Finite Group Databasebeta

← C2×#21456695 #30550693

Subgroups — C2×#21456695 #30550693

Order 15616.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840333C211yesmaximal, characteristic, complemented
2#21456695C2116yesmaximal, direct product factor
3C2×#16840097C211yesmaximal, characteristic, complemented
4C2×#16840100C211yesmaximal, characteristic, complemented
5C2×#16840083C211yesmaximal, characteristic, complemented
6C2×#16840092C211yesmaximal, characteristic, complemented
7C2×#16840018C211yesmaximal, characteristic, complemented
8C2×#16840006C211yesmaximal, characteristic, complemented
9C2×#16840001C211yesmaximal, characteristic, complemented
10C2×#16839989C211yesmaximal, characteristic, complemented
11C2×#16839924C211yesmaximal, characteristic, complemented
12C2×#16839924C211yesmaximal, characteristic, complemented
13C2×#16839917C211yesmaximal, characteristic, complemented
14C2×#16839900C211yesmaximal, characteristic, complemented
15C2×#16839729C211yesmaximal, characteristic, complemented
16C2×C61×#537C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758194C2211yescharacteristic
23C23×#92418C2211yescharacteristic
24#16840333—24no—
25#16840333C2218yescomplemented
26C2×#14519775—21no—
27C2×#14519764—21no—
28C2×#14519758—21no—
29C2×#14519758—21no—
30C2×#14519756C2211yescharacteristic
31C2×#14519756C2211yescharacteristic
32C2×#14519756C2211yescharacteristic
33C2×#14519756C2211yescharacteristic
34C2×#14519736C2211yescharacteristic
35#16840100C2218yescomplemented
36#16840097C2218yescomplemented
37#16840092C2218yescomplemented
38#16840083C2218yescomplemented
39#16840018C2218yescomplemented
40#16840006C2218yescomplemented
41#16840001C2218yescomplemented
42#16839989C2218yescomplemented
43#16839924C2218yescomplemented
44#16839924C2218yescomplemented
45#16839917C2218yescomplemented
46#16839900C2218yescomplemented
47C2×#14519710C2211yescharacteristic
48C2×#14519710C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×#14519708C2211yescharacteristic
51C2×#14519701C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519700C2211yescharacteristic
54C2×#14519700C2211yescharacteristic
55C2×#14519700C2211yescharacteristic
56C2×#14519700C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59#16839729C2218yescomplemented
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic
63C2×C22⋊#92418C2211yescharacteristic
64C22×#41×C61C2211yescharacteristic
65C22×#41×C61C2211yescharacteristic
66C61×#537—24no—
67C61×#537C2218yes—
68C2×C22⋊Q8×C61—21no—
69C2×C22⋊Q8×C61C2211yescharacteristic
70C2×C22⋊Q8×C61C2211yescharacteristic
71C2×#121×C61—21no—
72C2×#121×C61—21no—
73C2×#121×C61—21no—
74C2×#121×C61C2211yescharacteristic
75C2×#121×C61C2211yescharacteristic
76C22×C4⋊C4×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—22no—
79C22×Dic122—42no—
80C22×Dic122—42no—
81C22×Dic122C2311yescharacteristic
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2314yes—
84C23×Dic61—21no—
85C2×#11758202—42no—
86C2×#11758202—42no—
87C2×#11758202C2314yes—
88C2×#11758202C2314yes—
89C2×#11758200—42no—
90C2×#11758200—42no—
91C2×#11758200C2314yes—
92C2×#11758200C2314yes—
93C2×#11758194—42no—
94C2×#11758194C2314yes—
95C22×#92418—42no—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C22×#92418C2314yes—
101#14519775—28no—
102#14519764—28no—
103#14519758—28no—
104#14519758—28no—
105#14519756—22no—
106#14519756—22no—
107#14519756—22no—
108#14519756—22no—
109#14519756C2314yes—
