Finite Group Databasebeta

← C2×#21456922 #30551402

Subgroups — C2×#21456922 #30551402

Order 15616.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840338C211yesmaximal, characteristic, complemented
2#21456922C2116yesmaximal, direct product factor
3C2×#16840157C211yesmaximal, characteristic, complemented
4C2×#16840144C211yesmaximal, characteristic, complemented
5C2×#16840124C211yesmaximal, characteristic, complemented
6C2×#16840114C211yesmaximal, characteristic, complemented
7C2×#16839984C211yesmaximal, characteristic, complemented
8C2×#16839972C211yesmaximal, characteristic, complemented
9C2×#16839977C211yesmaximal, characteristic, complemented
10C2×#16839967C211yesmaximal, characteristic, complemented
11C2×#16839922C211yesmaximal, characteristic, complemented
12C2×#16839905C211yesmaximal, characteristic
13C2×#16839917C211yesmaximal, characteristic, complemented
14C2×#16839900C211yesmaximal, characteristic, complemented
15C2×#16839823C211yesmaximal, characteristic, complemented
16C2×C61×#542C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758200C2211yescharacteristic
24C22×#11758200C2211yescharacteristic
25C22×#11758201C2211yescharacteristic
26C22×#11758199C2211yescharacteristic
27#16840338—24no—
28#16840338C2218yescomplemented
29C2×#14519777C2211yescharacteristic
30C2×#14519777C2211yescharacteristic
31C2×#14519765C2211yescharacteristic
32C2×#14519765C2211yescharacteristic
33C2×#14519761—21no—
34C2×#14519761—21no—
35C2×#14519757—21no—
36C2×#14519757—21no—
37#16840157C2218yescomplemented
38#16840144C2218yescomplemented
39#16840124C2218yescomplemented
40#16840114C2218yescomplemented
41#16839984C2218yescomplemented
42#16839977C2218yescomplemented
43#16839972C2218yescomplemented
44#16839967C2218yescomplemented
45#16839922C2218yescomplemented
46#16839917C2218yescomplemented
47#16839905C2218yes—
48#16839900C2218yescomplemented
49#16839823C2218yescomplemented
50C2×C4⋊#92418C2211yescharacteristic
51C2×C4⋊#92418C2211yescharacteristic
52C2×#14519700C2211yescharacteristic
53C2×#14519700C2211yescharacteristic
54C2×#14519700C2211yescharacteristic
55C2×#14519700C2211yescharacteristic
56C2×#14519700C2211yescharacteristic
57C2×#14519700C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#542—24no—
65C61×#542C2218yescomplemented
66C2×C4⋊Q8×C61C2211yescharacteristic
67C2×#126×C61—21no—
68C2×#124×C61—21no—
69C2×#124×C61C2211yescharacteristic
70C2×#123×C61—21no—
71C2×C22⋊Q8×C61—21no—
72C2×C22⋊Q8×C61C2211yescharacteristic
73C2×#121×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C2×C4×D4×C61C2211yescharacteristic
76C2×#117×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122—22no—
83C22×Dic122—42no—
84C22×Dic122—42no—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2311yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2314yes—
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C2×#11758202—42no—
94C2×#11758202—42no—
95C2×#11758202—42no—
96C2×#11758202C2314yes—
97C2×#11758202C2314yes—
98C2×#11758202C2314yes—
99C2×#11758200—42no—
100C2×#11758200—42no—
101C2×#11758200—42no—
102C2×#11758200C2314yes—
103C2×#11758200C2314yes—
104C2×#11758200C2314yes—
105C2×#11758201—42no—
106C2×#11758201C2314yes—
107C2×#11758199—42no—
108C2×#11758199C2314yes—
109C22×#92418C2311yescharacteristic
110C22×#92418C2311yescharacteristic
