Finite Group Databasebeta

← #30616877

Subgroups — #30616877

Order 15616.

1476 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840831C211yesmaximal, characteristic, complemented
2C2×#16840801C211yesmaximal, characteristic, complemented
3C2×D8×#6923C211yesmaximal, characteristic, complemented
4#21462307C211yesmaximal, characteristic, complemented
5#21461815C211yesmaximal, characteristic, complemented
6#21461814C211yesmaximal, characteristic, complemented
7#21461806C211yesmaximal, characteristic, complemented
8#21461783C211yesmaximal, characteristic, complemented
9#21461782C211yesmaximal, characteristic, complemented
10#21461768C211yesmaximal, characteristic, complemented
11#21461659C211yesmaximal, characteristic, complemented
12#21461590C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic, complemented
15#449×D61C211yesmaximal, characteristic
16#16840831—24no—
17#16840831—24no—
18C2×Q8×#6923C2211yescharacteristic
19C2×Q8×#6923C2211yescharacteristic
20C2×D4×#6923—21no—
21C2×D4×#6923—21no—
22C2×D4×#6923C2211yescharacteristic
23C2×D4×#6923C2211yescharacteristic
24C2×D4×#6923C2211yescharacteristic
25C2×#14519856—21no—
26C2×#14519856C2211yescharacteristic
27C22×C4⋊#6923—21no—
28C22×C4⋊#6923C2211yescharacteristic
29#16840801—24no—
30D8×#6923—24no—
31C2×#14519846C2211yescharacteristic
32C2×#14519846C2211yescharacteristic
33C2×#14519840C2211yescharacteristic
34C2×#14519840C2211yescharacteristic
35C2×#14519839C2211yescharacteristic
36C2×#14519839C2211yescharacteristic
37C2×#14519839C2211yescharacteristic
38C2×#14519839C2211yescharacteristic
39D61⋊(C22⋊C8)C2211yescharacteristic
40C2×#14519831C2211yescharacteristic
41C2×C8×#6923C2211yescharacteristic
42#16840714—21no—
43#16840714C2211yescharacteristic
44#16840713C2211yescharacteristic
45#16840712—21no—
46#16840710—21no—
47#16840709—21no—
48#16840704C2211yescharacteristic
49C4⋊C4×#6923C2211yescharacteristic
50#16840636C2211yescharacteristic
51#16840636C2211yescharacteristic
52#16840635C2211yescharacteristic
53#16840635C2211yescharacteristic
54(C2×#6923)⋊C8C2211yescharacteristic
55(C2×#6923)⋊C8C2211yescharacteristic
56C2×#41×D61C2211yescharacteristic
57C2×SD16×D61C2211yescharacteristic
58C2×D8×D61C2211yescharacteristic
59#121×D61C2211yescharacteristic
60#16839910C411yescharacteristic, complemented
61#16839909C411yescharacteristic, complemented
62#16839908C411yescharacteristic, complemented
63#16839907C411yescharacteristic, complemented
64#16839906C411yescharacteristic, complemented
65#16839905C411yescharacteristic, complemented
66#16839904C411yescharacteristic, complemented
67#103×D61C2211yescharacteristic
68#102×D61C2211yescharacteristic
69C22⋊C8×D61C2211yescharacteristic
70C61×#449C411yescharacteristic, complemented
71C23×#6923—21no—
72C23×#6923—21no—
73C23×#6923—21no—
74C23×#6923—21no—
75C2×D61⋊C8C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77Q8×#6923—22no—