110#14519756C2314yes—
111#14519756C2314yes—
112#14519756C2314yes—
113#14519736—22no—
114#14519736C2314yes—
115C2×C4⋊Dic61C2311yescharacteristic
116C2×C4⋊Dic61C2311yescharacteristic
117C2×#11758196—21no—
118C2×#11758196—21no—
119C2×#11758196—21no—
120C2×#11758196—21no—
121C2×C22⋊Dic61—21no—
122C2×C22⋊Dic61—21no—
123C2×C22⋊Dic61—21no—
124C2×C22⋊Dic61—21no—
125C2×C22⋊Dic61—21no—
126C2×C4×Dic61—21no—
127#14519710C2314yes—
128#14519710C2314yes—
129#14519708C2314yes—
130#14519708C2314yes—
131#14519701C2314yes—
132#14519701C2314yes—
133#14519700C2314yes—
134#14519700C2314yes—
135#14519700C2314yes—
136#14519700C2314yes—
137#14519698C2314yes—
138#14519698C2314yes—
139C22⋊#92418C2314yes—
140C22⋊#92418C2314yes—
141C22⋊#92418C2314yes—
142C22⋊#92418C2314yes—
143C2×#41×C61—22no—
144C2×#41×C61—42no—
145C2×#41×C61—42no—
146C2×#41×C61—42no—
147C2×#41×C61—42no—
148C2×#41×C61D414yes—
149C2×#41×C61C2314yes—
150C2×#41×C61C2314yes—
151C22×Q8×C61D411yescharacteristic
152C22×Q8×C61C2311yescharacteristic
153C22×D4×C61—21no—
154C22×D4×C61—21no—
155C22×D4×C61—21no—
156C22×D4×C61D411yescharacteristic
157C22×D4×C61D411yescharacteristic
158C22×D4×C61D411yescharacteristic
159C22×D4×C61C2311yescharacteristic
160C23×C4×C61—21no—
161C23×C4×C61—21no—
162C23×C4×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C22⋊Q8×C61—28no—
166C22⋊Q8×C61—22no—
167C22⋊Q8×C61—22no—
168C22⋊Q8×C61C2314yes—
169C22⋊Q8×C61C2314yes—
170#121×C61—28no—
171#121×C61—28no—
172#121×C61—28no—
173#121×C61—22no—
174#121×C61—22no—
175#121×C61C2314yes—
176#121×C61C2314yes—
177C2×C4⋊C4×C61—22no—
178C2×C4⋊C4×C61—21no—
179C2×C4⋊C4×C61—21no—
180C2×C4⋊C4×C61—21no—
181C2×C4⋊C4×C61C2314yes—
182C2×C4⋊C4×C61C2311yescharacteristic
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185C2×C22⋊C4×C61—21no—
186C2×C22⋊C4×C61—21no—
187C2×C22⋊C4×C61—21no—
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C24×C61C2×D411yescharacteristic
191C24×C61C2×D411yescharacteristic
192#41×C61—48no—
193#41×C61—44no—
194#41×C61—44no—
195#41×C61—44no—
196#41×C61—44no—
197#41×C61—48no—
198C2×Q8×C61—21no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61—42no—
202C2×Q8×C61C2×D414yes—
203C2×Q8×C61C2412yes—
204C2×D4×C61—24no—
205C2×D4×C61—24no—
206C2×D4×C61—24no—
207C2×D4×C61—21no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61—42no—
211C2×D4×C61—42no—
212C2×D4×C61—42no—
213C2×D4×C61—44no—
214C2×D4×C61—82no—
215C2×D4×C61—82no—
216C2×D4×C61C2×D414yes—
217C2×D4×C61C2×D414yes—
218C2×D4×C61C2×D414yes—
219C2×D4×C61C2412yes—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61—22no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—24no—
230C22×C4×C61—24no—
231C22×C4×C61—44no—
232C22×C4×C61—82no—
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D412yes—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2412yes—
240C22×C4×C61C2412yes—
241C22×C4×C61C2412yes—
242C22×C4×C61C2411yescharacteristic
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—24no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—44no—
249C2×Dic122—22no—
250C2×Dic122—22no—
251C2×Dic122—22no—
252C2×Dic122—22no—
253C2×Dic122—21no—
254C2×Dic122—21no—
255C2×Dic122—24no—
256C2×Dic122—44no—
257C2×Dic122—44no—
258C2×Dic122—44no—
259C2×Dic122—48no—
260C2×Dic122C2412yes—
261C2×Dic122C2412yes—
262C4⋊C4×C61—24no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—24no—
266C4⋊C4×C61—24no—
267C4⋊C4×C61C2412yes—
268C4⋊C4×C61C2412yes—
269C22⋊C4×C61—24no—
270C22⋊C4×C61—24no—
