Finite Group Databasebeta

← #29688935

Subgroups — #29688935

Order 15616.

1502 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840271C211yesmaximal, characteristic
2C2×#16839728C211yesmaximal, characteristic, complemented
3C2×#16839727C211yesmaximal, characteristic, complemented
4#21446117C211yesmaximal, characteristic, complemented
5#21446115C211yesmaximal, characteristic, complemented
6#21446114C211yesmaximal, characteristic, complemented
7#21446113C211yesmaximal, characteristic, complemented
8#21446111C211yesmaximal, characteristic, complemented
9#21446110C211yesmaximal, characteristic, complemented
10#21446108C211yesmaximal, characteristic, complemented
11#21445889C211yesmaximal, characteristic, complemented
12#21445889C211yesmaximal, characteristic, complemented
13#21445728C211yesmaximal, characteristic, complemented
14#21445728C211yesmaximal, characteristic, complemented
15C61×#1869C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×#11758194C2211yescharacteristic, complemented
19C22×#11758189C2211yescharacteristic, complemented
20C22×C8×D61C2211yescharacteristic, complemented
21#16840271—24no—
22#16840271—24no—
23C2×#14519762C411yescharacteristic
24C2×#14519759C411yescharacteristic
25C2×#14519755C411yescharacteristic
26C2×#14519754C411yescharacteristic
27C2×#14519750C411yescharacteristic
28C2×#14519749C411yescharacteristic
29C2×#14519747C411yescharacteristic
30C2×#14519745C411yescharacteristic
31C2×C4×D244C2211yescharacteristic
32C2×C4×C22⋊D61C2211yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519734C2211yescharacteristic
35#16839728—24no—
36#16839727—24no—
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic, complemented
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48C2×#14519689C2211yescharacteristic, complemented
49C2×#14519689C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56C23×C8×C61C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic, complemented
61C61×#336C2211yescharacteristic, complemented
62C61×#336C2211yescharacteristic, complemented
63C24×D61C2×C411yescharacteristic
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222—41no—
68C2×#11758222D414yes—
69C2×#11758222D414yes—
70C22×Dic122C2×C411yescharacteristic
71C22×D244C2×C411yescharacteristic
72C22×D244C2×C411yescharacteristic
73C22×C22⋊D61C2×C411yescharacteristic
74C22×C22⋊D61C2×C411yescharacteristic
75C22×C22⋊D61C2×C411yescharacteristic
76C22×C22⋊D61C2×C411yescharacteristic
77C23×Dic61C2×C411yescharacteristic
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C2×#11758194—22no—
90C2×#11758194—41no—
91C2×#11758194—41no—
92C2×#11758189—22no—
93C2×#11758189—41no—
94C2×#11758189—41no—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C2×C8×D61—22no—
100C2×C8×D61—41no—
101C2×C8×D61—41no—
102#14519762—24no—
103#14519759—24no—
104#14519755—24no—
105#14519754—24no—
106#14519750—24no—
107#14519749—24no—
108#14519747—24no—
109#14519745—24no—
110C4×D244—22no—
111C4×D244—22no—
112C4×C22⋊D61—22no—
113C4×C22⋊D61—22no—
114C4×C22⋊D61—22no—
115C4×C22⋊D61—22no—
116#14519734—22no—
117#14519734—22no—
118C2×C4⋊Dic61C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×C22⋊Dic61C2×C411yescharacteristic
124C2×C22⋊Dic61C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×C4×Dic61C2311yescharacteristic
132C22⋊#92418—22no—
133C22⋊#92418—41no—
134C22⋊#92418—41no—
135#14519689—22no—
136#14519689—22no—
137#14519689—22no—
138#14519689—22no—
139#14519689—22no—
140#14519689—22no—
141#14519689—41no—
142#14519689—41no—
143#14519689—41no—
