Finite Group Databasebeta

← #30621758

Subgroups — #30621758

Order 15616.

1190 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C2×#16840753C211yesmaximal, characteristic, complemented
3#21462344C211yesmaximal, characteristic, complemented
4#21462324C211yesmaximal, characteristic, complemented
5#21461968C211yesmaximal, characteristic, complemented
6#21461909C211yesmaximal, characteristic, complemented
7#21461897C211yesmaximal, characteristic, complemented
8#21461835C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic, complemented
10#21461814C211yesmaximal, characteristic, complemented
11#21461785C211yesmaximal, characteristic, complemented
12#21461769C211yesmaximal, characteristic, complemented
13#21461592C211yesmaximal, characteristic, complemented
14#21461562C211yesmaximal, characteristic, complemented
15#449×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×D4×#6923—21no—
20C2×D4×#6923C2211yescharacteristic
21C22×C4⋊#6923C2211yescharacteristic
22SD16×#6923—24no—
23C2×#14519845C2211yescharacteristic
24C2×#14519845C2211yescharacteristic
25#16840753—24no—
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32C2×#14519831C2211yescharacteristic
33C2×C8×#6923C2211yescharacteristic
34#16840714—21no—
35#16840714—21no—
36#16840714C2211yescharacteristic
37#16840714C2211yescharacteristic
38#16840714C2211yescharacteristic
39#16840713C2211yescharacteristic
40#16840712—21no—
41#16840710—21no—
42#16840709—21no—
43#16840704—21no—
44#16840704C2211yescharacteristic
45C4⋊C4×#6923C2211yescharacteristic
46C4×C22⋊#6923—21no—
47C4×C22⋊#6923C2211yescharacteristic
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×#41×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56C2×D8×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16839910C411yescharacteristic, complemented
59#16839909C411yescharacteristic, complemented
60#16839908C411yescharacteristic, complemented
61#16839907C411yescharacteristic, complemented
62#16839906C411yescharacteristic, complemented
63#16839905C411yescharacteristic, complemented
64#16839904C411yescharacteristic, complemented
65#103×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#449C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C2×#11758213—21no—
72D61⋊M16—22no—
73D61⋊M16—41no—
74C2×#11758217—21no—
75C2×D61⋊C8C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77Q8×#6923—22no—
78Q8×#6923—22no—
79Q8×#6923—41no—
80Q8×#6923—41no—
81D4×#6923—22no—
82D4×#6923—41no—
83D4×#6923—44no—
84C2×C4⋊#6923—22no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923—21no—
88C2×C4⋊#6923—21no—
89C2×C4⋊#6923—41no—
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4⋊#6923C2311yescharacteristic
92C2×C4⋊#6923C2311yescharacteristic
93C2×C4⋊#6923C2311yescharacteristic
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923—21no—
99C2×C22⋊#6923—21no—
100C2×C22⋊#6923—21no—
101C2×C22⋊#6923—21no—
102C2×C22⋊#6923D411yescharacteristic
103C2×C22⋊#6923D411yescharacteristic
104C2×C4×#6923—21no—
105C2×C4×#6923—21no—
106C2×C4×#6923—21no—
107C2×C4×#6923C2311yescharacteristic
108C2×C4×#6923C2311yescharacteristic
109#14519845—22no—
110#14519845—41no—
111#14519840—22no—
112#14519840D414yescomplemented
113#14519839—22no—
114#14519839—22no—
115#14519839—22no—
116#14519839—41no—
117#14519831—41no—
118C8×#6923—22no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4—21no—