271C22⋊C4×C61—24no—
272C22⋊C4×C61—24no—
273C22⋊Dic61—24no—
274C22⋊Dic61—24no—
275C22⋊Dic61—24no—
276C22⋊Dic61—24no—
277C22⋊Dic61—24no—
278#11758202—44no—
279#11758202—44no—
280#11758200—44no—
281#11758200—44no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61C2412yes—
285C4⋊Dic61C2412yes—
286#11758196—24no—
287#11758196—24no—
288#11758196—24no—
289#11758196—24no—
290C4×Dic61—24no—
291#11758194—44no—
292C2×#92418—22no—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418—22no—
296C2×#92418—44no—
297C2×#92418C2412yes—
298C2×#92418C2412yes—
299C2×#92418C2412yes—
300C2×#92418C2412yes—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61C22×D412yes—
315C23×C61C22×D412yes—
316C23×C61C22×D412yes—
317C23×C61C22×D411yescharacteristic
318Q8×C61—22no—
319Q8×C61—22no—
320Q8×C61—44no—
321Q8×C61—42no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—44no—
325D4×C61—44no—
326D4×C61—44no—
327D4×C61—48no—
328D4×C61—42no—
329D4×C61—84no—
330D4×C61—84no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—24no—
335C2×C4×C61—24no—
336C2×C4×C61—24no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—48no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61—84no—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61H(5,𝔽2)12yes—
356C2×C4×C61H(5,𝔽2)12yes—
357C2×C4×C61C2511yescharacteristic
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—48no—
363C2×Dic61—42no—
364C2×Dic61—42no—
365C2×Dic61—42no—
366C2×Dic61—42no—
367Dic122—22no—
368Dic122—22no—
369Dic122—22no—
370Dic122—22no—
371Dic122—48no—
372Dic122—42no—
373Dic122—42no—
374#92418—22no—
375#92418—22no—
376#92418—22no—
377#92418—22no—
378C2×#3201—611nomaximal, Sylow
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—44no—
389C22×C61—44no—
390C22×C61—44no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—84no—
395C22×C61#53412yes—
396C22×C61#57712yes—
397C22×C61#57812yes—
398C22×C61C23×D411yescharacteristic
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—22no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61#53412yes—
406C4×C61C2×H(5,𝔽2)11yescharacteristic
407C4×C61C2×H(5,𝔽2)11yescharacteristic
408Dic61—42no—
409Dic61—42no—
410Dic61—42no—
411Dic61—42no—
412C2×#537D6111yescharacteristic
413C2×#536—611no—
414#3201—6116no—
415C2×#484—611no—
416C2×#485—611no—
417C2×#482—611no—
418C2×#483—611no—
419C2×#470—611no—
420C2×#468—611no—
421C2×#467—611no—
422C2×#465—611no—
423C2×#452—611no—
424C2×#452—611no—
425C2×#451—611no—
426C2×#448—611no—
427C2×#408—611no—
428C2×C61—42no—
429C2×C61—42no—
430C2×C61—42no—
431C2×C61—82no—
432C2×C61#320114yescomplemented
433C2×C61C2×#53411yescharacteristic
434C2×C61C2×#57711yescharacteristic
435C2×C61C2×#57811yescharacteristic
436C22×#41C2×D6111yescharacteristic
437C22×#41C2×D6111yescharacteristic
438C23×Q8—611no—
439C22×Q16—611no—
440C22×Q16—611no—
441C22×SD16—611no—
442C22×SD16—611no—
443C22×M16—611no—
444C23×C8—611no—
445#537—24no—
446#537C2×D6118yes—
447#536—618no—
448#536—1224no—
449C2×C4⋊Q8—1221no—
450C2×#124—1221no—
451C2×#123—1221no—
452C2×#123—1221no—
453C2×C22⋊Q8—21no—
454C2×C22⋊Q8—611no—
455C2×C22⋊Q8—611no—
456C2×C22⋊Q8—611no—
457C2×C22⋊Q8—611no—
458C2×C22⋊Q8C2×D6111yescharacteristic
459C2×C22⋊Q8C2×D6111yescharacteristic
460C2×#121—21no—
461C2×#121—21no—
462C2×#121—21no—
463C2×#121C2×D6111yescharacteristic
464C2×#121C2×D6111yescharacteristic
465C2×#117—611no—
466C22×C4⋊C4C2×D6111yescharacteristic
467#485—618no—
468#484—618no—
469#483—618no—
470#482—618no—
