Finite Group Databasebeta

← #30609313

Subgroups — #30609313

Order 15616.

1974 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840710C211yesmaximal, characteristic
2C2×#16840709C211yesmaximal, characteristic, complemented
3C2×#16840705C211yesmaximal, characteristic, complemented
4C2×#16840704C211yesmaximal, characteristic, complemented
5#21461006C211yesmaximal, characteristic, complemented
6#21461005C211yesmaximal, characteristic, complemented
7#21461005C211yesmaximal, characteristic, complemented
8#21461002C211yesmaximal, characteristic, complemented
9#21461002C211yesmaximal, characteristic, complemented
10#21461001C211yesmaximal, characteristic
11#21461000C211yesmaximal, characteristic, complemented
12#21461000C211yesmaximal, characteristic, complemented
13#21460999C211yesmaximal, characteristic, complemented
14#21460992C211yesmaximal, characteristic, complemented
15#386×D61C211yesmaximal, characteristic
16C24×#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C22⋊#6923C2211yescharacteristic
22C22×C22⋊#6923C2211yescharacteristic
23C22×C22⋊#6923C2211yescharacteristic
24C22×C22⋊#6923C2211yescharacteristic
25C22×C22⋊#6923C2211yescharacteristic
26C22×C22⋊#6923C2211yescharacteristic
27C22×C4×#6923C2211yescharacteristic
28#16840710—24no—
29#16840709—24no—
30#16840705—24no—
31#16840704—24no—
32C2×(C2×#6923)⋊C4C2211yescharacteristic
33C2×(C2×#6923)⋊C4C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36C2×(C2×#6923)⋊C4C2211yescharacteristic
37C2×(C2×#6923)⋊C4C2211yescharacteristic
38C2×(C2×#6923)⋊C4C2211yescharacteristic
39C2×(C2×#6923)⋊C4C2211yescharacteristic
40C2×(C2×#6923)⋊C4C2211yescharacteristic
41C2×(C2×#6923)⋊C4C2211yescharacteristic
42C2×(C2×#6923)⋊C4C2211yescharacteristic
43C2×(C2×#6923)⋊C4C2211yescharacteristic
44C2×(C2×#6923)⋊C4C2211yescharacteristic
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C2×(C2×#6923)⋊C4C2211yescharacteristic
47C2×(C2×#6923)⋊C4C2211yescharacteristic
48C22×D4×D61C2211yescharacteristic
49C23×C4×D61C2211yescharacteristic
50C2×C22⋊C4×D61C2211yescharacteristic
51C2×C22⋊C4×D61C2211yescharacteristic
52C2×C22⋊C4×D61C2211yescharacteristic
53#16839642C411yescharacteristic, complemented
54#16839641C411yescharacteristic, complemented
55#16839640C411yescharacteristic, complemented
56#16839640C411yescharacteristic, complemented
57#16839639C411yescharacteristic, complemented
58#16839638C411yescharacteristic, complemented
59#16839638C411yescharacteristic, complemented
60#95×D61C2211yescharacteristic
61#95×D61C2211yescharacteristic
62C61×#386C411yescharacteristic, complemented
63C23×#6923—22no—
64C23×#6923—22no—
65C23×#6923—22no—
66C23×#6923—41no—
67C23×#6923—41no—
68C23×#6923—41no—
69C23×#6923—41no—
70C23×#6923C2311yescharacteristic
71C23×#6923C2311yescharacteristic
72C23×#6923C2311yescharacteristic
73C23×#6923C2311yescharacteristic
74C23×#6923C2311yescharacteristic
75C23×#6923C2311yescharacteristic
76C23×#6923C2311yescharacteristic
77C23×#6923C2311yescharacteristic
78C2×C4⋊#6923—22no—
79C2×C4⋊#6923—22no—
80C2×C4⋊#6923—22no—
81C2×C4⋊#6923—22no—
82C2×C4⋊#6923—22no—
83C2×C4⋊#6923—41no—
84C2×C4⋊#6923—41no—
85C2×C4⋊#6923—41no—
86C2×C4⋊#6923—41no—
87C2×C22⋊#6923—22no—
88C2×C22⋊#6923—22no—
89C2×C22⋊#6923—22no—
90C2×C22⋊#6923—22no—
91C2×C22⋊#6923—22no—
92C2×C22⋊#6923—22no—
93C2×C22⋊#6923—22no—
94C2×C22⋊#6923—22no—
95C2×C22⋊#6923—22no—
96C2×C22⋊#6923—22no—
97C2×C22⋊#6923—41no—
98C2×C22⋊#6923—41no—
99C2×C22⋊#6923—41no—
100C2×C22⋊#6923—41no—
101C2×C22⋊#6923—41no—
102C2×C22⋊#6923—41no—
103C2×C22⋊#6923—41no—
104C2×C22⋊#6923—41no—
105C2×C22⋊#6923—41no—
106C2×C22⋊#6923—41no—
107C2×C22⋊#6923D414yes—
108C2×C4×#6923—41no—
