Finite Group Databasebeta

← #30609329

Subgroups — #30609329

Order 15616.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840709C211yesmaximal, characteristic
2C2×#16840707C211yesmaximal, characteristic, complemented
3#21461008C211yesmaximal, characteristic, complemented
4#21461005C211yesmaximal, characteristic, complemented
5#21461005C211yesmaximal, characteristic, complemented
6#21461004C211yesmaximal, characteristic, complemented
7#21461003C211yesmaximal, characteristic
8#21461002C211yesmaximal, characteristic
9#21461000C211yesmaximal, characteristic
10#21460999C211yesmaximal, characteristic, complemented
11#21460997C211yesmaximal, characteristic, complemented
12#21460994C211yesmaximal, characteristic, complemented
13#21460992C211yesmaximal, characteristic
14#21460992C211yesmaximal, characteristic
15#388×D61C211yesmaximal, characteristic
16C24×#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C22⋊#6923C2211yescharacteristic
22C22×C22⋊#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24#16840709—24no—
25#16840707—24no—
26C2×(C2×#6923)⋊C4C2211yescharacteristic
27C2×(C2×#6923)⋊C4C2211yescharacteristic
28C2×(C2×#6923)⋊C4C2211yescharacteristic
29C2×(C2×#6923)⋊C4C2211yescharacteristic
30C2×(C2×#6923)⋊C4C2211yescharacteristic
31C2×(C2×#6923)⋊C4C2211yescharacteristic
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×C4⋊C4×D61C2211yescharacteristic
47C2×C22⋊C4×D61C2211yescharacteristic
48C2×C22⋊C4×D61C2211yescharacteristic
49C2×C22⋊C4×D61C2211yescharacteristic
50C2×C42×D61C2211yescharacteristic
51#16839656C411yescharacteristic, complemented
52#16839655C411yescharacteristic, complemented
53#16839654C411yescharacteristic, complemented
54#16839653C411yescharacteristic, complemented
55#16839652C411yescharacteristic, complemented
56#16839651C411yescharacteristic, complemented
57#16839650C411yescharacteristic, complemented
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#388C411yescharacteristic, complemented
61C23×#6923—22no—
62C23×#6923—22no—
63C23×#6923—22no—
64C23×#6923—41no—
65C23×#6923—41no—
66C23×#6923—41no—
67C23×#6923—41no—
68C23×#6923C2311yescharacteristic
69C23×#6923C2311yescharacteristic
70C23×#6923C2311yescharacteristic
71C23×#6923C2311yescharacteristic
72C23×#6923C2311yescharacteristic
73C23×#6923C2311yescharacteristic
74C23×#6923C2311yescharacteristic
75C23×#6923C2311yescharacteristic
76C2×C4⋊#6923—22no—
77C2×C4⋊#6923—22no—
78C2×C4⋊#6923—22no—
79C2×C4⋊#6923—22no—
80C2×C4⋊#6923—22no—
81C2×C4⋊#6923—41no—
82C2×C4⋊#6923—41no—
83C2×C4⋊#6923—41no—
84C2×C4⋊#6923—41no—
85C2×C22⋊#6923—22no—
86C2×C22⋊#6923—22no—
87C2×C22⋊#6923—22no—
88C2×C22⋊#6923—22no—
89C2×C22⋊#6923—22no—
90C2×C22⋊#6923—41no—
91C2×C22⋊#6923—41no—
92C2×C22⋊#6923—41no—
93C2×C22⋊#6923—41no—
94C2×C4×#6923—22no—
95C2×C4×#6923—41no—
96C2×C4×#6923—41no—
97(C2×#6923)⋊C4—22no—
98(C2×#6923)⋊C4—22no—
99(C2×#6923)⋊C4—22no—
100(C2×#6923)⋊C4—22no—
101(C2×#6923)⋊C4—22no—
