Finite Group Databasebeta

← C2×#21456032 #30548275

Subgroups — C2×#21456032 #30548275

Order 15616.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840373C211yesmaximal, characteristic, complemented
2C2×#16840244C211yesmaximal, characteristic
3#21456032C2116yesmaximal, direct product factor
4C2×#16840096C211yesmaximal, characteristic, complemented
5C2×#16840091C211yesmaximal, characteristic, complemented
6C2×#16840069C211yesmaximal, characteristic, complemented
7C2×#16840063C211yesmaximal, characteristic, complemented
8C2×#16839964C211yesmaximal, characteristic, complemented
9C2×#16839923C211yesmaximal, characteristic
10C2×#16839923C211yesmaximal, characteristic
11C2×#16839869C211yesmaximal, characteristic, complemented
12C2×#16839865C211yesmaximal, characteristic, complemented
13C2×Q16×Dic61C211yesmaximal, characteristic, complemented
14C2×#16839847C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#462C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20#16840373—24no—
21#16840373C2218yescomplemented
22C2×#14519772—21no—
23C2×#14519772—21no—
24C2×#14519769C2211yescharacteristic
25C2×#14519767—21no—
26C2×#14519767—21no—
27C2×#14519753C2211yescharacteristic
28C2×#14519753C2211yescharacteristic
29#16840244—24no—
30#16840244C2218yes—
31C2×Q8×Dic61C2211yescharacteristic
32C2×Q8×Dic61C2211yescharacteristic
33C2×Q8×Dic61C2211yescharacteristic
34C2×C4×D244—21no—
35C2×C4×D244C2211yescharacteristic
36C2×#14519739—21no—
37C2×#14519739C2211yescharacteristic
38C2×#14519734—21no—
39C2×#14519734C2211yescharacteristic
40C2×C4⋊C4×D61—21no—
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840096C2218yescomplemented
43#16840091C2218yescomplemented
44#16840069C2218yescomplemented
45#16840063C2218yescomplemented
46#16839964C2218yescomplemented
47#16839923C2218yes—
48#16839923C2218yes—
49#16839869C2218yescomplemented
50#16839865C2218yescomplemented
51Q16×Dic61C2218yescomplemented
52#16839847C2218yescomplemented
53#16839822C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519701C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C2×C4⋊Q8×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#462C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C2×#11758226—24no—
78C2×#11758226—24no—
79C2×#11758226—22no—
80C2×#11758226C2314yes—
81C22×D244—21no—
82C22×D244C2311yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61C2311yescharacteristic
88C2×#11758201—24no—
89C2×#11758201—24no—
90C2×#11758201C2314yes—
91C2×#11758201C2314yes—
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94#14519772—28no—
95#14519772—28no—
96#14519769—22no—
97#14519769C2314yes—
98#14519767—28no—
99#14519767—28no—
100#14519753—22no—
101#14519753—22no—
102#14519753C2314yes—
103#14519753C2314yes—
104Q8×Dic61—22no—
105Q8×Dic61—22no—
106Q8×Dic61—22no—
107Q8×Dic61C2314yes—
108Q8×Dic61C2314yes—
109Q8×Dic61C2314yes—
110C4×D244—22no—
111C4×D244—28no—
112C4×D244C2314yes—
113#14519739—28no—
114#14519739—22no—
115#14519739C2314yes—
116#14519734—28no—
117#14519734D414yes—
118#14519734C2314yes—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196D411yescharacteristic
131C2×#11758196D411yescharacteristic
132C4⋊C4×D61—22no—
133C4⋊C4×D61—28no—
134C4⋊C4×D61C2314yes—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198D411yescharacteristic
140C2×#11758198D411yescharacteristic
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61C2311yescharacteristic
145#14519711C2314yes—
146#14519710C2314yes—
147#14519709C2314yes—
148#14519708C2314yes—
149C4⋊#92418C2314yes—
150#14519701C2314yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519701C2314yes—