122(C2×#6923)⋊C4D411yescharacteristic
123(C2×#6923)⋊C4D411yescharacteristic
124C2×#11758226C2×C411yescharacteristic, complemented
125C2×#11758222—21no—
126C2×#11758222C2×C411yescharacteristic, complemented
127C2×#11758224—21no—
128C2×#11758224C2×C411yescharacteristic, complemented
129#41×D61—22no—
130#41×D61—22no—
131#41×D61—41no—
132#41×D61—41no—
133C2×Q8×D61C2311yescharacteristic
134C2×D4×D61—21no—
135C2×D4×D61—21no—
136C2×D4×D61C2311yescharacteristic
137C2×D4×D61C2311yescharacteristic
138C22×C4×D61—21no—
139C22×C4×D61C2311yescharacteristic
140C2×#11758190C2×C411yescharacteristic, complemented
141C2×#11758200C2×C411yescharacteristic, complemented
142C2×#11758201C2×C411yescharacteristic, complemented
143SD16×D61—22no—
144SD16×D61—22no—
145C2×D488C2×C411yescharacteristic, complemented
146C2×#11758199C2×C411yescharacteristic, complemented
147C2×#11758199C2×C411yescharacteristic, complemented
148D8×D61—41no—
149D8×D61—41no—
150C2×C8×D61C2311yescharacteristic
151C2×C8×D61C2311yescharacteristic
152#14519752C2×C411yescharacteristic
153#14519751C2×C411yescharacteristic
154#14519750—21no—
155#14519749—21no—
156#14519748C2×C411yescharacteristic
157C4⋊C4×D61C2311yescharacteristic
158C22⋊C4×D61—21no—
159#14519702C2×C411yescharacteristic, complemented
160#14519701C2×C411yescharacteristic, complemented
161#14519700C2×C411yescharacteristic, complemented
162#14519699C2×C411yescharacteristic, complemented
163#14519698C2×C411yescharacteristic, complemented
164#14519697C2×C411yescharacteristic, complemented
165C22⋊#92418C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167#14519689C2×C411yescharacteristic, complemented
168C2×#41×C61C2×C411yescharacteristic, complemented
169C2×SD16×C61C2×C411yescharacteristic, complemented
170C2×D8×C61C2×C411yescharacteristic, complemented
171#121×C61C2×C411yescharacteristic
172#103×C61C2×C411yescharacteristic, complemented
173#102×C61C2×C411yescharacteristic, complemented
174C22⋊C8×C61C2×C411yescharacteristic, complemented
175C23×D61—21no—
176C23×D61—21no—
177C23×D61C2×D411yescharacteristic
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—21no—
182C22×#6923—42no—
183C22×#6923—42no—
184C22×#6923—42no—
185C22×#6923—42no—
186C22×#6923—81no—
187C22×#6923—81no—
188C22×#6923C2×D411yescharacteristic
189C22×#6923C2×D411yescharacteristic
190C22×#6923C2×D411yescharacteristic
191C22×#6923C2×D411yescharacteristic
192#41×C61—22no—
193#41×C61—41no—
194C2×Q8×C61C22×C411yescharacteristic
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61C22×C411yescharacteristic
198C2×D4×C61C22×C411yescharacteristic
199C22×C4×C61—21no—
200C22×C4×C61C22×C411yescharacteristic
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—21no—
207C22×Dic61—21no—
208C22×Dic61#4111yescharacteristic
209#11758226—22no—
210#11758226—41no—
211Q8×D61—21no—
212Q8×D61—21no—
213Q8×D61C2×D412yes—
214Q8×D61#4112yes—
215#11758224—22no—
216#11758224—41no—
217#11758224—42no—
218#11758224—42no—
219D4×D61—21no—
220D4×D61—21no—
221D4×D61—21no—
222D4×D61—21no—
223D4×D61—21no—
224D4×D61—21no—
225D4×D61—21no—
226D4×D61—21no—
227D4×D61—42no—
228D4×D61—42no—
229D4×D61—42no—
230D4×D61—42no—
231#11758222—22no—
232#11758222—42no—
233#11758222—42no—
234#11758222—41no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244C22×C411yescharacteristic
238C2×D244C22×C411yescharacteristic
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—42no—