102(C2×#6923)⋊C4—22no—
103(C2×#6923)⋊C4—22no—
104(C2×#6923)⋊C4—41no—
105(C2×#6923)⋊C4—41no—
106(C2×#6923)⋊C4—41no—
107(C2×#6923)⋊C4—41no—
108(C2×#6923)⋊C4—41no—
109(C2×#6923)⋊C4—41no—
110(C2×#6923)⋊C4—41no—
111(C2×#6923)⋊C4—41no—
112(C2×#6923)⋊C4—41no—
113(C2×#6923)⋊C4—41no—
114(C2×#6923)⋊C4—41no—
115(C2×#6923)⋊C4—41no—
116(C2×#6923)⋊C4D414yes—
117C24×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C2×C4⋊Dic61C2×C411yescharacteristic, complemented
125C2×#11758196C2×C411yescharacteristic, complemented
126C2×#11758196C2×C411yescharacteristic, complemented
127C4⋊C4×D61—41no—
128C4⋊C4×D61—41no—
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
138C22⋊C4×D61—22no—
139C22⋊C4×D61—22no—
140C22⋊C4×D61—22no—
141C22⋊C4×D61—22no—
142C22⋊C4×D61—41no—
143C22⋊C4×D61—41no—
144C2×C4×Dic61C2×C411yescharacteristic, complemented
145C2×C4×Dic61C2×C411yescharacteristic, complemented
146C2×C4×Dic61C2×C411yescharacteristic, complemented
147C42×D61—22no—
148C42×D61—22no—
149#14519684C2×C411yescharacteristic, complemented
150#14519684C2×C411yescharacteristic, complemented
151#14519684C2×C411yescharacteristic, complemented
152#14519684C2×C411yescharacteristic, complemented
153#14519684C2×C411yescharacteristic, complemented
154#14519684C2×C411yescharacteristic, complemented
155C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C22⋊C4×C61C2×C411yescharacteristic
158C2×C22⋊C4×C61C2×C411yescharacteristic
159C2×C42×C61C2×C411yescharacteristic, complemented
160#95×C61C2×C411yescharacteristic, complemented
161#95×C61C2×C411yescharacteristic, complemented
162C24×C61C22×C411yescharacteristic
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61C22×C411yescharacteristic
176C23×D61#4112yes—
177C23×D61#4112yes—
178C23×D61C2411yescharacteristic
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—21no—
182C22×#6923—21no—
183C22×#6923—21no—
184C22×#6923—21no—
185C22×#6923—21no—
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—21no—
192C22×#6923—21no—
193C22×#6923—21no—
194C22×#6923—21no—
195C22×#6923—21no—
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—21no—
200C22×#6923—21no—
201C22×#6923—21no—
202C22×#6923—21no—
203C22×#6923—21no—
204C22×#6923—21no—
205C22×#6923—21no—
206C22×#6923—21no—
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
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—44no—
232C22×#6923—44no—
233C22×#6923—44no—
234C22×#6923—44no—
235C22×#6923—44no—
236C22×#6923—44no—
237C22×#6923—44no—
238C22×#6923C2×D412yes—
239C22×#6923C2×D412yes—
240C22×#6923#4112yes—
241C22×#6923#4112yes—
242C22×C4×C61C22×C411yescharacteristic
243C22×C4×C61C22×C411yescharacteristic
244C22×C4×C61C22×C411yescharacteristic
245C22×C4×C61C22×C411yescharacteristic
246C22×C4×C61C22×C411yescharacteristic
247C22×C4×C61C22×C411yescharacteristic
248C22×Dic61C22×C411yescharacteristic
249C22×Dic61C22×C411yescharacteristic
250C22×Dic61C22×C411yescharacteristic
