Finite Group Databasebeta

← C2×#21458268 #30558554

Subgroups — C2×#21458268 #30558554

Order 15616.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840452C211yesmaximal, characteristic
2#21458268C2116yesmaximal, direct product factor
3C2×#16840168C211yesmaximal, characteristic, complemented
4C2×#16840097C211yesmaximal, characteristic, complemented
5C2×#16840100C211yesmaximal, characteristic, complemented
6C2×#16840092C211yesmaximal, characteristic, complemented
7C2×#16840090C211yesmaximal, characteristic, complemented
8C2×#16840069C211yesmaximal, characteristic, complemented
9C2×#16840044C211yesmaximal, characteristic, complemented
10C2×#16840018C211yesmaximal, characteristic, complemented
11C2×#16840001C211yesmaximal, characteristic, complemented
12C2×#16839867C211yesmaximal, characteristic, complemented
13C2×#16839834C211yesmaximal, characteristic
14C2×#16839802C211yesmaximal, characteristic, complemented
15C22×#14519708C211yesmaximal, characteristic, complemented
16C2×C61×#554C211yesmaximal, characteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20#16840452—24no—
21#16840452C2218yes—
22C2×#14519770—21no—
23C2×#14519769C2211yescharacteristic
24C2×#14519767—21no—
25C2×#14519758—21no—
26C2×#14519756C2211yescharacteristic
27C2×#14519756C2211yescharacteristic
28C2×C4×Dic122C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30C2×#14519733—21no—
31C22×C4⋊Dic61C2211yescharacteristic
32#16840168C2218yescomplemented
33#16840100C2218yescomplemented
34#16840097C2218yescomplemented
35#16840092C2218yescomplemented
36#16840090C2218yescomplemented
37#16840069C2218yescomplemented
38#16840044C2218yescomplemented
39#16840018C2218yescomplemented
40#16840001C2218yescomplemented
41#16839867C2218yescomplemented
42#16839834C2218yes—
43#16839802C2218yescomplemented
44C2×#14519710C2211yescharacteristic
45C2×#14519710C2211yescharacteristic
46C2×#14519710C2211yescharacteristic
47C2×#14519708C2211yescharacteristic
48C2×#14519708C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×#14519708C2211yescharacteristic
51C2×#14519708C2211yescharacteristic
52C2×#14519708C2211yescharacteristic
53C2×#14519708C2218yescomplemented
54C2×C4⋊#92418C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519701C2211yescharacteristic
57C2×#14519701C2211yescharacteristic
58C2×#14519700C2211yescharacteristic
59C2×#14519700C2211yescharacteristic
60C2×#14519700C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic
63C2×#14519688C2211yescharacteristic
64C61×#554—24no—
65C61×#554C2218yes—
66C2×C4⋊Q8×C61C2211yescharacteristic
67C2×#125×C61—21no—
68C2×C22⋊Q8×C61—21no—
69C2×C22⋊Q8×C61—21no—
70C2×C22⋊Q8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×D4×C61—21no—
74C2×C4×D4×C61C2211yescharacteristic
75C22×C4⋊C4×C61C2211yescharacteristic
76C22×C4⋊C4×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C23×Dic61—21no—
79C2×#11758202—24no—
80C2×#11758202C2314yes—
81C2×#11758194—24no—
82C2×#11758194C2314yes—
83C22×#92418—24no—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2314yes—
88C22×#92418C2311yescharacteristic
89#14519770—28no—
90#14519769—22no—
91#14519769C2314yes—
92#14519767—28no—
93#14519758—28no—
94#14519756—22no—
95#14519756—22no—
96#14519756C2314yes—
97#14519756C2314yes—
98C4×Dic122—22no—
99C4×Dic122C2314yes—
100#14519736—22no—
101#14519736C2314yes—
102#14519733—28no—
103C2×C4⋊Dic61—22no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61C2314yes—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×C22⋊Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119#14519710C2314yes—
120#14519710C2314yes—
121#14519710C2314yes—
122#14519708C2314yes—
123#14519708C2314yes—
124#14519708C2314yes—
125#14519708C2314yes—
126#14519708C2314yes—
127#14519708C2314yes—
128C4⋊#92418C2314yes—