144#14519689—41no—
145C22×D4×C61C2×C411yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61—22no—
149C22×C8×C61—41no—
150C22×C8×C61—41no—
151C22×C8×C61C2311yescharacteristic
152C22×C8×C61C2311yescharacteristic
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155C4×D4×C61—22no—
156C4×D4×C61—22no—
157C2×C4⋊C4×C61C2×C411yescharacteristic
158C2×C22⋊C4×C61C2×C411yescharacteristic
159C2×C22⋊C4×C61C2×C411yescharacteristic
160C2×C42×C61C2311yescharacteristic
161C22⋊C8×C61—22no—
162C22⋊C8×C61—41no—
163C22⋊C8×C61—41no—
164C24×C61C22×C411yescharacteristic
165C24×C61C22×C411yescharacteristic
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—41no—
170C23×D61—41no—
171C23×D61—41no—
172C23×D61—41no—
173C23×D61C22×C411yescharacteristic
174C23×D61C22×C411yescharacteristic
175C23×D61C22×C411yescharacteristic
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—41no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61C22×C411yescharacteristic
190C22×C4×C61C22×C411yescharacteristic
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—41no—
201C2×C22⋊D61—41no—
202C2×C22⋊D61—41no—
203C2×C22⋊D61—41no—
204C2×C22⋊D61—41no—
205C2×C22⋊D61—41no—
206C2×C22⋊D61C22⋊C414yes—
207C2×C22⋊D61C22⋊C414yes—
208C22×Dic61—22no—
209C22×Dic61—41no—
210C22×Dic61—41no—
211C22×Dic61C22×C411yescharacteristic
212C22×Dic61C22×C411yescharacteristic
213C22×Dic61C22×C411yescharacteristic
214C22×Dic61C22×C411yescharacteristic
215C22×Dic61C22×C411yescharacteristic
216#11758222—44no—
217#11758222—44no—
218#11758222—44no—
219#11758222—44no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—41no—
223C2×D244—41no—
224C2×D244—41no—
225C2×D244C22⋊C414yes—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—22no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—22no—
242C2×C4×D61—44no—
243C2×C4×D61—44no—
244C2×C4×D61—44no—
245C2×C4×D61—44no—
246C2×C4×D61—41no—
247C2×C4×D61—41no—
248C2×C4×D61—41no—
249C2×C4×D61—41no—
250C2×C4×D61C2×D412yes—
251C2×C4×D61C2×D412yes—
252C2×C4×D61C2×D412yes—
253C2×C4×D61C2×D412yes—
254C2×Dic122—41no—
255C2×Dic122—41no—
256C2×Dic122C22⋊C414yes—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—44no—
270C4⋊C4×C61—22no—
271C22⋊C4×C61—22no—
272C22⋊C4×C61—22no—
273C42×C61—21no—
274C42×C61—21no—
275C22⋊Dic61—22no—
276C22⋊Dic61—22no—
277#11758198—22no—
278#11758198—22no—
279#11758198—22no—
280#11758198—22no—
281#11758198—22no—
282#11758198—22no—
283C4⋊Dic61—22no—
284#11758196—22no—
285#11758196—22no—
286#11758196—22no—
287#11758196—22no—
288C4×Dic61—21no—
289C4×Dic61—21no—
290#11758194—44no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—21no—
301C2×#92418—21no—
302C2×#92418—21no—
303#11758189—44no—
304C8×D61—44no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61C2×C22⋊C412yes—
318C23×C61#13112yes—
319C23×C61C23×C411yescharacteristic
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—44no—
339C22×D61—44no—
340C22×D61—44no—
341C22×D61—44no—
342C22×D61—44no—
343C22×D61—44no—
344C22×D61—44no—
345C22×D61C2×C22⋊C412yes—
346C22×D61C2×C22⋊C412yes—
347C22×D61#13112yes—
348D4×C61—44no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61C2×C22⋊C412yes—
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61H(5,𝔽2)11yescharacteristic
372C2×C4×C61H(5,𝔽2)11yescharacteristic
373C2×C4×C61H(5,𝔽2)11yescharacteristic
374C2×C4×C61H(5,𝔽2)11yescharacteristic
375C22⋊D61—44no—
376C22⋊D61—44no—
377C22⋊D61—44no—
378C22⋊D61—44no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—44no—
393C2×Dic61C2×C22⋊C412yes—
394C2×Dic61C2×C22⋊C412yes—
395D244—44no—