154#14519699C2314yes—
155#14519699C2314yes—
156#14519689C2314yes—
157#14519689C2314yes—
158#14519687C2314yes—
159C8×Dic61C2314yes—
160C22×Q8×C61C2311yescharacteristic
161C22×Q8×C61C2311yescharacteristic
162C22×Q8×C61C2311yescharacteristic
163C2×Q16×C61—24no—
164C2×Q16×C61—24no—
165C2×Q16×C61C2314yes—
166C2×Q16×C61C2314yes—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4⋊Q8×C61—22no—
170C4⋊Q8×C61C2314yes—
171C4×Q8×C61—22no—
172C4×Q8×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179C4⋊C8×C61C2314yes—
180#103×C61C2314yes—
181#103×C61C2314yes—
182C23×D61—21no—
183C23×D61C2×D411yescharacteristic
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61#4114yes—
193C2×Q8×C61C2412yes—
194C2×Q8×C61C2412yes—
195C2×Q8×C61C2412yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209#11758226—216no—
210#11758226—28no—
211#11758226—28no—
212C2×D244—28no—
213C2×D244—24no—
214C2×D244—21no—
215C2×D244—22no—
216C2×D244#4114yes—
217C2×D244C2412yes—
218C2×C4×D61—28no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—82no—
226C2×C4×D61—82no—
227C2×C4×D61—82no—
228C2×C4×D61C2×D412yes—
229C2×C4×D61C2412yes—
230Q16×C61—28no—
231Q16×C61—28no—
232C2×C8×C61—22no—
233C2×C8×C61—22no—
234C2×C8×C61C2412yes—
235C2×C8×C61C2412yes—
236C4⋊C4×C61—24no—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61C2412yes—
241C42×C61—24no—
242C42×C61C2×D412yes—
243C42×C61C2412yes—
244#11758201—28no—
245#11758201—28no—
246#11758198—24no—
247#11758198—24no—
248#11758198—24no—
249#11758198—24no—
250#11758198C2×D414yes—
251#11758198C2×D414yes—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—24no—
256C4⋊Dic61—24no—
257C4⋊Dic61—24no—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196C2×D414yes—
267#11758196C2×D414yes—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61C2×D412yes—
272C4×Dic61C2412yes—
273C2×#92418—22no—
274C2×#92418—22no—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277C23×C61C22×D411yescharacteristic
278C22×D61—22no—
279C22×D61—24no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61C22×D412yes—
286Q8×C61—24no—
287Q8×C61—22no—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—42no—
293Q8×C61—42no—
294Q8×C61C2×#4114yes—
295C2×C4×C61—24no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D412yes—
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C2×#4112yes—
309C2×C4×C61C2×#4112yes—
310C2×C4×C61C2511yescharacteristic
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61C22×D412yes—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323D244—216no—
324D244—24no—
325D244—22no—
326D244C2×#4114yes—
327C4×D61—216no—
328C4×D61—24no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—84no—
332C4×D61—84no—
333C4×D61—84no—
334C8×C61—22no—
335C8×C61—22no—
336#92418—22no—
337#92418—22no—
338C2×#3120—611nomaximal, Sylow
339C22×C61#52512yes—
340C22×C61#57712yes—
341C22×C61#57812yes—
342C22×C61C23×D411yescharacteristic
343C2×D61—22no—
344C2×D61—24no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—44no—
348C2×D61—48no—
349C2×D61—42no—
350C2×D61—42no—
351C4×C61—24no—
352C4×C61—22no—
353C4×C61—22no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61#52512yes—
358C4×C61C22×#4111yescharacteristic
359C4×C61C22×#4111yescharacteristic
360Dic61—22no—
361Dic61—22no—
362Dic61—22no—
363Dic61—42no—
364Dic61—42no—
365Dic61—42no—
366C2×#541—611no—
367C2×#520—611no—
368#3120—6116no—
369C2×#484—611no—
370C2×#483—611no—
371C2×#479—611no—
372C2×#478—611no—
373C2×#462D6111yescharacteristic, complemented
374C2×#461—611no—
375C2×#452—611no—