109C2×C4×#6923—41no—
110C2×C4×#6923—41no—
111(C2×#6923)⋊C4—22no—
112(C2×#6923)⋊C4—22no—
113(C2×#6923)⋊C4—22no—
114(C2×#6923)⋊C4—22no—
115(C2×#6923)⋊C4—22no—
116(C2×#6923)⋊C4—22no—
117(C2×#6923)⋊C4—22no—
118(C2×#6923)⋊C4—22no—
119(C2×#6923)⋊C4—41no—
120(C2×#6923)⋊C4—41no—
121(C2×#6923)⋊C4—41no—
122(C2×#6923)⋊C4—41no—
123(C2×#6923)⋊C4—41no—
124(C2×#6923)⋊C4—41no—
125(C2×#6923)⋊C4—41no—
126(C2×#6923)⋊C4D414yescomplemented
127C24×D61C2311yescharacteristic
128C24×D61C2311yescharacteristic
129C22×D244C2×C411yescharacteristic
130C22×C22⋊D61C2×C411yescharacteristic
131C22×C22⋊D61C2×C411yescharacteristic
132C2×D4×D61—22no—
133C2×D4×D61—22no—
134C2×D4×D61—22no—
135C2×D4×D61—22no—
136C2×D4×D61—41no—
137C2×D4×D61—41no—
138C23×Dic61C2×C411yescharacteristic, complemented
139C22×C4×D61—22no—
140C22×C4×D61—22no—
141C22×C4×D61—22no—
142C22×C4×D61—22no—
143C22×C4×D61—41no—
144C22×C4×D61—41no—
145C22×C4×D61C2×C411yescharacteristic, complemented
146C22×C4×D61C2×C411yescharacteristic, complemented
147C22×C4×D61C2311yescharacteristic
148C22×C4×D61C2311yescharacteristic
149C22×C4×D61C2311yescharacteristic
150C22×C4×D61C2311yescharacteristic
151C22×C4×D61C2311yescharacteristic
152C2×C22⋊Dic61C2×C411yescharacteristic
153C2×C22⋊Dic61C2×C411yescharacteristic
154C2×C22⋊Dic61C2×C411yescharacteristic, complemented
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic, complemented
160C2×#11758198C2×C411yescharacteristic, complemented
161C22⋊C4×D61—22no—
162C22⋊C4×D61—22no—
163C22⋊C4×D61—41no—
164C22⋊C4×D61—41no—
165C22⋊C4×D61—41no—
166C22⋊C4×D61—41no—
167#14519684C2×C411yescharacteristic, complemented
168#14519684C2×C411yescharacteristic, complemented
169#14519684C2×C411yescharacteristic, complemented
170#14519684C2×C411yescharacteristic, complemented
171#14519684C2×C411yescharacteristic, complemented
172#14519684C2×C411yescharacteristic, complemented
173C22×D4×C61C2×C411yescharacteristic
174C23×C4×C61C2×C411yescharacteristic, complemented
175C2×C22⋊C4×C61C2×C411yescharacteristic
176C2×C22⋊C4×C61C2×C411yescharacteristic
177C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
178#95×C61C2×C411yescharacteristic, complemented
179#95×C61C2×C411yescharacteristic, complemented
180C24×C61C22×C411yescharacteristic
181C24×C61C22×C411yescharacteristic
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
206C23×D61C22×C411yescharacteristic
207C23×D61C22×C411yescharacteristic
208C23×D61C2×D412yes—
209C23×D61#4112yes—
210C23×D61#4112yes—
211C23×D61#4112yes—
212C23×D61C2411yescharacteristic
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—21no—
227C22×#6923—21no—
228C22×#6923—21no—
229C22×#6923—21no—
230C22×#6923—21no—
231C22×#6923—21no—
232C22×#6923—21no—
233C22×#6923—21no—
234C22×#6923—21no—
235C22×#6923—21no—
236C22×#6923—21no—
237C22×#6923—21no—
238C22×#6923—21no—
239C22×#6923—21no—
240C22×#6923—21no—
241C22×#6923—21no—
242C22×#6923—21no—
243C22×#6923—21no—
244C22×#6923—21no—
245C22×#6923—21no—
246C22×#6923—21no—
247C22×#6923—21no—
248C22×#6923—21no—
249C22×#6923—21no—
250C22×#6923—21no—
251C22×#6923—21no—
252C22×#6923—21no—
253C22×#6923—21no—
254C22×#6923—21no—
255C22×#6923—21no—
256C22×#6923—21no—
257C22×#6923—21no—
258C22×#6923—21no—
259C22×#6923—21no—
260C22×#6923—21no—
261C22×#6923—21no—
262C22×#6923—21no—
263C22×#6923—21no—
264C22×#6923—21no—
265C22×#6923—44no—
266C22×#6923—44no—
267C22×#6923—44no—
268C22×#6923—44no—
269C22×#6923—44no—
270C22×#6923—44no—
271C22×#6923—44no—
272C22×#6923C2×D412yes—
273C22×#6923C2×D412yes—
274C22×#6923C2×D412yes—
275C22×#6923C2×D412yes—
276C2×D4×C61—22no—
277C2×D4×C61—22no—
278C2×D4×C61—41no—
279C22×C4×C61—22no—
280C22×C4×C61—22no—
281C22×C4×C61—41no—