251C22×Dic61C22×C411yescharacteristic
252C22×Dic61C22×C411yescharacteristic
253C22×Dic61C22×C411yescharacteristic
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—21no—
284C2×C4×D61—21no—
285C2×C4×D61—21no—
286C2×C4×D61—21no—
287C2×C4×D61—21no—
288C2×C4×D61C2×D412yes—
289C2×C4×D61#4112yes—
290C22⋊#6923—44no—
291C22⋊#6923—44no—
292C22⋊#6923—44no—
293C4⋊#6923—44no—
294C4⋊#6923—44no—
295C4⋊#6923—44no—
296C4×#6923—44no—
297C4⋊C4×C61—41no—
298C22⋊C4×C61—22no—
299C22⋊C4×C61—22no—
300C22⋊C4×C61—41no—
301C42×C61—22no—
302C22⋊Dic61—22no—
303C22⋊Dic61—22no—
304C22⋊Dic61—41no—
305#11758198—22no—
306#11758198—22no—
307#11758198—22no—
308#11758198—22no—
309#11758198—41no—
310#11758198—41no—
311C4⋊Dic61—41no—
312#11758196—41no—
313#11758196—41no—
314C4×Dic61—22no—
315C4×Dic61—22no—
316C4×Dic61—22no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61—21no—
321C23×C61—21no—
322C23×C61—21no—
323C23×C61#11712yes—
324C23×C61C23×C411yescharacteristic
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61#11712yes—
360C22×D61C22×D411yescharacteristic
361C22×D61C2×#4111yescharacteristic
362C22×D61C2×#4111yescharacteristic
363C22×D61C2×#4111yescharacteristic
364C22×D61C2×#4111yescharacteristic
365C22×D61C2×#4111yescharacteristic
366C22×D61H(5,𝔽2)11yescharacteristic
367C22×D61H(5,𝔽2)11yescharacteristic
368C22×D61H(5,𝔽2)11yescharacteristic
369C22×D61H(5,𝔽2)11yescharacteristic
370C22×D61H(5,𝔽2)11yescharacteristic
371C22×D612−1+411yescharacteristic
372C22×D612−1+411yescharacteristic
373C22×D612−1+411yescharacteristic
374C2×#6923—22no—
375C2×#6923—22no—
376C2×#6923—22no—
377C2×#6923—22no—
378C2×#6923—22no—
379C2×#6923—22no—
380C2×#6923—22no—
381C2×#6923—22no—
382C2×#6923—22no—
383C2×#6923—22no—
384C2×#6923—22no—
385C2×#6923—22no—
386C2×#6923—416no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—41no—
398C2×#6923—41no—
399C2×#6923—41no—
400C2×#6923—41no—
401C2×#6923—41no—
402C2×#6923—41no—
403C2×#6923—41no—
404C2×#6923—41no—
405C2×#6923—41no—
406C2×#6923—41no—
407C2×#6923—41no—
408C2×#6923—41no—
409C2×#6923—41no—
410C2×#6923—41no—
411C2×#6923—41no—
412C2×#6923—41no—
413C2×#6923—41no—
414C2×#6923—41no—
415C2×#6923—41no—
416C2×#6923—41no—
417C2×#6923—41no—
418C2×#6923—41no—
419C2×#6923—41no—
420C2×#6923—41no—
421C2×#6923—41no—
422C2×#6923—41no—
423C2×#6923—41no—
424C2×#6923—41no—
425C2×#6923—41no—
426C2×#6923—41no—
427C2×#6923—41no—
428C2×#6923—41no—
429C2×#6923—41no—
430C2×#6923—41no—
431C2×C4×C61—21no—
432C2×C4×C61—21no—
433C2×C4×C61—21no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×C4×C61—21no—
442C2×C4×C61—21no—
443C2×C4×C61—21no—
444C2×C4×C61—21no—
445C2×C4×C61—21no—
446C2×C4×C61—21no—
447C2×C4×C61—21no—
448C2×C4×C61C4×D412yes—
449C2×Dic61—21no—
450C2×Dic61—21no—
451C2×Dic61—21no—
452C2×Dic61—21no—
453C2×Dic61—21no—
454C2×Dic61—21no—
455C2×Dic61—21no—
456C2×Dic61—21no—
457C2×Dic61—21no—
458C2×Dic61—21no—
459C2×Dic61—21no—
460C2×Dic61—21no—
461C2×Dic61—21no—
