Finite Group Databasebeta

← C2×#21457995 #30556640

Subgroups — C2×#21457995 #30556640

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840462C211yesmaximal, characteristic
2C2×Q8×D244C211yesmaximal, characteristic, complemented
3#21457995C2116yesmaximal, direct product factor
4C2×#16840131C211yesmaximal, characteristic, complemented
5C2×#16840099C211yesmaximal, characteristic, complemented
6C2×#16840105C211yesmaximal, characteristic, complemented
7C2×#16840069C211yesmaximal, characteristic, complemented
8C2×#16840007C211yesmaximal, characteristic, complemented
9C2×#16839990C211yesmaximal, characteristic, complemented
10C2×#16839967C211yesmaximal, characteristic, complemented
11C2×#16839899C211yesmaximal, characteristic, complemented
12C2×#16839899C211yesmaximal, characteristic, complemented
13C2×#16839835C211yesmaximal, characteristic, complemented
14C2×#16839769C211yesmaximal, characteristic, complemented
15C2×#103×D61C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840462—24no—
24#16840462C2218yes—
25Q8×D244—24no—
26Q8×D244C2218yescomplemented
27C2×#14519777—21no—
28C2×#14519777C2211yescharacteristic
29C2×#14519770—21no—
30C2×#14519769C2211yescharacteristic
31C2×#14519760—21no—
32C2×#14519757—21no—
33C2×#14519757—21no—
34C2×#14519757C2211yescharacteristic
35C2×#14519757C2211yescharacteristic
36C2×#14519750—21no—
37C2×#14519748C2211yescharacteristic
38C2×#14519748C2211yescharacteristic
39C2×C4×D244—21no—
40C2×C4×D244C2211yescharacteristic
41C2×C4×C22⋊D61—21no—
42C2×#14519735C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840131C2218yescomplemented
45#16840105C2218yescomplemented
46#16840099C2218yescomplemented
47#16840069C2218yescomplemented
48#16840007C2218yescomplemented
49#16839990C2218yescomplemented
50#16839967C2218yescomplemented
51#16839899C2218yescomplemented
52#16839899C2218yescomplemented
53#16839835C2218yescomplemented
54C2×#14519710C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56C2×C4⋊#92418C2211yescharacteristic
57#16839769C2218yescomplemented
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66#103×D61C2218yescomplemented
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#440C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C2×Q8×D61—22no—
82C2×Q8×D61—22no—
83C2×Q8×D61—24no—
84C2×Q8×D61—24no—
85C2×Q8×D61—42no—
86C2×Q8×D61—42no—
87C2×Q8×D61C2314yes—
88C2×Q8×D61C2314yes—
89C22×D244D411yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61C2311yescharacteristic
96C22×C4×D61C2311yescharacteristic
97C2×#11758200—42no—
98C2×#11758200—42no—
99C2×#11758200C2314yes—
100C2×#11758200C2314yes—
101C2×#11758189—42no—
102C2×#11758189C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105C2×C8×D61—42no—
106C2×C8×D61C2314yes—
107#14519777—22no—
108#14519777—28no—
109#14519777C2314yes—
110#14519770—28no—
111#14519769—22no—
112#14519769C2314yes—
113#14519760—28no—
114#14519757—22no—
115#14519757—22no—
116#14519757—28no—
117#14519757—28no—
118#14519757C2314yes—
119#14519757C2314yes—
120#14519750—28no—
121#14519748—22no—
122#14519748—22no—
123#14519748C2314yes—
124#14519748C2314yes—
125C4×D244—28no—
126C4×D244D414yes—
127C4×D244C2314yes—
128C4×C22⋊D61—28no—
129#14519735—22no—
130#14519735C2314yes—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61D411yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C4⋊C4×D61—22no—
142C4⋊C4×D61C2314yes—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198D411yescharacteristic
149C2×#11758198D411yescharacteristic
150C2×C4×Dic61—21no—
151#14519710C2314yes—
152#14519708C2314yes—
153C4⋊#92418C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519701C2314yes—
159#14519701C2314yes—
160#14519700C2314yes—
161#14519700C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164C22×Q8×C61C2311yescharacteristic
165C22×D4×C61C2311yescharacteristic
166C23×C4×C61—21no—
167C2×SD16×C61—24no—
168C2×SD16×C61C2314yes—
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C4×Q8×C61—22no—