78Q8×#6923—22no—
79Q8×#6923—22no—
80Q8×#6923D414yescomplemented
81D4×#6923—28no—
82D4×#6923—28no—
83D4×#6923—22no—
84D4×#6923—22no—
85D4×#6923—22no—
86D4×#6923—22no—
87D4×#6923—22no—
88D4×#6923D414yescomplemented
89#14519856—28no—
90#14519856—22no—
91#14519856—22no—
92C2×C4⋊#6923—28no—
93C2×C4⋊#6923—21no—
94C2×C4⋊#6923—21no—
95C2×C4⋊#6923—21no—
96C2×C4⋊#6923—22no—
97C2×C4⋊#6923—22no—
98C2×C4⋊#6923—21no—
99C2×C4⋊#6923D411yescharacteristic
100C2×C4⋊#6923D411yescharacteristic
101C2×C4⋊#6923C2311yescharacteristic
102C2×C4⋊#6923C2311yescharacteristic
103C2×C4⋊#6923C2311yescharacteristic
104C2×C4⋊#6923C2311yescharacteristic
105C2×C22⋊#6923—21no—
106C2×C22⋊#6923—21no—
107C2×C22⋊#6923—21no—
108C2×C22⋊#6923—21no—
109C2×C22⋊#6923—21no—
110C2×C22⋊#6923—21no—
111C2×C22⋊#6923D411yescharacteristic
112C2×C22⋊#6923D411yescharacteristic
113C2×C4×#6923—21no—
114C2×C4×#6923—21no—
115C2×C4×#6923—21no—
116C2×C4×#6923C2311yescharacteristic
117C2×C4×#6923C2311yescharacteristic
118#14519846—22no—
119#14519846—22no—
120#14519840—22no—
121#14519840—22no—
122#14519839—22no—
123#14519839—22no—
124#14519839—22no—
125#14519839—22no—
126#14519834—21no—
127C22⋊#92420—21no—
128#14519831—22no—
129C8×#6923—22no—
130(C2×#6923)⋊C4—21no—
131(C2×#6923)⋊C4—21no—
132(C2×#6923)⋊C4—21no—
133C2×#11758226C2×C411yescharacteristic, complemented
134C2×#11758222—21no—
135C2×#11758222C2×C411yescharacteristic, complemented
136C2×#11758224—21no—
137C2×#11758224C2×C411yescharacteristic, complemented
138#41×D61—22no—
139#41×D61—22no—
140#41×D61—22no—
141#41×D61—22no—
142C2×Q8×D61C2311yescharacteristic
143C2×D4×D61—21no—
144C2×D4×D61—21no—
145C2×D4×D61C2311yescharacteristic
146C2×D4×D61C2311yescharacteristic
147C22×C4×D61—21no—
148C22×C4×D61C2311yescharacteristic
149C2×#11758190C2×C411yescharacteristic, complemented
150C2×#11758200C2×C411yescharacteristic, complemented
151C2×#11758201C2×C411yescharacteristic, complemented
152SD16×D61—22no—
153SD16×D61—22no—
154C2×D488C2×C411yescharacteristic, complemented
155C2×#11758199C2×C411yescharacteristic, complemented
156C2×#11758199C2×C411yescharacteristic, complemented
157D8×D61—22no—
158D8×D61—22no—
159C2×C8×D61C2311yescharacteristic
160C2×C8×D61C2311yescharacteristic
161#14519752C2×C411yescharacteristic, complemented
162#14519751C2×C411yescharacteristic, complemented
163#14519750—21no—
164#14519749—21no—
165#14519748C2×C411yescharacteristic, complemented
166C4⋊C4×D61C2311yescharacteristic
167C22⋊C4×D61—21no—
168#14519702C2×C411yescharacteristic, complemented
169#14519701C2×C411yescharacteristic, complemented
170#14519700C2×C411yescharacteristic, complemented
171#14519699C2×C411yescharacteristic, complemented
172#14519698C2×C411yescharacteristic, complemented
173#14519697C2×C411yescharacteristic, complemented
174C22⋊#92418C2×C411yescharacteristic, complemented
175#14519689C2×C411yescharacteristic, complemented