396D244—44no—
397C4×D61—22no—
398C4×D61—22no—
399C4×D61—22no—
400C4×D61—22no—
401C4×D61—22no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—44no—
406C4×D61—44no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411Dic122—44no—
412C8×C61—41no—
413C8×C61—41no—
414C8×C61—41no—
415C8×C61—41no—
416#92418—41no—
417#92418—41no—
418#92418—41no—
419#92418—41no—
420#21744—611nomaximal, Sylow
421C22×C61—22no—
422C22×C61—22no—
423C22×C61—22no—
424C22×C61—22no—
425C22×C61—22no—
426C22×C61—22no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61C22×C22⋊C411yescharacteristic
436C22×C61#51811yescharacteristic
437C22×C61#51811yescharacteristic
438C22×C61C2×#13111yescharacteristic
439C22×C61C2×#13111yescharacteristic
440C22×C61#56811yescharacteristic
441C22×C61#56811yescharacteristic
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—22no—
445C2×D61—22no—
446C2×D61—22no—
447C2×D61—22no—
448C2×D61—22no—
449C2×D61—22no—
450C2×D61—22no—
451C2×D61—416no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—41no—
460C2×D61—41no—
461C2×D61—41no—
462C2×D61—41no—
463C2×D61—41no—
464C4×C61—22no—
465C4×C61—41no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61#53411yescharacteristic
469C4×C61#53411yescharacteristic
470C4×C61#53411yescharacteristic
471C4×C61#53411yescharacteristic
472Dic61—22no—
473Dic61—22no—
474Dic61—41no—
475Dic61—41no—
476Dic61—41no—
477C2×#525—611no—
478C2×#408—611no—
479C2×#408—611no—
480#1870—611no—
481#1870—611no—
482#1870—611no—
483#1870—611no—
484#1869—611no—
485#1869—611no—
486#1869—611no—
487#1869D6111yescharacteristic, complemented
488#1818—611no—
489#1818—611no—
490#1779—611no—
491#1779—611no—
492C2×C61—42no—
493C2×C61—42no—
494C2×C61#230811yescharacteristic
495C2×C61#288011yescharacteristic
496C2×C61#288011yescharacteristic
497C2×C61#297611yescharacteristic
498C2×C61#297611yescharacteristic
499C2×C61#297711yescharacteristic
500C2×C61#297811yescharacteristic
501D61—42no—
502D61—42no—
503D61—42no—
504C22×#41—611no—
505C24×C4—611no—
506C22×M16—611no—
507C22×M16—611no—
508C23×C8—611no—
509C23×C8C2×D6111yescharacteristic, complemented
510#525—1224no—
511#525—1224no—
512C2×#123—611no—
513C2×#123—611no—
514C2×C22⋊Q8—611no—
515C2×C22⋊Q8—611no—
516C2×#121—611no—
517C2×#121—611no—
518C2×#120—611no—
519C2×#120—611no—
520C2×C4×D4—611no—
521C2×C4×D4—611no—
522C2×C4×D4—611no—
523C2×C4×D4C2×D6111yescharacteristic
524C2×#117—611no—
525#408—1224no—
526#408—1224no—
527C2×C22⋊C8—611no—
528C2×C22⋊C8—611no—
529C2×C22⋊C8—611no—
530C2×C22⋊C8—611no—
531C2×C22⋊C8—611no—
532C2×C22⋊C8—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×C22⋊C8—611no—
536C2×C22⋊C8—611no—
537C2×C22⋊C8—611no—
538C2×C22⋊C8—611no—
539C2×C22⋊C8—611no—
540C2×C22⋊C8C2×D6111yescharacteristic
541C2×C22⋊C8C2×D6111yescharacteristic
542C2×C22⋊C8C2×D6111yescharacteristic, complemented
543#336—611no—
544#336—611no—
545#336—611no—
546#336—611no—
547#336—611no—
548#336—611no—
549#336C2×D6111yescharacteristic, complemented
550#336C2×D6111yescharacteristic, complemented
551C61#2174411yescharacteristic, complemented, Sylow
552C25—611no—
553C2×#41—614no—
554C2×#41—614no—
555C2×#41—2441no—
556C2×#41—2441no—
557C2×#41—2441no—
558C2×#41—2441no—
559C22×Q8—611no—
560C22×D4—611no—
561C22×D4—611no—
562C22×D4—611no—
563C22×D4—611no—
564C22×D4—611no—
565C22×D4—611no—
566C22×D4C4×D6111yescharacteristic
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—1222no—
574C23×C4—1222no—
575C23×C4—2441no—
576C23×C4—2441no—
577C23×C4—2441no—
578C23×C4—2441no—
579C23×C4C22×D6111yescharacteristic
