Finite Group Databasebeta

← C2×#21457479 #30555175

Subgroups — C2×#21457479 #30555175

Order 15616.

2794 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic, complemented
2C2×#16840431C211yesmaximal, characteristic
3C2×Q8×C22⋊D61C211yesmaximal, characteristic, complemented
4#21457479C2116yesmaximal, direct product factor
5C2×#16840133C211yesmaximal, characteristic, complemented
6C2×#16840008C211yesmaximal, characteristic, complemented
7C2×#16840005C211yesmaximal, characteristic, complemented
8C2×#16839970C211yesmaximal, characteristic, complemented
9C2×#16839960C211yesmaximal, characteristic, complemented
10C2×#16839924C211yesmaximal, characteristic, complemented
11C2×#16839923C211yesmaximal, characteristic, complemented
12C2×#16839901C211yesmaximal, characteristic, complemented
13C2×#16839899C211yesmaximal, characteristic, complemented
14C2×Q16×Dic61C211yesmaximal, characteristic, complemented
15C2×#16839838C211yesmaximal, characteristic, complemented
16C22×#137×C61C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C2×#14519809—28no—
20C2×#14519809C2218yescomplemented
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758200C2211yescharacteristic
24C22×#11758201C2211yescharacteristic
25C22×#11758201C2211yescharacteristic
26C22×#11758189C2211yescharacteristic
27#16840431—24no—
28#16840431C2218yes—
29Q8×C22⋊D61—24no—
30Q8×C22⋊D61C2218yescomplemented
31C2×#14519775—21no—
32C2×#14519775C2211yescharacteristic
33C2×#14519773—21no—
34C2×#14519773C2211yescharacteristic
35C2×#14519756—21no—
36C2×#14519756C2211yescharacteristic
37C2×#14519753—21no—
38C2×#14519753C2211yescharacteristic
39C2×#14519751—21no—
40C2×#14519751C2211yescharacteristic
41C2×#14519748—21no—
42C2×#14519748C2211yescharacteristic
43C2×Q8×Dic61C2211yescharacteristic
44C2×Q8×Dic61C2211yescharacteristic
45C2×C4×C22⋊D61—21no—
46C2×C4×C22⋊D61—21no—
47C2×C4×C22⋊D61C2211yescharacteristic
48#16840133C2218yescomplemented
49#16840008C2218yescomplemented
50#16840005C2218yescomplemented
51#16839970C2218yescomplemented
52#16839960C2218yescomplemented
53#16839924C2218yescomplemented
54#16839923C2218yescomplemented
55#16839901C2218yescomplemented
56#16839899C2218yescomplemented
57Q16×Dic61C2218yescomplemented
58#16839838C2218yescomplemented
59C2×#14519711C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×C22⋊#92418C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×C8×Dic61C2211yescharacteristic
70C22×#41×C61C2211yescharacteristic
71C23×Q8×C61C2211yescharacteristic
72C2×#137×C61—28no—
73C2×#137×C61C2218yescomplemented
74C22×Q16×C61C2211yescharacteristic
75C22×Q16×C61C2211yescharacteristic
76C22×SD16×C61C2211yescharacteristic
77C22×SD16×C61C2211yescharacteristic
78C22×M16×C61C2211yescharacteristic
79C2×#11758226—22no—
80C2×#11758226—24no—
81C2×#11758226—42no—
82C2×#11758226C2314yes—
83C22×Dic122—21no—
