Finite Group Databasebeta

← #29696130

Subgroups — #29696130

Order 15616.

1168 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840290C211yesmaximal, characteristic
2C2×#16839836C211yesmaximal, characteristic, complemented
3C2×#16839830C211yesmaximal, characteristic, complemented
4#21446757C211yesmaximal, characteristic, complemented
5#21446757C211yesmaximal, characteristic, complemented
6#21446115C211yesmaximal, characteristic, complemented
7#21446114C211yesmaximal, characteristic, complemented
8#21446110C211yesmaximal, characteristic, complemented
9#21446109C211yesmaximal, characteristic, complemented
10#21445889C211yesmaximal, characteristic, complemented
11#21445798C211yesmaximal, characteristic, complemented
12#21445580C211yesmaximal, characteristic, complemented
13#21445516C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1818C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840290—24no—
21#16840290—24no—
22C2×#14519772C411yescharacteristic
23C2×#14519770C411yescharacteristic
24C2×#14519767C411yescharacteristic
25C2×#14519763C411yescharacteristic
26C2×#14519762C411yescharacteristic
27C2×#14519759C411yescharacteristic
28C2×#14519755C411yescharacteristic
29C2×#14519750C411yescharacteristic
30C2×C4×Dic122C2211yescharacteristic
31C2×C4×D244C2211yescharacteristic
32C2×C4×C22⋊D61C2211yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519734C2211yescharacteristic
35C2×C42×D61C2211yescharacteristic
36#16839836—24no—
37#16839830—24no—
38C2×#14519706C2211yescharacteristic
39C2×#14519706C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519687C2211yescharacteristic
47C2×#14519687C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C2×#11758194—22no—
72C2×#11758194—22no—
73C2×#11758194—41no—
74C2×#11758189—22no—
75C2×#11758189—22no—
76C2×#11758189—41no—
77C22×#92418—22no—
78C22×#92418—22no—
79C22×#92418—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C2×C8×D61—22no—
85C2×C8×D61—22no—
86C2×C8×D61—41no—
87#14519772—24no—
88#14519770—24no—
89#14519767—24no—
90#14519763—24no—
91#14519762—24no—
92#14519759—24no—
93#14519755—24no—
94#14519750—24no—
95C4×Dic122—22no—
96C4×Dic122—22no—
97C4×D244—22no—
98C4×D244—22no—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101C4×C22⋊D61D414yes—
102C4×C22⋊D61D414yes—
103#14519734—22no—
104#14519734—22no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×C4⋊Dic61C2×C411yescharacteristic
107C2×#11758196C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196C2×C411yescharacteristic
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×C22⋊Dic61C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×C4×Dic61C2×C411yescharacteristic
122C2×C4×Dic61C2×C411yescharacteristic
123C2×C4×Dic61C2311yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125C42×D61—22no—
126C42×D61—22no—
127#14519706—22no—
128#14519706—22no—
129#14519689—22no—
130#14519689—22no—
131#14519689—22no—
132#14519689—22no—
133#14519689—41no—
134#14519689—41no—
135#14519687—22no—
136#14519687—22no—
137C23×C4×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142#117×C61—22no—
143#117×C61—22no—
144C2×C4⋊C4×C61C2×C411yescharacteristic
145C2×C4⋊C4×C61C2×C411yescharacteristic
146C2×C22⋊C4×C61C2×C411yescharacteristic
147C2×C22⋊C4×C61C2×C411yescharacteristic
148C2×C42×C61C2311yescharacteristic
149C2×C42×C61C2311yescharacteristic
150C22⋊C8×C61—22no—
151C22⋊C8×C61—22no—
152C24×C61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—41no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61C22⋊C414yes—
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—41no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—22no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—22no—
194C2×C4×D61—22no—
195C2×C4×D61—41no—
196C2×C4×D61—41no—
197C2×C4×D61—41no—
198C2×C4×D61C2×D412yes—
199C2×C4×D61C2×D412yes—
200C2×Dic122—22no—
201C2×Dic122—41no—
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—21no—
214C2×C8×C61—21no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C22⋊Dic61—22no—
224C22⋊Dic61C22⋊C414yes—
225#11758198—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
