Finite Group Databasebeta

← C2×#21457931 #30556604

Subgroups — C2×#21457931 #30556604

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×#16840467C211yesmaximal, characteristic, complemented
2C2×#16840419C211yesmaximal, characteristic
3#21457931C2116yesmaximal, direct product factor
4C2×#16840120C211yesmaximal, characteristic, complemented
5C2×#16840079C211yesmaximal, characteristic, complemented
6C2×#16840092C211yesmaximal, characteristic, complemented
7C2×#16840045C211yesmaximal, characteristic, complemented
8C2×#16840020C211yesmaximal, characteristic, complemented
9C2×#16839990C211yesmaximal, characteristic, complemented
10C2×#16839983C211yesmaximal, characteristic, complemented
11C2×#16839924C211yesmaximal, characteristic, complemented
12C2×#16839919C211yesmaximal, characteristic, complemented
13C2×#16839866C211yesmaximal, characteristic, complemented
14C2×#16839831C211yesmaximal, characteristic, complemented
15C2×#103×D61C211yesmaximal, characteristic, complemented
16C2×C61×#417C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840467—24no—
23#16840467C2218yescomplemented
24#16840419—24no—
25#16840419C2218yes—
26C2×#14519776C2211yescharacteristic
27C2×#14519767—21no—
28C2×#14519764—21no—
29C2×#14519764C2211yescharacteristic
30C2×#14519757C2211yescharacteristic
31C2×#14519756—21no—
32C2×#14519756—21no—
33C2×#14519756C2211yescharacteristic
34C2×#14519756C2211yescharacteristic
35C2×#14519755—21no—
36C2×#14519748—21no—
37C2×#14519748C2211yescharacteristic
38C2×Q8×Dic61C2211yescharacteristic
39C2×#14519742C2211yescharacteristic
40C2×C4×C22⋊D61—21no—
41C2×C4×C22⋊D61—21no—
42C2×C4×C22⋊D61C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840120C2218yescomplemented
45#16840092C2218yescomplemented
46#16840079C2218yescomplemented
47#16840045C2218yescomplemented
48#16840020C2218yescomplemented
49#16839990C2218yescomplemented
50#16839983C2218yescomplemented
51#16839924C2218yescomplemented
52#16839919C2218yescomplemented
53#16839866C2218yescomplemented
54#16839831C2218yescomplemented
55C2×#14519709C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64#103×D61C2218yescomplemented
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic
71C22×C4⋊C4×C61C2211yescharacteristic
72C61×#417C2218yescomplemented
73C2×#103×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C2×Q8×D61—22no—
82C2×Q8×D61—24no—
83C2×Q8×D61—42no—
84C2×Q8×D61C2314yes—
85C22×C22⋊D61—21no—
86C22×C22⋊D61D411yescharacteristic
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61C2311yescharacteristic
90C2×Dic244—42no—
91C2×Dic244C2314yes—
92C2×#11758202—24no—
93C2×#11758202C2314yes—
94C2×#11758200—42no—
95C2×#11758200C2314yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C2×C8×D61—42no—
99C2×C8×D61C2314yes—
100#14519776—22no—
101#14519776C2314yes—
102#14519767—28no—
103#14519764—28no—
104#14519764—22no—
105#14519764C2314yes—
106#14519757—22no—
107#14519757C2314yes—
108#14519756—22no—
109#14519756—22no—
110#14519756—28no—
111#14519756—28no—
112#14519756C2314yes—
113#14519756C2314yes—
114#14519755—28no—
115#14519748—28no—
116#14519748—22no—
117#14519748C2314yes—
118Q8×Dic61—22no—
119Q8×Dic61C2314yes—
120#14519742—22no—
121#14519742C2314yes—
122C4×C22⋊D61—28no—
123C4×C22⋊D61—28no—
124C4×C22⋊D61D414yes—
125C4×C22⋊D61C2314yes—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196D411yescharacteristic
136C4⋊C4×D61—22no—
137C4⋊C4×D61C2314yes—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61D411yescharacteristic
144C2×#11758198—21no—
145C2×#11758198D411yescharacteristic
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519709C2314yes—
150#14519708C2314yes—
151#14519708C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519701C2314yes—
156#14519700C2314yes—
157#14519700C2314yes—
158#14519698C2314yes—
159C22⋊#92418C2314yes—
160#14519689C2314yes—
161#14519687C2314yes—
162C2×#41×C61—22no—
163C2×#41×C61—24no—
164C2×#41×C61—42no—