376C2×#452—611no—
377C2×#441—611no—
378C2×#440—611no—
379C2×C4×Q16—611no—
380C2×C4×SD16—611no—
381C2×#433—611no—
382C2×C61#312014yescomplemented
383C2×C61C2×#52511yescharacteristic
384C2×C61C2×#57711yescharacteristic
385C2×C61C2×#57811yescharacteristic
386D61—42no—
387D61—44no—
388C22×#41—611no—
389C22×Q16C2×D6111yescharacteristic
390C22×Q16C2×D6111yescharacteristic
391C22×SD16—611no—
392C22×SD16—611no—
393#541—618no—
394#541—1224no—
395C2×C4⋊Q8C2×D6111yescharacteristic
396C2×#126—1221no—
397C2×#126—1221no—
398C2×#125—611no—
399C2×#125—1221no—
400C2×#125—1221no—
401C2×C22⋊Q8—611no—
402C2×C22⋊Q8—611no—
403#520—618no—
404#520—1224no—
405C2×C4×Q8—611no—
406C2×C4×Q8—611no—
407C2×C4×Q8—611no—
408C2×C4×Q8C2×D6111yescharacteristic
409C2×C4×D4—611no—
410C2×C4×D4—611no—
411C2×C4×D4—1221no—
412C2×C4×D4—1221no—
413C2×#117—611no—
414C2×#117—1221no—
415C22×C4⋊C4—611no—
416C22×C4⋊C4—1221no—
417#484—618no—
418#483—618no—
419#479—618no—
420#478—618no—
421#462C2×D6118yescomplemented
422#461—618no—
423#452—618no—
424#452—618no—
425#441—618no—
426#440—618no—
427C4×Q16—618no—
428C4×SD16—618no—
429#433—618no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#106—611no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8C2×D6111yescharacteristic
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103C2×D6111yescharacteristic
441C2×#103C2×D6111yescharacteristic
442C2×#102—611no—
443C2×#102—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×#97—611no—
447C2×C4×C8—611no—
448C61C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—614no—
450C2×#41—1222no—
451C2×#41—1224no—
452C2×#41—1224no—
453C22×Q8C22×D6111yescharacteristic
454C22×Q8C22×D6111yescharacteristic
455C22×Q8C22×D6111yescharacteristic
456C22×D4—611no—
457C22×D4—1221no—
458C23×C4—611no—
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4—1221no—
463C2×Q16—24no—
464C2×Q16—24no—
465C2×Q16C22×D6114yes—
466C2×Q16C22×D6114yes—
467C2×SD16—614no—
468C2×SD16—614no—
469C2×SD16—1224no—
470C2×SD16—1224no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8C22×D6114yes—
477#126—1228no—
478#126—1228no—
479#125—614no—
480#125—1228no—
481#125—1228no—
482#125—1222no—
483C22⋊Q8—614no—
484C22⋊Q8—614no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C4×Q8—22no—
488C4×Q8—614no—
489C4×Q8—614no—
490C4×Q8—614no—
491C4×Q8—1222no—
492C4×Q8—1222no—
493C4×Q8—1222no—
494C4×Q8C22×D6114yes—
495C4×D4—614no—
496C4×D4—614no—
497C4×D4—1228no—
498C4×D4—1222no—
499C4×D4—1228no—
500C4×D4—1222no—
501#117—614no—
502#117—614no—
503#117—1228no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—614no—
513C2×C4⋊C4—1228no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C42—21no—
531C2×C42—611no—
532C2×C42—1221no—
533C2×C42—1221no—
534C2×C42—1221no—
535C2×C42C22×D6111yescharacteristic
536#107—614no—
537#107—614no—
538#106—614no—
539#106—614no—
540C4⋊C8—614no—
541C4⋊C8C22×D6114yes—
542#103—614no—
543#103—614no—
544#103—614no—
545#103—614no—
546#103C22×D6114yes—
547#103C22×D6114yes—
548#102—614no—
549#102—614no—
550C22⋊C8—614no—
551C22⋊C8—614no—
552#97—614no—
553C4×C8—614no—
554C24—611no—
555C24—1221no—
556#41—1228no—
557#41—12216no—
558#41—1228no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8#1175822414yes—
568C2×Q8C23×D6112yes—
569C2×Q8C23×D6112yes—
570C2×Q8C23×D6112yes—
571C2×D4—614no—
572C2×D4—612no—
573C2×D4—1224no—
574C2×D4—1228no—
575C2×D4—1221no—
576C2×D4—1222no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—1224no—
587C22×C4—1224no—
588C22×C4—1228no—
589C22×C4—1224no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1224no—
