Finite Group Databasebeta

← #30620450

Subgroups — #30620450

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462621C211yesmaximal, characteristic, complemented
2#21462278C211yesmaximal, characteristic, complemented
3#21462007C211yesmaximal, characteristic, complemented
4#21462006C211yesmaximal, characteristic, complemented
5#21462005C211yesmaximal, characteristic, complemented
6#21461996C211yesmaximal, characteristic, complemented
7#21461996C211yesmaximal, characteristic, complemented
8#21461994C211yesmaximal, characteristic, complemented
9#21461694C211yesmaximal, characteristic
10#21461694C211yesmaximal, characteristic
11#21461692C211yesmaximal, characteristic
12#21461583C211yesmaximal, characteristic
13#21461583C211yesmaximal, characteristic
14C4×#14519842C211yesmaximal, characteristic
15#21459401C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840813—21no—
19#16840811—21no—
20#16840767C2211yescharacteristic
21#16840767C2211yescharacteristic
22#16840766C2211yescharacteristic
23C2×#14519842C2211yescharacteristic
24C2×#14519842C2211yescharacteristic
25C2×#14519842C2211yescharacteristic
26C2×#14519842C2211yescharacteristic
27C4×#11758213C2211yescharacteristic
28C4×#11758213C2211yescharacteristic
29C4×#11758213C2211yescharacteristic
30(C2×#6923)⋊Q8—21no—
31#16840713—21no—
32#16840711—21no—
33#16840711—21no—
34C4×C4⋊#6923C2211yescharacteristic
35C4×C4⋊#6923C2211yescharacteristic
36C4×C4⋊#6923C2211yescharacteristic
37#16840698C2211yescharacteristic
38#16840698C2211yescharacteristic
39C42×#6923C2211yescharacteristic
40#16840632C2211yescharacteristic
41#16840632C2211yescharacteristic
42#16840632C2211yescharacteristic
43#16840632C2211yescharacteristic
44#16840632C2211yescharacteristic
45#16840632C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50#16840632C2211yescharacteristic
51#16840632C2211yescharacteristic
52Q8×Dic122C411yescharacteristic, complemented
53#16840488C411yescharacteristic, complemented
54#16840488C411yescharacteristic, complemented
55#16840472—21no—
56#16840472C411yescharacteristic, complemented
57#16840468—21no—
58#16840468—21no—
59#16840468C411yescharacteristic, complemented
60#16840468C411yescharacteristic, complemented
61#16840427—21no—
62#16840427C411yescharacteristic, complemented
63#16840318—21no—
64#16840318—21no—
65#16840318C2211yescharacteristic
66#16840318C2211yescharacteristic
67#16840317—21no—
68#16840317C2211yescharacteristic
69C4×#11758226C2211yescharacteristic
70C4×#11758226C2211yescharacteristic
71C4×#11758226C2211yescharacteristic
72C4×Q8×D61—21no—
73C4×Q8×D61C2211yescharacteristic
74C61×#557C411yescharacteristic, complemented
75C2×#11758213C2311yescharacteristic
76C2×#11758213C2311yescharacteristic
77C2×#11758213C2311yescharacteristic
78C2×#11758213C2311yescharacteristic
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923C2311yescharacteristic
85C2×C4×#6923C2311yescharacteristic
86C2×C4×#6923C2311yescharacteristic
87C2×C4×#6923C2311yescharacteristic
88#14519844—21no—
89#14519844—21no—
90#14519844—21no—
91#14519844—21no—
92C4⋊#92420—21no—
93C4⋊#92420—21no—
94#14519842—22no—
95#14519842—22no—
96#14519842—22no—
97#14519842Q814yescomplemented
98#14519832—21no—
99#14519832—21no—
