Finite Group Databasebeta

← C4×#16839923 #29685641

Subgroups — C4×#16839923 #29685641

Order 15616.

1480 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758226C211yesmaximal, characteristic
2C2×#16839923C211yesmaximal, characteristic
3C2×C4×#11758201C211yesmaximal, characteristic, complemented
4C4×#14519753C211yesmaximal, characteristic, complemented
5#21446162C211yesmaximal, characteristic, complemented
6#21446150C211yesmaximal, characteristic, complemented
7#21446128C211yesmaximal, characteristic, complemented
8#21446085C211yesmaximal, characteristic, complemented
9#21446063C211yesmaximal, characteristic, complemented
10#21446015C211yesmaximal, characteristic, complemented
11#21445758C211yesmaximal, characteristic
12C4×#14519701C211yesmaximal, characteristic, complemented
13C4×#14519699C211yesmaximal, characteristic, complemented
14C4×#14519689C211yesmaximal, characteristic, complemented
15C2×C4×Q16×C61C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519753C2211yescharacteristic
19C4×#11758226—24no—
20C4×#11758226—24no—
21C2×Q8×Dic61C2211yescharacteristic
22C2×C4×D244—21no—
23C2×C4×D244C2211yescharacteristic
24C2×#14519739—21no—
25C2×#14519739C2211yescharacteristic
26C2×#14519735—21no—
27C2×#14519735C2211yescharacteristic
28C2×C42×D61—21no—
29C2×C42×D61C2211yescharacteristic
30#16839923C418yesdirect product factor
31C4×#11758201—24no—
32C2×#14519708C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839669C2211yescharacteristic
43#16839658C2211yescharacteristic
44#16839643—21no—
45#16839633—21no—
46#16839619C2211yescharacteristic
47C4×#11758196—21no—
48C4×C4⋊Dic61C2211yescharacteristic
49C4×#11758198—21no—
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×Q16×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C4×Q16×C61—24no—
60C2×#107×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C2×C4×C8×C61C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226C2×C414yes—
70C22×D244—21no—
71C22×D244C2311yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C2×#11758201—22no—
79C2×#11758201—22no—
80C2×#11758201C2×C414yescomplemented
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519753—22no—
84#14519753C2×C414yescomplemented
85Q8×Dic61—22no—
86Q8×Dic61—22no—
87C4×D244—28no—
88C4×D244—22no—
89C4×D244D414yes—
90#14519739—28no—
91#14519739—22no—
92#14519739—22no—
93#14519735—28no—
94#14519735—22no—
95#14519735—22no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C42×D61—28no—
114C42×D61—22no—
115C42×D61—22no—
116#14519708—22no—
117#14519701—22no—
118#14519701—22no—
119#14519701C2×C414yescomplemented
120#14519699—22no—
121#14519699C2×C414yescomplemented
122#14519697—22no—
123#14519689—22no—
124#14519689C2×C414yescomplemented
125C4×#92418—22no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131C22×Q8×C61C2311yescharacteristic
132C22×Q8×C61C2311yescharacteristic
133C2×Q16×C61—22no—
134C2×Q16×C61—22no—
135C2×Q16×C61C2×C414yescomplemented
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C4×Q8×C61—22no—
139C4×Q8×C61—22no—
140C4×Q8×C61—22no—
141C4×Q8×C61D414yes—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C42×C61—21no—
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#107×C61—22no—
150#103×C61—22no—
151#103×C61—22no—
152C4×C8×C61—22no—
153C23×D61—21no—
154C23×D61C2×D411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61C22×C412yes—
164C2×Q8×C61C22×C412yes—
165C2×Q8×C61C2×D412yes—