176#14519689C2×C411yescharacteristic, complemented
177C2×#41×C61C2×C411yescharacteristic, complemented
178C2×SD16×C61C2×C411yescharacteristic, complemented
179C2×D8×C61C2×C411yescharacteristic, complemented
180#121×C61C2×C411yescharacteristic, complemented
181#103×C61C2×C411yescharacteristic, complemented
182#102×C61C2×C411yescharacteristic, complemented
183C22⋊C8×C61C2×C411yescharacteristic, complemented
184C23×D61—21no—
185C23×D61—21no—
186C23×D61C2×D411yescharacteristic
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923—24no—
190C22×#6923—24no—
191C22×#6923—24no—
192C22×#6923—21no—
193C22×#6923—21no—
194C22×#6923—42no—
195C22×#6923—81no—
196C22×#6923—81no—
197C22×#6923—81no—
198C22×#6923—81no—
199C22×#6923—81no—
200C22×#6923—81no—
201C22×#6923—81no—
202C22×#6923—81no—
203C22×#6923C2×D411yescharacteristic
204C22×#6923C2×D411yescharacteristic
205C22×#6923C2×D411yescharacteristic
206C22×#6923C2×D411yescharacteristic
207#41×C61—22no—
208#41×C61—22no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61C22×C411yescharacteristic
213C2×D4×C61C22×C411yescharacteristic
214C22×C4×C61—21no—
215C22×C4×C61C22×C411yescharacteristic
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C22×Dic61—21no—
223C22×Dic61#4111yescharacteristic
224#11758226—22no—
225#11758226—22no—
226Q8×D61—21no—
227Q8×D61—21no—
228Q8×D61C2×D412yes—
229Q8×D61#4112yes—
230#11758224—24no—
231#11758224—24no—
232#11758224—22no—
233#11758224—22no—
234D4×D61—24no—
235D4×D61—24no—
236D4×D61—21no—
237D4×D61—21no—
238D4×D61—21no—
239D4×D61—21no—
240D4×D61—21no—
241D4×D61—21no—
242D4×D61—81no—
243D4×D61—81no—
244D4×D61C2×D412yes—
245D4×D61#4112yes—
246#11758222—24no—
247#11758222—24no—
248#11758222—22no—
249#11758222—22no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244C22×C411yescharacteristic
253C2×D244C22×C411yescharacteristic
254C2×C4×D61—24no—
255C2×C4×D61—24no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61C22×C411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61#4111yescharacteristic
267C2×C4×D61C2411yescharacteristic
268C2×Dic122—21no—
269C2×Dic122C22×C411yescharacteristic
270C22⋊#6923—24no—
271C22⋊#6923—24no—
272C22⋊#6923—22no—
273C22⋊#6923—22no—
274C22⋊#6923—42no—
275C22⋊#6923—81no—
276C22⋊#6923—81no—
277C22⋊#6923—81no—
278C2×#92420—21no—
279C2×#92420—21no—
280C4⋊#6923—24no—
281C4⋊#6923—24no—
282C4⋊#6923—22no—
283C4⋊#6923—24no—
284C4⋊#6923—22no—
285C4⋊#6923—21no—
286C4⋊#6923—21no—
287C4⋊#6923—21no—
288C4⋊#6923—21no—
289C4⋊#6923—21no—
290C4⋊#6923—21no—
291C4⋊#6923—81no—
292C4⋊#6923C2×D412yes—
293C4⋊#6923C2×D412yes—
294C4×#6923—24no—
295C4×#6923—24no—
296C4×#6923—21no—
297C4×#6923—21no—
298C4×#6923—81no—
299C4×#6923C2×D412yes—
300C4×#6923C2×D412yes—
301D61⋊C8—21no—
302D61⋊C8—21no—
303D61⋊C8—21no—
304D61⋊C8—21no—
305SD16×C61—22no—
306D8×C61—22no—
307C2×C8×C61C22×C411yescharacteristic
308C2×C8×C61C22×C411yescharacteristic