111C22×#92418C2311yescharacteristic
112C22×#92418C2311yescharacteristic
113#14519777—22no—
114#14519777—22no—
115#14519777C2314yes—
116#14519777C2314yes—
117#14519765—22no—
118#14519765—22no—
119#14519765C2314yes—
120#14519765C2314yes—
121#14519761—28no—
122#14519761—28no—
123#14519757—28no—
124#14519757—28no—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×#11758198—21no—
130C2×#11758198—21no—
131C2×#11758198—21no—
132C2×#11758198—21no—
133C4⋊#92418C2314yes—
134C4⋊#92418C2314yes—
135#14519700C2314yes—
136#14519700C2314yes—
137#14519700C2314yes—
138#14519700C2314yes—
139#14519700C2314yes—
140#14519700C2314yes—
141#14519697C2314yes—
142#14519697C2314yes—
143C22⋊#92418C2314yes—
144C22⋊#92418C2314yes—
145#14519688C2314yes—
146C4×#92418C2314yes—
147C22×Q8×C61—21no—
148C22×Q8×C61C2311yescharacteristic
149C22×D4×C61—21no—
150C22×D4×C61C2311yescharacteristic
151C23×C4×C61—21no—
152C23×C4×C61C2311yescharacteristic
153C4⋊Q8×C61—22no—
154C4⋊Q8×C61C2314yes—
155#126×C61—28no—
156#124×C61—28no—
157#124×C61—22no—
158#124×C61C2314yes—
159#123×C61—28no—
160C22⋊Q8×C61—22no—
161C22⋊Q8×C61—28no—
162C22⋊Q8×C61C2314yes—
163#121×C61—22no—
164#121×C61C2314yes—
165C4×Q8×C61—22no—
166C4×Q8×C61C2314yes—
167C4×D4×C61—22no—
168C4×D4×C61C2314yes—
169#117×C61D414yes—
170#117×C61C2314yes—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61D411yescharacteristic
175C2×C4⋊C4×C61D411yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61D411yescharacteristic
184C2×C22⋊C4×C61D411yescharacteristic
185C2×C42×C61—21no—
186C2×C42×C61C2311yescharacteristic
187C2×C42×C61C2311yescharacteristic
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C23×D61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—24no—
193C2×Q8×C61—22no—
194C2×Q8×C61—22no—
195C2×Q8×C61—82no—
196C2×Q8×C61C2412yes—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—82no—
202C2×D4×C61C2412yes—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—24no—
209C22×C4×C61—82no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2412yes—
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—24no—
219C2×C22⋊D61—44no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—24no—
224C22×Dic61—44no—
225#11758222—44no—
226#11758222—44no—
227#11758222—48no—
228C2×D244—22no—
229C2×D244—22no—
230C2×D244—21no—
231C2×D244C2412yes—
232C2×C4×D61—24no—
233C2×C4×D61—44no—
234C2×Dic122—22no—
235C2×Dic122—22no—
236C2×Dic122—22no—
237C2×Dic122—22no—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—24no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—44no—
245C2×Dic122—44no—
246C2×Dic122—44no—
247C2×Dic122—48no—
248C2×Dic122C2412yes—
249C2×Dic122C2412yes—
250C2×Dic122C2412yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C2×D414yes—
257C4⋊C4×C61C2×D414yes—
258C4⋊C4×C61C2412yes—
259C4⋊C4×C61C2412yes—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—24no—
265C22⋊C4×C61C2×D414yes—
266C22⋊C4×C61C2×D414yes—
267C42×C61—24no—
268C42×C61C2×D412yes—
269C42×C61C2×D412yes—
270C42×C61C2412yes—
271C42×C61C2412yes—
272#11758202—44no—
273#11758202—44no—
274#11758202—44no—
275#11758201—44no—
276#11758200—44no—
277#11758200—44no—
278#11758200—44no—
279#11758199—44no—
280#11758198—24no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284C4⋊Dic61—24no—
285C4⋊Dic61—24no—
286C4⋊Dic61—24no—