129#14519701C2314yes—
130#14519701C2314yes—
131#14519701C2314yes—
132#14519700C2314yes—
133#14519700C2314yes—
134#14519700C2314yes—
135C22⋊#92418C2314yes—
136C22⋊#92418C2314yes—
137#14519688C2314yes—
138C22×Q8×C61—21no—
139C22×Q8×C61C2311yescharacteristic
140C22×D4×C61D411yescharacteristic
141C23×C4×C61—21no—
142C23×C4×C61—21no—
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C4⋊Q8×C61—22no—
146C4⋊Q8×C61C2314yes—
147#125×C61—28no—
148C22⋊Q8×C61—22no—
149C22⋊Q8×C61—22no—
150C22⋊Q8×C61—28no—
151C22⋊Q8×C61—28no—
152C22⋊Q8×C61C2314yes—
153C22⋊Q8×C61C2314yes—
154C4×Q8×C61—22no—
155C4×Q8×C61C2314yes—
156C4×D4×C61—28no—
157C4×D4×C61D414yes—
158C4×D4×C61C2314yes—
159C2×C4⋊C4×C61—21no—
160C2×C4⋊C4×C61—22no—
161C2×C4⋊C4×C61—22no—
162C2×C4⋊C4×C61—21no—
163C2×C4⋊C4×C61—21no—
164C2×C4⋊C4×C61—21no—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61D411yescharacteristic
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2314yes—
171C2×C4⋊C4×C61C2314yes—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61D411yescharacteristic
176C2×C22⋊C4×C61D411yescharacteristic
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179C24×C61C2×D411yescharacteristic
180C24×C61C2×D411yescharacteristic
181C2×Q8×C61—21no—
182C2×Q8×C61—24no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61—82no—
186C2×Q8×C61C2412yes—
187C2×D4×C61—24no—
188C2×D4×C61C2×D414yes—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—24no—
198C22×C4×C61—24no—
199C22×C4×C61—82no—
200C22×C4×C61—82no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2×D412yes—
207C22×C4×C61C2412yes—
208C22×C4×C61C2412yes—
209C22×C4×C61C2411yescharacteristic
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—44no—
216C2×Dic122—22no—
217C2×Dic122—22no—
218C2×Dic122—21no—
219C2×Dic122C2412yes—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—24no—
222C4⋊C4×C61—24no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—24no—
228C4⋊C4×C61—24no—
229C4⋊C4×C61C2×D414yes—
230C4⋊C4×C61C2412yes—
231C4⋊C4×C61C2412yes—
232C4⋊C4×C61C2412yes—
233C22⋊C4×C61—24no—
234C22⋊C4×C61—24no—
235C22⋊C4×C61C2×D414yes—
236C22⋊C4×C61C2×D414yes—
237C42×C61—24no—
238C42×C61C2×D412yes—
239C42×C61C2412yes—
240C22⋊Dic61—24no—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243#11758202—28no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—24no—
247C4⋊Dic61—21no—
248C4⋊Dic61C2412yes—
249C4⋊Dic61C2412yes—
250C4⋊Dic61C2412yes—
251#11758196—24no—
252#11758196—24no—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256C4×Dic61—24no—
257C4×Dic61—24no—
258#11758194—28no—
259C2×#92418—22no—
260C2×#92418—22no—
261C2×#92418—22no—
262C2×#92418—28no—
263C2×#92418#4114yes—
264C2×#92418C2412yes—
265C2×#92418C2412yes—
266C2×#92418C2412yes—
267C2×#92418C2412yes—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61#13714yes—
274C23×C61C22×D412yes—
275C23×C61C22×D412yes—
276C23×C61C22×D411yescharacteristic
277Q8×C61—22no—
278Q8×C61—22no—
279Q8×C61—42no—
280Q8×C61—84no—
281D4×C61—28no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—84no—
301C2×C4×C61—84no—
302C2×C4×C61C22×D412yes—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D412yes—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C2×#4112yes—
308C2×C4×C612−1+412yes—
309C2×C4×C61C2511yescharacteristic
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—42no—
315C2×Dic61—48no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319Dic122—22no—
320Dic122—22no—
321Dic122—42no—
322#92418—22no—
323#92418—22no—
324#92418—22no—
325#92418C2×#4114yes—
326C2×#3344—611nomaximal, Sylow
327C22×C61—28no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—44no—
334C22×C61#54712yes—
335C22×C61C2×#13714yes—
336C22×C61C2×#13712yes—
337C22×C61#57712yes—
338C22×C61C23×D411yescharacteristic
339C4×C61—22no—