166C2×Q8×C61#4112yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180#11758226—28no—
181#11758226—28no—
182#11758226—28no—
183#11758226—28no—
184C2×D244—24no—
185C2×D244—24no—
186C2×D244—24no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244C22×C412yes—
191C2×D244C2×D412yes—
192C2×D244#4112yes—
193C2×C4×D61—24no—
194C2×C4×D61—24no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—24no—
200C2×C4×D61—24no—
201C2×C4×D61—24no—
202C2×C4×D61—22no—
203C2×C4×D61—22no—
204C2×C4×D61—22no—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—41no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61C22×C412yes—
213C2×C4×D61#4112yes—
214Q16×C61—28no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61C22×C412yes—
221C4⋊C4×C61—24no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—42no—
226C4⋊C4×C61C2×D412yes—
227C42×C61—24no—
228C42×C61—42no—
229C42×C61C2×D412yes—
230C42×C61C2×D412yes—
231#11758201—28no—
232#11758198—24no—
233#11758198—24no—
234#11758198—24no—
235#11758198—24no—
236#11758198—42no—
237C4⋊Dic61—24no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61C22×C412yes—
243C4⋊Dic61C2×D412yes—
244#11758196—24no—
245#11758196—42no—
246C4×Dic61—24no—
247C4×Dic61—24no—
248C4×Dic61—22no—
249C4×Dic61—22no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252C4×Dic61—42no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418C22×C412yes—
259C23×C61C22×D411yescharacteristic
260C22×D61—22no—
261C22×D61—21no—
262C22×D61—22no—
263C22×D61—21no—
264C22×D61—22no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61C4×D412yes—
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—22no—
278Q8×C61—22no—
279Q8×C61—41no—
280Q8×C61—41no—
281Q8×C61C4×D414yes—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61#12012yes—
297C2×C4×C61#12012yes—
298C2×C4×C61#13512yes—
299C2×C4×C61#13712yes—
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61C4×D412yes—
323C2×Dic61#13512yes—
324D244—216no—
325D244—22no—
326D244—22no—
327D244—22no—
328D244C4×D414yes—
329C4×D61—216no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—44no—
335C4×D61—48no—
336C4×D61—44no—
337C4×D61—48no—
338C8×C61—22no—
339C8×C61—41no—
340#92418—22no—
341#92418—41no—
342C4×#452—611nomaximal, Sylow
343C22×C61C2×C4×D411yescharacteristic
344C22×C61C2×#12011yescharacteristic
345C22×C61#52511yescharacteristic
346C22×C61C2×#13511yescharacteristic
347C22×C61C2×#13511yescharacteristic
348C22×C61C2×#13711yescharacteristic
349C22×C61#57511yescharacteristic
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—24no—
354C2×D61—41no—
355C2×D61—42no—
356C2×D61—41no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—41no—
361C2×D61—42no—
362C2×D61—41no—
363C2×D61—42no—
364C4×C61—22no—
365C4×C61—24no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61—81no—
369C4×C61#45214yescomplemented
370C4×C61C2×C4×D411yescharacteristic
371C4×C61C2×C4×D411yescharacteristic
372C4×C61#52511yescharacteristic
373C4×C61#52511yescharacteristic
374Dic61—22no—
375Dic61—22no—
376Dic61—42no—
377Dic61—41no—
378Dic61—42no—
379Dic61—81no—
380C2×C4×#41—611no—
381C2×#452—611no—
382C2×C4×Q16D6111yescharacteristic, complemented
383C2×C4×SD16—611no—
384C4×C22⋊Q8—611no—
385#1878—611no—
386#1877—611no—
387#1873—611no—
388#1865—611no—
389#1862—611no—
390#1854—611no—
391#1788—611no—
392C4×#103—611no—
393C4×#102—611no—
394C4×C22⋊C8—611no—
395C2×C61C4×#12011yescharacteristic
396C2×C61C4×#13511yescharacteristic
397C2×C61C4×#13711yescharacteristic
398C2×C61C2×#45211yescharacteristic