287C4⋊Dic61—24no—
288C2×#92418—22no—
289C2×#92418—22no—
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418C2412yes—
293C2×#92418C2412yes—
294C2×#92418C2412yes—
295C2×#92418C2412yes—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61C22×D412yes—
304C23×C61C22×D411yescharacteristic
305C22×D61—22no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—42no—
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—42no—
312Q8×C61—84no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—42no—
316D4×C61—84no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—24no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61—84no—
332C2×C4×C61C22×D412yes—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D412yes—
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61H(5,𝔽2)12yes—
339C2×C4×C61H(5,𝔽2)12yes—
340C2×C4×C61C2511yescharacteristic
341C22⋊D61—48no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—48no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349D244—22no—
350D244—22no—
351D244—42no—
352C4×D61—48no—
353Dic122—22no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—22no—
359Dic122—48no—
360Dic122—42no—
361Dic122—42no—
362Dic122—42no—
363#92418—22no—
364#92418—22no—
365#92418—22no—
366#92418—22no—
367C2×#3225—611nomaximal, Sylow
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—44no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—84no—
376C22×C61#53512yes—
377C22×C61#57712yes—
378C22×C61#57812yes—
379C22×C61C23×D411yescharacteristic
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—84no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61#53512yes—
393C4×C61C2×H(5,𝔽2)11yescharacteristic
394C4×C61C2×H(5,𝔽2)11yescharacteristic
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#542D6111yescharacteristic, complemented
399C2×#536—611no—
400#3225—6116no—
401C2×#497—611no—
402C2×#495—611no—
403C2×#489—611no—
404C2×#487—611no—
405C2×#464—611no—
406C2×#462—611no—
407C2×#463—611no—
408C2×#461—611no—
409C2×#452—611no—
410C2×#449—611no—
411C2×#451—611no—
412C2×#448—611no—
413C2×#433—611no—
414C2×C61—42no—
415C2×C61—82no—
416C2×C61#322514yescomplemented
417C2×C61C2×#53511yescharacteristic
418C2×C61C2×#57711yescharacteristic
419C2×C61C2×#57811yescharacteristic
420D61—82no—
421C22×#41—611no—
422C23×Q8—611no—
423C22×Q16—611no—
424C22×Q16—611no—
425C22×Q16—611no—
426C22×SD16—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C22×SD16—611no—
430C22×D8—611no—
431#542—24no—
432#542C2×D6118yescomplemented
433#536—618no—
434#536—1224no—
435C2×C4⋊Q8—611no—
436C2×C4⋊Q8—611no—
437C2×C4⋊Q8C2×D6111yescharacteristic
438C2×#126—21no—
439C2×#124—21no—
440C2×#124—611no—
441C2×#124—611no—
442C2×#124C2×D6111yescharacteristic
443C2×#123—21no—
444C2×#123—1221no—
445C2×#123—1221no—
446C2×C22⋊Q8—21no—
447C2×C22⋊Q8—1221no—
448C2×C22⋊Q8—1221no—
449C2×C22⋊Q8C2×D6111yescharacteristic
450C2×#121C2×D6111yescharacteristic
451C2×C4×Q8C2×D6111yescharacteristic
452C2×C4×D4C2×D6111yescharacteristic
453C2×#117C2×D6111yescharacteristic
454#497—618no—
455#495—618no—
456#489—618no—
457#487—618no—
458#464—618no—
459#463—618no—
460#462—618no—
461#461—618no—
462#452—618no—
463#451—618no—
464#449—618no—
465#448—618no—
466#433—618no—
467C2×C4⋊C8—611no—
468C2×C4⋊C8—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×C22⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×#97—611no—
