Finite Group Databasebeta

← C2×#21458200 #30558462

Subgroups — C2×#21458200 #30558462

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic
2C2×#16840452C211yesmaximal, characteristic, complemented
3#21458200C2116yesmaximal, direct product factor
4C2×#16840164C211yesmaximal, characteristic, complemented
5C2×#16840098C211yesmaximal, characteristic, complemented
6C2×#16840104C211yesmaximal, characteristic, complemented
7C2×#16840087C211yesmaximal, characteristic, complemented
8C2×#16840076C211yesmaximal, characteristic, complemented
9C2×#16840070C211yesmaximal, characteristic, complemented
10C2×#16840063C211yesmaximal, characteristic, complemented
11C2×#16839991C211yesmaximal, characteristic, complemented
12C2×#16839991C211yesmaximal, characteristic, complemented
13C2×C4×#11758190C211yesmaximal, characteristic, complemented
14C2×#16839800C211yesmaximal, characteristic, complemented
15C22×#14519709C211yesmaximal, characteristic, complemented
16C2×C8×D4×C61C211yesmaximal, characteristic, complemented
17C22×#11758190C2211yescharacteristic
18#16840458—24no—
19#16840458C2218yes—
20#16840452—24no—
21#16840452C2218yescomplemented
22C2×#14519772—21no—
23C2×#14519770—21no—
24C2×#14519769C2211yescharacteristic
25C2×#14519769C2211yescharacteristic
26C2×#14519767—21no—
27C2×#14519759—21no—
28C2×#14519758—21no—
29C2×#14519756C2211yescharacteristic
30C2×#14519756C2211yescharacteristic
31C2×#14519751C2211yescharacteristic
32C2×#14519751C2211yescharacteristic
33C2×#14519749—21no—
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×#14519737—21no—
37C2×#14519736C2211yescharacteristic
38C2×#14519736C2211yescharacteristic
39C2×#14519733—21no—
40C22×C4⋊Dic61C2211yescharacteristic
41C22×C4⋊Dic61C2211yescharacteristic
42#16840164C2218yescomplemented
43#16840104C2218yescomplemented
44#16840098C2218yescomplemented
45#16840087C2218yescomplemented
46#16840076C2218yescomplemented
47#16840070C2218yescomplemented
48#16840063C2218yescomplemented
49#16839991C2218yescomplemented
50#16839991C2218yescomplemented
51C4×#11758190C2218yescomplemented
52#16839800C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519711C2211yescharacteristic
56C2×#14519711C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519709C2211yescharacteristic
59C2×#14519709C2211yescharacteristic
60C2×#14519709C2211yescharacteristic
61C2×#14519709C2211yescharacteristic
62C2×#14519709C2218yescomplemented
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C23×C8×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C8×D4×C61C2218yescomplemented
73C2×C4⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C23×Dic61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C2×#11758190—24no—
85C2×#11758190C2314yes—
86#14519772—28no—
87#14519770—28no—
88#14519769—22no—
89#14519769—22no—
90#14519769C2314yes—
91#14519769C2314yes—
92#14519767—28no—
93#14519759—28no—
94#14519758—28no—
95#14519756—22no—
96#14519756—22no—
97#14519756C2314yes—
98#14519756C2314yes—
99#14519751—22no—
100#14519751—22no—
101#14519751C2314yes—
102#14519751C2314yes—
103#14519749—28no—
104C4×Dic122—22no—
105C4×Dic122C2314yes—
106C4×D244—22no—
107C4×D244C2314yes—
108#14519737—28no—
109#14519736—22no—
110#14519736—22no—
111#14519736C2314yes—
112#14519736C2314yes—
113#14519733—28no—
114C2×C4⋊Dic61—22no—
115C2×C4⋊Dic61—22no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61C2314yes—
119C2×C4⋊Dic61C2314yes—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143#14519711C2314yes—
144#14519711C2314yes—
145#14519711C2314yes—
146#14519711C2314yes—
147#14519709C2314yes—
148#14519709C2314yes—
149#14519709C2314yes—
150#14519709C2314yes—
151#14519709C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519699C2314yes—