165C2×#41×C61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61—21no—
171C23×C4×C61C2311yescharacteristic
172C2×M16×C61—42no—
173C2×M16×C61C2314yes—
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176C2×C4⋊C4×C61—22no—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2314yes—
180C2×C4⋊C4×C61C2311yescharacteristic
181#103×C61C2314yes—
182#103×C61C2314yes—
183#102×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C23×D61C2×D411yescharacteristic
188#41×C61—28no—
189#41×C61—44no—
190#41×C61—48no—
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61#4114yes—
194C2×Q8×C61C2412yes—
195C2×D4×C61—24no—
196C2×D4×C61—21no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—44no—
200C2×D4×C61C2412yes—
201C22×C4×C61—21no—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—24no—
207C22×C4×C61—24no—
208C22×C4×C61—44no—
209C22×C4×C61—82no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2411yescharacteristic
214C2×C22⋊D61—24no—
215C2×C22⋊D61—24no—
216C2×C22⋊D61—44no—
217C2×C22⋊D61C2×D414yes—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225Q8×D61—28no—
226Q8×D61—44no—
227Q8×D61—48no—
228C2×C4×D61—22no—
229C2×C4×D61—22no—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—44no—
233C2×C4×D61—82no—
234C2×C4×D61C2×D412yes—
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—82no—
246C2×Dic122C2412yes—
247C2×Dic122C2412yes—
248M16×C61—44no—
249C2×C8×C61—22no—
250C2×C8×C61—22no—
251C2×C8×C61C2412yes—
252C2×C8×C61C2412yes—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C2412yes—
257C4⋊C4×C61C2412yes—
258C22⋊Dic61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261C22⋊Dic61—24no—
262C22⋊Dic61—24no—
263C22⋊Dic61C2×D414yes—
264#11758202—28no—
265#11758200—44no—
266#11758198—24no—
267#11758198C2×D414yes—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—24no—
271C4⋊Dic61—24no—
272C4⋊Dic61C2412yes—
273C4⋊Dic61C2412yes—
274#11758196—24no—
275#11758196—24no—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196C2×D414yes—
280C4×Dic61—24no—
281C4×Dic61—24no—
282C4×Dic61C2×D412yes—
283C4×Dic61C2412yes—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418C2412yes—
287C2×#92418C2412yes—
288Dic244—44no—
289C8×D61—44no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61C22×D412yes—
298C23×C61C22×D411yescharacteristic
299C22×D61—22no—
300C22×D61—22no—
301C22×D61#13714yes—
302C22×D61C22×D412yes—
303Q8×C61—24no—
304Q8×C61—22no—
305Q8×C61C2×#4114yes—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—48no—
309D4×C61—42no—
310C2×C4×C61—24no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—24no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—48no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—84no—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4112yes—
325C2×C4×C61H(5,𝔽2)12yes—
326C2×C4×C61C2511yescharacteristic
327C22⋊D61—28no—
328C22⋊D61—48no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61C22×D412yes—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343C4×D61—24no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—48no—
347C4×D61—84no—
348Dic122—22no—
349Dic122—22no—
350Dic122—22no—
351Dic122—22no—
352Dic122—48no—
353Dic122—42no—
354Dic122—42no—
355Dic122—84no—
356C8×C61—22no—
357C8×C61—22no—
358#92418—22no—
359#92418—22no—
360C2×#3316—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—44no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—84no—
369C22×C61#54612yes—
370C22×C61C2×#13712yes—
371C22×C61#57712yes—
372C22×C61C23×D411yescharacteristic
373C2×D61—22no—
374C2×D61—28no—
375C2×D61—22no—
376C2×D61C2×#13714yes—
377C4×C61—24no—
378C4×C61—22no—
379C4×C61—42no—
380C4×C61—42no—
381C4×C61#54612yes—
382C4×C61C22×#4111yescharacteristic
383C4×C61C2×H(5,𝔽2)11yescharacteristic
384Dic61—22no—
385Dic61—22no—
386Dic61—22no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390Dic61—42no—
391C2×#554—611no—
392C2×#548—611no—
393#3316—6116no—
394C2×#489—611no—
