Finite Group Databasebeta

← #30609317

Subgroups — #30609317

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840712C211yesmaximal, characteristic, complemented
2C2×#16840710C211yesmaximal, characteristic
3C2×#16840709C211yesmaximal, characteristic, complemented
4C2×#16840706C211yesmaximal, characteristic, complemented
5#21461004C211yesmaximal, characteristic, complemented
6#21461003C211yesmaximal, characteristic, complemented
7#21461002C211yesmaximal, characteristic, complemented
8#21461002C211yesmaximal, characteristic, complemented
9#21461002C211yesmaximal, characteristic, complemented
10#21461001C211yesmaximal, characteristic
11#21461000C211yesmaximal, characteristic, complemented
12#21460998C211yesmaximal, characteristic, complemented
13#21460995C211yesmaximal, characteristic, complemented
14#21460992C211yesmaximal, characteristic, complemented
15#390×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#16840712—24no—
29#16840710—24no—
30#16840709—24no—
31#16840706—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
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×C22⋊C4×D61C2211yescharacteristic
51C2×C22⋊C4×D61C2211yescharacteristic
52C2×C22⋊C4×D61C2211yescharacteristic
53C2×C22⋊C4×D61C2211yescharacteristic
54C2×C42×D61C2211yescharacteristic
55#16839665C411yescharacteristic, complemented
56#16839664C411yescharacteristic, complemented
57#16839663C411yescharacteristic, complemented
58#16839662C411yescharacteristic, complemented
59#16839662C411yescharacteristic, complemented
60#16839662C411yescharacteristic, complemented
61#16839662C411yescharacteristic, complemented
62C61×#390C411yescharacteristic, 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—41no—
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⋊#6923—41no—
108C2×C4×#6923—22no—
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)⋊C4D414yes—
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—
138C22×C4×D61C2311yescharacteristic
139C22×C4×D61C2311yescharacteristic
140C22×C4×D61C2311yescharacteristic
141C22×C4×D61C2311yescharacteristic
142C22×C4×D61C2311yescharacteristic
143C2×C4⋊Dic61C2×C411yescharacteristic, complemented
144C2×#11758196C2×C411yescharacteristic, complemented
145C2×#11758196C2×C411yescharacteristic, complemented
146C4⋊C4×D61—41no—
147C4⋊C4×D61—41no—
148C2×C22⋊Dic61C2×C411yescharacteristic
149C2×C22⋊Dic61C2×C411yescharacteristic
150C2×C22⋊Dic61C2×C411yescharacteristic, complemented
151C2×C22⋊Dic61C2×C411yescharacteristic, complemented
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic, complemented
157C2×#11758198C2×C411yescharacteristic, complemented
158C2×#11758198C2×C411yescharacteristic, complemented
159C2×#11758198C2×C411yescharacteristic, complemented
160C22⋊C4×D61—22no—
161C22⋊C4×D61—22no—
162C22⋊C4×D61—22no—
163C22⋊C4×D61—22no—
164C22⋊C4×D61—41no—
165C22⋊C4×D61—41no—
166C22⋊C4×D61—41no—
167C22⋊C4×D61—41no—
168C2×C4×Dic61C2×C411yescharacteristic, complemented
169C2×C4×Dic61C2×C411yescharacteristic, complemented
170C2×C4×Dic61C2×C411yescharacteristic, complemented
171C42×D61—22no—