309C4⋊C4×C61C22×C411yescharacteristic
310C22⋊C4×C61—21no—
311C22⋊Dic61—21no—
312#11758201—22no—
313#11758200—22no—
314#11758199—22no—
315#11758199—22no—
316#11758198—21no—
317#11758198—21no—
318C4⋊Dic61C22×C411yescharacteristic
319#11758196—21no—
320C2×#92418C22×C411yescharacteristic
321C2×#92418C22×C411yescharacteristic
322D488—22no—
323#11758190—22no—
324C8×D61—21no—
325C8×D61—21no—
326C8×D61—21no—
327C8×D61—21no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61C4×D411yescharacteristic
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—22no—
334C22×D61—21no—
335C22×D61—22no—
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61C4×D411yescharacteristic
352C22×D61C22×D411yescharacteristic
353C2×#6923—21no—
354C2×#6923—21no—
355C2×#6923—21no—
356C2×#6923—21no—
357C2×#6923—21no—
358C2×#6923—21no—
359C2×#6923—22no—
360C2×#6923—22no—
361C2×#6923—21no—
362C2×#6923—21no—
363C2×#6923—21no—
364C2×#6923—21no—
365C2×#6923—41no—
366C2×#6923—41no—
367C2×#6923—41no—
368C2×#6923—41no—
369C2×#6923—41no—
370C2×#6923—41no—
371C2×#6923—41no—
372C2×#6923—41no—
373C2×#6923—41no—
374C2×#6923—41no—
375C2×#6923—84no—
376C2×#6923—84no—
377C2×#6923—84no—
378C2×#6923—84no—
379C2×#6923#12012yes—
380C2×#6923#12012yes—
381Q8×C61—21no—
382Q8×C61C4×D412yes—
383D4×C61—24no—
384D4×C61—21no—
385D4×C61—21no—
386D4×C61—21no—
387D4×C61—81no—
388D4×C61C4×D412yes—
389C2×C4×C61—24no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61C4×D411yescharacteristic
395C2×C4×C61C23×C411yescharacteristic
396C22⋊D61—24no—
397C22⋊D61—24no—
398C22⋊D61—22no—
399C22⋊D61—22no—
400C22⋊D61—41no—
401C22⋊D61—41no—
402C22⋊D61—81no—
403C22⋊D61—81no—
404C2×Dic61—24no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61C4×D411yescharacteristic
410C2×Dic61C2×#4111yescharacteristic
411D244—24no—
412D244—21no—
413D244—21no—
414D244—21no—
415D244—81no—
416D244C4×D412yes—
417C4×D61—24no—
418C4×D61—24no—
419C4×D61—22no—
420C4×D61—21no—
421C4×D61—21no—
422C4×D61—22no—
423C4×D61—21no—
424C4×D61—21no—
425C4×D61—21no—
426C4×D61—21no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61C22×D411yescharacteristic
430C4×D61C22×D411yescharacteristic
431C4×D61C2×#4111yescharacteristic
432C4×D61C2×#4111yescharacteristic
433Dic122—21no—
434Dic122—22no—
435Dic122—22no—
436Dic122C4×D412yes—
437#92420—41no—
438#92420—41no—
439C8×C61—21no—
440C8×C61—21no—
441#92418—21no—
442#92418—21no—
443#21460—611nomaximal, Sylow
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—22no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61C2×C4×D411yescharacteristic
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—22no—
458C2×D61—41no—
459C2×D61—41no—
460C2×D61—41no—
461C2×D61—42no—
462C2×D61—41no—
463C2×D61—42no—
464C2×D61—41no—
465C2×D61—42no—
466C2×D61—41no—
467C2×D61—42no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—81no—
472C2×D61—81no—
473C2×D61—81no—
