Finite Group Databasebeta

← #29685034

Subgroups — #29685034

Order 15616.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840296C211yesmaximal, characteristic
2C2×#16839824C211yesmaximal, characteristic, complemented
3C2×#16839719C211yesmaximal, characteristic, complemented
4#21446757C211yesmaximal, characteristic, complemented
5#21446753C211yesmaximal, characteristic, complemented
6#21446615C211yesmaximal, characteristic, complemented
7#21446611C211yesmaximal, characteristic, complemented
8#21446115C211yesmaximal, characteristic, complemented
9#21446113C211yesmaximal, characteristic, complemented
10#21446110C211yesmaximal, characteristic, complemented
11#21446108C211yesmaximal, characteristic, complemented
12#21445588C211yesmaximal, characteristic, complemented
13#21445588C211yesmaximal, characteristic, complemented
14C4×C22⋊#92418C211yesmaximal, characteristic, complemented
15C61×#1749C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840296—24no—
19#16840296—24no—
20C2×#14519771C411yescharacteristic
21C2×#14519771C411yescharacteristic
22C2×#14519769C411yescharacteristic
23C2×#14519765C411yescharacteristic
24C2×#14519760C411yescharacteristic
25C2×#14519760C411yescharacteristic
26C2×#14519756C411yescharacteristic
27C2×#14519751C411yescharacteristic
28C2×C4×Dic122C2211yescharacteristic
29C2×C4×D244C2211yescharacteristic
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×C4×C22⋊D61C2211yescharacteristic
32C2×#14519734C2211yescharacteristic
33C2×#14519734C2211yescharacteristic
34#16839824—24no—
35C2×#14519706C2211yescharacteristic
36C2×#14519706C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45#16839719—24no—
46C2×#14519687C2211yescharacteristic
47C2×C4×#92418C2211yescharacteristic
48C2×C4×#92418C2211yescharacteristic
49C2×C8×Dic61C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758189—22no—
70C2×#11758189—22no—
71C2×#11758189—22no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C2×C8×D61—22no—
77C2×C8×D61—22no—
78C2×C8×D61—22no—
79#14519771—24no—
80#14519771—24no—
81#14519769—24no—
82#14519765—24no—
83#14519760—24no—
84#14519760—24no—
85#14519756—24no—
86#14519751—24no—
87C4×Dic122—22no—
88C4×Dic122—22no—
89C4×D244—22no—
90C4×D244—22no—
91C4×C22⋊D61—22no—
92C4×C22⋊D61—22no—
93C4×C22⋊D61—22no—
94C4×C22⋊D61—22no—
95#14519734—22no—
96#14519734—22no—
97#14519734D414yes—
98#14519734D414yes—
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C2×#11758196C2×C411yescharacteristic
107C2×#11758196C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120C2×C4×Dic61C2311yescharacteristic
121#14519706—22no—
122#14519706—22no—
123C22⋊#92418—22no—
124C22⋊#92418—22no—
125#14519689—22no—
126#14519689—22no—
127#14519689—22no—
128#14519689—22no—
129#14519689—22no—
130#14519689—22no—
131#14519687—22no—
132C4×#92418—22no—
133C4×#92418—22no—
134C8×Dic61—22no—
135C23×C4×C61C2×C411yescharacteristic
136C23×C4×C61C2×C411yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C2×C42×C61—22no—
143C2×C42×C61—22no—
144C2×C42×C61C2×C411yescharacteristic
145C2×C42×C61C2×C411yescharacteristic
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C22⋊C8×C61—22no—
149C22⋊C8×C61—22no—
150#97×C61—22no—
151#97×C61—22no—
152C24×C61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—41no—
166C22×C4×C61—41no—
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C2411yescharacteristic
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—41no—
178C2×C22⋊D61—41no—
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—41no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61C2×D412yes—
199C2×C4×D61C2×D412yes—
200C2×Dic122—22no—
201C2×Dic122—22no—
202C2×Dic122—41no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61#4112yes—
214C2×C8×C61#4112yes—
215C42×C61—22no—
216C42×C61—22no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61C2×D412yes—
220C42×C61C2×D412yes—
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223#11758198—22no—
224#11758198—22no—
225#11758198—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198C22⋊C414yes—