84C22×Dic122C2311yescharacteristic
85C2×Q8×D61—22no—
86C2×Q8×D61—24no—
87C2×Q8×D61—42no—
88C2×Q8×D61C2314yes—
89C22×D244—21no—
90C22×D244C2311yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C22×C22⋊D61D411yescharacteristic
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C22×C4×D61C2311yescharacteristic
99#14519809—232no—
100C2×#11758202—24no—
101C2×#11758202C2314yes—
102C2×#11758190—24no—
103C2×#11758190C2314yes—
104C2×#11758200—42no—
105C2×#11758200C2314yes—
106C2×#11758201—24no—
107C2×#11758201—42no—
108C2×#11758201C2314yes—
109C2×#11758201C2314yes—
110C2×#11758189—24no—
111C2×#11758189C2314yes—
112C22×#92418C2311yescharacteristic
113C22×#92418C2311yescharacteristic
114#14519775—28no—
115#14519775—22no—
116#14519775C2314yes—
117#14519773—28no—
118#14519773—22no—
119#14519773C2314yes—
120#14519756—22no—
121#14519756—28no—
122#14519756C2314yes—
123#14519753—22no—
124#14519753—28no—
125#14519753C2314yes—
126#14519751—22no—
127#14519751—28no—
128#14519751C2314yes—
129#14519748—22no—
130#14519748—28no—
131#14519748C2314yes—
132Q8×Dic61—22no—
133Q8×Dic61—22no—
134Q8×Dic61C2314yes—
135Q8×Dic61C2314yes—
136C4×C22⋊D61—28no—
137C4×C22⋊D61—28no—
138C4×C22⋊D61D414yes—
139C4×C22⋊D61C2314yes—
140C2×C4⋊Dic61—21no—
141C2×C4⋊Dic61—21no—
142C2×C4⋊Dic61C2311yescharacteristic
143C2×C4⋊Dic61C2311yescharacteristic
144C2×#11758196—21no—
145C2×#11758196—21no—
146C2×#11758196—21no—
147C2×#11758196—21no—
148C2×#11758196D411yescharacteristic
149C2×C22⋊Dic61—21no—
150C2×C22⋊Dic61—21no—
151C2×C22⋊Dic61D411yescharacteristic
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198D411yescharacteristic
155C2×C4×Dic61—21no—
156C2×C4×Dic61—21no—
157C2×C4×Dic61C2311yescharacteristic
158#14519711C2314yes—
159#14519706C2314yes—
160#14519702C2314yes—
161#14519701C2314yes—
162#14519701C2314yes—
163#14519701C2314yes—
164#14519699C2314yes—
165#14519698C2314yes—
166C22⋊#92418C2314yes—
167#14519689C2314yes—
168C8×Dic61C2314yes—
169C2×#41×C61—22no—
170C2×#41×C61—24no—
171C2×#41×C61—42no—
172C2×#41×C61C2314yes—
173C22×Q8×C61—21no—
174C22×Q8×C61—22no—
175C22×Q8×C61—24no—
176C22×Q8×C61—42no—
177C22×Q8×C61C2311yescharacteristic
178C22×Q8×C61C2314yes—
179C22×Q8×C61C2311yescharacteristic
180C22×Q8×C61C2311yescharacteristic
181C22×D4×C61—21no—
182C22×D4×C61C2311yescharacteristic
183C23×C4×C61—21no—
184C23×C4×C61—21no—
185C23×C4×C61C2311yescharacteristic
186#137×C61—232no—
187C2×Q16×C61—24no—
188C2×Q16×C61D418yescomplemented
189C2×Q16×C61C2314yes—
190C2×Q16×C61C2314yes—
191C2×SD16×C61—24no—
192C2×SD16×C61—24no—
193C2×SD16×C61C2314yes—
194C2×SD16×C61C2314yes—
195C2×M16×C61—24no—
196C2×M16×C61C2314yes—
197C22×C8×C61C2311yescharacteristic
198C22×C8×C61C2311yescharacteristic
199C24×C61—21no—
200C24×C61C2×D411yescharacteristic
201C23×D61—21no—
202C23×D61C2×D411yescharacteristic
203#41×C61—28no—