474C2×D61—81no—
475C2×D61C2×#12011yescharacteristic
476C2×D61#52511yescharacteristic
477C2×D61#57611yescharacteristic
478C2×D61#57611yescharacteristic
479C2×D61#57711yescharacteristic
480C2×D61#57811yescharacteristic
481#6923—22no—
482#6923—22no—
483#6923—41no—
484#6923—42no—
485#6923—42no—
486#6923—41no—
487#6923—81no—
488#6923—81no—
489C4×C61—22no—
490C4×C61—21no—
491C4×C61—41no—
492C4×C61C2×C4×D411yescharacteristic
493C4×C61C2×C4×D411yescharacteristic
494Dic61—22no—
495Dic61—21no—
496Dic61—41no—
497Dic61#52511yescharacteristic
498Dic61#52511yescharacteristic
499C2×#520—611no—
500C2×#449—611no—
501C2×#440—611no—
502C2×C4×D8—611no—
503#2324—611no—
504#1880—611no—
505#1879—611no—
506#1874—611no—
507#1863—611no—
508#1862—611no—
509#1852—611no—
510#1788—611no—
511#1762—611no—
512C4×#103—611no—
513#1750—611no—
514C2×C61—41no—
515C2×C61—42no—
516C2×C61—81no—
517C2×C61C4×#12011yescharacteristic
518C2×C61#294611yescharacteristic
519C2×C61#295111yescharacteristic
520D61—41no—
521D61—42no—
522D61—81no—
523D61#300811yescharacteristic
524D61#301311yescharacteristic
525D61#311911yescharacteristic
526D61#312411yescharacteristic
527C22×#41—611no—
528C22×SD16—611no—
529C22×D8—611no—
530C2×#121—611no—
531#520—1224no—
532#520—1224no—
533C2×C4×Q8—611no—
534C2×C4×Q8—611no—
535C2×C4×D4—611no—
536C2×C4×D4—611no—
537C2×C4×D4—611no—
538C2×C4×D4—1221no—
539C2×C4×D4—1221no—
540C2×#117—611no—
541C2×#117—1221no—
542C22×C4⋊C4—611no—
543C22×C4⋊C4—1221no—
544#449—611no—
545#449—611no—
546#449—611no—
547#449—611no—
548#449—611no—
549#449—611no—
550#449—611no—
551#449#692311yescharacteristic, complemented
552#440—1224no—
553C4×D8—1224no—
554C2×#107—611no—
555C2×#107—611no—
556C2×#103—611no—
557C2×#103—611no—
558C2×#103—611no—
559C2×#102—611no—
560C2×#102—611no—
561C2×#102—611no—
562C2×#102—611no—
563C2×#102—611no—
564C2×C22⋊C8—611no—
565C2×C22⋊C8—611no—
566C2×#97—611no—
567C2×C4×C8—611no—
568#390—611no—
569#390—1221no—
570#389—611no—
571#388—1221no—
572#386—1221no—
573#385—1221no—
574#380—611no—
575C4×C4⋊C4—611no—
576#340—611no—
577#340—611no—
578#340—611no—
579#340—611no—
580#336—611no—
581#336—611no—
582C61#2146011yescharacteristic, complemented, Sylow
583C2×#41—611no—
584C2×#41—611no—
585C2×#41—611no—
586C2×#41—1221no—
587C2×#41—1221no—
588C2×#41—1222no—
589C2×#41—1222no—
590C2×#41—1222no—
591C2×#41—1222no—
592C2×#41C2×#692311yescharacteristic, complemented
593C22×Q8—611no—
594C22×D4—611no—
595C22×D4—611no—
596C22×D4—1221no—
597C22×D4—1221no—
598C23×C4—611no—
599C23×C4—1221no—
600C23×C4—1221no—
601C23×C4—1221no—
602C23×C4—1221no—
603C23×C4—1221no—
604C2×SD16—611no—
605C2×SD16—611no—
606C2×SD16—611no—
607C2×SD16—1222no—
608C2×SD16—1222no—
609C2×SD16C2×#692311yescharacteristic, complemented
610C2×D8—611no—
611C2×D8—611no—
612C2×D8—611no—
613C2×D8—1222no—
614C2×D8—1222no—
615C2×D8C2×#692311yescharacteristic, complemented
616C22×C8—611no—