248C2×C4×D61—42no—
249C2×C4×D61C22×C411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61#4111yescharacteristic
252C2×C4×D61C2411yescharacteristic
253C2×Dic122—21no—
254C2×Dic122C22×C411yescharacteristic
255C22⋊#6923—22no—
256C22⋊#6923—41no—
257C22⋊#6923—42no—
258C22⋊#6923—42no—
259C22⋊#6923—42no—
260C22⋊#6923—42no—
261C22⋊#6923—81no—
262C22⋊#6923—81no—
263C22⋊#6923—81no—
264C22⋊#6923—81no—
265#11758217—42no—
266C2×#92420—21no—
267C2×#92420—21no—
268C4⋊#6923—21no—
269C4⋊#6923—21no—
270C4⋊#6923—21no—
271C4⋊#6923—21no—
272C4⋊#6923—21no—
273C4⋊#6923—21no—
274C4⋊#6923—21no—
275C4⋊#6923—42no—
276C4⋊#6923—42no—
277C4⋊#6923—42no—
278C4⋊#6923—42no—
279C4⋊#6923C2×D412yes—
280C4×#6923—21no—
281C4×#6923—21no—
282C4×#6923—21no—
283C4×#6923—21no—
284C4×#6923—42no—
285C4×#6923—42no—
286C4×#6923—42no—
287#11758213—42no—
288D61⋊C8—21no—
289D61⋊C8—21no—
290D61⋊C8—21no—
291D61⋊C8C2×D412yes—
292SD16×C61—22no—
293D8×C61—41no—
294C2×C8×C61C22×C411yescharacteristic
295C2×C8×C61C22×C411yescharacteristic
296C4⋊C4×C61C22×C411yescharacteristic
297C22⋊C4×C61—21no—
298C22⋊Dic61—21no—
299#11758201—22no—
300#11758200—22no—
301#11758199—41no—
302#11758199—41no—
303#11758198—21no—
304#11758198—21no—
305C4⋊Dic61C22×C411yescharacteristic
306#11758196—21no—
307C2×#92418C22×C411yescharacteristic
308C2×#92418C22×C411yescharacteristic
309D488—41no—
310#11758190—22no—
311C8×D61—21no—
312C8×D61—21no—
313C8×D61—21no—
314C8×D61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61C4×D411yescharacteristic
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61C4×D411yescharacteristic
339C22×D61C22×D411yescharacteristic
340C2×#6923—21no—
341C2×#6923—21no—
342C2×#6923—21no—
343C2×#6923—22no—
344C2×#6923—21no—
345C2×#6923—21no—
346C2×#6923—21no—
347C2×#6923—21no—
348C2×#6923—21no—
349C2×#6923—21no—
350C2×#6923—21no—
351C2×#6923—21no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923—41no—
363C2×#6923—84no—
364C2×#6923—84no—
365C2×#6923AGL(1,ℤ/8)12yes—
366Q8×C61—21no—
367Q8×C61C4×D412yescomplemented
368D4×C61—21no—
369D4×C61—21no—
370D4×C61—21no—
371D4×C61—21no—
372D4×C61—42no—
373D4×C61—42no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—42no—
379C2×C4×C61C4×D411yescharacteristic
380C2×C4×C61C23×C411yescharacteristic
381C22⋊D61—42no—
382C22⋊D61—42no—
383C22⋊D61—42no—
384C22⋊D61—42no—
385C22⋊D61—41no—
386C22⋊D61—41no—
387C22⋊D61—41no—
388C22⋊D61—41no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—42no—
394C2×Dic61C4×D411yescharacteristic
395C2×Dic61C2×#4111yescharacteristic
396D244—21no—
397D244—21no—
398D244—21no—
399D244—21no—
400D244—42no—
401D244—42no—
402C4×D61—22no—
403C4×D61—21no—
404C4×D61—22no—
405C4×D61—21no—
406C4×D61—21no—
407C4×D61—21no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—42no—
411C4×D61—42no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61C22×D411yescharacteristic
415C4×D61C2×#4111yescharacteristic
416C4×D61H(5,𝔽2)11yescharacteristic
417C4×D61H(5,𝔽2)11yescharacteristic
418Dic122—21no—
419Dic122—22no—
420Dic122—22no—
421Dic122C4×D412yescomplemented
422#92420—22no—
423#92420—41no—
424C8×C61—21no—
425C8×C61—21no—
426#92418—21no—
427#92418—21no—
428#22883—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61C2×C4×D411yescharacteristic
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61—81no—
459C2×D61—81no—
460C2×D61D4211yescharacteristic
461C2×D61#54611yescharacteristic