282C22×C4×C61C22×C411yescharacteristic
283C22×C4×C61C22×C411yescharacteristic
284C22×C4×C61C22×C411yescharacteristic
285C22×C4×C61C22×C411yescharacteristic
286C22×C4×C61C22×C411yescharacteristic
287C2×C22⋊D61—22no—
288C2×C22⋊D61—22no—
289C2×C22⋊D61—22no—
290C2×C22⋊D61—22no—
291C2×C22⋊D61—41no—
292C2×C22⋊D61—41no—
293C22×Dic61—22no—
294C22×Dic61—22no—
295C22×Dic61—41no—
296C22×Dic61C22×C411yescharacteristic
297C22×Dic61C22×C411yescharacteristic
298C22×Dic61C22×C411yescharacteristic
299C22×Dic61C22×C411yescharacteristic
300C22×Dic61C22×C411yescharacteristic
301D4×D61—44no—
302D4×D61—44no—
303D4×D61—44no—
304D4×D61—44no—
305C2×D244—22no—
306C2×D244—22no—
307C2×D244—41no—
308C2×C4×D61—21no—
309C2×C4×D61—21no—
310C2×C4×D61—21no—
311C2×C4×D61—21no—
312C2×C4×D61—22no—
313C2×C4×D61—22no—
314C2×C4×D61—21no—
315C2×C4×D61—21no—
316C2×C4×D61—21no—
317C2×C4×D61—21no—
318C2×C4×D61—21no—
319C2×C4×D61—21no—
320C2×C4×D61—21no—
321C2×C4×D61—21no—
322C2×C4×D61—21no—
323C2×C4×D61—21no—
324C2×C4×D61—21no—
325C2×C4×D61—21no—
326C2×C4×D61—21no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—21no—
333C2×C4×D61—21no—
334C2×C4×D61—21no—
335C2×C4×D61—21no—
336C2×C4×D61—21no—
337C2×C4×D61—21no—
338C2×C4×D61—22no—
339C2×C4×D61—22no—
340C2×C4×D61—44no—
341C2×C4×D61—44no—
342C2×C4×D61—44no—
343C2×C4×D61—44no—
344C2×C4×D61—41no—
345C2×C4×D61—41no—
346C2×C4×D61C2×D412yes—
347C2×C4×D61#4112yes—
348C22⋊#6923—44no—
349C22⋊#6923—44no—
350C22⋊#6923—44no—
351C22⋊#6923—44no—
352C22⋊#6923—44no—
353C22⋊#6923—44no—
354C22⋊#6923—44no—
355C4⋊#6923—44no—
356C4⋊#6923—44no—
357C4⋊#6923—44no—
358C4×#6923—44no—
359C22⋊C4×C61—22no—
360C22⋊C4×C61—41no—
361C22⋊C4×C61—41no—
362C22⋊Dic61—22no—
363C22⋊Dic61—41no—
364C22⋊Dic61—41no—
365#11758198—22no—
366#11758198—22no—
367#11758198—41no—
368#11758198—41no—
369#11758198—41no—
370#11758198—41no—
371C23×C61—21no—
372C23×C61—21no—
373C23×C61—21no—
374C23×C61—21no—
375C23×C61—21no—
376C23×C61—21no—
377C23×C61—21no—
378C23×C61—21no—
379C23×C61—21no—
380C23×C61—21no—
381C23×C61—21no—
382C23×C61—21no—
383C23×C61#11712yes—
384C23×C61C4×D412yes—
385C23×C61C23×C411yescharacteristic
386C22×D61—21no—
387C22×D61—21no—
388C22×D61—21no—
389C22×D61—21no—
390C22×D61—21no—
391C22×D61—21no—
392C22×D61—21no—
393C22×D61—21no—
394C22×D61—21no—
395C22×D61—21no—
396C22×D61—21no—
397C22×D61—21no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—22no—
401C22×D61—22no—
402C22×D61—22no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—22no—
409C22×D61—22no—
410C22×D61—22no—
411C22×D61—22no—
412C22×D61—22no—
413C22×D61—22no—
414C22×D61—22no—
415C22×D61—22no—
416C22×D61—22no—
417C22×D61—22no—
418C22×D61—22no—
419C22×D61—22no—
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—41no—
423C22×D61—41no—
424C22×D61—41no—
425C22×D61—41no—
426C22×D61—41no—
427C22×D61—41no—
428C22×D61—41no—
429C22×D61—41no—
430C22×D61—41no—
431C22×D61—41no—
432C22×D61—41no—
433C22×D61—41no—
434C22×D61—41no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—41no—
451C22×D61—41no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61#11712yes—
455C22×D61C4×D412yes—
456C22×D61C22×D411yescharacteristic
457C22×D61C22×D411yescharacteristic
458C22×D61C2×#4111yescharacteristic
459C22×D61C2×#4111yescharacteristic
460C22×D61C2×#4111yescharacteristic
461C22×D61C2×#4111yescharacteristic
462C22×D61H(5,𝔽2)11yescharacteristic
463C22×D61H(5,𝔽2)11yescharacteristic
464C22×D61H(5,𝔽2)11yescharacteristic
465C22×D61H(5,𝔽2)11yescharacteristic
466C22×D61H(5,𝔽2)11yescharacteristic
467C22×D61H(5,𝔽2)11yescharacteristic
468C22×D612−1+411yescharacteristic
469C22×D612−1+411yescharacteristic
470C2×#6923—22no—