172C4×Q8×C61C2314yes—
173C4×D4×C61—22no—
174C4×D4×C61C2314yes—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C42×C61—21no—
180C2×C42×C61C2311yescharacteristic
181#107×C61C2314yes—
182#103×C61C2314yes—
183#102×C61C2314yes—
184#97×C61C2314yes—
185C24×C61—21no—
186C23×D61C2×D411yescharacteristic
187C23×D61C2×D411yescharacteristic
188C2×Q8×C61—21no—
189C2×Q8×C61—22no—
190C2×Q8×C61#4114yes—
191C2×Q8×C61C2412yes—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61C2412yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—24no—
200C22×C4×C61—82no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—44no—
207C2×C22⋊D61—82no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214Q8×D61—28no—
215Q8×D61—28no—
216Q8×D61—44no—
217Q8×D61—44no—
218Q8×D61—48no—
219Q8×D61—48no—
220C2×D244—24no—
221C2×D244C2×D414yes—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—24no—
227C2×C4×D61—24no—
228C2×C4×D61—24no—
229C2×C4×D61—44no—
230C2×C4×D61—44no—
231C2×C4×D61—82no—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2412yes—
235C2×C4×D61C2412yes—
236C2×Dic122—22no—
237C2×Dic122—22no—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—24no—
243C2×Dic122—24no—
244C2×Dic122—44no—
245C2×Dic122—44no—
246C2×Dic122C2412yes—
247C2×Dic122C2412yes—
248SD16×C61—28no—
249C2×C8×C61—22no—
250C2×C8×C61—22no—
251C2×C8×C61C2412yes—
252C2×C8×C61C2412yes—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C2412yes—
257C4⋊C4×C61C2412yes—
258C22⋊C4×C61—24no—
259C42×C61—24no—
260C42×C61C2×D412yes—
261C42×C61C2412yes—
262C22⋊Dic61—24no—
263C22⋊Dic61—24no—
264#11758200—44no—
265#11758200—44no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198C2×D414yes—
270#11758198C2×D414yes—
271C4⋊Dic61—21no—
272C4⋊Dic61—24no—
273C4⋊Dic61—24no—
274C4⋊Dic61—21no—
275C4⋊Dic61—24no—
276C4⋊Dic61—24no—
277C4⋊Dic61C2×D414yes—
278C4⋊Dic61C2412yes—
279C4⋊Dic61C2412yes—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283C4×Dic61—24no—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418C2412yes—
287C2×#92418C2412yes—
288#11758189—44no—
289C8×D61—44no—
290C23×C61—22no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61C22×D411yescharacteristic
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61#13714yes—
301C22×D61C22×D412yes—
302C22×D61C22×D412yes—
303Q8×C61—24no—
304Q8×C61—22no—
305Q8×C61C2×#4114yes—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—42no—
309C2×C4×C61—24no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—84no—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4112yes—
322C2×C4×C61H(5,𝔽2)12yes—
323C2×C4×C61C2511yescharacteristic
324C22⋊D61—48no—
325C22⋊D61—84no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61C22×D412yes—
337C2×Dic61C22×D412yes—
338D244—28no—
339C4×D61—24no—
340C4×D61—24no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—48no—
346C4×D61—48no—
347C4×D61—84no—
348Dic122—22no—
349Dic122—22no—
350Dic122—22no—
351Dic122—22no—
352Dic122—48no—
353Dic122—48no—
354Dic122—42no—
355Dic122—42no—
356C8×C61—22no—
357C8×C61—22no—
358#92418—22no—
359#92418—22no—
360C2×#3320—611nomaximal, Sylow
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—84no—
365C22×C61#54612yes—
366C22×C61C2×#13712yes—
367C22×C61#57712yes—
368C22×C61C23×D411yescharacteristic
369C2×D61—22no—
370C2×D61—28no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—44no—
376C2×D61C2×#13714yes—
377C4×C61—24no—
378C4×C61—22no—
379C4×C61—22no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61#54612yes—
383C4×C61C22×#4111yescharacteristic
384C4×C61C2×H(5,𝔽2)11yescharacteristic
385Dic61—22no—
386Dic61—22no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390Dic61—42no—
391C2×#553—611no—
392C2×D4×Q8—611no—
393#3320—6116no—
394C2×#491—611no—
395C2×#484—611no—
396C2×#485—611no—
397C2×#479—611no—
398C2×#468—611no—
399C2×#465—611no—
400C2×#461—611no—
401C2×#448—611no—
402C2×#448—611no—
403C2×#440D6111yescharacteristic, complemented
404C2×#435—611no—
405C2×#419—611no—