462C2×Dic61—21no—
463C2×Dic61—21no—
464C2×Dic61—21no—
465C2×Dic61—21no—
466C2×Dic61C4×D412yes—
467C4×D61—22no—
468C4×D61—22no—
469C4×D61—22no—
470C4×D61—22no—
471C4×D61—41no—
472C4×D61—41no—
473C4×D61—41no—
474C4×D61—41no—
475C4×D61—41no—
476C4×D61—41no—
477C4×D61—41no—
478C4×D61—41no—
479C4×D61—41no—
480C4×D61—41no—
481C4×D61—41no—
482C4×D61—41no—
483C4×D61—41no—
484C4×D61—41no—
485C4×D61—41no—
486C4×D61—41no—
487C4×D61—41no—
488C4×D61—41no—
489C4×D61—41no—
490C4×D61—41no—
491#14389—611nomaximal, Sylow
492C22×C61—22no—
493C22×C61—22no—
494C22×C61—22no—
495C22×C61—41no—
496C22×C61—41no—
497C22×C61—41no—
498C22×C61—41no—
499C22×C61C2×#11711yescharacteristic
500C22×C61C2×C4×D411yescharacteristic
501C22×C61C4×#4111yescharacteristic
502C22×C61#51811yescharacteristic
503C22×C61#52011yescharacteristic
504C22×C61#52011yescharacteristic
505C22×C61#52011yescharacteristic
506C2×D61—22no—
507C2×D61—22no—
508C2×D61—22no—
509C2×D61—41no—
510C2×D61—41no—
511C2×D61—41no—
512C2×D61—41no—
513C2×D61—42no—
514C2×D61—42no—
515C2×D61—42no—
516C2×D61—42no—
517C2×D61—42no—
518C2×D61—42no—
519C2×D61—42no—
520C2×D61—42no—
521C2×D61#53511yescharacteristic
522C2×D61#53711yescharacteristic
523C2×D61#53811yescharacteristic
524C2×D61#53811yescharacteristic
525C2×D61#53811yescharacteristic
526C2×D61#53811yescharacteristic
527C2×D61#53911yescharacteristic
528C2×D61#53911yescharacteristic
529C2×D61#54011yescharacteristic
530C2×D61#54211yescharacteristic
531C2×D61#54211yescharacteristic
532C2×D61#54211yescharacteristic
533C2×D61#54611yescharacteristic
534C2×D61#54611yescharacteristic
535C2×D61#54711yescharacteristic
536C2×D61#54811yescharacteristic
537C2×D61#55111yescharacteristic
538C2×D61#55111yescharacteristic
539C2×D61#55111yescharacteristic
540C2×D61#55211yescharacteristic
541C2×D61#55211yescharacteristic
542C2×D61#55211yescharacteristic
543C2×D61#55211yescharacteristic
544C2×D61#55311yescharacteristic
545C2×D61#56011yescharacteristic
546C2×D61#56311yescharacteristic
547C2×D61#56311yescharacteristic
548C2×D61#56311yescharacteristic
549#6923—42no—
550#6923—42no—
551#6923—42no—
552#6923—42no—
553#6923—81no—
554#6923—81no—
555#6923—81no—
556#6923—81no—
557C4×C61—22no—
558C4×C61—41no—
559C4×C61—41no—
560C4×C61—41no—
561C4×C61—41no—
562C4×C61—41no—
563Dic61—22no—
564Dic61—41no—
565Dic61—41no—
566Dic61—41no—
567Dic61—41no—
568Dic61—41no—
569C2×#388—611no—
570C2×#385—611no—
571C2×#383—611no—
572#1445—611no—
573#1442—611no—
574#1442—611no—
575#1441—611no—
576#1440—611no—
577#1439—611no—
578#1437—611no—
579#1436—611no—
580C4⋊#95—611no—
581#1434—611no—
582C22⋊#95—611no—
583C22⋊#95—611no—
584C2×C61—42no—
585C2×C61#231811yescharacteristic
586C2×C61#232411yescharacteristic
587C2×C61#233711yescharacteristic
588C2×C61#234311yescharacteristic
589C2×C61#235211yescharacteristic
590C2×C61#235911yescharacteristic
591C2×C61#238311yescharacteristic
592D61—42no—
593D61#268511yescharacteristic