399C2×C61#300211yescharacteristic
400C2×C61#310211yescharacteristic
401C2×C61#310711yescharacteristic
402D61—42no—
403D61—44no—
404C22×#41—611no—
405C22×Q16C2×D6111yescharacteristic
406C22×SD16—611no—
407C2×C22⋊Q8—611no—
408C4×#41—1224no—
409C4×#41—1224no—
410C2×C4×Q8—611no—
411C2×C4×Q8C2×D6111yescharacteristic
412C2×C4×Q8C2×D6111yescharacteristic
413C2×C4×D4—611no—
414C2×C4×D4—611no—
415C2×C4×D4—1221no—
416C2×C4×D4—1221no—
417C2×#117—611no—
418C2×#117—1221no—
419C22×C42—611no—
420C22×C42—1221no—
421#452—618no—
422C4×Q16—24no—
423C4×SD16—1224no—
424C2×#107C2×D6111yescharacteristic
425C2×#106—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103C2×D6111yescharacteristic
430C2×#103C2×D6111yescharacteristic
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C4×C8—611no—
437C2×C4×C8C2×D6111yescharacteristic
438#391—611no—
439#389—611no—
440#387—1221no—
441#385—1221no—
442#380—611no—
443C4×C4⋊C4—611no—
444C4×C4⋊C4—1221no—
445C4×C22⋊C4—1221no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450#336—611no—
451#336—611no—
452C61C4×#45211yescharacteristic, complemented, Sylow
453C2×#41—614no—
454C2×#41—1222no—
455C2×#41—1222no—
456C2×#41—1222no—
457C2×#41—1222no—
458C2×#41—1222no—
459C22×Q8C22×D6111yescharacteristic
460C22×Q8C22×D6111yescharacteristic
461C22×D4—611no—
462C22×D4—1221no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C2×Q16—22no—
470C2×Q16—22no—
471C2×Q16C4×D6114yescomplemented
472C2×SD16—614no—
473C2×SD16—1222no—
474C2×SD16—1222no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479C22⋊Q8—614no—
480C22⋊Q8—1222no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—1222no—
485C4×Q8—1222no—
486C4×Q8C22⋊D6114yes—
487C4×D4—614no—
488C4×D4—1228no—
489C4×D4—1222no—
490C4×D4—1228no—
491C4×D4—1222no—
492C4×D4—1222no—
493#117—1222no—
494#117—1228no—
495#117—1222no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C42—21no—
512C2×C42—21no—
513C2×C42—611no—
514C2×C42—611no—
515C2×C42—611no—
516C2×C42—1228no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1222no—
520C2×C42—1222no—
521C2×C42—1221no—
522C2×C42C22×D6111yescharacteristic
523#107—22no—
524#106—1222no—
525#103—22no—
526#103—22no—
527#103—614no—
528#103—1222no—
529#103—1222no—
530#102—614no—
531#102—1222no—
532#102—1222no—
533C22⋊C8—614no—
534C22⋊C8—1222no—
535C4×C8—22no—
536C4×C8—1222no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542C24—611no—
543C24—1221no—
544#41—1228no—
545#41—1228no—
546#41—1228no—
547#41—1228no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8C2×C4×D6112yes—
557C2×Q8C2×C4×D6112yes—
558C2×Q8#1175822212yes—
559C2×Q8C2×C22⋊D6112yes—
560C2×D4—612no—
561C2×D4—612no—
562C2×D4—612no—
563C2×D4—1224no—
564C2×D4—1224no—
565C2×D4—1224no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—611no—
578C22×C4—1224no—
579C22×C4—1222no—
580C22×C4—1224no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1222no—
590C22×C4—1224no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1221no—
595C22×C4—2441no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4D4×D6111yescharacteristic
601C22×C4D4×D6111yescharacteristic
602C22×C4C23×D6111yescharacteristic
603Q16—28no—
604SD16—1228no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—612no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8C2×C4×D6112yes—
617C4⋊C4—21no—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—42no—
622C4⋊C4—612no—
623C4⋊C4—612no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—2442no—