480C2×C4×C8—611no—
481C61C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—614no—
483C2×#41—1222no—
484C2×#41—2442no—
485C2×#41—2442no—
486C22×Q8—21no—
487C22×Q8—611no—
488C22×Q8—611no—
489C22×Q8—611no—
490C22×Q8—614no—
491C22×Q8—1221no—
492C22×Q8—1222no—
493C22×Q8—2442no—
494C22×Q8—2442no—
495C22×Q8C22×D6111yescharacteristic
496C22×D4—21no—
497C22×D4—611no—
498C22×D4—1221no—
499C22×D4C22×D6111yescharacteristic
500C23×C4—21no—
501C23×C4—1221no—
502C23×C4—1221no—
503C23×C4C22×D6111yescharacteristic
504C2×Q16—614no—
505C2×Q16—614no—
506C2×Q16—614no—
507C2×Q16—2442no—
508C2×Q16—2442no—
509C2×Q16—2442no—
510C2×SD16—614no—
511C2×SD16—614no—
512C2×SD16—614no—
513C2×SD16—614no—
514C2×SD16—2442no—
515C2×SD16—2442no—
516C2×SD16—2442no—
517C2×SD16—2442no—
518C2×D8—614no—
519C2×D8—2442no—
520C22×C8—611no—
521C22×C8—611no—
522C22×C8—611no—
523C22×C8—611no—
524C4⋊Q8—22no—
525C4⋊Q8—614no—
526C4⋊Q8—614no—
527C4⋊Q8—1222no—
528C4⋊Q8—1222no—
529C4⋊Q8C22×D6114yes—
530#126—28no—
531#124—28no—
532#124—22no—
533#124—614no—
534#124—614no—
535#124—1222no—
536#124—1222no—
537#124C22×D6114yes—
538#123—28no—
539#123—1228no—
540#123—1228no—
541C22⋊Q8—22no—
542C22⋊Q8—28no—
543C22⋊Q8—1228no—
544C22⋊Q8—1228no—
545C22⋊Q8C22×D6114yes—
546#121—22no—
547#121C22×D6114yes—
548C4×Q8—22no—
549C4×Q8C22×D6114yes—
550C4×D4—22no—
551C4×D4C22×D6114yes—
552#117C22⋊D6114yes—
553#117C22×D6114yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4C22⋊D6111yescharacteristic
562C2×C4⋊C4C22⋊D6111yescharacteristic
563C2×C4⋊C4C22×D6111yescharacteristic
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4C22⋊D6111yescharacteristic
575C2×C22⋊C4C22⋊D6111yescharacteristic
576C2×C42—21no—
577C2×C42C22×D6111yescharacteristic
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—614no—
580C4⋊C8—614no—
581#103—614no—
582#103—614no—
583#103—614no—
584#103—614no—
585#103—614no—
586#103—614no—
587#102—614no—
588#102—614no—
589C22⋊C8—614no—
590C22⋊C8—614no—
591#97—614no—
592C4×C8—614no—
593C24—21no—
594C24—1221no—
595C24C2×C22⋊D6111yescharacteristic
596#41—2444no—
597#41—2444no—
598#41—2448no—
599C2×Q8—21no—
600C2×Q8—24no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—82no—
604C2×Q8—612no—
605C2×Q8—612no—
606C2×Q8—612no—
607C2×Q8—1224no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1222no—
612C2×Q8—1222no—
613C2×Q8—1222no—
614C2×Q8—1222no—
615C2×Q8—1222no—
616C2×Q8—1222no—
617C2×Q8—2444no—
618C2×Q8—2444no—
619C2×Q8—2444no—
620C2×Q8—2448no—
621C2×Q8C23×D6112yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—82no—
627C2×D4—612no—
628C2×D4—1224no—
629C2×D4—1221no—
630C2×D4—1222no—
631C2×D4—1222no—
632C2×D4—2444no—
633C2×D4C23×D6112yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—82no—
641C22×C4—1224no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1224no—
646C22×C4—2444no—
647C22×C4—2444no—
648C22×C4C2×C22⋊D6112yes—
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C2×C22⋊D6111yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C2×C22⋊D6111yescharacteristic
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656Q16—2444no—
657Q16—2444no—
658Q16—2444no—
659SD16—2444no—
660SD16—2444no—
661SD16—2444no—
662SD16—2444no—
663D8—2444no—
664C2×C8—612no—
665C2×C8—612no—
666C2×C8—612no—
667C2×C8—612no—