156#14519699C2314yes—
157#14519699C2314yes—
158C22×D4×C61D411yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C22×C8×C61—24no—
162C22×C8×C61—24no—
163C22×C8×C61C2314yes—
164C22×C8×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4×D4×C61D414yes—
170C4×D4×C61C2314yes—
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C22⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61D411yescharacteristic
174C2×C42×C61C2311yescharacteristic
175C4⋊C8×C61C2314yes—
176C22⋊C8×C61C2314yes—
177C22⋊C8×C61C2314yes—
178C4×C8×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182C2×D4×C61—24no—
183C2×D4×C61C2×D414yes—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—44no—
200C2×C22⋊D61—82no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—24no—
210C22×Dic61—44no—
211C22×Dic61—82no—
212C2×D244—22no—
213C2×D244—22no—
214C2×D244—21no—
215C2×D244C2412yes—
216C2×C4×D61—24no—
217C2×C4×D61—82no—
218C2×Dic122—22no—
219C2×Dic122—22no—
220C2×Dic122—21no—
221C2×Dic122C2412yes—
222C2×C8×C61—22no—
223C2×C8×C61—22no—
224C2×C8×C61—22no—
225C2×C8×C61—28no—
226C2×C8×C61—28no—
227C2×C8×C61#4114yes—
228C2×C8×C61C2412yes—
229C2×C8×C61C2412yes—
230C2×C8×C61C2412yes—
231C2×C8×C61C2412yes—
232C4⋊C4×C61C2×D414yes—
233C22⋊C4×C61C2×D414yes—
234C22⋊C4×C61C2×D414yes—
235C42×C61C2×D412yes—
236C42×C61C2412yes—
237C22⋊Dic61—24no—
238C22⋊Dic61—24no—
239C22⋊Dic61—24no—
240C22⋊Dic61—24no—
241#11758198—24no—
242#11758198—24no—
243#11758198—24no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—24no—
249C4⋊Dic61—24no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C2412yes—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255C4⋊Dic61C2412yes—
256C4⋊Dic61C2412yes—
257C4⋊Dic61C2412yes—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61—24no—
268#11758190—28no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61#13514yes—
275C23×C61C22×D412yes—
276C23×C61C22×D412yes—
277C23×C61C22×D411yescharacteristic
278C22×D61—22no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282D4×C61—28no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—24no—
288C2×C4×C61—24no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61C22×D412yes—
294C2×C4×C61C22×D412yes—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D412yes—
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C2×#4112yes—
299C2×C4×C612−1+412yes—
300C2×C4×C61C2511yescharacteristic
301C22⋊D61—48no—
302C22⋊D61—84no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—42no—
311C2×Dic61—48no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—84no—
319D244—22no—
320D244—22no—
321D244—42no—
322C4×D61—84no—
323Dic122—22no—
324Dic122—22no—
325Dic122—42no—
326C8×C61—22no—
327C8×C61—22no—
328C8×C61—22no—
329C8×C61C2×#4114yes—
330C2×#3337—611nomaximal, Sylow
331C22×C61—28no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—44no—
338C22×C61#54712yes—
339C22×C61C2×#13514yes—
340C22×C61C2×#13512yes—
341C22×C61#57712yes—
342C22×C61C23×D411yescharacteristic
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—84no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—22no—
350C4×C61—22no—
351C4×C61#54712yes—
352C4×C61C22×#4111yescharacteristic
353C4×C61C2×2−1+411yescharacteristic
354Dic61—42no—
355Dic61—42no—
356Dic61—42no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#553—611no—
362C2×#552—611no—
363#3337—6116no—
364C2×#499—611no—
365C2×#484—611no—
366C2×#485—611no—
367C2×#482—611no—
368C2×#480—611no—
369C2×#479—611no—
370C2×#478—611no—
371C2×#465—611no—
372C2×#465—611no—
373C2×C4×SD16—611no—
374C2×C8×D4D6111yescharacteristic, complemented
375C2×#427—611no—
376C22×#106—611no—
377C2×C61—24no—
378C2×C61—42no—
379C2×C61#333714yescomplemented