471C2×#6923—22no—
472C2×#6923—22no—
473C2×#6923—22no—
474C2×#6923—22no—
475C2×#6923—22no—
476C2×#6923—22no—
477C2×#6923—22no—
478C2×#6923—22no—
479C2×#6923—22no—
480C2×#6923—22no—
481C2×#6923—22no—
482C2×#6923—416no—
483C2×#6923—41no—
484C2×#6923—41no—
485C2×#6923—41no—
486C2×#6923—41no—
487C2×#6923—41no—
488C2×#6923—41no—
489C2×#6923—41no—
490C2×#6923—41no—
491C2×#6923—41no—
492C2×#6923—41no—
493C2×#6923—41no—
494C2×#6923—41no—
495C2×#6923—41no—
496C2×#6923—41no—
497C2×#6923—41no—
498C2×#6923—41no—
499C2×#6923—41no—
500C2×#6923—41no—
501C2×#6923—41no—
502C2×#6923—41no—
503C2×#6923—41no—
504C2×#6923—41no—
505C2×#6923—41no—
506C2×#6923—41no—
507C2×#6923—41no—
508C2×#6923—41no—
509C2×#6923—41no—
510C2×#6923—41no—
511C2×#6923—41no—
512C2×#6923—41no—
513C2×#6923—41no—
514C2×#6923—41no—
515C2×#6923—41no—
516C2×#6923—41no—
517C2×#6923—41no—
518C2×#6923—41no—
519C2×#6923—41no—
520C2×#6923—41no—
521C2×#6923—41no—
522C2×#6923—41no—
523C2×#6923—41no—
524C2×#6923—41no—
525C2×#6923—41no—
526C2×#6923—41no—
527D4×C61—44no—
528C2×C4×C61—21no—
529C2×C4×C61—21no—
530C2×C4×C61—21no—
531C2×C4×C61—21no—
532C2×C4×C61—21no—
533C2×C4×C61—21no—
534C2×C4×C61—21no—
535C2×C4×C61—21no—
536C2×C4×C61—21no—
537C2×C4×C61—21no—
538C2×C4×C61—21no—
539C2×C4×C61—21no—
540C2×C4×C61—21no—
541C2×C4×C61—21no—
542C2×C4×C61—44no—
543C2×C4×C61C4×D412yes—
544C22⋊D61—44no—
545C22⋊D61—44no—
546C2×Dic61—21no—
547C2×Dic61—21no—
548C2×Dic61—21no—
549C2×Dic61—21no—
550C2×Dic61—21no—
551C2×Dic61—21no—
552C2×Dic61—21no—
553C2×Dic61—21no—
554C2×Dic61—21no—
555C2×Dic61—21no—
556C2×Dic61—21no—
557C2×Dic61—21no—
558C2×Dic61—21no—
559C2×Dic61—21no—
560C2×Dic61—44no—
561C2×Dic61C4×D412yes—
562D244—44no—
563C4×D61—22no—
564C4×D61—22no—
565C4×D61—22no—
566C4×D61—22no—
567C4×D61—44no—
568C4×D61—44no—
569C4×D61—41no—
570C4×D61—41no—
571C4×D61—41no—
572C4×D61—41no—
573C4×D61—41no—
574C4×D61—41no—
575C4×D61—41no—
576C4×D61—41no—
577C4×D61—41no—
578C4×D61—41no—
579C4×D61—41no—
580C4×D61—41no—
581C4×D61—41no—
582C4×D61—41no—
583C4×D61—41no—
584C4×D61—41no—
585#14373—611nomaximal, Sylow
586C22×C61—22no—
587C22×C61—22no—
588C22×C61—22no—
589C22×C61—22no—
590C22×C61—22no—
591C22×C61—22no—
592C22×C61—41no—
593C22×C61—41no—
594C22×C61—41no—
595C22×C61—41no—
596C22×C61—41no—
597C22×C61—41no—
598C22×C61—41no—
599C22×C61—41no—
600C22×C61C2×#11711yescharacteristic
601C22×C61C2×C4×D411yescharacteristic
602C22×C61C2×C4×D411yescharacteristic
603C22×C61#51811yescharacteristic
604C22×C61#51811yescharacteristic
605C22×C61#52011yescharacteristic
606C22×C61#52011yescharacteristic
607C2×D61—22no—
608C2×D61—22no—
609C2×D61—22no—
610C2×D61—22no—
611C2×D61—22no—
612C2×D61—22no—
613C2×D61—41no—
614C2×D61—41no—
615C2×D61—41no—
616C2×D61—41no—
617C2×D61—41no—
618C2×D61—41no—
619C2×D61—41no—
620C2×D61—41no—
621C2×D61—42no—
622C2×D61—42no—
623C2×D61—42no—
624C2×D61—42no—
625C2×D61—42no—
626C2×D61—42no—
627C2×D61—42no—
628C2×D61—42no—
629C2×D61—42no—
630C2×D61—42no—
631C2×D61—42no—
632C2×D61—42no—
633C2×D61—42no—
634C2×D61—42no—
635C2×D61—42no—
636C2×D61—42no—
637C2×D61#53411yescharacteristic
638C2×D61#53511yescharacteristic
639C2×D61#53611yescharacteristic
640C2×D61#53711yescharacteristic
641C2×D61#53811yescharacteristic
642C2×D61#53811yescharacteristic
643C2×D61#53911yescharacteristic
644C2×D61#53911yescharacteristic
645C2×D61#53911yescharacteristic
646C2×D61#53911yescharacteristic
647C2×D61#54011yescharacteristic
648C2×D61#54211yescharacteristic
649C2×D61D4211yescharacteristic
650C2×D61#54611yescharacteristic
651C2×D61#54611yescharacteristic
652C2×D61#54611yescharacteristic
653C2×D61#54611yescharacteristic
654C2×D61#54611yescharacteristic