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#11758196C22⋊C414yes—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C4×Dic61C2×D412yes—
244C4×Dic61C2×D412yes—
245#11758194—44no—
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—21no—
256C2×#92418—44no—
257C2×#92418#4112yes—
258C2×#92418#4112yes—
259#11758189—44no—
260C8×D61—44no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61C2×C22⋊C412yes—
268C23×C61C23×C411yescharacteristic
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×D61—21no—
281C22×D61C2×C22⋊C412yes—
282C22×D61#13112yes—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61C2×C22⋊C412yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C612−1+411yescharacteristic
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—44no—
334C4×D61—44no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339Dic122—44no—
340C8×C61—41no—
341C8×C61—41no—
342C8×C61—41no—
343C8×C61—41no—
344#92418—22no—
345#92418—22no—
346#92418—41no—
347#92418—41no—
348#22475—611nomaximal, Sylow
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61C22×C22⋊C411yescharacteristic
357C22×C61C4×#4111yescharacteristic
358C22×C61#52011yescharacteristic
359C22×C61C2×#13111yescharacteristic
360C22×C61#56811yescharacteristic
361C22×C61#56811yescharacteristic
362C22×C61#56811yescharacteristic
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C4×C61—22no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61—41no—
382C4×C61#54611yescharacteristic
383C4×C61#54611yescharacteristic
384C4×C61#54711yescharacteristic
385C4×C61#54711yescharacteristic
386Dic61—22no—
387Dic61—22no—
388Dic61—22no—
389Dic61—41no—
390Dic61—41no—
391Dic61—41no—
392C2×#529—611no—
393C2×#435—611no—
394C2×#435—611no—
395#1985—611no—
396#1985—611no—
397#1870—611no—
398#1870—611no—
399#1869—611no—
400#1869—611no—
401#1818—611no—
402#1818D6111yescharacteristic, complemented
403#1797—611no—
404#1749—611no—
405#1729—611no—
406#1729—611no—
407C2×C61—42no—
408C2×C61#233911yescharacteristic
409C2×C61#287911yescharacteristic
410C2×C61#288011yescharacteristic
411C2×C61#296711yescharacteristic
412C2×C61#296811yescharacteristic
413C2×C61#299211yescharacteristic
414C2×C61#299511yescharacteristic
415D61—42no—
416D61—42no—
417C22×M16—611no—
418C22×M16—611no—
419C23×C8—611no—
420C23×C8—611no—
421#529—1224no—
422#529—1224no—
423C2×#126—611no—
424C2×#126—611no—
425C2×#125—611no—
426C2×#124—611no—
427C2×#123—611no—
428C2×#123—611no—
429C2×C22⋊Q8—611no—
430C2×#121—611no—
431C2×C4×Q8—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×#117—611no—
436C2×#117C2×D6111yescharacteristic
437C22×C42—611no—
438#435—1224no—
439#435—1224no—
440C2×C4⋊C8—611no—
441C2×C4⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8C2×D6111yescharacteristic
449C2×C22⋊C8C2×D6111yescharacteristic
450C2×#97—611no—
451C2×#97—611no—
452#336—611no—
453#336—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
462#336C2×D6111yescharacteristic
463#336C2×D6111yescharacteristic
464C61#2247511yescharacteristic, complemented, Sylow
465C22×Q8—611no—
466C22×D4—611no—
467C22×D4—611no—
468C22×D4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4C22×D6111yescharacteristic
474C2×M16—1222no—
475C2×M16—1222no—
476C2×M16—1222no—
477C2×M16—1222no—
478C2×M16—2441no—
479C2×M16—2441no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8—1222no—
485C22×C8—1222no—
486C22×C8—1222no—
487C22×C8—1222no—
488C22×C8—2441no—
489C22×C8—2441no—
490C22×C8C22×D6111yescharacteristic
491C22×C8C22×D6111yescharacteristic
492C22×C8C22×D6111yescharacteristic
493C22×C8C22×D6111yescharacteristic
494#126—1224no—
495#126—1224no—
496#125—1224no—
497#124—1224no—
498#123—1224no—
499#123—1224no—
500C22⋊Q8—1224no—
501#121—1224no—
502C4×Q8—1222no—
503C4×Q8—1222no—
504C4×D4—614no—
505C4×D4—614no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510#117—22no—
511#117—22no—
512#117—1222no—
513#117—1222no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4C4×D6111yescharacteristic
523C2×C4⋊C4C4×D6111yescharacteristic
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4C4×D6111yescharacteristic