580C23×C4C22×D6111yescharacteristic
581C2×M16—1222no—
582C2×M16—1222no—
583C2×M16—2441no—
584C2×M16—2441no—
585C2×M16—2441no—
586C2×M16—2441no—
587C22×C8—22no—
588C22×C8—41no—
589C22×C8—41no—
590C22×C8—611no—
591C22×C8—611no—
592C22×C8—611no—
593C22×C8—611no—
594C22×C8—1222no—
595C22×C8—2441no—
596C22×C8—2441no—
597C22×C8C22×D6111yescharacteristic
598C22×C8C22×D6111yescharacteristic
599C22×C8C22×D6111yescharacteristic
600C22×C8C22×D6111yescharacteristic
601#123—1224no—
602#123—1224no—
603C22⋊Q8—1224no—
604C22⋊Q8—1224no—
605#121—1224no—
606#121—1224no—
607#120—1224no—
608#120—1224no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—1222no—
612C4×D4—1222no—
613C4×D4—1222no—
614C4×D4—1222no—
615C4×D4—1222no—
616C4×D4—1222no—
617#117—1222no—
618#117—1222no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—611no—
624C2×C4⋊C4C4×D6111yescharacteristic
625C2×C22⋊C4—611no—
626C2×C22⋊C4—611no—
627C2×C22⋊C4—611no—
628C2×C22⋊C4—611no—
629C2×C22⋊C4—611no—
630C2×C22⋊C4—611no—
631C2×C22⋊C4—611no—
632C2×C22⋊C4—611no—
633C2×C22⋊C4C4×D6111yescharacteristic
634C2×C22⋊C4C4×D6111yescharacteristic
635C2×C42—611no—
636C2×C42C22×D6111yescharacteristic
637C22⋊C8—22no—
638C22⋊C8—41no—
639C22⋊C8—41no—
640C22⋊C8—1222no—
641C22⋊C8—1222no—
642C22⋊C8—1222no—
643C22⋊C8—1222no—
644C22⋊C8—1222no—
645C22⋊C8—1222no—
646C22⋊C8—1222no—
647C22⋊C8—2441no—
648C22⋊C8—2441no—
649C22⋊C8—2441no—
650C22⋊C8—2441no—
651C22⋊C8—2441no—
652C22⋊C8—2441no—
653C24—611no—
654C24—611no—
655C24—611no—
656C24—1222no—
657C24—1222no—
658C24—1222no—
659C24—2441no—
660C24—2441no—
661C24—2441no—
662C24—2441no—
663C24C2×C4×D6111yescharacteristic
664C24C2×C4×D6111yescharacteristic
665#41—2444no—
666#41—2444no—
667#41—2444no—
668#41—2444no—
669C2×Q8—614no—
670C2×Q8—2441no—
671C2×Q8—2441no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—41no—
675C2×D4—614no—
676C2×D4—614no—
677C2×D4—614no—
678C2×D4—1222no—
679C2×D4—1222no—
680C2×D4—1222no—
681C2×D4—1222no—
682C2×D4—1222no—
683C2×D4—1222no—
684C2×D4—2441no—
685C2×D4—2441no—
686C2×D4—2441no—
687C2×D4—2441no—
688C2×D4—2441no—
689C2×D4—2441no—
690C2×D4—2441no—
691C2×D4—2441no—
692C2×D4—2441no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—612no—
706C22×C4—612no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1222no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—2441no—
730C22×C4—2441no—
731C22×C4—2441no—
732C22×C4—2441no—
733C22×C4—2444no—
734C22×C4—2444no—
735C22×C4—2444no—
736C22×C4—2444no—
737C22×C4—2441no—
738C22×C4—2441no—
739C22×C4C2×C4×D6111yescharacteristic
740C22×C4C2×C4×D6111yescharacteristic
741C22×C4C2×C4×D6111yescharacteristic
742C22×C4C2×C4×D6111yescharacteristic
743C22×C4D4×D6112yes—
744C22×C4D4×D6112yes—
745C22×C4C23×D6111yescharacteristic
746M16—2444no—
747M16—2444no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—44no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—1221no—
769C2×C8—1221no—
770C2×C8—1221no—
771C2×C8—1221no—
772C2×C8—1221no—
773C2×C8—2444no—
774C4⋊C4—22no—
775C4⋊C4—1222no—
776C4⋊C4—1222no—
777C4⋊C4—1222no—
778C4⋊C4—1222no—
779C4⋊C4—1222no—
780C22⋊C4—22no—
781C22⋊C4—22no—
782C22⋊C4—1222no—
783C22⋊C4—1222no—
784C22⋊C4—1222no—
785C22⋊C4—1222no—
786C22⋊C4—1222no—
787C22⋊C4—1222no—
788C22⋊C4—1222no—
789C22⋊C4—1222no—
790C42—21no—
791C42—21no—
792C42—1221no—
793C42—1221no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—612no—
807C23—612no—
808C23—612no—
809C23—1221no—
810C23—1221no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—1221no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1221no—