655C2×D61#54811yescharacteristic
656C2×D61#55111yescharacteristic
657C2×D61#55111yescharacteristic
658C2×D61#55111yescharacteristic
659C2×D61#55211yescharacteristic
660C2×D61#55311yescharacteristic
661C2×D61#56011yescharacteristic
662C2×D61#56011yescharacteristic
663C2×D61#56211yescharacteristic
664C2×D61#56211yescharacteristic
665#6923—42no—
666#6923—42no—
667#6923—42no—
668#6923—42no—
669#6923—81no—
670#6923—81no—
671#6923—81no—
672#6923—81no—
673C4×C61—22no—
674C4×C61—41no—
675C4×C61—41no—
676C4×C61—41no—
677C4×C61—41no—
678Dic61—22no—
679Dic61—41no—
680Dic61—41no—
681Dic61—41no—
682Dic61—41no—
683C2×#386—611no—
684C2×#386—611no—
685C2×#385—611no—
686C2×#381—611no—
687C2×#380—611no—
688#1443—611no—
689#1442—611no—
690#1442—611no—
691#1439—611no—
692#1439—611no—
693#1438—611no—
694#1437—611no—
695#1437—611no—
696#1436—611no—
697C22⋊#95—611no—
698C2×C61—42no—
699C2×C61—42no—
700C2×C61#231811yescharacteristic
701C2×C61#232211yescharacteristic
702C2×C61#232411yescharacteristic
703C2×C61#234211yescharacteristic
704C2×C61#235211yescharacteristic
705C2×C61#235811yescharacteristic
706C2×C61#237711yescharacteristic
707D61—42no—
708D61—42no—
709D61#267811yescharacteristic
710D61#268111yescharacteristic
711D61#268711yescharacteristic
712D61#268811yescharacteristic
713D61#269311yescharacteristic
714D61#269611yescharacteristic
715D61#274311yescharacteristic
716D61#274611yescharacteristic
717C23×D4—611no—
718C24×C4—611no—
719C24×C4—611no—
720C22×C4⋊C4—611no—
721C22×C4⋊C4—611no—
722C22×C4⋊C4—611no—
723C22×C22⋊C4—611no—
724C22×C22⋊C4—611no—
725C22×C22⋊C4—611no—
726C22×C22⋊C4—611no—
727C22×C22⋊C4—611no—
728C22×C22⋊C4—611no—
729C22×C22⋊C4—611no—
730C22×C22⋊C4—611no—
731C22×C22⋊C4—611no—
732C22×C22⋊C4—611no—
733C22×C42—611no—
734#386—611no—
735#386—611no—
736#386—611no—
737#386—611no—
738#386—611no—
739#386—611no—
740#386—611no—
741#386—1224no—
742#386#692311yescharacteristic, complemented
743#385—1224no—
744#381—1224no—
745#380—1224no—
746C2×#95—611no—
747C2×#95—611no—
748C2×#95—611no—
749C2×#95—611no—
750C2×#95—611no—
751C2×#95—611no—
752C2×#95—611no—
753C2×#95—611no—
754C2×#95—611no—
755C2×#95—611no—
756C2×#95—611no—
757C2×#95—611no—
758C2×#95—611no—
759C2×#95—611no—
760C2×#95—611no—
761C2×#95—611no—
762C2×#95—611no—
763C2×#95—611no—
764C61#1437311yescharacteristic, complemented, Sylow
765C25—611no—
766C25—611no—
767C22×D4—611no—
768C22×D4—611no—
769C22×D4—611no—
770C22×D4—1222no—
771C22×D4—1222no—
772C22×D4—1222no—
773C22×D4—1222no—
774C22×D4—2441no—
775C22×D4—2441no—
776C22×D4C2×#692311yescharacteristic
777C23×C4—611no—
778C23×C4—611no—
779C23×C4—611no—
780C23×C4—611no—
781C23×C4—611no—
782C23×C4—611no—
783C23×C4—611no—
784C23×C4—611no—
785C23×C4—611no—
786C23×C4—611no—
787C23×C4—611no—
788C23×C4—611no—
789C23×C4—611no—
790C23×C4—611no—
791C23×C4—611no—
792C23×C4—611no—
793C23×C4—1222no—
794C23×C4—1222no—
795C23×C4—1222no—
796C23×C4—1222no—
797C23×C4—1222no—
798C23×C4—1222no—
799C23×C4—1222no—
800C23×C4—2441no—
801C23×C4—2441no—
802C23×C4—2441no—
803C23×C4—2441no—
804C23×C4—2441no—
805C23×C4—2441no—
806C23×C4C2×#692311yescharacteristic, complemented
807C2×C4⋊C4—1222no—
808C2×C4⋊C4—1222no—
809C2×C4⋊C4—1222no—
810C2×C4⋊C4—1222no—
811C2×C4⋊C4—1222no—
812C2×C4⋊C4—2441no—
813C2×C4⋊C4—2441no—
814C2×C4⋊C4—2441no—
815C2×C4⋊C4—2441no—
816C2×C22⋊C4—611no—
817C2×C22⋊C4—611no—
818C2×C22⋊C4—611no—
819C2×C22⋊C4—614no—
820C2×C22⋊C4—611no—
821C2×C22⋊C4—611no—
822C2×C22⋊C4—611no—
823C2×C22⋊C4—611no—
824C2×C22⋊C4—611no—
825C2×C22⋊C4—611no—
826C2×C22⋊C4—1222no—
827C2×C22⋊C4—1222no—
828C2×C22⋊C4—1222no—
829C2×C22⋊C4—1222no—
830C2×C22⋊C4—1222no—
831C2×C22⋊C4—1222no—
832C2×C22⋊C4—1222no—