594D61#269511yescharacteristic
595D61#270211yescharacteristic
596D61#272311yescharacteristic
597D61#273811yescharacteristic
598D61#274911yescharacteristic
599D61#276411yescharacteristic
600D61#277011yescharacteristic
601C24×C4—611no—
602C22×C4⋊C4—611no—
603C22×C4⋊C4—611no—
604C22×C4⋊C4—611no—
605C22×C4⋊C4—611no—
606C22×C22⋊C4—611no—
607C22×C22⋊C4—611no—
608C22×C22⋊C4—611no—
609C22×C22⋊C4—611no—
610C22×C22⋊C4—611no—
611C22×C22⋊C4—611no—
612C22×C42—611no—
613C22×C42—611no—
614#388—611no—
615#388—611no—
616#388—611no—
617#388—611no—
618#388—611no—
619#388—611no—
620#388—611no—
621#388#692311yescharacteristic, complemented
622#385—1224no—
623#383—1224no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95—611no—
646C61#1438911yescharacteristic, complemented, Sylow
647C25—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—611no—
651C23×C4—611no—
652C23×C4—611no—
653C23×C4—611no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—611no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—1222no—
663C23×C4—1222no—
664C23×C4—1222no—
665C23×C4—2441no—
666C23×C4—2441no—
667C23×C4—2441no—
668C23×C4—2441no—
669C2×C4⋊C4—611no—
670C2×C4⋊C4—611no—
671C2×C4⋊C4—611no—
672C2×C4⋊C4—1222no—
673C2×C4⋊C4—1222no—
674C2×C4⋊C4—1222no—
675C2×C4⋊C4—1222no—
676C2×C4⋊C4—1222no—
677C2×C4⋊C4—2441no—
678C2×C4⋊C4—2441no—
679C2×C4⋊C4—2441no—
680C2×C4⋊C4—2441no—
681C2×C4⋊C4—2441no—
682C2×C4⋊C4—2441no—
683C2×C4⋊C4C2×#692311yescharacteristic, complemented
684C2×C22⋊C4—611no—
685C2×C22⋊C4—611no—
686C2×C22⋊C4—611no—
687C2×C22⋊C4—611no—
688C2×C22⋊C4—611no—
689C2×C22⋊C4—611no—
690C2×C22⋊C4—611no—
691C2×C22⋊C4—611no—
692C2×C22⋊C4—611no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4—1222no—
695C2×C22⋊C4—1222no—
696C2×C22⋊C4—1222no—
697C2×C22⋊C4—1222no—
698C2×C22⋊C4—1222no—
699C2×C22⋊C4—1222no—
700C2×C22⋊C4—1222no—
701C2×C22⋊C4—1222no—
702C2×C22⋊C4—2441no—
703C2×C22⋊C4—2441no—
704C2×C22⋊C4—2441no—
705C2×C22⋊C4—2441no—
706C2×C22⋊C4—2441no—
707C2×C22⋊C4—2441no—
708C2×C22⋊C4C2×#692311yescharacteristic
709C2×C22⋊C4C2×#692311yescharacteristic
710C2×C22⋊C4C2×#692311yescharacteristic
711C2×C42—611no—
712C2×C42—611no—
713C2×C42—611no—
714C2×C42—1222no—
715C2×C42—1222no—
716C2×C42—1222no—
717C2×C42—2441no—
718C2×C42—2441no—
719C2×C42C2×#692311yescharacteristic, complemented
720#95—614no—
721#95—611no—
722#95—611no—
723#95—611no—
724#95—611no—
725#95—611no—
726#95—611no—
727#95—1222no—
728#95—1222no—
729#95—1222no—
730#95—1222no—
731#95—1222no—
732#95—1222no—
733#95—1222no—
734#95—2441no—
735#95—2441no—
736#95—2441no—
737#95—2441no—
738#95—2441no—
739#95—2441no—
740#95—2441no—
741#95—2441no—
742#95—2441no—
743#95—2441no—
744#95—2441no—
745#95—2441no—
746#95C2×#692311yescharacteristic, complemented
747#95C2×#692311yescharacteristic, complemented
748C24—611no—
749C24—612no—
750C24—612no—
751C24—611no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24C22×#692311yescharacteristic