395C2×#481—611no—
396C2×#483—611no—
397C2×#475—611no—
398C2×#470—611no—
399C2×#465—611no—
400C2×#464—611no—
401C2×#452—611no—
402C2×#451—611no—
403C2×#441—611no—
404C2×#435—611no—
405C2×#417D6111yescharacteristic, complemented
406C22×#103—611no—
407C2×C61—42no—
408C2×C61—82no—
409C2×C61#331614yescomplemented
410C2×C61C2×#54611yescharacteristic
411C2×C61C22×#13711yescharacteristic
412C2×C61C2×#57711yescharacteristic
413D61—24no—
414C22×#41C2×D6111yescharacteristic
415C23×Q8—611no—
416C22×Q16—611no—
417C22×Q16—611no—
418C22×SD16—611no—
419C22×M16C2×D6111yescharacteristic
420C23×C8—611no—
421#554—618no—
422#554—1224no—
423#548—618no—
424#548—1224no—
425C2×C4⋊Q8—611no—
426C2×#125—1221no—
427C2×#124—611no—
428C2×#124—1221no—
429C2×C22⋊Q8—611no—
430C2×C22⋊Q8—611no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8—1221no—
434C2×C22⋊Q8—1221no—
435C2×#121—611no—
436C2×#121—1221no—
437C2×C4×Q8—611no—
438C2×C4×Q8—611no—
439C2×C4×D4—611no—
440C2×C4×D4—1221no—
441C2×C4×D4—1221no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4C2×D6111yescharacteristic
444#489—618no—
445#483—618no—
446#481—618no—
447#475—618no—
448#470—618no—
449#465—618no—
450#464—618no—
451#452—618no—
452#451—618no—
453#441—618no—
454#435—618no—
455C2×#106—611no—
456C2×#106—611no—
457C2×#106—611no—
458C2×C4⋊C8—611no—
459#417C2×D6118yescomplemented
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—618no—
466C2×#103C2×D6111yescharacteristic
467C2×#103C2×D6111yescharacteristic
468C2×#102—611no—
469C2×#102C2×D6111yescharacteristic
470C2×#102C2×D6111yescharacteristic
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×#97—611no—
474C61C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—42no—
478C2×#41C22×D6114yes—
479C22×Q8—614no—
480C22×Q8—611no—
481C22×Q8—611no—
482C22×Q8—1221no—
483C22×Q8—1221no—
484C22×Q8—1222no—
485C22×Q8—1224no—
486C22×Q8—2442no—
487C22×Q8C22×D6111yescharacteristic
488C22×D4—21no—
489C22×D4—611no—
490C22×D4—1221no—
491C22×D4C22×D6111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—611no—
495C23×C4—1221no—
496C23×C4—1221no—
497C23×C4C22×D6111yescharacteristic
498C2×Q16—614no—
499C2×Q16—614no—
500C2×Q16—1224no—
501C2×Q16—2442no—
502C2×SD16—614no—
503C2×SD16—2442no—
504C2×M16—42no—
505C2×M16C22×D6114yes—
506C22×C8—611no—
507C22×C8—611no—
508C22×C8—614no—
509C22×C8—2442no—
510C22×C8C22×D6111yescharacteristic
511C22×C8C22×D6111yescharacteristic
512C4⋊Q8—614no—
513C4⋊Q8—1222no—
514#125—1228no—
515#124—614no—
516#124—1222no—
517#124—1228no—
518C22⋊Q8—614no—
519C22⋊Q8—614no—
520C22⋊Q8—614no—
521C22⋊Q8—1228no—
522C22⋊Q8—1228no—
523C22⋊Q8—1222no—
524C22⋊Q8—1228no—
525C22⋊Q8—1222no—
526C22⋊Q8—1222no—
527#121—614no—
528#121—1222no—
529#121—1228no—
530C4×Q8—614no—
531C4×Q8—614no—
532C4×Q8—1222no—
533C4×Q8—1222no—
534C4×D4—614no—
535C4×D4—614no—
536C4×D4—1228no—
537C4×D4—1228no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—614no—
544C2×C4⋊C4—1222no—
545C2×C4⋊C4—1221no—
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⋊C4C22×D6111yescharacteristic
553C2×C4⋊C4C22×D6111yescharacteristic
554C2×C4⋊C4C22×D6114yes—
555C2×C22⋊C4—611no—
556C2×C22⋊C4—611no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C42—611no—
564C2×C42—1221no—
565C2×C42—1221no—
566#106—614no—
567#106—614no—
568#106—614no—
569C4⋊C8—614no—
570#103—614no—
571#103—614no—
572#103—614no—
573#103—614no—
574#103—614no—
575#103C22×D6114yes—
576#103C22×D6114yes—
577#102—614no—
578#102C22×D6114yes—
579#102C22×D6114yes—
580C22⋊C8—614no—
581C22⋊C8—614no—
582#97—614no—
583C24—21no—
584C24—611no—
585C24D4×D6111yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—612no—
592C2×Q8—612no—
593C2×Q8—1224no—
594C2×Q8—1224no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1228no—
598C2×Q8—1222no—
599C2×Q8—1222no—
600C2×Q8—1222no—
601C2×Q8—1222no—
602C2×Q8—4882no—
603C2×Q8—2444no—
604C2×Q8—2444no—
605C2×Q8—2448no—
606C2×Q8#1175822214yes—