380C2×C61C2×#54711yescharacteristic
381C2×C61C22×#13511yescharacteristic
382C2×C61C2×#57711yescharacteristic
383D61—82no—
384C22×SD16—611no—
385C23×C8C2×D6111yescharacteristic
386C23×C8C2×D6111yescharacteristic
387#553—618no—
388#553—1224no—
389#552—618no—
390#552—1224no—
391C2×#126—1221no—
392C2×#126—1221no—
393C2×#125—611no—
394C2×#125—611no—
395C2×#125—1221no—
396C2×#123—1221no—
397C2×#123—1221no—
398C2×C22⋊Q8—611no—
399C2×C22⋊Q8—611no—
400C2×#121—611no—
401C2×#121—611no—
402C2×#121—1221no—
403C2×C4×Q8—611no—
404C2×C4×D4—611no—
405C2×C4×D4—1221no—
406C2×C4×D4C2×D6111yescharacteristic
407C2×#117—611no—
408C2×#117—611no—
409C2×#117—1221no—
410C22×C4⋊C4—611no—
411C22×C4⋊C4—611no—
412#499—618no—
413#485—618no—
414#484—618no—
415#482—618no—
416#480—618no—
417#479—618no—
418#478—618no—
419#465—618no—
420#465—618no—
421C4×SD16—618no—
422C8×D4C2×D6118yescomplemented
423#427—618no—
424C2×#107—611no—
425C2×#107—611no—
426C2×#107—611no—
427C2×#107—611no—
428C2×#106—611no—
429C2×#106—611no—
430C2×#106—618no—
431C2×#106—611no—
432C2×#106—611no—
433C2×#106—611no—
434C2×C4⋊C8C2×D6111yescharacteristic
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×C22⋊C8C2×D6111yescharacteristic
442C2×C22⋊C8C2×D6111yescharacteristic
443C2×C4×C8C2×D6111yescharacteristic
444C61C2×#333711yescharacteristic, complemented, Sylow
445C22×Q8—611no—
446C22×D4—611no—
447C22×D4—1221no—
448C22×D4—1221no—
449C22×D4D24411yescharacteristic
450C23×C4—1221no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4C22×D6111yescharacteristic
454C23×C4C22×D6111yescharacteristic
455C2×SD16—614no—
456C2×SD16—1224no—
457C22×C8—24no—
458C22×C8—24no—
459C22×C8C22×D6111yescharacteristic
460C22×C8C22×D6111yescharacteristic
461C22×C8C22×D6114yes—
462C22×C8C22×D6114yes—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465#126—1228no—
466#126—1228no—
467#125—614no—
468#125—614no—
469#125—1228no—
470#125—1222no—
471#125—1222no—
472#123—1228no—
473#123—1228no—
474C22⋊Q8—614no—
475C22⋊Q8—614no—
476C22⋊Q8—1222no—
477C22⋊Q8—1222no—
478#121—614no—
479#121—614no—
480#121—1228no—
481#121—1222no—
482#121—1222no—
483C4×Q8—614no—
484C4×Q8—1222no—
485C4×D4—614no—
486C4×D4—1228no—
487C4×D4—1222no—
488C4×D4D24414yes—
489C4×D4C22×D6114yes—
490#117—614no—
491#117—614no—
492#117—1222no—
493#117—1222no—
494#117—1228no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—614no—
500C2×C4⋊C4—614no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4D24411yescharacteristic
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4D24411yescharacteristic
523C2×C22⋊C4D24411yescharacteristic
524C2×C42—1221no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42C22×D6111yescharacteristic
528#107—614no—
529#107—614no—
530#107—614no—
531#107—614no—
532#106—614no—
533#106—614no—
534#106—614no—
535#106—614no—
536#106—614no—
537C4⋊C8C22×D6114yes—
538#103—614no—
539#103—614no—
540#103—614no—
541#102—614no—
542#102—614no—
543#102—614no—
544C22⋊C8C22×D6114yes—
545C22⋊C8C22×D6114yes—
546C4×C8C22×D6114yes—
547C24—1221no—
548C24C2×D24411yescharacteristic
549C24C2×D24411yescharacteristic
550C2×Q8—612no—
551C2×Q8—1221no—
552C2×Q8—1222no—
553C2×Q8—1222no—
554C2×D4—24no—
555C2×D4—612no—
556C2×D4—1224no—
557C2×D4—1224no—
558C2×D4—1221no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—4882no—
562C2×D4—2444no—
563C2×D4C2×D24414yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—1224no—
569C22×C4—1224no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1224no—
578C22×C4—4882no—
579C22×C4—4882no—
580C22×C4—2444no—
581C22×C4C2×D24412yes—
582C22×C4C2×D24412yes—
583C22×C4C2×D24411yescharacteristic
584C22×C4C2×D24411yescharacteristic
585C22×C4C2×D24411yescharacteristic