462C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
463C2×D61#57511yescharacteristic
464C2×D61#57711yescharacteristic
465C2×D61#57711yescharacteristic
466#6923—22no—
467#6923—41no—
468#6923—42no—
469#6923—41no—
470#6923—41no—
471#6923—81no—
472#6923—81no—
473#6923—81no—
474C4×C61—22no—
475C4×C61—21no—
476C4×C61—41no—
477C4×C61C2×C4×D411yescharacteristic
478C4×C61#51811yescharacteristic
479Dic61—22no—
480Dic61—21no—
481Dic61—41no—
482Dic61#54611yescharacteristic
483Dic61#55111yescharacteristic
484C2×#449—611no—
485C2×C4×SD16—611no—
486C2×#417—611no—
487#2361—611no—
488#2341—611no—
489#1972—611no—
490#1934—611no—
491#1926—611no—
492#1895—611no—
493#1880—611no—
494#1879—611no—
495#1865—611no—
496#1853—611no—
497#1763—611no—
498#1753—611no—
499C2×C61—41no—
500C2×C61—81no—
501C2×C61—81no—
502C2×C61#235811yescharacteristic
503C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
504C2×C61#295211yescharacteristic
505D61—41no—
506D61—81no—
507D61—81no—
508D61#326511yescharacteristic
509D61#327111yescharacteristic
510D61#332611yescharacteristic
511D61#333211yescharacteristic
512C22×#41—611no—
513C22×SD16—611no—
514C22×D8—611no—
515C22×M16—611no—
516C2×#121—611no—
517C2×C4×Q8—611no—
518C2×C4×Q8—611no—
519C2×C4×D4—611no—
520C2×C4×D4—1221no—
521C22×C4⋊C4—611no—
522#449—611no—
523#449—611no—
524#449—611no—
525#449—611no—
526#449—611no—
527#449—611no—
528#449—611no—
529#449#692311yescharacteristic, complemented
530C4×SD16—1224no—
531C2×#106—611no—
532C2×#106—611no—
533#417—1224no—
534C2×#103—611no—
535C2×#103—611no—
536C2×#103—611no—
537C2×#102—611no—
538C2×#102—611no—
539C2×#102—611no—
540C2×#102—611no—
541C2×#102—611no—
542C2×C22⋊C8—611no—
543C2×#97—611no—
544C2×C4×C8—611no—
545#390—611no—
546#390—611no—
547#390—611no—
548#390—1221no—
549#390—1221no—
550#389—611no—
551#388—1221no—
552#386—1221no—
553#385—1221no—
554#380—611no—
555#380—1221no—
556C4×C4⋊C4—611no—
557C4×C22⋊C4—611no—
558C4×C22⋊C4—1221no—
559#340—611no—
560#340—611no—
561#340—611no—
562#340—611no—
563#336—611no—
564#336—611no—
565C61#2288311yescharacteristic, complemented, Sylow
566C2×#41—611no—
567C2×#41—611no—
568C2×#41—611no—
569C2×#41—1221no—
570C2×#41—1221no—
571C2×#41—1222no—
572C2×#41—1222no—
573C2×#41—2441no—
574C2×#41—2441no—
575C2×#41C2×#692311yescharacteristic, complemented
576C22×Q8—611no—
577C22×D4—611no—
578C22×D4—611no—
579C22×D4—1221no—
580C22×D4—1221no—
581C23×C4—611no—
582C23×C4—1221no—
583C23×C4—1221no—
584C23×C4—1221no—
585C2×SD16—611no—
586C2×SD16—611no—
587C2×SD16—611no—
588C2×SD16—1222no—
589C2×SD16—1222no—
590C2×SD16C2×#692311yescharacteristic, complemented
591C2×D8—611no—
592C2×D8—611no—
593C2×D8—611no—
594C2×D8—2441no—
595C2×D8—2441no—
596C2×D8C2×#692311yescharacteristic, complemented
597C2×M16—1222no—
598C2×M16—1221no—
599C2×M16—1221no—
600C2×M16—2441no—
601C22×C8—611no—
602C22×C8—611no—
603C22×C8—611no—
604C22×C8—611no—
605#121—611no—
606#121—611no—
607#121—611no—
608#121—1221no—
609#121—1221no—
610#121C2×#692311yescharacteristic
611C4×Q8—1222no—
612C4×Q8—1222no—
613C4×Q8—2441no—
614C4×Q8—2441no—
615C4×D4—1222no—
616C4×D4—2441no—
617C4×D4—2444no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—1222no—
624C2×C4⋊C4—1221no—
625C2×C4⋊C4—1221no—
626C2×C4⋊C4—1221no—
627C2×C4⋊C4—1221no—
628C2×C4⋊C4—2441no—
629C2×C22⋊C4—611no—
630C2×C22⋊C4—611no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C42—611no—