821C23—1221no—
822C23—1221no—
823C23—1221no—
824C23—1221no—
825C23—1221no—
826C23—1221no—
827C23—2444no—
828C23—2444no—
829C23—2444no—
830C23—2444no—
831C23—2444no—
832C23—2444no—
833C23—2444no—
834C23C22⋊C4×D6112yes—
835C23#1451978312yes—
836C23C22×C4×D6111yescharacteristic
837Q8—2444no—
838D4—44no—
839D4—2444no—
840D4—2444no—
841D4—2444no—
842D4—2444no—
843D4—2444no—
844D4—2444no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—612no—
865C2×C4—612no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—2444no—
888C2×C4—2444no—
889C2×C4—2444no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4C22⋊C4×D6112yes—
895C2×C4C2×D4×D6111yescharacteristic
896C2×C4C2×D4×D6111yescharacteristic
897C2×C4#1451982211yescharacteristic
898C2×C4#1451982211yescharacteristic
899C2×C4#1451982311yescharacteristic
900C2×C4#1451982311yescharacteristic
901C8—41no—
902C8—41no—
903C8—41no—
904C8—41no—
905C8—2441no—
906C8—2441no—
907C8—2441no—
908C8—2441no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—1222no—
924C22—1222no—
925C22—1222no—
926C22—1222no—
927C22—1222no—
928C22—1222no—
929C22—1222no—
930C22—1222no—
931C22—1222no—
932C22—24416no—
933C22—2441no—
934C22—2441no—
935C22—2441no—
936C22—2441no—
937C22—2441no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22—2441no—
942C22—2441no—
943C22—2441no—
944C22—2441no—
945C22C2×C22⋊C4×D6111yescharacteristic
946C22#1684023411yescharacteristic
947C22#1684023411yescharacteristic
948C22#131×D6111yescharacteristic
949C22C2×#1451978311yescharacteristic
950C22#1684052711yescharacteristic
951C22#1684052811yescharacteristic
952C4—22no—
953C4—41no—
954C4—41no—
955C4—41no—
956C4—1222no—
957C4—1222no—
958C4—2441no—
959C4—2441no—
960C4—2441no—
961C4#1684032011yescharacteristic
962C4#1684032011yescharacteristic
963C4#1684032211yescharacteristic
964C4#1684032311yescharacteristic
965C2—42no—
966C2—42no—
967C2—2442no—
968C2—2442no—
969C2—2442no—
970C2#2144839311yescharacteristic
971C2#2145426511yescharacteristic
972C2#2145426711yescharacteristic
973C2#2145486111yescharacteristic
974C2#2145486611yescharacteristic
975C2#2145487211yescharacteristic
976C2#2145487811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1869C2
prime radicalC2×#16840271C2
cosocleC22×C4×C61C24
hypercenter#1869D61
hypocenterC61#21744
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×#16839728C2semidirect
3. C2×#16839727C2semidirect
4. #21446117C2semidirect
5. #21446115C2semidirect
6. #21446114C2semidirect
7. #21446113C2semidirect
8. #21446111C2semidirect
9. #21446110C2semidirect
10. #21446108C2semidirect
11. #21445889C2semidirect
12. #21445889C2semidirect
13. #21445728C2semidirect
14. #21445728C2semidirect
15. C61×#1869C2semidirect
18. C22×#11758194C22semidirect
19. C22×#11758189C22semidirect
20. C22×C8×D61C22semidirect
39. C2×C22⋊#92418C22semidirect
48. C2×#14519689C22semidirect
49. C2×#14519689C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
54. #16839516C22semidirect
55. #16839516C22semidirect
56. C23×C8×C61C22semidirect
60. C2×C22⋊C8×C61C22semidirect
61. C61×#336C22semidirect
62. C61×#336C22semidirect
487. #1869D61semidirect
509. C23×C8C2×D61semidirect
542. C2×C22⋊C8C2×D61semidirect
549. #336C2×D61semidirect
550. #336C2×D61semidirect
551. C61#21744semidirect

Maximal subgroups

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

subgroupindex
C2×#168402712
C2×#168397282
C2×#168397272
#214461172
#214461152
#214461142
#214461132
#214461112
#214461102
#214461082
#214458892
#214457282
C61×#18692
#2174461