586C22×C4C2×D24411yescharacteristic
587C22×C4C23×D6112yes—
588C22×C4C23×D6112yes—
589C22×C4C23×D6111yescharacteristic
590SD16—1228no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—28no—
595C2×C8—28no—
596C2×C8#1175822414yes—
597C2×C8C23×D6112yes—
598C2×C8C23×D6112yes—
599C2×C8C23×D6112yes—
600C2×C8C23×D6112yes—
601C4⋊C4—612no—
602C4⋊C4—612no—
603C4⋊C4—612no—
604C4⋊C4—612no—
605C4⋊C4—612no—
606C4⋊C4—612no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1224no—
616C4⋊C4—1224no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4C2×D24414yes—
623C22⋊C4—1224no—
624C22⋊C4—1224no—
625C22⋊C4—1224no—
626C22⋊C4—1224no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4C2×D24414yes—
631C22⋊C4C2×D24414yes—
632C42—1224no—
633C42—1224no—
634C42—1224no—
635C42C2×D24412yes—
636C42C23×D6112yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—1222no—
643C23—2442no—
644C23—2442no—
645C23—2442no—
646C23#1451979914yes—
647C23C22×D24412yes—
648C23C22×D24412yes—
649C23C22×D24411yescharacteristic
650Q8—1222no—
651Q8—1222no—
652Q8—2442no—
653D4—28no—
654D4—1222no—
655D4—1222no—
656D4—4884no—
657D4—2448no—
658D4—2442no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—4884no—
677C2×C4—4884no—
678C2×C4—2448no—
679C2×C4—2442no—
680C2×C4—2442no—
681C2×C4—2442no—
682C2×C4—2442no—
683C2×C4—2442no—
684C2×C4—2442no—
685C2×C4—2442no—
686C2×C4C22×D24412yes—
687C2×C4C22×D24412yes—
688C2×C4C22×D24412yes—
689C2×C4C22×D24412yes—
690C2×C4C22×D24411yescharacteristic
691C2×C4C2×#1175822412yes—
692C2×C4#1451982412yes—
693C2×C4C24×D6111yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8C2×#1175822414yes—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—4884no—
706C22—2442no—
707C22—2442no—
708C22—2442no—
709C22#1684041612yes—
710C22C2×#1451979914yes—
711C22C2×#1451979912yes—
712C22#1684057412yes—
713C22C23×D24411yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—2442no—
719C4—2442no—
720C4—2442no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4—2442no—
725C4#1684041612yes—
726C4C22×#1175822411yescharacteristic
727C4C2×#1451982411yescharacteristic
728C2—24no—
729C2—42no—
730C2—4882no—
731C2#2145820014yesdirect product factor
732C2C2×#1684041611yescharacteristic
733C2C22×#1451979911yescharacteristic
734C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C8×D4×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840458C2
hypercenterC2×C8×D4D61
hypocenterC61C2×#3337
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×#16840452C2semidirect
3. #21458200C2direct (N × H)
4. C2×#16840164C2semidirect
5. C2×#16840098C2semidirect
6. C2×#16840104C2semidirect
7. C2×#16840087C2semidirect
8. C2×#16840076C2semidirect
9. C2×#16840070C2semidirect
10. C2×#16840063C2semidirect
11. C2×#16839991C2semidirect
12. C2×#16839991C2semidirect
13. C2×C4×#11758190C2semidirect
14. C2×#16839800C2semidirect
15. C22×#14519709C2semidirect
16. C2×C8×D4×C61C2semidirect
21. #16840452C22semidirect
42. #16840164C22semidirect
43. #16840104C22semidirect
44. #16840098C22semidirect
45. #16840087C22semidirect
46. #16840076C22semidirect
47. #16840070C22semidirect
48. #16840063C22semidirect
49. #16839991C22semidirect
50. #16839991C22semidirect
51. C4×#11758190C22semidirect
52. #16839800C22semidirect
62. C2×#14519709C22semidirect
72. C8×D4×C61C22semidirect
374. C2×C8×D4D61semidirect
379. C2×C61#3337semidirect
422. C8×D4C2×D61semidirect
444. C61C2×#3337semidirect
731. C2#21458200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404582
C2×#168404522
#214582002
C2×#168401642
C2×#168400982
C2×#168401042
C2×#168400872
C2×#168400762
C2×#168400702
C2×#168400632
C2×#168399912
C2×C4×#117581902
C2×#168398002
C22×#145197092
C2×C8×D4×C612
C2×#333761