765C22×C4—611no—
766C22×C4—612no—
767C22×C4—612no—
768C22×C4—612no—
769C22×C4—612no—
770C22×C4—612no—
771C22×C4—612no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—2444no—
864C22×C4—2444no—
865C22×C4—2444no—
866C22×C4—2444no—
867C22×C4—2444no—
868C22×C4—2444no—
869C22×C4—2444no—
870C22×C4C22×#692311yescharacteristic
871C22×C4C22×#692311yescharacteristic
872C22×C4C22×#692311yescharacteristic
873C22×C4C22×#692311yescharacteristic
874C22×C4C22×#692311yescharacteristic
875C22×C4C22×#692311yescharacteristic
876C4⋊C4—41no—
877C4⋊C4—2441no—
878C4⋊C4—2441no—
879C4⋊C4—2441no—
880C4⋊C4—2444no—
881C4⋊C4—2444no—
882C4⋊C4—2444no—
883C22⋊C4—22no—
884C22⋊C4—22no—
885C22⋊C4—41no—
886C22⋊C4—1222no—
887C22⋊C4—1222no—
888C22⋊C4—1222no—
889C22⋊C4—1222no—
890C22⋊C4—1222no—
891C22⋊C4—1222no—
892C22⋊C4—2441no—
893C22⋊C4—2441no—
894C22⋊C4—2441no—
895C22⋊C4—2444no—
896C22⋊C4—2444no—
897C22⋊C4—2444no—
898C42—22no—
899C42—1222no—
900C42—1222no—
901C42—1222no—
902C42—2444no—
903C23—21no—
904C23—21no—
905C23—21no—
906C23—21no—
907C23—21no—
908C23—21no—
909C23—611no—
910C23—611no—
911C23—611no—
912C23—611no—
913C23—611no—
914C23—611no—
915C23—611no—
916C23—611no—
917C23—611no—
918C23—611no—
919C23—611no—
920C23—611no—
921C23—611no—
922C23—611no—
923C23—612no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—1222no—
931C23—1222no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—1222no—
936C23—1221no—
937C23—1221no—
938C23—1221no—
939C23—1221no—
940C23—1221no—
941C23—1221no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23—2441no—
948C23—2441no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23#1451985612yes—
959C23C23×#692311yescharacteristic
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—612no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1221no—
983C2×C4—1221no—
984C2×C4—1222no—
985C2×C4—1222no—
986C2×C4—1222no—
987C2×C4—1222no—
988C2×C4—1222no—
989C2×C4—1222no—
990C2×C4—1222no—
991C2×C4—1222no—
992C2×C4—1222no—
993C2×C4—1222no—
994C2×C4—1222no—
995C2×C4—1222no—
996C2×C4—1221no—
997C2×C4—1221no—
998C2×C4—1221no—
999C2×C4—1221no—
1000C2×C4—1221no—
1001C2×C4—1221no—
1002C2×C4—1221no—
1003C2×C4—1221no—
1004C2×C4—1221no—
1005C2×C4—1221no—
1006C2×C4—1221no—
1007C2×C4—1221no—
1008C2×C4—1221no—
1009C2×C4—1221no—
1010C2×C4—1221no—
1011C2×C4—2441no—
1012C2×C4—2441no—
1013C2×C4—2441no—
1014C2×C4—2441no—
1015C2×C4—2441no—
1016C2×C4—2441no—
1017C2×C4—2441no—
1018C2×C4—2441no—
1019C2×C4—2441no—
1020C2×C4—2441no—
1021C2×C4—2441no—
1022C2×C4—2441no—
1023C2×C4—2441no—
1024C2×C4—2441no—
1025C2×C4—2441no—
1026C2×C4—2441no—
1027C2×C4—2441no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4—2441no—
1031C2×C4—2441no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—24416no—
1076C2×C4D4×#692312yes—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—41no—
1084C22—611no—
1085C22—611no—
1086C22—611no—
1087C22—611no—
1088C22—611no—
1089C22—611no—
1090C22—611no—