204#41×C61—44no—
205#41×C61—48no—
206C2×Q8×C61—21no—
207C2×Q8×C61—21no—
208C2×Q8×C61—24no—
209C2×Q8×C61—21no—
210C2×Q8×C61—22no—
211C2×Q8×C61—22no—
212C2×Q8×C61—28no—
213C2×Q8×C61—22no—
214C2×Q8×C61—22no—
215C2×Q8×C61—44no—
216C2×Q8×C61—44no—
217C2×Q8×C61—48no—
218C2×Q8×C61C2×D414yes—
219C2×Q8×C61C2×D414yes—
220C2×Q8×C61C2412yes—
221C2×Q8×C61C2412yes—
222C2×Q8×C61C2412yes—
223C2×D4×C61—24no—
224C2×D4×C61—22no—
225C2×D4×C61—21no—
226C2×D4×C61—22no—
227C2×D4×C61—44no—
228C2×D4×C61C2412yes—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—22no—
232C22×C4×C61—22no—
233C22×C4×C61—21no—
234C22×C4×C61—24no—
235C22×C4×C61—24no—
236C22×C4×C61—44no—
237C22×C4×C61—44no—
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2412yes—
241C22×C4×C61C2411yescharacteristic
242C2×C22⋊D61—24no—
243C2×C22⋊D61—24no—
244C2×C22⋊D61—24no—
245C2×C22⋊D61—24no—
246C2×C22⋊D61—24no—
247C2×C22⋊D61—44no—
248C2×C22⋊D61—82no—
249C2×C22⋊D61—82no—
250C2×C22⋊D61—82no—
251C2×C22⋊D61C2×D414yes—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61C2×D411yescharacteristic
256C22×Dic61C2×D411yescharacteristic
257C22×Dic61C2×D411yescharacteristic
258#11758226—28no—
259#11758226—44no—
260#11758226—48no—
261Q8×D61—28no—
262Q8×D61—44no—
263Q8×D61—48no—
264C2×D244—22no—
265C2×D244—22no—
266C2×D244—24no—
267C2×D244—21no—
268C2×D244—44no—
269C2×D244C2412yes—
270C2×C4×D61—22no—
271C2×C4×D61—22no—
272C2×C4×D61—24no—
273C2×C4×D61—24no—
274C2×C4×D61—44no—
275C2×C4×D61—44no—
276C2×C4×D61C2×D412yes—
277C2×C4×D61C2412yes—
278C2×Dic122—22no—
279C2×Dic122—22no—
280C2×Dic122—21no—
281C2×Dic122—24no—
282C2×Dic122—44no—
283C2×Dic122C2412yes—
284Q16×C61—28no—
285Q16×C61C2×D4116yescomplemented
286SD16×C61—28no—
287SD16×C61—28no—
288M16×C61—28no—
289C2×C8×C61—22no—
290C2×C8×C61C2×D414yes—
291C2×C8×C61C2412yes—
292C2×C8×C61C2412yes—
293C22⋊Dic61—24no—
294C22⋊Dic61—24no—
295C22⋊Dic61C2×D414yes—
296#11758202—28no—
297#11758201—28no—
298#11758201—44no—
299#11758200—44no—
300#11758198—24no—
301#11758198—24no—
302#11758198C2×D414yes—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—24no—
306C4⋊Dic61—24no—
307C4⋊Dic61C2412yes—
308C4⋊Dic61C2412yes—
309#11758196—24no—
310#11758196—24no—
311#11758196—24no—
312#11758196—24no—
313#11758196C2×D414yes—
314C4×Dic61—24no—
315C4×Dic61—24no—
316C4×Dic61C2×D412yes—
317C4×Dic61C2412yes—
318C2×#92418—22no—
319C2×#92418—22no—
320C2×#92418C2412yes—
321C2×#92418C2412yes—
322#11758190—28no—
323#11758189—28no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—42no—
329C23×C61—42no—
330C23×C61—42no—
331C23×C61C22×D412yes—
332C23×C61C22×D411yescharacteristic
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61C22×D412yes—
341Q8×C61—24no—
342Q8×C61—24no—
343Q8×C61—22no—
344Q8×C61—22no—
345Q8×C61—22no—
346Q8×C61—22no—
347Q8×C61—48no—
348Q8×C61—42no—
349Q8×C61C22×D414yes—
350Q8×C61C22×D414yes—