833C2×C22⋊C4—1222no—
834C2×C22⋊C4—1222no—
835C2×C22⋊C4—1222no—
836C2×C22⋊C4—1222no—
837C2×C22⋊C4—1222no—
838C2×C22⋊C4—2441no—
839C2×C22⋊C4—2441no—
840C2×C22⋊C4—2441no—
841C2×C22⋊C4—2441no—
842C2×C22⋊C4—2441no—
843C2×C22⋊C4—2441no—
844C2×C22⋊C4—2441no—
845C2×C22⋊C4—2441no—
846C2×C22⋊C4—2441no—
847C2×C22⋊C4—2441no—
848C2×C22⋊C4—2441no—
849C2×C22⋊C4—2441no—
850C2×C22⋊C4—2441no—
851C2×C22⋊C4—2441no—
852C2×C22⋊C4C2×#692311yescharacteristic
853C2×C22⋊C4C2×#692311yescharacteristic
854C2×C22⋊C4C2×#692311yescharacteristic, complemented
855C2×C42—2441no—
856C2×C42—2441no—
857C2×C42—2441no—
858#95—614no—
859#95—611no—
860#95—611no—
861#95—611no—
862#95—611no—
863#95—611no—
864#95—611no—
865#95—1222no—
866#95—1222no—
867#95—1222no—
868#95—1222no—
869#95—1222no—
870#95—1222no—
871#95—1222no—
872#95—1222no—
873#95—2441no—
874#95—2441no—
875#95—2441no—
876#95—2441no—
877#95—2441no—
878#95—2441no—
879#95—2441no—
880#95C2×#692311yescharacteristic, complemented
881#95C2×#692311yescharacteristic, complemented
882C24—611no—
883C24—612no—
884C24—612no—
885C24—612no—
886C24—612no—
887C24—611no—
888C24—611no—
889C24—1221no—
890C24—1221no—
891C24—1221no—
892C24—1221no—
893C24—1221no—
894C24—1221no—
895C24—1221no—
896C24—1221no—
897C24—1221no—
898C24—1221no—
899C24—1221no—
900C24—1221no—
901C24—1221no—
902C24—1221no—
903C24—1221no—
904C24—1221no—
905C24—1221no—
906C24—1221no—
907C24—1221no—
908C24—1221no—
909C24—1221no—
910C24—1221no—
911C24—1221no—
912C24—1221no—
913C24C22×#692311yescharacteristic
914C24C22×#692311yescharacteristic
915C2×D4—22no—
916C2×D4—22no—
917C2×D4—41no—
918C2×D4—1222no—
919C2×D4—1222no—
920C2×D4—1222no—
921C2×D4—1222no—
922C2×D4—1222no—
923C2×D4—1222no—
924C2×D4—2441no—
925C2×D4—2441no—
926C2×D4—2441no—
927C2×D4—2444no—
928C2×D4—2444no—
929C2×D4—2444no—
930C2×D4—2444no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—41no—
934C22×C4—611no—
935C22×C4—612no—
936C22×C4—612no—
937C22×C4—612no—
938C22×C4—612no—
939C22×C4—612no—
940C22×C4—612no—
941C22×C4—611no—
942C22×C4—611no—
943C22×C4—611no—
944C22×C4—611no—
945C22×C4—1222no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1222no—
968C22×C4—1222no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1222no—
977C22×C4—1221no—
978C22×C4—1221no—
979C22×C4—1221no—
980C22×C4—1221no—
981C22×C4—1221no—
982C22×C4—1221no—
983C22×C4—1221no—
984C22×C4—1221no—
985C22×C4—1221no—
986C22×C4—1221no—
987C22×C4—1221no—
988C22×C4—1221no—
989C22×C4—1221no—
990C22×C4—1221no—
991C22×C4—1221no—
992C22×C4—1221no—
993C22×C4—1221no—
994C22×C4—1221no—
995C22×C4—1221no—
996C22×C4—1221no—
997C22×C4—1221no—
998C22×C4—1221no—
999C22×C4—1221no—
1000C22×C4—1221no—
1001C22×C4—1222no—
1002C22×C4—1222no—
1003C22×C4—1221no—
1004C22×C4—1221no—
1005C22×C4—1221no—
1006C22×C4—1221no—
1007C22×C4—1221no—
1008C22×C4—1221no—
1009C22×C4—1221no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1221no—
1014C22×C4—1221no—
1015C22×C4—1221no—
1016C22×C4—1221no—
1017C22×C4—1221no—
1018C22×C4—1221no—
1019C22×C4—1221no—
1020C22×C4—1221no—
1021C22×C4—1221no—
1022C22×C4—1221no—
1023C22×C4—1221no—
1024C22×C4—1221no—
1025C22×C4—1221no—
1026C22×C4—1221no—
1027C22×C4—1221no—
1028C22×C4—1221no—
1029C22×C4—1221no—
1030C22×C4—1221no—
1031C22×C4—2441no—
1032C22×C4—2441no—
1033C22×C4—2444no—
1034C22×C4—2444no—
1035C22×C4—2444no—
1036C22×C4—2444no—
1037C22×C4—2441no—
1038C22×C4—2444no—
1039C22×C4—2444no—
1040C22×C4—2444no—
1041C22×C4—2444no—
1042C22×C4—2444no—
1043C22×C4—2444no—
1044C22×C4—2444no—
1045C22×C4C22×#692311yescharacteristic
1046C22×C4C22×#692311yescharacteristic
1047C22×C4C22×#692311yescharacteristic
1048C22×C4C22×#692311yescharacteristic