471#470—618no—
472#468—618no—
473#467—618no—
474#465—618no—
475#452—618no—
476#452—618no—
477#451—618no—
478#448—618no—
479C2×#107—611no—
480C2×#107—611no—
481C2×#106—611no—
482C2×#106—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#103—611no—
487C2×#103—611no—
488C2×#103—611no—
489C2×#102—611no—
490C2×#102—611no—
491#408—618no—
492C2×C22⋊C8—611no—
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×C22⋊C8—611no—
496C61C2×#320111yescharacteristic, complemented, Sylow
497C2×#41—22no—
498C2×#41—42no—
499C2×#41—42no—
500C2×#41—42no—
501C2×#41—42no—
502C2×#41C22⋊D6114yes—
503C2×#41C22×D6114yes—
504C2×#41C22×D6114yes—
505C22×Q8—611no—
506C22×Q8—611no—
507C22×Q8—614no—
508C22×Q8—1221no—
509C22×Q8—1222no—
510C22×Q8—2442no—
511C22×Q8—2442no—
512C22×Q8C22⋊D6111yescharacteristic
513C22×Q8C22×D6111yescharacteristic
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4C22⋊D6111yescharacteristic
518C22×D4C22⋊D6111yescharacteristic
519C22×D4C22⋊D6111yescharacteristic
520C22×D4C22×D6111yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—1221no—
524C23×C4C22×D6111yescharacteristic
525C23×C4C22×D6111yescharacteristic
526C23×C4C22×D6111yescharacteristic
527C2×Q16—614no—
528C2×Q16—614no—
529C2×Q16—2442no—
530C2×Q16—2442no—
531C2×SD16—614no—
532C2×SD16—614no—
533C2×SD16—2442no—
534C2×SD16—2442no—
535C2×M16—614no—
536C2×M16—2442no—
537C22×C8—611no—
538C22×C8—611no—
539C22×C8—611no—
540C22×C8—611no—
541C22×C8—614no—
542C22×C8—2442no—
543C4⋊Q8—1228no—
544#124—1228no—
545#123—1228no—
546#123—1228no—
547C22⋊Q8—28no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—614no—
551C22⋊Q8—614no—
552C22⋊Q8—614no—
553C22⋊Q8—614no—
554C22⋊Q8—1222no—
555C22⋊Q8—1222no—
556C22⋊Q8—1222no—
557C22⋊Q8—1222no—
558C22⋊Q8C22×D6114yes—
559C22⋊Q8C22×D6114yes—
560#121—28no—
561#121—28no—
562#121—28no—
563#121—22no—
564#121—22no—
565#121C22×D6114yes—
566#121C22×D6114yes—
567#117—614no—
568#117—1222no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4C22×D6111yescharacteristic
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C4⋊C4C22×D6114yes—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—1221no—
592#107—614no—
593#107—614no—
594#106—614no—
595#106—614no—
596#103—614no—
597#103—614no—
598#103—614no—
599#103—614no—
600#103—614no—
601#103—614no—
602#102—614no—
603#102—614no—
604C22⋊C8—614no—
605C22⋊C8—614no—
606C22⋊C8—614no—
607C22⋊C8—614no—
608C24—21no—
609C24C2×C22⋊D6111yescharacteristic
610C24C2×C22⋊D6111yescharacteristic
611C24C2×C22⋊D6111yescharacteristic
612#41—48no—
613#41—44no—
614#41—44no—
615#41—44no—
616#41—44no—
617#41—48no—
618C2×Q8—21no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—42no—
622C2×Q8—612no—
623C2×Q8—612no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1224no—
627C2×Q8—1222no—
628C2×Q8—1222no—
629C2×Q8—1222no—
630C2×Q8—1222no—
631C2×Q8—2444no—
632C2×Q8—2444no—
633C2×Q8—2444no—
634C2×Q8—2448no—
635C2×Q8C2×C22⋊D6114yes—
636C2×Q8C23×D6112yes—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—44no—
647C2×D4—82no—
648C2×D4—82no—
649C2×D4C2×C22⋊D6114yes—
650C2×D4C2×C22⋊D6114yes—
651C2×D4C2×C22⋊D6114yes—
652C2×D4C23×D6112yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—44no—
665C22×C4—82no—
666C22×C4—1224no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—2444no—
672C22×C4C2×C22⋊D6112yes—
673C22×C4C2×C22⋊D6112yes—
674C22×C4C2×C22⋊D6112yes—
675C22×C4C2×C22⋊D6111yescharacteristic
676C22×C4C2×C22⋊D6111yescharacteristic