351D4×C61—22no—
352D4×C61—22no—
353D4×C61—48no—
354D4×C61—42no—
355C2×C4×C61—24no—
356C2×C4×C61—24no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—24no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—48no—
365C2×C4×C61—48no—
366C2×C4×C61—42no—
367C2×C4×C61C22×D412yes—
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D412yes—
370C2×C4×C61H(5,𝔽2)12yes—
371C2×C4×C61C2511yescharacteristic
372C22⋊D61—28no—
373C22⋊D61—48no—
374C22⋊D61—84no—
375C22⋊D61—84no—
376C22⋊D61—84no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—42no—
383C2×Dic61—42no—
384C2×Dic61—42no—
385C2×Dic61#13714yescomplemented
386C2×Dic61C22×D412yes—
387C2×Dic61C22×D412yes—
388C2×Dic61C22×D412yes—
389D244—22no—
390D244—22no—
391D244—48no—
392D244—42no—
393C4×D61—24no—
394C4×D61—22no—
395C4×D61—22no—
396C4×D61—48no—
397C4×D61—48no—
398Dic122—22no—
399Dic122—22no—
400Dic122—48no—
401Dic122—42no—
402C8×C61—22no—
403C8×C61C22×D414yes—
404#92418—22no—
405#92418—22no—
406C2×#3278—611nomaximal, Sylow
407C22×C61—22no—
408C22×C61—22no—
409C22×C61—22no—
410C22×C61—44no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—84no—
415C22×C61D4212yes—
416C22×C61C2×#13712yes—
417C22×C61#57712yes—
418C22×C61C23×D411yescharacteristic
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—44no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—84no—
427C4×C61—24no—
428C4×C61—24no—
429C4×C61—22no—
430C4×C61—42no—
431C4×C61D4212yes—
432C4×C61C23×D411yescharacteristic
433C4×C61C2×H(5,𝔽2)11yescharacteristic
434Dic61—22no—
435Dic61—22no—
436Dic61—42no—
437Dic61—42no—
438Dic61—42no—
439Dic61C2×#13714yescomplemented
440C22×#137—611no—
441C22×#137D6111yescharacteristic, complemented
442C2×#550—611no—
443C2×D4×Q8—611no—
444#3278—6116no—
445C2×#492—611no—
446C2×#468—611no—
447C2×#468—611no—
448C2×#462—611no—
449C2×#460—611no—
450C2×#452—611no—
451C2×#452—611no—
452C2×#448—611no—
453C2×#448—611no—
454C2×C4×Q16—611no—
455C2×#436—611no—
456C2×C61—42no—
457C2×C61—82no—
458C2×C61#327814yescomplemented
459C2×C61C2×D4211yescharacteristic
460C2×C61C22×#13711yescharacteristic
461C2×C61C2×#57711yescharacteristic
462D61—42no—
463D61—82no—
464C22×#41—611no—
465C22×#41C2×D6111yescharacteristic
466C23×Q8—611no—
467C23×Q8C2×D6111yescharacteristic
468C2×#137—28no—
469C2×#137—618no—
470C2×#137—1228no—
471C2×#137C2×D6118yescomplemented
472C22×Q16—611no—
473C22×Q16C2×D6111yescharacteristic
474C22×Q16C2×D6111yescharacteristic
475C22×SD16—611no—
476C22×SD16—611no—
477C22×SD16—611no—
478C22×SD16—611no—
479C22×SD16C2×D6111yescharacteristic
480C22×SD16C2×D6111yescharacteristic
481C22×M16—611no—
482C22×M16C2×D6111yescharacteristic
483#550—618no—
484#550—1224no—
485D4×Q8—618no—
486D4×Q8—1224no—
487C2×C4⋊Q8—611no—
488C2×C4⋊Q8—1221no—
489C2×#127—611no—
490C2×#127—1221no—
491C2×C22⋊Q8—611no—
492C2×C22⋊Q8—611no—
493C2×C22⋊Q8—1221no—