641C2×C42—611no—
642C2×C42—1221no—
643C2×C42—1221no—
644C2×C42—1221no—
645#106—1222no—
646#106—2441no—
647#103—614no—
648#103—611no—
649#103—611no—
650#103—611no—
651#103—1222no—
652#103C2×#692311yescharacteristic, complemented
653#102—611no—
654#102—611no—
655#102—611no—
656#102—1222no—
657#102—1222no—
658#102—1222no—
659#102—2441no—
660#102C2×#692311yescharacteristic, complemented
661C22⋊C8—611no—
662C22⋊C8—611no—
663C22⋊C8—611no—
664C22⋊C8C2×#692311yescharacteristic, complemented
665#97—2441no—
666C4×C8—1222no—
667#95—611no—
668#95—611no—
669#95—1221no—
670#95—1221no—
671#95—1221no—
672C24—611no—
673C24—1221no—
674C24—1221no—
675#41—22no—
676#41—41no—
677#41—1222no—
678#41—1222no—
679#41—1222no—
680#41—2441no—
681#41—2442no—
682#41—2442no—
683#41—2441no—
684#41—2442no—
685#41—2442no—
686#41—2441no—
687C2×Q8—612no—
688C2×Q8—612no—
689C2×Q8—611no—
690C2×Q8—1221no—
691C2×Q8—1221no—
692C2×Q8—1221no—
693C2×Q8C22×#692311yescharacteristic
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—611no—
697C2×D4—611no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—2442no—
715C2×D4—2442no—
716C2×D4—2442no—
717C2×D4—2442no—
718C2×D4C22×#692311yescharacteristic
719C2×D4C22×#692311yescharacteristic
720C22×C4—21no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—4881no—
744C22×C4—4881no—
745C22×C4—2442no—
746C22×C4—2442no—
747C22×C4—2442no—
748C22×C4—2442no—
749C22×C4—2442no—
750C22×C4—2442no—
751C22×C4C22×#692311yescharacteristic
752SD16—22no—
753SD16—1222no—
754SD16—1222no—
755SD16—1222no—
756D8—41no—
757D8—2441no—
758D8—2441no—
759D8—2441no—
760M16—2442no—
761M16—2442no—
762C2×C8—612no—
763C2×C8—611no—
764C2×C8—611no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—1221no—
769C2×C8—1221no—
770C2×C8—1221no—
771C2×C8—1221no—
772C2×C8—1221no—
773C2×C8—1221no—
774C2×C8C22×#692311yescharacteristic
775C2×C8C22×#692311yescharacteristic
776C4⋊C4—612no—
777C4⋊C4—611no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—2442no—
787C4⋊C4—2442no—
788C4⋊C4—2442no—
789C4⋊C4—2442no—
790C4⋊C4C22×#692311yescharacteristic
791C22⋊C4—21no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1222no—
795C22⋊C4—1221no—
796C22⋊C4—4881no—
797C22⋊C4—4881no—
798C22⋊C4—4881no—
799C22⋊C4—4881no—
800C22⋊C4—2442no—
801C22⋊C4—2441no—
802C22⋊C4—2442no—
803C22⋊C4—2442no—
804C22⋊C4—2442no—
805C42—1221no—
806C42—1221no—
807C42—1221no—
808C42—1221no—
809C42—2442no—
810C42—2442no—
811C42—2442no—
812C23—21no—
813C23—21no—
814C23—611no—
815C23—611no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1221no—
821C23—1221no—
822C23—1221no—
823C23—1221no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23—2441no—
830C23—2441no—
831C23—2441no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23D4×#692311yescharacteristic
837Q8—21no—
838Q8—612no—
839Q8—1222no—
840Q8—1222no—
841Q8—1221no—
842Q8D4×#692312yescomplemented
843D4—21no—
844D4—21no—
845D4—21no—
846D4—21no—
847D4—42no—
848D4—42no—
849D4—1221no—
850D4—1221no—
851D4—1221no—
852D4—1221no—
853D4—2442no—
854D4—2442no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2442no—
860D4—2442no—
861D4—2442no—
862D4—2442no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—42no—
868C2×C4—611no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—612no—
874C2×C4—611no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—1221no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1222no—