230#11758198C22⋊C414yes—
231C4⋊Dic61—22no—
232C4⋊Dic61—22no—
233#11758196—22no—
234#11758196—22no—
235#11758196—22no—
236#11758196—22no—
237#11758196—22no—
238#11758196—22no—
239#11758196C22⋊C414yes—
240#11758196C22⋊C414yes—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C4×Dic61C2×D412yes—
244C4×Dic61C2×D412yes—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418#4112yes—
256C2×#92418#4112yes—
257#11758189—28no—
258C8×D61—28no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61#13112yes—
266C23×C61C23×C411yescharacteristic
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61C2×C22⋊C412yes—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—44no—
294C2×C4×C61—44no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61C2×C22⋊C412yes—
300C2×C4×C61C2×C22⋊C412yes—
301C2×C4×C61#13112yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C22⋊D61—44no—
309C22⋊D61—44no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61C2×C22⋊C412yes—
326C2×Dic61C2×C22⋊C412yes—
327C2×Dic61C2×C22⋊C412yes—
328D244—44no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337Dic122—44no—
338C8×C61—22no—
339C8×C61—22no—
340C8×C61—41no—
341C8×C61—41no—
342#92418—22no—
343#92418—22no—
344#92418—41no—
345#92418—41no—
346#21381—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61C22×C22⋊C411yescharacteristic
355C22×C61C4×#4111yescharacteristic
356C22×C61C4×#4111yescharacteristic
357C22×C61C2×#13111yescharacteristic
358C22×C61C2×#13111yescharacteristic
359C22×C61#56811yescharacteristic
360C22×C61#56811yescharacteristic
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C4×C61—22no—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61#52511yescharacteristic
381C4×C61#52511yescharacteristic
382C4×C61#53211yescharacteristic
383C4×C61#53211yescharacteristic
384Dic61—22no—
385Dic61—22no—
386Dic61—22no—
387Dic61—41no—
388Dic61—41no—
389Dic61—41no—
390C2×#529—611no—
391C2×#433—611no—
392C2×#405—611no—
393#1985—611no—
394#1984—611no—
395#1955—611no—
396#1954—611no—
397#1870—611no—
398#1870—611no—
399#1869—611no—
400#1869—611no—
401#1750—611no—
402#1750—611no—
403#1749D6111yescharacteristic, complemented
404C4×C22⋊C8—611no—
405C2×C61—42no—
406C2×C61#229711yescharacteristic
407C2×C61#288011yescharacteristic
408C2×C61#288011yescharacteristic
409C2×C61#296611yescharacteristic
410C2×C61#296711yescharacteristic
411C2×C61#296811yescharacteristic
412C2×C61#296911yescharacteristic
413D61—42no—
414D61—81no—
415C22×M16—611no—
416C23×C8—611no—
417#529—1224no—
418#529—1224no—
419C2×#126—611no—
420C2×#126—611no—
421C2×#125—611no—
422C2×#124—611no—
423C2×#123—611no—
424C2×#123—611no—
425C2×C22⋊Q8—611no—
426C2×#121—611no—
427C2×C4×Q8—611no—
428C2×C4×D4—611no—
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×#117—611no—
432C2×#117—611no—
433C22×C42C2×D6111yescharacteristic
434#433—1224no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437C2×C22⋊C8—611no—
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8C2×D6111yescharacteristic
446C2×C22⋊C8C2×D6111yescharacteristic
447#405—1224no—
448C2×#97—611no—
449C2×#97C2×D6111yescharacteristic
450C2×#97C2×D6111yescharacteristic
451C2×C4×C8—611no—
452C2×C4×C8—611no—
453C2×C4×C8—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336—611no—
460#336C2×D6111yescharacteristic
461#336C2×D6111yescharacteristic
462C61#2138111yescharacteristic, complemented, Sylow
463C22×Q8—611no—
464C22×D4—611no—
465C22×D4—611no—
466C22×D4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4C4×D6111yescharacteristic
470C23×C4C4×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C2×M16—1222no—
473C2×M16—1222no—
474C2×M16—1222no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—1222no—
480C22×C8—1222no—
481C22×C8—1222no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486#126—1224no—
487#126—1224no—
488#125—1224no—
489#124—1224no—
490#123—1224no—
491#123—1224no—
492C22⋊Q8—1224no—
493#121—1224no—
494C4×Q8—1222no—
495C4×Q8—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502#117—614no—
503#117—614no—
504#117—1222no—