406C22×#103—611no—
407C2×C61—82no—
408C2×C61#332014yescomplemented
409C2×C61C2×#54611yescharacteristic
410C2×C61C22×#13711yescharacteristic
411C2×C61C2×#57711yescharacteristic
412D61—24no—
413D61—42no—
414C23×Q8—611no—
415C23×Q8—611no—
416C22×SD16—611no—
417C22×SD16—611no—
418C22×SD16C2×D6111yescharacteristic
419C22×M16—611no—
420C23×C8—611no—
421#553—618no—
422#553—1224no—
423D4×Q8—618no—
424D4×Q8—1224no—
425C2×C4⋊Q8—611no—
426C2×C4⋊Q8—1221no—
427C2×#126—1221no—
428C2×#125—611no—
429C2×#123—1221no—
430C2×C22⋊Q8—611no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8—1221no—
434C2×#121—611no—
435C2×#121—611no—
436C2×#121—1221no—
437C2×C4×Q8C2×D6111yescharacteristic
438C2×C4×D4—611no—
439C2×C4×D4—1221no—
440C2×C4×D4—1221no—
441C2×C4×D4C2×D6111yescharacteristic
442C2×#117—611no—
443C22×C4⋊C4—611no—
444#491—618no—
445#485—618no—
446#484—618no—
447#479—618no—
448#468—618no—
449#465—618no—
450#461—618no—
451#448—618no—
452#448—618no—
453#440C2×D6118yescomplemented
454#435—618no—
455C2×#107—611no—
456C2×#107C2×D6111yescharacteristic
457C2×#106—611no—
458C2×C4⋊C8—611no—
459#419—618no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103—618no—
469C2×#103C2×D6111yescharacteristic
470C2×#102C2×D6111yescharacteristic
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×#97C2×D6111yescharacteristic
474C61C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—614no—
476C22×Q8—614no—
477C22×Q8—611no—
478C22×Q8—611no—
479C22×Q8—1221no—
480C22×Q8—1221no—
481C22×Q8—1222no—
482C22×Q8—1222no—
483C22×Q8—1224no—
484C22×Q8—1224no—
485C22×Q8—2442no—
486C22×Q8—2442no—
487C22×Q8C22×D6111yescharacteristic
488C22×D4—611no—
489C22×D4—1221no—
490C22×D4—1221no—
491C22×D4C22×D6111yescharacteristic
492C23×C4—21no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—1221no—
496C23×C4—1221no—
497C23×C4—1221no—
498C2×SD16—24no—
499C2×SD16—614no—
500C2×SD16—614no—
501C2×SD16—2442no—
502C2×SD16—2442no—
503C2×SD16C22×D6114yes—
504C2×M16—614no—
505C2×M16—2442no—
506C22×C8—611no—
507C22×C8—611no—
508C22×C8—614no—
509C22×C8—2442no—
510C22×C8C22×D6111yescharacteristic
511C22×C8C22×D6111yescharacteristic
512C4⋊Q8—614no—
513C4⋊Q8—1228no—
514C4⋊Q8—1222no—
515#126—1228no—
516#125—614no—
517#125—1222no—
518#123—1228no—
519C22⋊Q8—614no—
520C22⋊Q8—614no—
521C22⋊Q8—1228no—
522C22⋊Q8—1228no—
523C22⋊Q8—1222no—
524C22⋊Q8—1222no—
525#121—614no—
526#121—614no—
527#121—1228no—
528#121—1222no—
529#121—1222no—
530C4×Q8—22no—
531C4×Q8C22×D6114yes—
532C4×D4—22no—
533C4×D4—614no—
534C4×D4—614no—
535C4×D4—1228no—
536C4×D4—1228no—
537C4×D4C22×D6114yes—
538#117—614no—
539#117—1222no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—614no—
545C2×C4⋊C4—1222no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4C22×D6111yescharacteristic
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—611no—
557C2×C22⋊C4—611no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C42—21no—
564C2×C42—1221no—
565C2×C42C22×D6111yescharacteristic
566#107—614no—
567#107C22×D6114yes—
568#106—614no—
569C4⋊C8—614no—
570#103—614no—
571#103—614no—
572#103—614no—
573#103—614no—
574#103—614no—
575#103—614no—
576#103—614no—
577#103—614no—
578#103C22×D6114yes—
579#102C22×D6114yes—
580C22⋊C8—614no—
581C22⋊C8—614no—
582#97C22×D6114yes—
583C24—21no—
584C24—611no—
585C24—611no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—612no—
589C2×Q8—612no—
590C2×Q8—1224no—
591C2×Q8—1224no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1228no—
595C2×Q8—1228no—
596C2×Q8—1222no—
597C2×Q8—1222no—
598C2×Q8—1222no—
599C2×Q8—1222no—
600C2×Q8—2444no—
601C2×Q8—2444no—
602C2×Q8—2444no—
603C2×Q8—2444no—
604C2×Q8—2448no—
605C2×Q8—2448no—
606C2×Q8#1175822214yes—
607C2×Q8C23×D6112yes—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—614no—
612C2×D4—1224no—
613C2×D4—1224no—
614C2×D4—1224no—
615C2×D4—4882no—
616C2×D4—2444no—