1091C22—611no—
1092C22—611no—
1093C22—611no—
1094C22—611no—
1095C22—611no—
1096C22—611no—
1097C22—611no—
1098C22—611no—
1099C22—611no—
1100C22—611no—
1101C22—611no—
1102C22—611no—
1103C22—611no—
1104C22—611no—
1105C22—611no—
1106C22—611no—
1107C22—611no—
1108C22—611no—
1109C22—611no—
1110C22—611no—
1111C22—611no—
1112C22—1222no—
1113C22—1222no—
1114C22—1222no—
1115C22—2442no—
1116C22—2442no—
1117C22—2442no—
1118C22—2442no—
1119C22—2442no—
1120C22—2442no—
1121C22—2442no—
1122C22—2442no—
1123C22—2441no—
1124C22—2441no—
1125C22—2441no—
1126C22—2441no—
1127C22C2×#1451985611yescharacteristic
1128C22C2×D4×#692311yescharacteristic
1129C22#41×#692311yescharacteristic
1130C22#1684082911yescharacteristic
1131C22#1684083111yescharacteristic
1132C22#1684083111yescharacteristic
1133C22#1684083111yescharacteristic
1134C4—22no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—1222no—
1141C4—4881no—
1142C4—4881no—
1143C4—4881no—
1144C4—4881no—
1145C4—2442no—
1146C4—2442no—
1147C4—2442no—
1148C4—2442no—
1149C4—2441no—
1150C4—2441no—
1151C4—2441no—
1152C4—2441no—
1153C4—2441no—
1154C2—42no—
1155C2—611no—
1156C2—611no—
1157C2—611no—
1158C2—611no—
1159C2—611no—
1160C2—611no—
1161C2—611no—
1162C2—611no—
1163C2—2442no—
1164C2#2146230111yescharacteristic
1165C2#2146230711yescharacteristic
1166C2#2146232011yescharacteristic
1167C2#2146232611yescharacteristic
1168C2#2146233511yescharacteristic
1169C2#2146234211yescharacteristic
1170C2#2146236611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#388C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#388#6923
hypocenterC61#14389
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#16840707C2semidirect
3. #21461008C2semidirect
4. #21461005C2semidirect
5. #21461005C2semidirect
6. #21461004C2semidirect
10. #21460999C2semidirect
11. #21460997C2semidirect
12. #21460994C2semidirect
51. #16839656C4semidirect
52. #16839655C4semidirect
53. #16839654C4semidirect
54. #16839653C4semidirect
55. #16839652C4semidirect
56. #16839651C4semidirect
57. #16839650C4semidirect
60. C61×#388C4semidirect
124. C2×C4⋊Dic61C2×C4semidirect
125. C2×#11758196C2×C4semidirect
126. C2×#11758196C2×C4semidirect
144. C2×C4×Dic61C2×C4semidirect
145. C2×C4×Dic61C2×C4semidirect
146. C2×C4×Dic61C2×C4semidirect
149. #14519684C2×C4semidirect
150. #14519684C2×C4semidirect
151. #14519684C2×C4semidirect
152. #14519684C2×C4semidirect
153. #14519684C2×C4semidirect
154. #14519684C2×C4semidirect
155. C2×C4⋊C4×C61C2×C4semidirect
159. C2×C42×C61C2×C4semidirect
160. #95×C61C2×C4semidirect
161. #95×C61C2×C4semidirect
621. #388#6923semidirect
646. C61#14389semidirect
683. C2×C4⋊C4C2×#6923semidirect
719. C2×C42C2×#6923semidirect
746. #95C2×#6923semidirect
747. #95C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407092
C2×#168407072
#214610082
#214610052
#214610042
#214610032
#214610022
#214610002
#214609992
#214609972
#214609942
#214609922
#388×D612
#1438961