172C42×D61—22no—
173C22×D4×C61C2×C411yescharacteristic
174C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
175C2×C22⋊C4×C61C2×C411yescharacteristic
176C2×C22⋊C4×C61C2×C411yescharacteristic
177C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
178C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
179C2×C42×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×D61—21no—
207C23×D61—21no—
208C23×D61C22×C411yescharacteristic
209C23×D61C22×C411yescharacteristic
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×C61C22×C411yescharacteristic
280C22×C4×C61C22×C411yescharacteristic
281C22×C4×C61C22×C411yescharacteristic
282C22×C4×C61C22×C411yescharacteristic
283C22×C4×C61C22×C411yescharacteristic
284C2×C22⋊D61—22no—
285C2×C22⋊D61—22no—
286C2×C22⋊D61—22no—
287C2×C22⋊D61—22no—
288C2×C22⋊D61—41no—
289C2×C22⋊D61—41no—
290C22×Dic61C22×C411yescharacteristic
291C22×Dic61C22×C411yescharacteristic
292C22×Dic61C22×C411yescharacteristic
293C22×Dic61C22×C411yescharacteristic
294C22×Dic61C22×C411yescharacteristic
295D4×D61—44no—
296D4×D61—44no—
297D4×D61—44no—
298D4×D61—44no—
299C2×D244—22no—
300C2×D244—22no—
301C2×D244—41no—
302C2×C4×D61—21no—
303C2×C4×D61—21no—
304C2×C4×D61—21no—
305C2×C4×D61—21no—
306C2×C4×D61—21no—
307C2×C4×D61—21no—
308C2×C4×D61—21no—
309C2×C4×D61—21no—
310C2×C4×D61—21no—
311C2×C4×D61—21no—
312C2×C4×D61—21no—
313C2×C4×D61—21no—
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×D61C2×D412yes—
329C2×C4×D61C2×D412yes—
330C2×C4×D61#4112yes—
331C2×C4×D61#4112yes—
332C22⋊#6923—44no—
333C22⋊#6923—44no—
334C22⋊#6923—44no—
335C22⋊#6923—44no—
336C22⋊#6923—44no—
337C22⋊#6923—44no—
338C22⋊#6923—44no—
339C4⋊#6923—44no—
340C4⋊#6923—44no—
341C4⋊#6923—44no—
342C4×#6923—44no—
343C4⋊C4×C61—41no—
344C22⋊C4×C61—22no—
345C22⋊C4×C61—22no—
346C22⋊C4×C61—41no—
347C22⋊C4×C61—41no—
348C42×C61—22no—
349C22⋊Dic61—22no—
350C22⋊Dic61—22no—
351C22⋊Dic61—41no—
352C22⋊Dic61—41no—
353#11758198—22no—
354#11758198—22no—
355#11758198—22no—
356#11758198—22no—
357#11758198—41no—
358#11758198—41no—
359#11758198—41no—
360#11758198—41no—
361C4⋊Dic61—41no—
362#11758196—41no—
363#11758196—41no—
364C4×Dic61—22no—
365C4×Dic61—22no—
366C4×Dic61—22no—
367C23×C61—21no—
368C23×C61—21no—
369C23×C61—21no—
370C23×C61—21no—
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#11712yes—
381C23×C61C23×C411yescharacteristic
382C22×D61—21no—
383C22×D61—21no—
384C22×D61—21no—
385C22×D61—21no—
386C22×D61—21no—
387C22×D61—21no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—21no—
401C22×D61—21no—
402C22×D61—21no—
403C22×D61—21no—
404C22×D61—21no—
405C22×D61—21no—
406C22×D61—21no—
407C22×D61—41no—
408C22×D61—41no—
409C22×D61—41no—
410C22×D61—41no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61—41no—
417C22×D61—41no—
418C22×D61—41no—
419C22×D61—41no—
420C22×D61—41no—
421C22×D61—41no—
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#11712yes—
452C22×D61C22×D411yescharacteristic
453C22×D61C22×D411yescharacteristic
454C22×D61C2×#4111yescharacteristic
455C22×D61C2×#4111yescharacteristic
456C22×D61C2×#4111yescharacteristic