340C4×C61—22no—
341C4×C61—22no—
342C4×C61—22no—
343C4×C61—42no—
344C4×C61—42no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61#54712yes—
348C4×C61C22×#4111yescharacteristic
349C4×C61C2×2−1+411yescharacteristic
350Dic61—42no—
351Dic61—42no—
352Dic61—42no—
353Dic61—42no—
354C2×#554D6111yescharacteristic
355C2×#552—611no—
356#3344—6116no—
357C2×#501—611no—
358C2×#484—611no—
359C2×#485—611no—
360C2×#483—611no—
361C2×#483—611no—
362C2×#479—611no—
363C2×#475—611no—
364C2×#470—611no—
365C2×#467—611no—
366C2×#441—611no—
367C2×#435—611no—
368C2×#428—611no—
369C22×#106—611no—
370C2×C61—24no—
371C2×C61—42no—
372C2×C61#334414yescomplemented
373C2×C61C2×#54711yescharacteristic
374C2×C61C22×#13711yescharacteristic
375C2×C61C2×#57711yescharacteristic
376C22×Q16—611no—
377C22×M16—611no—
378C23×C8—611no—
379#554—24no—
380#554C2×D6118yes—
381#552—618no—
382#552—1224no—
383C2×C4⋊Q8C2×D6111yescharacteristic
384C2×#126—1221no—
385C2×#125—21no—
386C2×#125—611no—
387C2×#125—1221no—
388C2×#123—1221no—
389C2×C22⋊Q8—21no—
390C2×C22⋊Q8—21no—
391C2×C22⋊Q8—611no—
392C2×C22⋊Q8—611no—
393C2×C22⋊Q8C2×D6111yescharacteristic
394C2×C22⋊Q8C2×D6111yescharacteristic
395C2×C4×Q8—611no—
396C2×C4×Q8C2×D6111yescharacteristic
397C2×C4×D4—21no—
398C2×C4×D4C2×D6111yescharacteristic
399C2×#117—611no—
400C2×#117—1221no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4C2×D6111yescharacteristic
403C22×C4⋊C4C2×D6111yescharacteristic
404#501—618no—
405#485—618no—
406#484—618no—
407#483—618no—
408#483—618no—
409#479—618no—
410#475—618no—
411#470—618no—
412#467—618no—
413#441—618no—
414#435—618no—
415#428—618no—
416C2×#107—611no—
417C2×#107—611no—
418C2×#107—611no—
419C2×#106—611no—
420C2×#106—611no—
421C2×#106—611no—
422C2×#106—611no—
423C2×#106—618no—
424C2×#106—611no—
425C2×#106—611no—
426C2×C4⋊C8—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×C22⋊C8—611no—
434C2×C22⋊C8—611no—
435C2×#97—611no—
436C61C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—21no—
438C22×Q8—611no—
439C22×Q8C22×D6111yescharacteristic
440C22×D4C22⋊D6111yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—1221no—
444C23×C4C22×D6111yescharacteristic
445C23×C4C22×D6111yescharacteristic
446C2×Q16—614no—
447C2×Q16—1224no—
448C2×M16—614no—
449C2×M16—1224no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8—614no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—1224no—
456C4⋊Q8—22no—
457C4⋊Q8C22×D6114yes—
458#126—1228no—
459#125—28no—
460#125—614no—
461#125—1228no—
462#125—1222no—
463#123—1228no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—28no—
467C22⋊Q8—28no—
468C22⋊Q8—614no—
469C22⋊Q8—614no—
470C22⋊Q8—1222no—
471C22⋊Q8—1222no—
472C22⋊Q8C22×D6114yes—
473C22⋊Q8C22×D6114yes—
474C4×Q8—22no—
475C4×Q8—614no—
476C4×Q8—1222no—
477C4×Q8C22×D6114yes—
478C4×D4—28no—
479C4×D4C22⋊D6114yes—
480C4×D4C22×D6114yes—
481#117—614no—
482#117—1222no—
483#117—1228no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—614no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4C22⋊D6111yescharacteristic
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6114yes—
508C2×C4⋊C4C22×D6114yes—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4C22⋊D6111yescharacteristic
515C2×C22⋊C4C22⋊D6111yescharacteristic
516C2×C42—21no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42C22×D6111yescharacteristic
520#107—614no—
521#107—614no—
522#107—614no—
523#106—614no—
524#106—614no—
525#106—614no—
526#106—614no—
527#106—614no—
528#106—614no—
529C4⋊C8—614no—
530#103—614no—
531#103—614no—
532#103—614no—
533#103—614no—
534#103—614no—
535#103—614no—
536C22⋊C8—614no—
537C22⋊C8—614no—
538#97—614no—
539C24C2×C22⋊D6111yescharacteristic
540C24C2×C22⋊D6111yescharacteristic
541C2×Q8—21no—
542C2×Q8—24no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—82no—