505#117—1222no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—611no—
529C2×C42—611no—
530C2×C42C4×D6111yescharacteristic
531C2×C42C4×D6111yescharacteristic
532C2×C42C22×D6111yescharacteristic
533C2×C42C22×D6111yescharacteristic
534C4⋊C8—1222no—
535C4⋊C8—1222no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—1222no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542C22⋊C8—1222no—
543C22⋊C8—1222no—
544C22⋊C8—1222no—
545C22⋊C8—1222no—
546#97—22no—
547#97—22no—
548#97—1222no—
549C4×C8—1222no—
550C4×C8—1222no—
551C4×C8—1222no—
552C24—611no—
553C24—611no—
554C24C2×C4×D6111yescharacteristic
555C2×Q8—1222no—
556C2×Q8—1222no—
557C2×Q8—2441no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—2441no—
565C2×D4—2441no—
566C2×D4—2441no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×C4×D6111yescharacteristic
601C22×C4C2×C4×D6111yescharacteristic
602C22×C4C23×D6111yescharacteristic
603M16—1228no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—612no—
615C2×C8—612no—
616C2×C8—1228no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8#1175822212yes—
628C2×C8#1175822212yes—
629C4⋊C4—614no—
630C4⋊C4—614no—
631C4⋊C4—1222no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C22⋊C4—614no—
640C22⋊C4—614no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C42—21no—
650C42—21no—
651C42—22no—
652C42—22no—
653C42—612no—
654C42—612no—
655C42—1221no—
656C42—1221no—
657C42D4×D6112yes—
658C42D4×D6112yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—612no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23#1451978512yes—
680C23C22×C4×D6111yescharacteristic
681Q8—2444no—
682D4—2444no—
683D4—2444no—
684D4—2444no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—612no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4C22⋊C4×D6112yes—
730C2×C4C22⋊C4×D6112yes—
731C2×C4#1451978512yes—
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×D4×D6111yescharacteristic
734C2×C4#41×D6111yescharacteristic
735C2×C4#41×D6111yescharacteristic
736C2×C4C2×#1175822211yescharacteristic
737C2×C4C2×#1175822211yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C8—1222no—
743C8—1222no—
744C8—2441no—
745C8—2441no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—1222no—
754C22—1222no—
755C22—1222no—
756C22—2441no—
757C22—2441no—
758C22—2441no—
759C22—2441no—
760C22—2441no—
761C22—2441no—
762C22—2441no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22C2×C22⋊C4×D6111yescharacteristic
768C22#1684023011yescharacteristic
769C22C4×#1175822211yescharacteristic
770C22C2×#1451978511yescharacteristic
771C22C2×#1451978511yescharacteristic
772C22#1684052811yescharacteristic
773C22#1684052811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—41no—
779C4—1222no—
780C4—1222no—
781C4—1222no—
782C4—2441no—
783C4—2441no—
784C4—2441no—
785C4#1684027111yescharacteristic
786C4#1684027111yescharacteristic
787C4#1684030911yescharacteristic
788C4#1684030911yescharacteristic
789C2—42no—
790C2—4881no—
791C2—2442no—
792C2#2144830511yescharacteristic
793C2#2145426911yescharacteristic
794C2#2145426911yescharacteristic
795C2#2145478811yescharacteristic
796C2#2145479911yescharacteristic
797C2#2145481311yescharacteristic
798C2#2145482311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1749C2
prime radicalC2×#14519751C4
cosocleC22×C4×C61C24
hypercenter#1749D61
hypocenterC61#21381
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#16839824C2semidirect
3. C2×#16839719C2semidirect
4. #21446757C2semidirect
5. #21446753C2semidirect
6. #21446615C2semidirect
7. #21446611C2semidirect
8. #21446115C2semidirect
9. #21446113C2semidirect
10. #21446110C2semidirect
11. #21446108C2semidirect
12. #21445588C2semidirect
13. #21445588C2semidirect
14. C4×C22⋊#92418C2semidirect
15. C61×#1749C2semidirect
403. #1749D61semidirect
462. C61#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#168402962
C2×#168398242
C2×#168397192
#214467572
#214467532
#214466152
#214466112
#214461152
#214461132
#214461102
#214461082
#214455882
C4×C22⋊#924182
C61×#17492
#2138161