457C22×D61C2×#4111yescharacteristic
458C22×D61H(5,𝔽2)11yescharacteristic
459C22×D61H(5,𝔽2)11yescharacteristic
460C22×D61H(5,𝔽2)11yescharacteristic
461C22×D61H(5,𝔽2)11yescharacteristic
462C22×D61H(5,𝔽2)11yescharacteristic
463C22×D61H(5,𝔽2)11yescharacteristic
464C22×D612−1+411yescharacteristic
465C22×D612−1+411yescharacteristic
466C2×#6923—22no—
467C2×#6923—22no—
468C2×#6923—22no—
469C2×#6923—22no—
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—416no—
479C2×#6923—41no—
480C2×#6923—41no—
481C2×#6923—41no—
482C2×#6923—41no—
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—
523D4×C61—44no—
524C2×C4×C61—21no—
525C2×C4×C61—21no—
526C2×C4×C61—21no—
527C2×C4×C61—21no—
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×C61C4×D412yes—
538C2×C4×C61C4×D412yes—
539C22⋊D61—44no—
540C22⋊D61—44no—
541C2×Dic61—21no—
542C2×Dic61—21no—
543C2×Dic61—21no—
544C2×Dic61—21no—
545C2×Dic61—21no—
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×Dic61C4×D412yes—
555C2×Dic61C4×D412yes—
556D244—44no—
557C4×D61—22no—
558C4×D61—22no—
559C4×D61—22no—
560C4×D61—22no—
561C4×D61—22no—
562C4×D61—22no—
563C4×D61—22no—
564C4×D61—22no—
565C4×D61—41no—
566C4×D61—41no—
567C4×D61—41no—
568C4×D61—41no—
569C4×D61—41no—
570C4×D61—41no—
571C4×D61—41no—
572C4×D61—41no—
573C4×D61—41no—
574C4×D61—41no—
575C4×D61—41no—
576C4×D61—41no—
577#14377—611nomaximal, Sylow
578C22×C61—22no—
579C22×C61—22no—
580C22×C61—22no—
581C22×C61—41no—
582C22×C61—41no—
583C22×C61—41no—
584C22×C61—41no—
585C22×C61—41no—
586C22×C61—41no—
587C22×C61—41no—
588C22×C61—41no—
589C22×C61—41no—
590C22×C61—41no—
591C22×C61—41no—
592C22×C61C2×#11711yescharacteristic
593C22×C61C2×C4×D411yescharacteristic
594C22×C61C2×C4×D411yescharacteristic
595C22×C61#51811yescharacteristic
596C22×C61#51811yescharacteristic
597C22×C61#52011yescharacteristic
598C22×C61#52011yescharacteristic
599C2×D61—22no—
600C2×D61—22no—
601C2×D61—22no—
602C2×D61—41no—
603C2×D61—41no—
604C2×D61—41no—
605C2×D61—41no—
606C2×D61—42no—
607C2×D61—42no—
608C2×D61—42no—
609C2×D61—42no—
610C2×D61—42no—
611C2×D61—42no—
612C2×D61—42no—
613C2×D61—42no—
614C2×D61—41no—
615C2×D61—41no—
616C2×D61—41no—
617C2×D61—41no—
618C2×D61—41no—
619C2×D61—41no—
620C2×D61—41no—
621C2×D61—81no—
622C2×D61—81no—
623C2×D61—81no—
624C2×D61—81no—
625C2×D61—81no—
626C2×D61—81no—
627C2×D61—81no—
628C2×D61—81no—
629C2×D61#53511yescharacteristic
630C2×D61#53511yescharacteristic
631C2×D61#53511yescharacteristic
632C2×D61#53711yescharacteristic
633C2×D61#53811yescharacteristic
634C2×D61#53811yescharacteristic
635C2×D61#53911yescharacteristic
636C2×D61#53911yescharacteristic
637C2×D61#54011yescharacteristic
638C2×D61#54011yescharacteristic
639C2×D61#54011yescharacteristic
640C2×D61#54211yescharacteristic
641C2×D61D4211yescharacteristic
642C2×D61#54611yescharacteristic
643C2×D61#54611yescharacteristic
644C2×D61#54611yescharacteristic
645C2×D61#54711yescharacteristic
646C2×D61#54811yescharacteristic
647C2×D61#54811yescharacteristic
648C2×D61#55111yescharacteristic
649C2×D61#55111yescharacteristic