546C2×Q8—612no—
547C2×Q8—1221no—
548C2×Q8—1222no—
549C2×Q8—1222no—
550C2×Q8C23×D6112yes—
551C2×D4—24no—
552C2×D4C2×C22⋊D6114yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—1224no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—2444no—
571C22×C4C2×C22⋊D6112yes—
572C22×C4C2×C22⋊D6112yes—
573C22×C4C2×C22⋊D6111yescharacteristic
574C22×C4C2×C22⋊D6111yescharacteristic
575C22×C4C2×C22⋊D6111yescharacteristic
576C22×C4C2×C22⋊D6111yescharacteristic
577C22×C4C23×D6112yes—
578C22×C4C23×D6112yes—
579C22×C4C23×D6111yescharacteristic
580Q16—1228no—
581M16—1228no—
582C2×C8—614no—
583C2×C8—612no—
584C2×C8—612no—
585C2×C8—612no—
586C2×C8—612no—
587C2×C8—1228no—
588C2×C8—1222no—
589C2×C8—1222no—
590C2×C8—1222no—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—612no—
601C4⋊C4—612no—
602C4⋊C4—612no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1224no—
606C4⋊C4—1221no—
607C4⋊C4—1224no—
608C4⋊C4—1224no—
609C4⋊C4—1224no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4C2×C22⋊D6114yes—
613C4⋊C4C23×D6112yes—
614C4⋊C4C23×D6112yes—
615C4⋊C4C23×D6112yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1224no—
619C22⋊C4—1224no—
620C22⋊C4—1224no—
621C22⋊C4C2×C22⋊D6114yes—
622C22⋊C4C2×C22⋊D6114yes—
623C42—24no—
624C42—1224no—
625C42—1224no—
626C42C2×C22⋊D6112yes—
627C42C23×D6112yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1451980814yes—
634C23C22×C22⋊D6112yes—
635C23C22×C22⋊D6112yes—
636C23C22×C22⋊D6111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—84no—
641Q8—1222no—
642Q8—1222no—
643Q8—2442no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—2448no—
670C2×C4—2442no—
671C2×C4—2442no—
672C2×C4—2442no—
673C2×C4—2442no—
674C2×C4C22×C22⋊D6112yes—
675C2×C4C22×C22⋊D6112yes—
676C2×C4C22×C22⋊D6112yes—
677C2×C4C22×C22⋊D6112yes—
678C2×C4C22×C22⋊D6111yescharacteristic
679C2×C4#41×D6112yes—
680C2×C4#1451982412yes—
681C2×C4C24×D6111yescharacteristic
682C8—614no—
683C8—1222no—
684C8—1222no—
685C8—1222no—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1684041112yes—
694C22C2×#1451980814yes—
695C22C2×#1451980812yes—
696C22#1684057312yes—
697C22C23×C22⋊D6111yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—2442no—
707C4—2442no—
708C4—2442no—
709C4—2442no—
710C4#1684041112yes—
711C4C2×#41×D6111yescharacteristic
712C4C2×#1451982411yescharacteristic
713C2—24no—
714C2—42no—
715C2#2145826814yesdirect product factor
716C2C2×#1684041111yescharacteristic
717C2C22×#1451980811yescharacteristic
718C2C2×#1684057311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#554C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenterC2×#554D61
hypocenterC61C2×#3344
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #21458268C2direct (N × H)
3. C2×#16840168C2semidirect
4. C2×#16840097C2semidirect
5. C2×#16840100C2semidirect
6. C2×#16840092C2semidirect
7. C2×#16840090C2semidirect
8. C2×#16840069C2semidirect
9. C2×#16840044C2semidirect
10. C2×#16840018C2semidirect
11. C2×#16840001C2semidirect
12. C2×#16839867C2semidirect
14. C2×#16839802C2semidirect
15. C22×#14519708C2semidirect
32. #16840168C22semidirect
33. #16840100C22semidirect
34. #16840097C22semidirect
35. #16840092C22semidirect
36. #16840090C22semidirect
37. #16840069C22semidirect
38. #16840044C22semidirect
39. #16840018C22semidirect
40. #16840001C22semidirect
41. #16839867C22semidirect
43. #16839802C22semidirect
53. C2×#14519708C22semidirect
372. C2×C61#3344semidirect
436. C61C2×#3344semidirect
715. C2#21458268direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404522
#214582682
C2×#168401682
C2×#168400972
C2×#168401002
C2×#168400922
C2×#168400902
C2×#168400692
C2×#168400442
C2×#168400182
C2×#168400012
C2×#168398672
C2×#168398342
C2×#168398022
C22×#145197082
C2×C61×#5542
C2×#334461