494C2×C22⋊Q8—1221no—
495C2×#121—611no—
496C2×#121—611no—
497C2×#121—1221no—
498C2×#121—1221no—
499C2×C4×Q8—611no—
500C2×C4×Q8—611no—
501C2×C4×D4—611no—
502C2×C4×D4—1221no—
503C2×C4×D4—1221no—
504#492—618no—
505#468—618no—
506#468—618no—
507#462—618no—
508#460—618no—
509#452—618no—
510#452—618no—
511#448—618no—
512#448—618no—
513C4×Q16—618no—
514#436—618no—
515C2×#107—611no—
516C2×C4⋊C8—611no—
517C2×#103—611no—
518C2×#103—611no—
519C2×#103—611no—
520C2×#103—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×C22⋊C8—611no—
524C2×C22⋊C8—611no—
525C2×C4×C8—611no—
526C61C2×#327811yescharacteristic, complemented, Sylow
527C2×#41—22no—
528C2×#41—24no—
529C2×#41—42no—
530C2×#41—614no—
531C2×#41—1222no—
532C2×#41—1224no—
533C2×#41—2442no—
534C2×#41C22×D6114yes—
535C22×Q8—21no—
536C22×Q8—22no—
537C22×Q8—24no—
538C22×Q8—42no—
539C22×Q8—614no—
540C22×Q8—611no—
541C22×Q8—1221no—
542C22×Q8—1222no—
543C22×Q8—1224no—
544C22×Q8—2442no—
545C22×Q8C22×D6111yescharacteristic
546C22×Q8C22×D6114yes—
547C22×Q8C22×D6111yescharacteristic
548C22×Q8C22×D6111yescharacteristic
549C22×D4—21no—
550C22×D4—611no—
551C22×D4—611no—
552C22×D4—1221no—
553C22×D4—1221no—
554C22×D4—1221no—
555C22×D4—1221no—
556C22×D4—1221no—
557C22×D4C22×D6111yescharacteristic
558C23×C4—21no—
559C23×C4—21no—
560C23×C4—611no—
561C23×C4—1221no—
562C23×C4—1221no—
563C23×C4C22×D6111yescharacteristic
564#137—232no—
565#137—12232no—
566C2×Q16—24no—
567C2×Q16—614no—
568C2×Q16—1224no—
569C2×Q16C22⋊D6118yescomplemented
570C2×Q16C22×D6114yes—
571C2×Q16C22×D6114yes—
572C2×SD16—24no—
573C2×SD16—24no—
574C2×SD16—614no—
575C2×SD16—614no—
576C2×SD16—614no—
577C2×SD16—614no—
578C2×SD16—1224no—
579C2×SD16—1224no—
580C2×SD16—2442no—
581C2×SD16—2442no—
582C2×SD16C22×D6114yes—
583C2×SD16C22×D6114yes—
584C2×M16—24no—
585C2×M16—614no—
586C2×M16—1224no—
587C2×M16C22×D6114yes—
588C22×C8—611no—
589C22×C8—611no—
590C22×C8C22×D6111yescharacteristic
591C22×C8C22×D6111yescharacteristic
592C4⋊Q8—614no—
593C4⋊Q8—1222no—
594C4⋊Q8—1228no—
595#127—614no—
596#127—1222no—
597#127—1228no—
598C22⋊Q8—614no—
599C22⋊Q8—614no—
600C22⋊Q8—1228no—
601C22⋊Q8—1228no—
602C22⋊Q8—1222no—
603C22⋊Q8—1222no—
604#121—614no—
605#121—614no—
606#121—1228no—
607#121—1228no—
608#121—1222no—
609#121—1222no—
610C4×Q8—614no—
611C4×Q8—614no—
612C4×Q8—1222no—
613C4×Q8—1222no—
614C4×D4—614no—
615C4×D4—614no—
616C4×D4—1228no—
617C4×D4—1228no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1221no—
623C2×C4⋊C4—1221no—
624C2×C4⋊C4—1221no—
625C2×C4⋊C4—1221no—
626C2×C4⋊C4—1221no—
627C2×C22⋊C4—611no—
628C2×C22⋊C4—611no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C42—611no—
634C2×C42—1221no—
635C2×C42—1221no—
636#107—614no—
637C4⋊C8—614no—
638#103—614no—
639#103—614no—
640#103—614no—
641#103—614no—
642#102—614no—
643#102—614no—
644C22⋊C8—614no—
645C22⋊C8—614no—