650C2×D61#55211yescharacteristic
651C2×D61#55311yescharacteristic
652C2×D61#55311yescharacteristic
653C2×D61H(3,𝔽4)11yescharacteristic
654C2×D61#56211yescharacteristic
655C2×D61#56211yescharacteristic
656C2×D61#56311yescharacteristic
657#6923—42no—
658#6923—42no—
659#6923—42no—
660#6923—42no—
661#6923—81no—
662#6923—81no—
663#6923—81no—
664#6923—81no—
665C4×C61—22no—
666C4×C61—22no—
667C4×C61—41no—
668C4×C61—41no—
669C4×C61—41no—
670Dic61—22no—
671Dic61—22no—
672Dic61—41no—
673Dic61—41no—
674Dic61—41no—
675C2×#390—611no—
676C2×#388—611no—
677C2×#386—611no—
678C2×#385—611no—
679C2×#382—611no—
680#1441—611no—
681#1440—611no—
682#1439—611no—
683#1439—611no—
684#1439—611no—
685#1438—611no—
686#1437—611no—
687#1436—611no—
688#1434—611no—
689C22⋊#95—611no—
690C2×C61—42no—
691C2×C61—81no—
692C2×C61#231811yescharacteristic
693C2×C61#232411yescharacteristic
694C2×C61#232811yescharacteristic
695C2×C61#234211yescharacteristic
696C2×C61#235211yescharacteristic
697C2×C61#236111yescharacteristic
698C2×C61#237911yescharacteristic
699D61—42no—
700D61—81no—
701D61#267011yescharacteristic
702D61#267611yescharacteristic
703D61#270611yescharacteristic
704D61#270711yescharacteristic
705D61#271111yescharacteristic
706D61#272311yescharacteristic
707D61#275311yescharacteristic
708D61#276111yescharacteristic
709C23×D4—611no—
710C24×C4—611no—
711C22×C4⋊C4—611no—
712C22×C4⋊C4—611no—
713C22×C4⋊C4—611no—
714C22×C4⋊C4—611no—
715C22×C22⋊C4—611no—
716C22×C22⋊C4—611no—
717C22×C22⋊C4—611no—
718C22×C22⋊C4—611no—
719C22×C22⋊C4—611no—
720C22×C22⋊C4—611no—
721C22×C22⋊C4—611no—
722C22×C22⋊C4—611no—
723C22×C22⋊C4—611no—
724C22×C22⋊C4—611no—
725C22×C22⋊C4—611no—
726C22×C42—611no—
727C22×C42—611no—
728#390—611no—
729#390—611no—
730#390—611no—
731#390—611no—
732#390—611no—
733#390—611no—
734#390—611no—
735#390#692311yescharacteristic, complemented
736#388—1224no—
737#386—1224no—
738#385—1224no—
739#382—1224no—
740C2×#95—611no—
741C2×#95—611no—
742C2×#95—611no—
743C2×#95—611no—
744C2×#95—611no—
745C2×#95—611no—
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—
756C61#1437711yescharacteristic, complemented, Sylow
757C25—611no—
758C25—611no—
759C22×D4—611no—
760C22×D4—611no—
761C22×D4—611no—
762C22×D4—1222no—
763C22×D4—1222no—
764C22×D4—1222no—
765C22×D4—1222no—
766C22×D4—2441no—
767C22×D4—2441no—
768C22×D4C2×#692311yescharacteristic
769C23×C4—611no—
770C23×C4—611no—
771C23×C4—611no—
772C23×C4—611no—
773C23×C4—611no—
774C23×C4—611no—
775C23×C4—611no—
776C23×C4—611no—
777C23×C4—611no—
778C23×C4—611no—
779C23×C4—611no—
780C23×C4—611no—
781C23×C4—611no—
782C23×C4—1222no—
783C23×C4—1222no—
784C23×C4—1222no—
785C23×C4—2441no—
786C23×C4—2441no—
787C23×C4—2441no—
788C23×C4—2441no—
789C2×C4⋊C4—611no—
790C2×C4⋊C4—611no—
791C2×C4⋊C4—611no—
792C2×C4⋊C4—1222no—
793C2×C4⋊C4—1222no—
794C2×C4⋊C4—1222no—
795C2×C4⋊C4—1222no—
796C2×C4⋊C4—1222no—
797C2×C4⋊C4—2441no—
798C2×C4⋊C4—2441no—
799C2×C4⋊C4—2441no—
800C2×C4⋊C4—2441no—
801C2×C4⋊C4—2441no—
802C2×C4⋊C4—2441no—
803C2×C4⋊C4C2×#692311yescharacteristic, complemented
804C2×C22⋊C4—611no—
805C2×C22⋊C4—611no—