607C2×Q8C23×D6112yes—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—44no—
613C2×D4—614no—
614C2×D4—1224no—
615C2×D4—1224no—
616C2×D4—2444no—
617C2×D4C23×D6112yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—44no—
626C22×C4—82no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—612no—
631C22×C4—612no—
632C22×C4—1224no—
633C22×C4—1224no—
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×C4D4×D6112yes—
643C22×C4D4×D6111yescharacteristic
644C22×C4C23×D6112yes—
645C22×C4C23×D6111yescharacteristic
646Q16—1228no—
647Q16—2444no—
648SD16—2444no—
649M16—44no—
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—21no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—614no—
663C4⋊C4—612no—
664C4⋊C4—612no—
665C4⋊C4—1224no—
666C4⋊C4—1224no—
667C4⋊C4—1224no—
668C4⋊C4—1224no—
669C4⋊C4—1224no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1224no—
673C4⋊C4—1224no—
674C4⋊C4C23×D6112yes—
675C4⋊C4C23×D6112yes—
676C22⋊C4—614no—
677C22⋊C4—614no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—1224no—
684C42—612no—
685C42—612no—
686C42—1224no—
687C42—1224no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—614no—
696C23—612no—
697C23—1222no—
698C23—1222no—
699C23C2×D4×D6112yes—
700C23C2×D4×D6111yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—1222no—
704Q8—1222no—
705Q8—1222no—
706Q8—1222no—
707Q8—4884no—
708Q8—2448no—
709Q8—2442no—
710Q8—2442no—
711Q8C2×#1175822214yes—
712D4—22no—
713D4—22no—
714D4—48no—
715D4—42no—
716D4—1228no—
717D4—2448no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—84no—
730C2×C4—612no—
731C2×C4—612no—
732C2×C4—612no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1224no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—4884no—
744C2×C4—2448no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4C2×D4×D6112yes—
750C2×C4C2×D4×D6111yescharacteristic
751C2×C4C2×#1175822212yes—
752C2×C4#1451982212yes—
753C2×C4C24×D6111yescharacteristic
754C8—22no—
755C8—22no—
756C8—1222no—
757C8—1222no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—614no—
767C22—1228no—
768C22—1222no—
769C22—1222no—
770C22#1684040212yes—
771C22#137×D6112yes—
772C22#1684057212yes—
773C22C22×D4×D6111yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—1222no—
779C4—1222no—
780C4—1222no—
781C4—2442no—
782C4—2442no—
783C4—2442no—
784C4—2442no—
785C4#1684040212yes—
786C4C22×#1175822211yescharacteristic
787C4C2×#1451982211yescharacteristic
788C2—42no—
789C2—82no—
790C2—1224no—
791C2#2145793114yesdirect product factor
792C2C2×#1684040211yescharacteristic
793C2C2×#137×D6111yescharacteristic
794C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC2×#16840419C2
hypercenterC2×#417D61
hypocenterC61C2×#3316
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#16840467C2semidirect
3. #21457931C2direct (N × H)
4. C2×#16840120C2semidirect
5. C2×#16840079C2semidirect
6. C2×#16840092C2semidirect
7. C2×#16840045C2semidirect
8. C2×#16840020C2semidirect
9. C2×#16839990C2semidirect
10. C2×#16839983C2semidirect
11. C2×#16839924C2semidirect
12. C2×#16839919C2semidirect
13. C2×#16839866C2semidirect
14. C2×#16839831C2semidirect
15. C2×#103×D61C2semidirect
16. C2×C61×#417C2semidirect
23. #16840467C22semidirect
44. #16840120C22semidirect
45. #16840092C22semidirect
46. #16840079C22semidirect
47. #16840045C22semidirect
48. #16840020C22semidirect
49. #16839990C22semidirect
50. #16839983C22semidirect
51. #16839924C22semidirect
52. #16839919C22semidirect
53. #16839866C22semidirect
54. #16839831C22semidirect
64. #103×D61C22semidirect
72. C61×#417C22semidirect
405. C2×#417D61semidirect
409. C2×C61#3316semidirect
459. #417C2×D61semidirect
474. C61C2×#3316semidirect
791. C2#21457931direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404672
C2×#168404192
#214579312
C2×#168401202
C2×#168400792
C2×#168400922
C2×#168400452
C2×#168400202
C2×#168399902
C2×#168399832
C2×#168399242
C2×#168399192
C2×#168398662
C2×#168398312
C2×#103×D612
C2×C61×#4172
C2×#331661