646C4×C8—614no—
647C24—21no—
648C24—611no—
649C24—1221no—
650C24D4×D6111yescharacteristic
651#41—28no—
652#41—44no—
653#41—48no—
654#41—1228no—
655#41—2444no—
656#41—2448no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—24no—
660C2×Q8—21no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—28no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×Q8—48no—
669C2×Q8—612no—
670C2×Q8—1224no—
671C2×Q8—1221no—
672C2×Q8—1228no—
673C2×Q8—1222no—
674C2×Q8—1222no—
675C2×Q8—2444no—
676C2×Q8—2444no—
677C2×Q8—2448no—
678C2×Q8C2×C22⋊D6114yes—
679C2×Q8C2×C22⋊D6114yes—
680C2×Q8C23×D6112yes—
681C2×Q8C23×D6112yes—
682C2×Q8C23×D6112yes—
683C2×D4—24no—
684C2×D4—21no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—44no—
688C2×D4—614no—
689C2×D4—612no—
690C2×D4—1224no—
691C2×D4—1224no—
692C2×D4—1224no—
693C2×D4—1224no—
694C2×D4—1224no—
695C2×D4—1224no—
696C2×D4—1221no—
697C2×D4—1222no—
698C2×D4—1222no—
699C2×D4—4882no—
700C2×D4—4882no—
701C2×D4—4882no—
702C2×D4—2444no—
703C2×D4—2444no—
704C2×D4C23×D6112yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—24no—
710C22×C4—21no—
711C22×C4—24no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—612no—
718C22×C4—612no—
719C22×C4—1224no—
720C22×C4—1224no—
721C22×C4—1222no—
722C22×C4—1222no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—2444no—
727C22×C4—2444no—
728C22×C4D4×D6112yes—
729C22×C4D4×D6111yescharacteristic
730C22×C4C23×D6112yes—
731C22×C4C23×D6111yescharacteristic
732Q16—28no—
733Q16—1228no—
734Q16C2×C22⋊D61116yescomplemented
735SD16—28no—
736SD16—28no—
737SD16—1228no—
738SD16—1228no—
739SD16—2444no—
740SD16—2444no—
741M16—28no—
742M16—1228no—
743C2×C8—22no—
744C2×C8—612no—
745C2×C8—612no—
746C2×C8—1222no—
747C2×C8—1222no—
748C2×C8C2×C22⋊D6114yes—
749C2×C8C23×D6112yes—
750C2×C8C23×D6112yes—
751C4⋊C4—614no—
752C4⋊C4—612no—
753C4⋊C4—612no—
754C4⋊C4—1224no—
755C4⋊C4—1224no—
756C4⋊C4—1224no—
757C4⋊C4—1224no—
758C4⋊C4—1224no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1224no—
762C22⋊C4—614no—
763C22⋊C4—614no—
764C22⋊C4—1224no—
765C22⋊C4—1224no—
766C22⋊C4—1224no—
767C22⋊C4—1224no—
768C42—612no—
769C42—612no—
770C42—1224no—
771C42—1224no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—612no—
780C23—1222no—
781C23—1222no—
782C23—1222no—
783C23—1222no—
784C23—2442no—
785C23—2442no—
786C23—2442no—
787C23C2×D4×D6112yes—
788C23C2×D4×D6111yescharacteristic
789Q8—22no—
790Q8—22no—
791Q8—24no—
792Q8—24no—
793Q8—22no—
794Q8—22no—
795Q8—48no—
796Q8—42no—
797Q8—1222no—
798Q8—1222no—
799Q8—2448no—
800Q8—2442no—
801Q8C22×C22⋊D6114yes—
802Q8C22×C22⋊D6114yes—
803D4—22no—
804D4—22no—
805D4—48no—
806D4—42no—
807D4—1228no—
808D4—1222no—
809D4—1222no—
810D4—4884no—
811D4—4884no—
812D4—4884no—
813D4—2448no—
814D4—2448no—
815D4—2442no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—48no—
826C2×C4—48no—
827C2×C4—42no—