897C2×C4—1221no—
898C2×C4—1221no—
899C2×C4—4884no—
900C2×C4—4884no—
901C2×C4—2442no—
902C2×C4—2442no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2442no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4D4×#692311yescharacteristic
918C2×C4C23×#692311yescharacteristic
919C8—21no—
920C8—21no—
921C8—1222no—
922C8—1221no—
923C8—1221no—
924C8—2441no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—611no—
935C22—611no—
936C22—611no—
937C22—611no—
938C22—611no—
939C22—611no—
940C22—1221no—
941C22—1221no—
942C22—1221no—
943C22—4881no—
944C22—4881no—
945C22—4881no—
946C22—4881no—
947C22—4881no—
948C22—4881no—
949C22—4881no—
950C22—4881no—
951C22—2441no—
952C22—2441no—
953C22—2441no—
954C22—2441no—
955C22—2441no—
956C22—2441no—
957C22—2441no—
958C22—2441no—
959C22—2441no—
960C22—2441no—
961C22C2×D4×#692311yescharacteristic
962C4—21no—
963C4—22no—
964C4—41no—
965C4—611no—
966C4—611no—
967C4—1222no—
968C4—1221no—
969C4—1222no—
970C4—4881no—
971C4—4881no—
972C4—4881no—
973C4—2441no—
974C4—2441no—
975C4—2441no—
976C4—2442no—
977C4—2441no—
978C4C2×D4×#692311yescharacteristic
979C4#1684082911yescharacteristic
980C2—41no—
981C2—81no—
982C2—81no—
983C2—611no—
984C2—611no—
985C2—611no—
986C2—611no—
987C2—4881no—
988C2—4881no—
989C2—2441no—
990C2#2146234111yescharacteristic
991C2AGL(1,ℤ/8)×#692311yescharacteristic
992C2#2146258211yescharacteristic
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#22883
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×SD16×#6923C2semidirect
2. C2×#16840753C2semidirect
3. #21462344C2semidirect
4. #21462324C2semidirect
5. #21461968C2semidirect
6. #21461909C2semidirect
7. #21461897C2semidirect
8. #21461835C2semidirect
9. #21461815C2semidirect
10. #21461814C2semidirect
11. #21461785C2semidirect
12. #21461769C2semidirect
13. #21461592C2semidirect
14. #21461562C2semidirect
58. #16839910C4semidirect
59. #16839909C4semidirect
60. #16839908C4semidirect
61. #16839907C4semidirect
62. #16839906C4semidirect
63. #16839905C4semidirect
64. #16839904C4semidirect
68. C61×#449C4semidirect
112. #14519840D4semidirect
124. C2×#11758226C2×C4semidirect
126. C2×#11758222C2×C4semidirect
128. C2×#11758224C2×C4semidirect
140. C2×#11758190C2×C4semidirect
141. C2×#11758200C2×C4semidirect
142. C2×#11758201C2×C4semidirect
145. C2×D488C2×C4semidirect
146. C2×#11758199C2×C4semidirect
147. C2×#11758199C2×C4semidirect
159. #14519702C2×C4semidirect
160. #14519701C2×C4semidirect
161. #14519700C2×C4semidirect
162. #14519699C2×C4semidirect
163. #14519698C2×C4semidirect
164. #14519697C2×C4semidirect
165. C22⋊#92418C2×C4semidirect
166. #14519689C2×C4semidirect
167. #14519689C2×C4semidirect
168. C2×#41×C61C2×C4semidirect
169. C2×SD16×C61C2×C4semidirect
170. C2×D8×C61C2×C4semidirect
172. #103×C61C2×C4semidirect
173. #102×C61C2×C4semidirect
174. C22⋊C8×C61C2×C4semidirect
367. Q8×C61C4×D4semidirect
421. Dic122C4×D4semidirect
529. #449#6923semidirect
565. C61#22883semidirect
575. C2×#41C2×#6923semidirect
590. C2×SD16C2×#6923semidirect
596. C2×D8C2×#6923semidirect
652. #103C2×#6923semidirect
660. #102C2×#6923semidirect
664. C22⋊C8C2×#6923semidirect
842. Q8D4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
C2×#168407532
#214623442
#214623242
#214619682
#214619092
#214618972
#214618352
#214618152
#214618142
#214617852
#214617692
#214615922
#214615622
#449×D612
#2288361