1049C22×C4C22×#692311yescharacteristic
1050C4⋊C4—2444no—
1051C4⋊C4—2444no—
1052C4⋊C4—2444no—
1053C22⋊C4—22no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—1222no—
1057C22⋊C4—1222no—
1058C22⋊C4—1222no—
1059C22⋊C4—2441no—
1060C22⋊C4—2441no—
1061C22⋊C4—2441no—
1062C22⋊C4—2441no—
1063C22⋊C4—2441no—
1064C22⋊C4—2441no—
1065C22⋊C4—2444no—
1066C22⋊C4—2444no—
1067C22⋊C4—2444no—
1068C22⋊C4—2444no—
1069C22⋊C4—2444no—
1070C22⋊C4—2444no—
1071C22⋊C4—2444no—
1072C42—2444no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—611no—
1086C23—611no—
1087C23—611no—
1088C23—611no—
1089C23—611no—
1090C23—611no—
1091C23—611no—
1092C23—611no—
1093C23—611no—
1094C23—611no—
1095C23—611no—
1096C23—611no—
1097C23—611no—
1098C23—611no—
1099C23—612no—
1100C23—612no—
1101C23—1222no—
1102C23—1222no—
1103C23—1222no—
1104C23—1222no—
1105C23—1222no—
1106C23—1222no—
1107C23—1222no—
1108C23—1222no—
1109C23—1222no—
1110C23—1222no—
1111C23—1222no—
1112C23—1222no—
1113C23—1222no—
1114C23—1222no—
1115C23—1222no—
1116C23—1222no—
1117C23—1222no—
1118C23—1222no—
1119C23—1222no—
1120C23—1222no—
1121C23—1222no—
1122C23—1222no—
1123C23—1222no—
1124C23—1222no—
1125C23—1221no—
1126C23—1221no—
1127C23—1221no—
1128C23—1221no—
1129C23—1221no—
1130C23—1221no—
1131C23—1221no—
1132C23—1221no—
1133C23—1221no—
1134C23—1221no—
1135C23—1221no—
1136C23—1221no—
1137C23—2441no—
1138C23—2441no—
1139C23—2441no—
1140C23—2441no—
1141C23—2441no—
1142C23—2441no—
1143C23—2441no—
1144C23—2441no—
1145C23—2441no—
1146C23—2441no—
1147C23—2441no—
1148C23—2441no—
1149C23—2441no—
1150C23—2441no—
1151C23—2441no—
1152C23—2441no—
1153C23—2441no—
1154C23—2441no—
1155C23—2441no—
1156C23—2441no—
1157C23—2441no—
1158C23—2441no—
1159C23—2441no—
1160C23—2441no—
1161C23—2441no—
1162C23—2441no—
1163C23—2441no—
1164C23—2441no—
1165C23—2441no—
1166C23—2441no—
1167C23—2441no—
1168C23—2441no—
1169C23#1451985612yes—
1170C23D4×#692312yes—
1171C23C23×#692311yescharacteristic
1172D4—44no—
1173D4—2444no—
1174D4—2444no—
1175D4—2444no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—44no—
1191C2×C4—612no—
1192C2×C4—1222no—
1193C2×C4—1222no—
1194C2×C4—1222no—
1195C2×C4—1222no—
1196C2×C4—1221no—
1197C2×C4—1221no—
1198C2×C4—1222no—
1199C2×C4—1222no—
1200C2×C4—1222no—
1201C2×C4—1222no—
1202C2×C4—1222no—
1203C2×C4—1222no—
1204C2×C4—1222no—
1205C2×C4—1222no—
1206C2×C4—1222no—
1207C2×C4—1222no—
1208C2×C4—1222no—
1209C2×C4—1222no—
1210C2×C4—1221no—
1211C2×C4—1221no—
1212C2×C4—1221no—
1213C2×C4—1221no—
1214C2×C4—1221no—
1215C2×C4—1221no—
1216C2×C4—1221no—
1217C2×C4—1221no—
1218C2×C4—1221no—
1219C2×C4—1221no—
1220C2×C4—1221no—
1221C2×C4—1221no—
1222C2×C4—2444no—
1223C2×C4—2444no—
1224C2×C4—2441no—
1225C2×C4—2441no—
1226C2×C4—2441no—
1227C2×C4—2441no—
1228C2×C4—2441no—
1229C2×C4—2441no—
1230C2×C4—2441no—
1231C2×C4—2441no—
1232C2×C4—2441no—
1233C2×C4—2441no—
1234C2×C4—2441no—
1235C2×C4—2441no—
1236C2×C4—2441no—
1237C2×C4—2441no—
1238C2×C4—2441no—
1239C2×C4—2441no—
1240C2×C4—2444no—
1241C2×C4—2441no—
1242C2×C4—2441no—
1243C2×C4—2441no—
1244C2×C4—2441no—
1245C2×C4—2441no—
1246C2×C4—2441no—
1247C2×C4—2441no—
1248C2×C4—2441no—
1249C2×C4—2441no—
1250C2×C4—2441no—
1251C2×C4—2441no—
1252C2×C4—2441no—
1253C2×C4—2441no—
1254C2×C4—2441no—
1255C2×C4—2441no—
1256C2×C4—2441no—
1257C2×C4—2441no—
1258C2×C4—2441no—
1259C2×C4—2441no—
1260C2×C4—2441no—
1261C2×C4—2441no—
1262C2×C4—2441no—
1263C2×C4—2441no—
1264C2×C4—2441no—
1265C2×C4—2441no—
1266C2×C4—2441no—
1267C2×C4—2441no—
1268C2×C4—2441no—
1269C2×C4—2441no—
1270C2×C4—2441no—
1271C2×C4—2441no—
1272C2×C4—2441no—
1273C2×C4—2441no—
1274C2×C4—2441no—
1275C2×C4—2441no—
1276C2×C4—2441no—
1277C2×C4—2441no—