828C2×C4—614no—
829C2×C4—612no—
830C2×C4—612no—
831C2×C4—612no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1224no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—2448no—
841C2×C4—2448no—
842C2×C4—2442no—
843C2×C4—2442no—
844C2×C4—2442no—
845C2×C4C2×D4×D6112yes—
846C2×C4C2×D4×D6111yescharacteristic
847C2×C4C22×C22⋊D6112yes—
848C2×C4#1451982212yes—
849C2×C4C24×D6111yescharacteristic
850C8—22no—
851C8—1222no—
852C8—1222no—
853C8C22×C22⋊D6114yes—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—44no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—84no—
862C22—1222no—
863C22—1222no—
864C22—1222no—
865C22—4884no—
866C22—2442no—
867C22—2442no—
868C22—2442no—
869C22—2444no—
870C22D4×C22⋊D6112yes—
871C22#137×D6112yes—
872C22#1684057112yes—
873C22C22×D4×D6111yescharacteristic
874C4—22no—
875C4—24no—
876C4—24no—
877C4—42no—
878C4—614no—
879C4—1222no—
880C4—1222no—
881C4—2442no—
882C4—2442no—
883C4—2442no—
884C4D4×C22⋊D6112yes—
885C4C23×C22⋊D6111yescharacteristic
886C4C2×#1451982211yescharacteristic
887C2—42no—
888C2—82no—
889C2—4882no—
890C2—2442no—
891C2#2145747914yesdirect product factor
892C2C2×D4×C22⋊D6111yescharacteristic
893C2C2×#137×D6111yescharacteristic
894C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC22×#137×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840431C2
hypercenterC22×#137D61
hypocenterC61C2×#3278
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#14519809C2semidirect
3. C2×Q8×C22⋊D61C2semidirect
4. #21457479C2direct (N × H)
5. C2×#16840133C2semidirect
6. C2×#16840008C2semidirect
7. C2×#16840005C2semidirect
8. C2×#16839970C2semidirect
9. C2×#16839960C2semidirect
10. C2×#16839924C2semidirect
11. C2×#16839923C2semidirect
12. C2×#16839901C2semidirect
13. C2×#16839899C2semidirect
14. C2×Q16×Dic61C2semidirect
15. C2×#16839838C2semidirect
16. C22×#137×C61C2semidirect
20. C2×#14519809C22semidirect
30. Q8×C22⋊D61C22semidirect
48. #16840133C22semidirect
49. #16840008C22semidirect
50. #16840005C22semidirect
51. #16839970C22semidirect
52. #16839960C22semidirect
53. #16839924C22semidirect
54. #16839923C22semidirect
55. #16839901C22semidirect
56. #16839899C22semidirect
57. Q16×Dic61C22semidirect
58. #16839838C22semidirect
73. C2×#137×C61C22semidirect
188. C2×Q16×C61D4semidirect
285. Q16×C61C2×D4semidirect
385. C2×Dic61#137semidirect
439. Dic61C2×#137semidirect
441. C22×#137D61semidirect
458. C2×C61#3278semidirect
471. C2×#137C2×D61semidirect
526. C61C2×#3278semidirect
569. C2×Q16C22⋊D61semidirect
734. Q16C2×C22⋊D61semidirect
891. C2#21457479direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198092
C2×#168404312
C2×Q8×C22⋊D612
#214574792
C2×#168401332
C2×#168400082
C2×#168400052
C2×#168399702
C2×#168399602
C2×#168399242
C2×#168399232
C2×#168399012
C2×#168398992
C2×Q16×Dic612
C2×#168398382
C22×#137×C612
C2×#327861