677C22×C4C2×C22⋊D6111yescharacteristic
678C22×C4C23×D6112yes—
679C22×C4C23×D6112yes—
680C22×C4C23×D6112yes—
681C22×C4C23×D6111yescharacteristic
682Q16—2444no—
683Q16—2444no—
684SD16—2444no—
685SD16—2444no—
686M16—2444no—
687C2×C8—612no—
688C2×C8—612no—
689C2×C8—612no—
690C2×C8—612no—
691C2×C8—1222no—
692C2×C8—1222no—
693C2×C8—1222no—
694C2×C8—1222no—
695C2×C8—2444no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—612no—
702C4⋊C4—612no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1224no—
706C4⋊C4—1224no—
707C4⋊C4—1224no—
708C4⋊C4—1224no—
709C4⋊C4C23×D6112yes—
710C4⋊C4C23×D6112yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C42—1224no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23C22×C22⋊D6112yes—
735C23C22×C22⋊D6112yes—
736C23C22×C22⋊D6112yes—
737C23C22×C22⋊D6111yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—44no—
741Q8—42no—
742Q8—1222no—
743Q8—1222no—
744Q8—1222no—
745Q8—1222no—
746Q8—2448no—
747Q8—2442no—
748Q8—2442no—
749D4—22no—
750D4—22no—
751D4—44no—
752D4—44no—
753D4—44no—
754D4—48no—
755D4—42no—
756D4—84no—
757D4—84no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—48no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—84no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—2448no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4—2442no—
786C2×C4—2442no—
787C2×C4C22×C22⋊D6112yes—
788C2×C4C22×C22⋊D6112yes—
789C2×C4C22×C22⋊D6112yes—
790C2×C4C22×C22⋊D6111yescharacteristic
791C2×C4#1451982212yes—
792C2×C4#1451982212yes—
793C2×C4C24×D6111yescharacteristic
794C8—1222no—
795C8—1222no—
796C8—1222no—
797C8—1222no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—84no—
814C22#1684032112yes—
815C22#1684057312yes—
816C22#1684057712yes—
817C22C23×C22⋊D6111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—2442no—
825C4—2442no—
826C4—2442no—
827C4—2442no—
828C4#1684032112yes—
829C4C2×#1451982211yescharacteristic
830C4C2×#1451982211yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—82no—
835C2#2145669514yesdirect product factor
836C2C2×#1684032111yescharacteristic
837C2C2×#1684057311yescharacteristic
838C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
Fitting, prime radicalC2×C61×#537C2
socleC23×C61C22×D4
hypercenterC2×#537D61
hypocenterC61C2×#3201
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16840333C2semidirect
2. #21456695C2direct (N × H)
3. C2×#16840097C2semidirect
4. C2×#16840100C2semidirect
5. C2×#16840083C2semidirect
6. C2×#16840092C2semidirect
7. C2×#16840018C2semidirect
8. C2×#16840006C2semidirect
9. C2×#16840001C2semidirect
10. C2×#16839989C2semidirect
11. C2×#16839924C2semidirect
12. C2×#16839924C2semidirect
13. C2×#16839917C2semidirect
14. C2×#16839900C2semidirect
15. C2×#16839729C2semidirect
25. #16840333C22semidirect
35. #16840100C22semidirect
36. #16840097C22semidirect
37. #16840092C22semidirect
38. #16840083C22semidirect
39. #16840018C22semidirect
40. #16840006C22semidirect
41. #16840001C22semidirect
42. #16839989C22semidirect
43. #16839924C22semidirect
44. #16839924C22semidirect
45. #16839917C22semidirect
46. #16839900C22semidirect
59. #16839729C22semidirect
432. C2×C61#3201semidirect
496. C61C2×#3201semidirect
835. C2#21456695direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403332
#214566952
C2×#168400972
C2×#168401002
C2×#168400832
C2×#168400922
C2×#168400182
C2×#168400062
C2×#168400012
C2×#168399892
C2×#168399242
C2×#168399172
C2×#168399002
C2×#168397292
C2×C61×#5372
C2×#320161