617C2×D4C23×D6112yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—82no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—612no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—1224no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—4882no—
641C22×C4—2444no—
642C22×C4—2444no—
643C22×C4D4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4C23×D6111yescharacteristic
646SD16—28no—
647SD16—2444no—
648SD16—2444no—
649M16—2444no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—612no—
653C2×C8—612no—
654C2×C8—1222no—
655C2×C8—1222no—
656C2×C8—2444no—
657C2×C8C23×D6112yes—
658C2×C8C23×D6112yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—614no—
663C4⋊C4—612no—
664C4⋊C4—612no—
665C4⋊C4—1224no—
666C4⋊C4—1224no—
667C4⋊C4—1224no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1224no—
671C4⋊C4—1224no—
672C4⋊C4—1224no—
673C4⋊C4—1224no—
674C4⋊C4C23×D6112yes—
675C4⋊C4C23×D6112yes—
676C22⋊C4—24no—
677C22⋊C4—614no—
678C22⋊C4—614no—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—1224no—
684C42—24no—
685C42—1224no—
686C42D4×D6112yes—
687C42C23×D6112yes—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—614no—
693C23—612no—
694C23—612no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23C2×D4×D6111yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—1222no—
704Q8—1222no—
705Q8—1222no—
706Q8—1222no—
707Q8—2448no—
708Q8—2448no—
709Q8—2442no—
710Q8—2442no—
711Q8C2×#1175822214yes—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—1228no—
716D4—4884no—
717D4—2448no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—84no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1224no—
736C2×C4—1224no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—4884no—
742C2×C4—2448no—
743C2×C4—2448no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4C2×D4×D6112yes—
749C2×C4C2×D4×D6112yes—
750C2×C4C2×D4×D6111yescharacteristic
751C2×C4C2×#1175822212yes—
752C2×C4#1451982312yes—
753C2×C4C24×D6111yescharacteristic
754C8—22no—
755C8—22no—
756C8—1222no—
757C8—1222no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22—614no—
763C22—1222no—
764C22—1228no—
765C22—1222no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—2444no—
770C22#1684040812yes—
771C22#137×D6112yes—
772C22#1684057212yes—
773C22C22×D4×D6111yescharacteristic
774C4—24no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—1222no—
780C4—1222no—
781C4—2442no—
782C4—2442no—
783C4—2442no—
784C4—2442no—
785C4#1684040812yes—
786C4C22×#1175822211yescharacteristic
787C4C2×#1451982311yescharacteristic
788C2—82no—
789C2—1224no—
790C2—2442no—
791C2#2145799514yesdirect product factor
792C2C2×#1684040811yescharacteristic
793C2C2×#137×D6111yescharacteristic
794C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#16840462C2
hypercenterC2×#440D61
hypocenterC61C2×#3320
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×Q8×D244C2semidirect
3. #21457995C2direct (N × H)
4. C2×#16840131C2semidirect
5. C2×#16840099C2semidirect
6. C2×#16840105C2semidirect
7. C2×#16840069C2semidirect
8. C2×#16840007C2semidirect
9. C2×#16839990C2semidirect
10. C2×#16839967C2semidirect
11. C2×#16839899C2semidirect
12. C2×#16839899C2semidirect
13. C2×#16839835C2semidirect
14. C2×#16839769C2semidirect
15. C2×#103×D61C2semidirect
16. C2×C61×#440C2semidirect
26. Q8×D244C22semidirect
44. #16840131C22semidirect
45. #16840105C22semidirect
46. #16840099C22semidirect
47. #16840069C22semidirect
48. #16840007C22semidirect
49. #16839990C22semidirect
50. #16839967C22semidirect
51. #16839899C22semidirect
52. #16839899C22semidirect
53. #16839835C22semidirect
57. #16839769C22semidirect
66. #103×D61C22semidirect
72. C61×#440C22semidirect
403. C2×#440D61semidirect
408. C2×C61#3320semidirect
453. #440C2×D61semidirect
474. C61C2×#3320semidirect
791. C2#21457995direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404622
C2×Q8×D2442
#214579952
C2×#168401312
C2×#168400992
C2×#168401052
C2×#168400692
C2×#168400072
C2×#168399902
C2×#168399672
C2×#168398992
C2×#168398352
C2×#168397692
C2×#103×D612
C2×C61×#4402
C2×#332061