806C2×C22⋊C4—611no—
807C2×C22⋊C4—611no—
808C2×C22⋊C4—611no—
809C2×C22⋊C4—611no—
810C2×C22⋊C4—611no—
811C2×C22⋊C4—611no—
812C2×C22⋊C4—611no—
813C2×C22⋊C4—611no—
814C2×C22⋊C4—611no—
815C2×C22⋊C4—611no—
816C2×C22⋊C4—1222no—
817C2×C22⋊C4—1222no—
818C2×C22⋊C4—1222no—
819C2×C22⋊C4—1222no—
820C2×C22⋊C4—1222no—
821C2×C22⋊C4—1222no—
822C2×C22⋊C4—1222no—
823C2×C22⋊C4—1222no—
824C2×C22⋊C4—1222no—
825C2×C22⋊C4—1222no—
826C2×C22⋊C4—1222no—
827C2×C22⋊C4—1222no—
828C2×C22⋊C4—1222no—
829C2×C22⋊C4—2441no—
830C2×C22⋊C4—2441no—
831C2×C22⋊C4—2441no—
832C2×C22⋊C4—2441no—
833C2×C22⋊C4—2441no—
834C2×C22⋊C4—2441no—
835C2×C22⋊C4—2441no—
836C2×C22⋊C4—2441no—
837C2×C22⋊C4—2441no—
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⋊C4C2×#692311yescharacteristic
846C2×C22⋊C4C2×#692311yescharacteristic
847C2×C22⋊C4C2×#692311yescharacteristic, complemented
848C2×C22⋊C4C2×#692311yescharacteristic, complemented
849C2×C42—611no—
850C2×C42—611no—
851C2×C42—611no—
852C2×C42—1222no—
853C2×C42—1222no—
854C2×C42—1222no—
855C2×C42—2441no—
856C2×C42—2441no—
857C2×C42C2×#692311yescharacteristic, complemented
858#95—614no—
859#95—614no—
860#95—1222no—
861#95—1222no—
862#95—1222no—
863#95—1222no—
864#95—1222no—
865#95—1222no—
866#95—1222no—
867#95—1222no—
868#95—2441no—
869#95—2441no—
870#95—2441no—
871#95—2441no—
872#95—2441no—
873#95—2441no—
874C24—611no—
875C24—612no—
876C24—612no—
877C24—611no—
878C24—611no—
879C24—1221no—
880C24—1221no—
881C24—1221no—
882C24—1221no—
883C24—1221no—
884C24—1221no—
885C24—1221no—
886C24—1221no—
887C24—1221no—
888C24—1221no—
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—
905C24C22×#692311yescharacteristic
906C24C22×#692311yescharacteristic
907C2×D4—22no—
908C2×D4—22no—
909C2×D4—41no—
910C2×D4—1222no—
911C2×D4—1222no—
912C2×D4—1222no—
913C2×D4—1222no—
914C2×D4—1222no—
915C2×D4—1222no—
916C2×D4—2441no—
917C2×D4—2444no—
918C2×D4—2444no—
919C2×D4—2444no—
920C2×D4—2444no—
921C2×D4—2441no—
922C2×D4—2441no—
923C22×C4—611no—
924C22×C4—611no—
925C22×C4—612no—
926C22×C4—612no—
927C22×C4—612no—
928C22×C4—612no—
929C22×C4—612no—
930C22×C4—612no—
931C22×C4—612no—
932C22×C4—612no—
933C22×C4—611no—
934C22×C4—611no—
935C22×C4—611no—
936C22×C4—1221no—
937C22×C4—1221no—
938C22×C4—1221no—
939C22×C4—1221no—
940C22×C4—1221no—
941C22×C4—1221no—
942C22×C4—1221no—
943C22×C4—1221no—
944C22×C4—1221no—
945C22×C4—1221no—
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—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1221no—
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—1221no—
1002C22×C4—1221no—
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—2444no—
1015C22×C4—2444no—
1016C22×C4—2444no—
1017C22×C4—2444no—
1018C22×C4—2444no—
1019C22×C4—2444no—
1020C22×C4—2444no—
1021C22×C4C22×#692311yescharacteristic
1022C22×C4C22×#692311yescharacteristic
1023C22×C4C22×#692311yescharacteristic
1024C22×C4C22×#692311yescharacteristic
1025C22×C4C22×#692311yescharacteristic
1026C4⋊C4—41no—
1027C4⋊C4—2441no—
1028C4⋊C4—2441no—
1029C4⋊C4—2441no—
1030C4⋊C4—2444no—
1031C4⋊C4—2444no—
1032C4⋊C4—2444no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—1222no—