533C2×C22⋊C4C4×D6111yescharacteristic
534C2×C42—611no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—1222no—
539C2×C42—1222no—
540C2×C42C22×D6111yescharacteristic
541C2×C42C22×D6111yescharacteristic
542C4⋊C8—1222no—
543C4⋊C8—1222no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—1222no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549C22⋊C8—1222no—
550C22⋊C8—2441no—
551C22⋊C8—2441no—
552#97—1222no—
553#97—1222no—
554C24—611no—
555C24—611no—
556C24C2×C4×D6111yescharacteristic
557C2×Q8—1222no—
558C2×Q8—2441no—
559C2×Q8—2441no—
560C2×D4—614no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—2441no—
566C2×D4—2441no—
567C2×D4—2441no—
568C2×D4—2441no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—2441no—
595C22×C4—2441no—
596C22×C4—2441no—
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×C4×D6111yescharacteristic
601C22×C4C2×C4×D6111yescharacteristic
602C22×C4D4×D6112yes—
603C22×C4D4×D6112yes—
604C22×C4C23×D6111yescharacteristic
605M16—2444no—
606M16—2444no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—612no—
620C2×C8—612no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—2444no—
632C2×C8—2444no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—614no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C4⋊C4—1222no—
640C4⋊C4—1222no—
641C4⋊C4—1222no—
642C4⋊C4—1222no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—614no—
646C22⋊C4—614no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—612no—
658C42—612no—
659C42—1222no—
660C42—1222no—
661C42—1221no—
662C42—1221no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—612no—
670C23—612no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23C22⋊C4×D6112yes—
684C23C22×C4×D6111yescharacteristic
685Q8—2444no—
686D4—2444no—
687D4—2444no—
688D4—2444no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—2444no—
730C2×C4—2444no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4C22⋊C4×D6112yes—
736C2×C4C2×D4×D6111yescharacteristic
737C2×C4C2×D4×D6111yescharacteristic
738C2×C4#41×D6111yescharacteristic
739C2×C4#41×D6111yescharacteristic
740C2×C4#1451982311yescharacteristic
741C2×C4#1451982411yescharacteristic
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—1222no—
747C8—1222no—
748C8—2441no—
749C8—2441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—1222no—
758C22—1222no—
759C22—1222no—
760C22—1222no—
761C22—1222no—
762C22—1222no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22—2441no—
768C22—2441no—
769C22—2441no—
770C22—2441no—
771C22C2×C22⋊C4×D6111yescharacteristic
772C22#1684023011yescharacteristic
773C22#1684024211yescharacteristic
774C22#131×D6111yescharacteristic
775C22#1684052711yescharacteristic
776C22#1684052711yescharacteristic
777C22#1684052711yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—1222no—
784C4—1222no—
785C4—1222no—
786C4—2441no—
787C4—2441no—
788C4—2441no—
789C4#1684040411yescharacteristic
790C4#1684040411yescharacteristic
791C4#1684041011yescharacteristic
792C4#1684041011yescharacteristic
793C2—42no—
794C2—2442no—
795C2—2442no—
796C2#2144864311yescharacteristic
797C2#2145426111yescharacteristic
798C2#2145426711yescharacteristic
799C2#2145480211yescharacteristic
800C2#2145481111yescharacteristic
801C2#2145495311yescharacteristic
802C2#2145498411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1818C2
prime radicalC2×#14519750C4
cosocleC22×C4×C61C24
hypercenter#1818D61
hypocenterC61#22475
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
2. C2×#16839836C2semidirect
3. C2×#16839830C2semidirect
4. #21446757C2semidirect
5. #21446757C2semidirect
6. #21446115C2semidirect
7. #21446114C2semidirect
8. #21446110C2semidirect
9. #21446109C2semidirect
10. #21445889C2semidirect
11. #21445798C2semidirect
12. #21445580C2semidirect
13. #21445516C2semidirect
14. #21445514C2semidirect
15. C61×#1818C2semidirect
402. #1818D61semidirect
464. C61#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#168402902
C2×#168398362
C2×#168398302
#214467572
#214461152
#214461142
#214461102
#214461092
#214458892
#214457982
#214455802
#214455162
#214455142
C61×#18182
#2247561