668C2×C8—1222no—
669C2×C8—1222no—
670C2×C8—1222no—
671C2×C8—1222no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4C2×C22⋊D6114yes—
682C4⋊C4C2×C22⋊D6114yes—
683C4⋊C4C23×D6112yes—
684C4⋊C4C23×D6112yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C22⋊C4C2×C22⋊D6114yes—
695C22⋊C4C2×C22⋊D6114yes—
696C42—24no—
697C42C2×C22⋊D6112yes—
698C42C2×C22⋊D6112yes—
699C42C23×D6112yes—
700C42C23×D6112yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—1222no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23C22×C22⋊D6112yes—
713C23C22×C22⋊D6111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—1222no—
719Q8—1222no—
720Q8—1222no—
721Q8—1222no—
722Q8—1222no—
723Q8—1222no—
724Q8—2448no—
725Q8—2442no—
726Q8—2442no—
727Q8—2442no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—84no—
732D4—1222no—
733D4—1222no—
734D4—2448no—
735D4—2442no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—84no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—2448no—
755C2×C4—2448no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4C22×C22⋊D6112yes—
760C2×C4C22×C22⋊D6112yes—
761C2×C4C22×C22⋊D6112yes—
762C2×C4C22×C22⋊D6112yes—
763C2×C4C22×C22⋊D6112yes—
764C2×C4C22×C22⋊D6111yescharacteristic
765C2×C4#1451982312yes—
766C2×C4#1451982312yes—
767C2×C4C24×D6111yescharacteristic
768C8—1222no—
769C8—1222no—
770C8—1222no—
771C8—1222no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—4884no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22#1684032612yes—
785C22#1684057312yes—
786C22#1684057712yes—
787C22C23×C22⋊D6111yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—2442no—
797C4—2442no—
798C4—2442no—
799C4#1684032612yes—
800C4C2×#1451982311yescharacteristic
801C4C2×#1451982311yescharacteristic
802C2—42no—
803C2—82no—
804C2—4882no—
805C2#2145692214yesdirect product factor
806C2C2×#1684032611yescharacteristic
807C2C2×#1684057311yescharacteristic
808C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#542C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
hypercenterC2×#542D61
hypocenterC61C2×#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16840338C2semidirect
2. #21456922C2direct (N × H)
3. C2×#16840157C2semidirect
4. C2×#16840144C2semidirect
5. C2×#16840124C2semidirect
6. C2×#16840114C2semidirect
7. C2×#16839984C2semidirect
8. C2×#16839972C2semidirect
9. C2×#16839977C2semidirect
10. C2×#16839967C2semidirect
11. C2×#16839922C2semidirect
13. C2×#16839917C2semidirect
14. C2×#16839900C2semidirect
15. C2×#16839823C2semidirect
16. C2×C61×#542C2semidirect
28. #16840338C22semidirect
37. #16840157C22semidirect
38. #16840144C22semidirect
39. #16840124C22semidirect
40. #16840114C22semidirect
41. #16839984C22semidirect
42. #16839977C22semidirect
43. #16839972C22semidirect
44. #16839967C22semidirect
45. #16839922C22semidirect
46. #16839917C22semidirect
48. #16839900C22semidirect
49. #16839823C22semidirect
65. C61×#542C22semidirect
398. C2×#542D61semidirect
416. C2×C61#3225semidirect
432. #542C2×D61semidirect
481. C61C2×#3225semidirect
805. C2#21456922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403382
#214569222
C2×#168401572
C2×#168401442
C2×#168401242
C2×#168401142
C2×#168399842
C2×#168399722
C2×#168399772
C2×#168399672
C2×#168399222
C2×#168399052
C2×#168399172
C2×#168399002
C2×#168398232
C2×C61×#5422
C2×#322561