631C4⋊C4C2×C22⋊D6112yes—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—2442no—
637C42—24no—
638C42—42no—
639C42—1224no—
640C42—1224no—
641C42—1221no—
642C42—1221no—
643C42—1222no—
644C42—1222no—
645C42—2442no—
646C42D4×D6112yes—
647C42C2×C22⋊D6112yes—
648C23—612no—
649C23—1222no—
650C23—1222no—
651C23—1221no—
652C23—1222no—
653C23—1221no—
654C23—1221no—
655C23—1221no—
656C23—1221no—
657C23—1221no—
658C23—2441no—
659C23—2441no—
660C23—2441no—
661C23—2441no—
662C23C2×D4×D6111yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—41no—
669Q8—41no—
670Q8C4×C22⋊D6114yes—
671D4—614no—
672D4—12216no—
673D4—1222no—
674D4—1222no—
675D4—1222no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—12216no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—2444no—
707C2×C4—2448no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2444no—
716C2×C4—2448no—
717C2×C4#1451974512yes—
718C2×C4#1451974512yes—
719C2×C4#1451980012yes—
720C2×C4#1451980912yes—
721C2×C4C22×C4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C22×C22⋊D6111yescharacteristic
724C2×C4#41×D6111yescharacteristic
725C2×C4#41×D6111yescharacteristic
726C2×C4C2×#1175822211yescharacteristic
727C8—22no—
728C8—41no—
729C8—1222no—
730C8—2441no—
731C22—1222no—
732C22—1224no—
733C22—1222no—
734C22—1222no—
735C22—2441no—
736C22—2442no—
737C22—2442no—
738C22—2441no—
739C22—2442no—
740C22—2441no—
741C22—2442no—
742C22—2441no—
743C22—2442no—
744C22—2442no—
745C22C4×D4×D6111yescharacteristic
746C22C2×#1451974511yescharacteristic
747C22#1684027111yescharacteristic
748C22#135×D6111yescharacteristic
749C22C2×#1451980011yescharacteristic
750C22C2×#1451980911yescharacteristic
751C22#1684055911yescharacteristic
752C4—24no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—81no—
757C4—1222no—
758C4—1222no—
759C4—4881no—
760C4—2441no—
761C4—2442no—
762C4—2442no—
763C4#1683992314yesdirect product factor
764C4C4×D4×D6111yescharacteristic
765C4C2×C4×C22⋊D6111yescharacteristic
766C4#1684026911yescharacteristic
767C4#1684027111yescharacteristic
768C2—2442no—
769C2—2444no—
770C2C4×#1451974511yescharacteristic
771C2C4×#1451980011yescharacteristic
772C2C4×#1451980911yescharacteristic
773C2C2×#1683992311yescharacteristic
774C2#2145503311yescharacteristic
775C2#2145584311yescharacteristic
776C2#2145588811yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×Q16×C61C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenterC2×C4×Q16D61
hypocenterC61C4×#452
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758201C2semidirect
4. C4×#14519753C2semidirect
5. #21446162C2semidirect
6. #21446150C2semidirect
7. #21446128C2semidirect
8. #21446085C2semidirect
9. #21446063C2semidirect
10. #21446015C2semidirect
12. C4×#14519701C2semidirect
13. C4×#14519699C2semidirect
14. C4×#14519689C2semidirect
15. C2×C4×Q16×C61C2semidirect
30. #16839923C4direct (N × H)
80. C2×#11758201C2×C4semidirect
84. #14519753C2×C4semidirect
119. #14519701C2×C4semidirect
121. #14519699C2×C4semidirect
124. #14519689C2×C4semidirect
135. C2×Q16×C61C2×C4semidirect
369. C4×C61#452semidirect
382. C2×C4×Q16D61semidirect
452. C61C4×#452semidirect
471. C2×Q16C4×D61semidirect
763. C4#16839923direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#117582262
C2×#168399232
C2×C4×#117582012
C4×#145197532
#214461622
#214461502
#214461282
#214460852
#214460632
#214460152
#214457582
C4×#145197012
C4×#145196992
C4×#145196892
C2×C4×Q16×C612
C4×#45261