617C22×C8—611no—
618C22×C8—611no—
619C22×C8—611no—
620#121—611no—
621#121—611no—
622#121—611no—
623#121—1221no—
624#121—1221no—
625#121C2×#692311yescharacteristic, complemented
626C4×Q8—614no—
627C4×Q8—1222no—
628C4×Q8—1222no—
629C4×Q8—1222no—
630C4×D4—614no—
631C4×D4—1222no—
632C4×D4—1222no—
633C4×D4—1222no—
634C4×D4—1222no—
635C4×D4—1222no—
636C4×D4—1228no—
637C4×D4—1228no—
638#117—1222no—
639#117—1222no—
640#117—1228no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—611no—
647C2×C4⋊C4—611no—
648C2×C4⋊C4—1222no—
649C2×C4⋊C4—1222no—
650C2×C4⋊C4—1221no—
651C2×C4⋊C4—1221no—
652C2×C4⋊C4—1221no—
653C2×C4⋊C4—1228no—
654C2×C4⋊C4—1221no—
655C2×C22⋊C4—611no—
656C2×C22⋊C4—611no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C22⋊C4—1221no—
660C2×C22⋊C4—1221no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C42—611no—
665C2×C42—611no—
666C2×C42—1221no—
667C2×C42—1221no—
668C2×C42—1221no—
669#107—1222no—
670#107—1222no—
671#103—611no—
672#103—611no—
673#103—611no—
674#103—1222no—
675#103—1222no—
676#103C2×#692311yescharacteristic, complemented
677#102—611no—
678#102—611no—
679#102—611no—
680#102—1222no—
681#102—1222no—
682#102—1222no—
683#102—1222no—
684#102C2×#692311yescharacteristic, complemented
685C22⋊C8—611no—
686C22⋊C8—611no—
687C22⋊C8—611no—
688C22⋊C8—1221no—
689C22⋊C8—1221no—
690C22⋊C8C2×#692311yescharacteristic, complemented
691#97—1222no—
692C4×C8—1222no—
693#95—1221no—
694#95—1221no—
695#95—1221no—
696C24—611no—
697C24—1221no—
698C24—1221no—
699#41—22no—
700#41—22no—
701#41—1222no—
702#41—1222no—
703#41—1224no—
704#41—1224no—
705#41—1222no—
706#41—1224no—
707#41—1224no—
708#41—1222no—
709#41—1222no—
710#41—1222no—
711C2×Q8—612no—
712C2×Q8—612no—
713C2×Q8—611no—
714C2×Q8—1221no—
715C2×Q8—1221no—
716C2×Q8—1221no—
717C2×Q8C22×#692311yescharacteristic
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—612no—
721C2×D4—612no—
722C2×D4—611no—
723C2×D4—611no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1221no—
728C2×D4—1221no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1224no—
735C2×D4—1224no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—4881no—
741C2×D4—4881no—
742C2×D4C22×#692311yescharacteristic
743C2×D4C22×#692311yescharacteristic
744C22×C4—21no—
745C22×C4—611no—
746C22×C4—611no—
747C22×C4—611no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1224no—
761C22×C4—1224no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1224no—
765C22×C4—1221no—
766C22×C4—1224no—
767C22×C4—1224no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—4881no—
773C22×C4—4881no—
774C22×C4—4881no—
775C22×C4—4881no—
776C22×C4—4881no—
777C22×C4—4881no—
778C22×C4—4881no—
779C22×C4—4881no—
780C22×C4—2442no—
781C22×C4C22×#692311yescharacteristic
782SD16—22no—
783SD16—1222no—
784SD16—1222no—
785SD16—1222no—
786D8—22no—
787D8—1222no—
788D8—1222no—
789D8—1222no—
790C2×C8—611no—
791C2×C8—611no—