1038C22⋊C4—1222no—
1039C22⋊C4—1222no—
1040C22⋊C4—1222no—
1041C22⋊C4—1222no—
1042C22⋊C4—1222no—
1043C22⋊C4—2441no—
1044C22⋊C4—2441no—
1045C22⋊C4—2441no—
1046C22⋊C4—2441no—
1047C22⋊C4—2441no—
1048C22⋊C4—2441no—
1049C22⋊C4—2444no—
1050C22⋊C4—2444no—
1051C22⋊C4—2444no—
1052C22⋊C4—2444no—
1053C22⋊C4—2444no—
1054C22⋊C4—2444no—
1055C22⋊C4—2444no—
1056C42—22no—
1057C42—1222no—
1058C42—1222no—
1059C42—1222no—
1060C42—2444no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—611no—
1075C23—611no—
1076C23—611no—
1077C23—611no—
1078C23—611no—
1079C23—611no—
1080C23—611no—
1081C23—611no—
1082C23—611no—
1083C23—611no—
1084C23—611no—
1085C23—611no—
1086C23—611no—
1087C23—611no—
1088C23—612no—
1089C23—1222no—
1090C23—1222no—
1091C23—1222no—
1092C23—1222no—
1093C23—1222no—
1094C23—1222no—
1095C23—1222no—
1096C23—1222no—
1097C23—1222no—
1098C23—1222no—
1099C23—1222no—
1100C23—1222no—
1101C23—1221no—
1102C23—1221no—
1103C23—1221no—
1104C23—1221no—
1105C23—1221no—
1106C23—1221no—
1107C23—1221no—
1108C23—1221no—
1109C23—1221no—
1110C23—1221no—
1111C23—1221no—
1112C23—1221no—
1113C23—1221no—
1114C23—2441no—
1115C23—2441no—
1116C23—2441no—
1117C23—2441no—
1118C23—2441no—
1119C23—2441no—
1120C23—2441no—
1121C23—2441no—
1122C23—2441no—
1123C23—2441no—
1124C23—2441no—
1125C23—2441no—
1126C23—2441no—
1127C23—2441no—
1128C23—2441no—
1129C23—2441no—
1130C23—2441no—
1131C23—2441no—
1132C23—2441no—
1133C23—2441no—
1134C23—2441no—
1135C23—2441no—
1136C23—2441no—
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#1451985612yes—
1159C23C23×#692311yescharacteristic
1160D4—44no—
1161D4—2444no—
1162D4—2444no—
1163D4—2444no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—612no—
1178C2×C4—612no—
1179C2×C4—1222no—
1180C2×C4—1222no—
1181C2×C4—1222no—
1182C2×C4—1222no—
1183C2×C4—1222no—
1184C2×C4—1222no—
1185C2×C4—1222no—
1186C2×C4—1222no—
1187C2×C4—1221no—
1188C2×C4—1221no—
1189C2×C4—1221no—
1190C2×C4—1221no—
1191C2×C4—1222no—
1192C2×C4—1222no—
1193C2×C4—1222no—
1194C2×C4—1222no—
1195C2×C4—1222no—
1196C2×C4—1222no—
1197C2×C4—1222no—
1198C2×C4—1222no—
1199C2×C4—1222no—
1200C2×C4—1222no—
1201C2×C4—1222no—
1202C2×C4—1222no—
1203C2×C4—1221no—
1204C2×C4—1221no—
1205C2×C4—1221no—
1206C2×C4—1221no—
1207C2×C4—1221no—
1208C2×C4—1221no—
1209C2×C4—1221no—
1210C2×C4—1221no—
1211C2×C4—1221no—
1212C2×C4—2441no—
1213C2×C4—2441no—
1214C2×C4—2441no—
1215C2×C4—2441no—
1216C2×C4—2441no—
1217C2×C4—2441no—
1218C2×C4—2441no—
1219C2×C4—2441no—
1220C2×C4—2441no—
1221C2×C4—2441no—
1222C2×C4—2441no—
1223C2×C4—2441no—
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—2441no—
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—24416no—
1269C2×C4D4×#692312yes—
1270C2×C4D4×#692312yes—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—611no—
1286C22—611no—
1287C22—611no—
1288C22—611no—
1289C22—611no—
1290C22—611no—
1291C22—611no—
1292C22—611no—
1293C22—611no—
1294C22—611no—
1295C22—611no—
1296C22—611no—
1297C22—611no—
1298C22—611no—
1299C22—611no—
1300C22—611no—
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—1222no—