596C22×C4—4882no—
597C22×C4—4882no—
598C22×C4—4882no—
599C22×C4D4×D6111yescharacteristic
600C22×C4D4×D6111yescharacteristic
601C22×C4C23×D6111yescharacteristic
602Q16—28no—
603Q16—28no—
604SD16—1228no—
605SD16—1228no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—612no—
609C2×C8—612no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8C23×D6112yes—
613C2×C8C23×D6112yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—614no—
619C4⋊C4—614no—
620C4⋊C4—612no—
621C4⋊C4—612no—
622C4⋊C4—612no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4C23×D6112yes—
635C22⋊C4—614no—
636C22⋊C4—614no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C22⋊C4—1224no—
641C42—24no—
642C42—612no—
643C42—612no—
644C42—1224no—
645C42—1224no—
646C42—1224no—
647C42D4×D6112yes—
648C42C23×D6112yes—
649C23—612no—
650C23—1224no—
651C23—1222no—
652C23—1222no—
653C23—1222no—
654C23—1222no—
655C23—2442no—
656C23—2442no—
657C23C2×D4×D6111yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8—42no—
665Q8—42no—
666Q8C2×#1175822414yes—
667D4—614no—
668D4—12216no—
669D4—1224no—
670D4—1222no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—612no—
682C2×C4—612no—
683C2×C4—612no—
684C2×C4—12216no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1224no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—4884no—
695C2×C4—4884no—
696C2×C4—4884no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4C2×D4×D6112yes—
701C2×C4C2×D4×D6112yes—
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4#41×D6112yes—
704C2×C4C2×#1175822412yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—22no—
708C8—1222no—
709C8—1222no—
710C22—1222no—
711C22—1222no—
712C22—1224no—
713C22—1222no—
714C22—2442no—
715C22—2442no—
716C22—2444no—
717C22—2448no—
718C22#1684027212yes—
719C22#1684057112yes—
720C22#1684057512yes—
721C22C22×D4×D6111yescharacteristic
722C4—22no—
723C4—22no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—1222no—
729C4—1222no—
730C4—1222no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C4#1684027212yes—
735C4C2×#41×D6111yescharacteristic
736C4C22×#1175822411yescharacteristic
737C2—2442no—
738C2—2444no—
739C2#2145603214yesdirect product factor
740C2C2×#1684027211yescharacteristic
741C2C2×#1684057111yescharacteristic
742C2C2×#1684057511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#462C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
hypercenterC2×#462D61
hypocenterC61C2×#3120
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#16840373C2semidirect
3. #21456032C2direct (N × H)
4. C2×#16840096C2semidirect
5. C2×#16840091C2semidirect
6. C2×#16840069C2semidirect
7. C2×#16840063C2semidirect
8. C2×#16839964C2semidirect
11. C2×#16839869C2semidirect
12. C2×#16839865C2semidirect
13. C2×Q16×Dic61C2semidirect
14. C2×#16839847C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#462C2semidirect
21. #16840373C22semidirect
42. #16840096C22semidirect
43. #16840091C22semidirect
44. #16840069C22semidirect
45. #16840063C22semidirect
46. #16839964C22semidirect
49. #16839869C22semidirect
50. #16839865C22semidirect
51. Q16×Dic61C22semidirect
52. #16839847C22semidirect
53. #16839822C22semidirect
73. C61×#462C22semidirect
373. C2×#462D61semidirect
382. C2×C61#3120semidirect
421. #462C2×D61semidirect
448. C61C2×#3120semidirect
739. C2#21456032direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403732
C2×#168402442
#214560322
C2×#168400962
C2×#168400912
C2×#168400692
C2×#168400632
C2×#168399642
C2×#168399232
C2×#168398692
C2×#168398652
C2×Q16×Dic612
C2×#168398472
C2×#168398222
C2×C61×#4622
C2×#312061