792C2×C8—1221no—
793C2×C8—1221no—
794C2×C8—1221no—
795C2×C8—1221no—
796C2×C8—1221no—
797C2×C8—1221no—
798C2×C8—1221no—
799C2×C8—1221no—
800C2×C8—1221no—
801C2×C8—1221no—
802C2×C8C22×#692311yescharacteristic
803C2×C8C22×#692311yescharacteristic
804C4⋊C4—612no—
805C4⋊C4—612no—
806C4⋊C4—611no—
807C4⋊C4—1221no—
808C4⋊C4—1222no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4—1222no—
812C4⋊C4—1224no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—1224no—
818C4⋊C4—1224no—
819C4⋊C4—4881no—
820C4⋊C4C22×#692311yescharacteristic
821C22⋊C4—21no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1222no—
825C22⋊C4—1222no—
826C22⋊C4—1224no—
827C22⋊C4—1224no—
828C22⋊C4—1221no—
829C22⋊C4—4881no—
830C22⋊C4—4881no—
831C22⋊C4—4881no—
832C22⋊C4—2442no—
833C42—612no—
834C42—612no—
835C42—1221no—
836C42—1221no—
837C42—1224no—
838C42—1224no—
839C42—4881no—
840C23—21no—
841C23—21no—
842C23—611no—
843C23—611no—
844C23—1222no—
845C23—1221no—
846C23—1221no—
847C23—1222no—
848C23—1221no—
849C23—1221no—
850C23—1221no—
851C23—1221no—
852C23—1221no—
853C23—1221no—
854C23—2441no—
855C23—2441no—
856C23—2441no—
857C23—2441no—
858C23—2441no—
859C23—2441no—
860C23—2441no—
861C23—2441no—
862C23—2441no—
863C23—2441no—
864C23D4×#692311yescharacteristic
865Q8—21no—
866Q8—612no—
867Q8—1222no—
868Q8—1222no—
869Q8—1221no—
870Q8D4×#692312yes—
871D4—24no—
872D4—21no—
873D4—21no—
874D4—21no—
875D4—81no—
876D4—612no—
877D4—1224no—
878D4—1222no—
879D4—1222no—
880D4—1224no—
881D4—1224no—
882D4—1221no—
883D4—1221no—
884D4—1221no—
885D4—4881no—
886D4—4881no—
887D4—4881no—
888D4—2441no—
889D4—2441no—
890D4D4×#692312yes—
891C2×C4—24no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—611no—
897C2×C4—611no—
898C2×C4—611no—
899C2×C4—611no—
900C2×C4—611no—
901C2×C4—612no—
902C2×C4—612no—
903C2×C4—611no—
904C2×C4—1221no—
905C2×C4—1221no—
906C2×C4—1222no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1222no—
910C2×C4—1224no—
911C2×C4—1224no—
912C2×C4—1221no—
913C2×C4—1221no—
914C2×C4—1224no—
915C2×C4—1221no—
916C2×C4—1221no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—1221no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—1221no—
926C2×C4—1221no—
927C2×C4—1221no—
928C2×C4—1221no—
929C2×C4—1221no—
930C2×C4—1221no—
931C2×C4—4884no—
932C2×C4—4884no—
933C2×C4—4884no—
934C2×C4—4884no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4D4×#692311yescharacteristic
948C2×C4C23×#692311yescharacteristic
949C8—21no—
950C8—21no—
951C8—1221no—
952C8—1221no—
953C8—2441no—
954C8—2441no—
955C22—21no—
956C22—22no—
957C22—21no—
958C22—21no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—611no—
965C22—611no—
966C22—611no—
967C22—611no—
968C22—611no—
969C22—611no—
970C22—1222no—
971C22—1221no—
972C22—1221no—
973C22—1221no—
974C22—4881no—
975C22—4881no—
976C22—4881no—
977C22—4881no—
978C22—2441no—
979C22—2442no—
980C22—2441no—
981C22—2441no—