1314C22—1222no—
1315C22—1222no—
1316C22—4881no—
1317C22—4881no—
1318C22—4881no—
1319C22—4881no—
1320C22—4881no—
1321C22—4881no—
1322C22—4881no—
1323C22—4881no—
1324C22—2442no—
1325C22—2442no—
1326C22—2442no—
1327C22—2442no—
1328C22—2442no—
1329C22—2442no—
1330C22—2442no—
1331C22—2442no—
1332C22—2441no—
1333C22—2441no—
1334C22—2441no—
1335C22—2441no—
1336C22—2441no—
1337C22—2441no—
1338C22—2441no—
1339C22—2441no—
1340C22—2441no—
1341C22—2441no—
1342C22—2441no—
1343C22C2×#1451985611yescharacteristic
1344C22C2×D4×#692311yescharacteristic
1345C22C2×D4×#692311yescharacteristic
1346C22#1684082911yescharacteristic
1347C22#1684082911yescharacteristic
1348C22#1684083111yescharacteristic
1349C22#1684083111yescharacteristic
1350C4—22no—
1351C4—22no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—1222no—
1356C4—1222no—
1357C4—4881no—
1358C4—4881no—
1359C4—4881no—
1360C4—4881no—
1361C4—2442no—
1362C4—2442no—
1363C4—2442no—
1364C4—2442no—
1365C4—2441no—
1366C4—2441no—
1367C4—2441no—
1368C2—42no—
1369C2—81no—
1370C2—611no—
1371C2—611no—
1372C2—611no—
1373C2—611no—
1374C2—611no—
1375C2—611no—
1376C2—611no—
1377C2—611no—
1378C2—4881no—
1379C2—2442no—
1380C2#2146230111yescharacteristic
1381C2#2146230711yescharacteristic
1382C2#2146231111yescharacteristic
1383C2#2146232511yescharacteristic
1384C2#2146233511yescharacteristic
1385C2#2146234411yescharacteristic
1386C2#2146236211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#390C4
prime radicalC22×D4×D61C22
cosocleC23×D61C24
hypercenter#390#6923
hypocenterC61#14377
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#16840712C2semidirect
3. C2×#16840709C2semidirect
4. C2×#16840706C2semidirect
5. #21461004C2semidirect
6. #21461003C2semidirect
7. #21461002C2semidirect
8. #21461002C2semidirect
9. #21461002C2semidirect
11. #21461000C2semidirect
12. #21460998C2semidirect
13. #21460995C2semidirect
14. #21460992C2semidirect
55. #16839665C4semidirect
56. #16839664C4semidirect
57. #16839663C4semidirect
58. #16839662C4semidirect
59. #16839662C4semidirect
60. #16839662C4semidirect
61. #16839662C4semidirect
62. C61×#390C4semidirect
126. (C2×#6923)⋊C4D4semidirect
143. C2×C4⋊Dic61C2×C4semidirect
144. C2×#11758196C2×C4semidirect
145. C2×#11758196C2×C4semidirect
150. C2×C22⋊Dic61C2×C4semidirect
151. C2×C22⋊Dic61C2×C4semidirect
156. C2×#11758198C2×C4semidirect
157. C2×#11758198C2×C4semidirect
158. C2×#11758198C2×C4semidirect
159. C2×#11758198C2×C4semidirect
168. C2×C4×Dic61C2×C4semidirect
169. C2×C4×Dic61C2×C4semidirect
170. C2×C4×Dic61C2×C4semidirect
174. C2×C4⋊C4×C61C2×C4semidirect
177. C2×C22⋊C4×C61C2×C4semidirect
178. C2×C22⋊C4×C61C2×C4semidirect
179. C2×C42×C61C2×C4semidirect
735. #390#6923semidirect
756. C61#14377semidirect
803. C2×C4⋊C4C2×#6923semidirect
847. C2×C22⋊C4C2×#6923semidirect
848. C2×C22⋊C4C2×#6923semidirect
857. C2×C42C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407122
C2×#168407102
C2×#168407092
C2×#168407062
#214610042
#214610032
#214610022
#214610012
#214610002
#214609982
#214609952
#214609922
#390×D612
#1437761