1278C2×C4—2441no—
1279C2×C4—2441no—
1280C2×C4—2441no—
1281C2×C4—2441no—
1282C2×C4—2441no—
1283C2×C4—2441no—
1284C2×C4—2441no—
1285C2×C4—24416no—
1286C2×C4D4×#692312yes—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—611no—
1302C22—611no—
1303C22—611no—
1304C22—611no—
1305C22—611no—
1306C22—611no—
1307C22—611no—
1308C22—611no—
1309C22—611no—
1310C22—611no—
1311C22—611no—
1312C22—611no—
1313C22—611no—
1314C22—611no—
1315C22—611no—
1316C22—611no—
1317C22—611no—
1318C22—611no—
1319C22—611no—
1320C22—611no—
1321C22—611no—
1322C22—611no—
1323C22—611no—
1324C22—611no—
1325C22—611no—
1326C22—611no—
1327C22—611no—
1328C22—611no—
1329C22—1222no—
1330C22—1222no—
1331C22—1222no—
1332C22—1222no—
1333C22—1222no—
1334C22—1222no—
1335C22—2442no—
1336C22—2442no—
1337C22—2442no—
1338C22—2442no—
1339C22—2442no—
1340C22—2442no—
1341C22—2442no—
1342C22—2442no—
1343C22—2442no—
1344C22—2442no—
1345C22—2442no—
1346C22—2442no—
1347C22—2442no—
1348C22—2442no—
1349C22—2442no—
1350C22—2442no—
1351C22—2441no—
1352C22—2441no—
1353C22—2441no—
1354C22—2441no—
1355C22—2441no—
1356C22—2441no—
1357C22—2441no—
1358C22—2441no—
1359C22C2×#1451985611yescharacteristic
1360C22C2×D4×#692311yescharacteristic
1361C22C2×D4×#692311yescharacteristic
1362C22#1684082911yescharacteristic
1363C22#1684082911yescharacteristic
1364C22#1684083111yescharacteristic
1365C22#1684083111yescharacteristic
1366C4—22no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—1222no—
1372C4—4881no—
1373C4—4881no—
1374C4—4881no—
1375C4—4881no—
1376C4—2442no—
1377C4—2442no—
1378C4—2442no—
1379C4—2442no—
1380C4—2441no—
1381C4—2441no—
1382C4—2441no—
1383C4—2441no—
1384C2—42no—
1385C2—42no—
1386C2—611no—
1387C2—611no—
1388C2—611no—
1389C2—611no—
1390C2—611no—
1391C2—611no—
1392C2—611no—
1393C2—611no—
1394C2—2442no—
1395C2—2442no—
1396C2#2146230111yescharacteristic
1397C2#2146230511yescharacteristic
1398C2#2146230711yescharacteristic
1399C2#2146232511yescharacteristic
1400C2#2146233511yescharacteristic
1401C2#2146234111yescharacteristic
1402C2#2146236011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#386C4
prime radicalC22×D4×D61C22
cosocleC23×D61C24
hypercenter#386#6923
hypocenterC61#14373
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16840709C2semidirect
3. C2×#16840705C2semidirect
4. C2×#16840704C2semidirect
5. #21461006C2semidirect
6. #21461005C2semidirect
7. #21461005C2semidirect
8. #21461002C2semidirect
9. #21461002C2semidirect
11. #21461000C2semidirect
12. #21461000C2semidirect
13. #21460999C2semidirect
14. #21460992C2semidirect
53. #16839642C4semidirect
54. #16839641C4semidirect
55. #16839640C4semidirect
56. #16839640C4semidirect
57. #16839639C4semidirect
58. #16839638C4semidirect
59. #16839638C4semidirect
62. C61×#386C4semidirect
126. (C2×#6923)⋊C4D4semidirect
138. C23×Dic61C2×C4semidirect
145. C22×C4×D61C2×C4semidirect
146. C22×C4×D61C2×C4semidirect
154. C2×C22⋊Dic61C2×C4semidirect
159. C2×#11758198C2×C4semidirect
160. C2×#11758198C2×C4semidirect
167. #14519684C2×C4semidirect
168. #14519684C2×C4semidirect
169. #14519684C2×C4semidirect
170. #14519684C2×C4semidirect
171. #14519684C2×C4semidirect
172. #14519684C2×C4semidirect
174. C23×C4×C61C2×C4semidirect
177. C2×C22⋊C4×C61C2×C4semidirect
178. #95×C61C2×C4semidirect
179. #95×C61C2×C4semidirect
742. #386#6923semidirect
764. C61#14373semidirect
806. C23×C4C2×#6923semidirect
854. C2×C22⋊C4C2×#6923semidirect
880. #95C2×#6923semidirect
881. #95C2×#6923semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168407102
C2×#168407092
C2×#168407052
C2×#168407042
#214610062
#214610052
#214610022
#214610012
#214610002
#214609992
#214609922
#386×D612
#1437361