982C22—2441no—
983C22—2442no—
984C22—2442no—
985C22—2442no—
986C22—2441no—
987C22—2441no—
988C22—2441no—
989C22—2441no—
990C22—2441no—
991C22C2×D4×#692311yescharacteristic
992C4—21no—
993C4—22no—
994C4—41no—
995C4—611no—
996C4—611no—
997C4—1222no—
998C4—1222no—
999C4—1221no—
1000C4—1222no—
1001C4—4881no—
1002C4—4881no—
1003C4—2441no—
1004C4—2441no—
1005C4—2442no—
1006C4—2442no—
1007C4—2441no—
1008C4C2×D4×#692311yescharacteristic
1009C4C2×D4×#692311yescharacteristic
1010C2—41no—
1011C2—42no—
1012C2—81no—
1013C2—611no—
1014C2—611no—
1015C2—611no—
1016C2—611no—
1017C2—4881no—
1018C2—2441no—
1019C2—2442no—
1020C2#120×#692311yescharacteristic
1021C2#2146257611yescharacteristic
1022C2#2146258111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#449C4
socleC22×C61C2×C4×D4
prime radical#449×D61C2
cosocleC2×C4×D61C24
hypercenter#449#6923
hypocenterC61#21460
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#16840831C2semidirect
2. C2×#16840801C2semidirect
3. C2×D8×#6923C2semidirect
4. #21462307C2semidirect
5. #21461815C2semidirect
6. #21461814C2semidirect
7. #21461806C2semidirect
8. #21461783C2semidirect
9. #21461782C2semidirect
10. #21461768C2semidirect
11. #21461659C2semidirect
12. #21461590C2semidirect
13. #103×#6923C2semidirect
14. #21461550C2semidirect
60. #16839910C4semidirect
61. #16839909C4semidirect
62. #16839908C4semidirect
63. #16839907C4semidirect
64. #16839906C4semidirect
65. #16839905C4semidirect
66. #16839904C4semidirect
70. C61×#449C4semidirect
80. Q8×#6923D4semidirect
88. D4×#6923D4semidirect
133. C2×#11758226C2×C4semidirect
135. C2×#11758222C2×C4semidirect
137. C2×#11758224C2×C4semidirect
149. C2×#11758190C2×C4semidirect
150. C2×#11758200C2×C4semidirect
151. C2×#11758201C2×C4semidirect
154. C2×D488C2×C4semidirect
155. C2×#11758199C2×C4semidirect
156. C2×#11758199C2×C4semidirect
161. #14519752C2×C4semidirect
162. #14519751C2×C4semidirect
165. #14519748C2×C4semidirect
168. #14519702C2×C4semidirect
169. #14519701C2×C4semidirect
170. #14519700C2×C4semidirect
171. #14519699C2×C4semidirect
172. #14519698C2×C4semidirect
173. #14519697C2×C4semidirect
174. C22⋊#92418C2×C4semidirect
175. #14519689C2×C4semidirect
176. #14519689C2×C4semidirect
177. C2×#41×C61C2×C4semidirect
178. C2×SD16×C61C2×C4semidirect
179. C2×D8×C61C2×C4semidirect
180. #121×C61C2×C4semidirect
181. #103×C61C2×C4semidirect
182. #102×C61C2×C4semidirect
183. C22⋊C8×C61C2×C4semidirect
551. #449#6923semidirect
582. C61#21460semidirect
592. C2×#41C2×#6923semidirect
609. C2×SD16C2×#6923semidirect
615. C2×D8C2×#6923semidirect
625. #121C2×#6923semidirect
676. #103C2×#6923semidirect
684. #102C2×#6923semidirect
690. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408312
C2×#168408012
C2×D8×#69232
#214623072
#214618152
#214618142
#214618062
#214617832
#214617822
#214617682
#214616592
#214615902
#103×#69232
#214615502
#449×D612
#2146061