100#14519832—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111C2×#11758226C2311yescharacteristic
112C2×Q8×D61—21no—
113C2×Q8×D61D411yescharacteristic
114#14519777—21no—
115#14519777C2×C411yescharacteristic
116#14519776—21no—
117#14519776—21no—
118#14519776—21no—
119#14519776—21no—
120#14519776C2×C411yescharacteristic
121#14519776C2×C411yescharacteristic
122#14519776C2×C411yescharacteristic
123#14519776C2×C411yescharacteristic
124#14519769—21no—
125#14519769—21no—
126#14519769C2×C411yescharacteristic
127#14519769C2×C411yescharacteristic
128#14519768—21no—
129#14519768—21no—
130#14519768C2×C411yescharacteristic
131#14519768C2×C411yescharacteristic
132#14519757—21no—
133#14519757—21no—
134#14519757—21no—
135#14519755—21no—
136#14519755—21no—
137#14519755—21no—
138#14519755—21no—
139#14519755—21no—
140#14519755—21no—
141#14519755—21no—
142#14519755—21no—
143#14519755—21no—
144#14519755—21no—
145#14519755—21no—
146#14519755—21no—
147#14519753—21no—
148#14519753—21no—
149#14519753—21no—
150Q8×Dic61—21no—
151Q8×Dic61C2×C411yescharacteristic
152Q8×Dic61C2×C411yescharacteristic
153Q8×Dic61C2×C411yescharacteristic
154Q8×Dic61D411yescharacteristic
155C4×Dic122—21no—
156C4×Dic122—21no—
157C4×Dic122—21no—
158C4×Dic122C2×C411yescharacteristic
159C4×Dic122C2×C411yescharacteristic
160C4×Dic122C2×C411yescharacteristic
161#14519742—21no—
162#14519742—21no—
163#14519742—21no—
164#14519742—21no—
165#14519742—21no—
166#14519742D411yescharacteristic
167#14519742D411yescharacteristic
168#14519742D411yescharacteristic
169C4×D244—21no—
170C4×D244—21no—
171C4×D244—21no—
172C4×D244C2×C411yescharacteristic
173C4×D244C2×C411yescharacteristic
174C4×D244C2×C411yescharacteristic
175#14519739—21no—
176#14519739—21no—
177#14519739—21no—
178#14519739C2×C411yescharacteristic
179#14519739C2×C411yescharacteristic
180#14519739C2×C411yescharacteristic
181#14519735—21no—
182#14519735—21no—
183#14519735—21no—
184#14519735C2311yescharacteristic
185#14519735C2311yescharacteristic
186#14519735C2311yescharacteristic
187C4⋊C4×D61—21no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61D411yescharacteristic
191C4⋊C4×D61D411yescharacteristic
192C4⋊C4×D61D411yescharacteristic
193C42×D61—21no—
194C42×D61—21no—
195C42×D61—21no—
196C42×D61C2311yescharacteristic
197C42×D61C2311yescharacteristic
198C42×D61C2311yescharacteristic
199C4⋊Q8×C61—21no—
200C4⋊Q8×C61C2×C411yescharacteristic
201#125×C61—21no—
202#125×C61—21no—
203#125×C61C2×C411yescharacteristic
204#125×C61C2×C411yescharacteristic
205C4×Q8×C61—21no—
206C4×Q8×C61C2×C411yescharacteristic
207C4×Q8×C61C2×C411yescharacteristic
208C4×Q8×C61C2×C411yescharacteristic
209C4×Q8×C61C2×C411yescharacteristic
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61C22⋊C411yescharacteristic
216C2×Q8×C61C22×C411yescharacteristic
217#11758226—21no—
218#11758226—21no—
219#11758226C2×Q812yes—
220#11758226#4112yes—
221Q8×D61—42no—
222Q8×D61—44no—
223C2×D244—21no—
224C2×D244C22×C411yescharacteristic
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2411yescharacteristic
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122C22⋊C411yescharacteristic
245C2×Dic122C22⋊C411yescharacteristic
246C2×Dic122C22⋊C411yescharacteristic
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—21no—
250C2×#92420—21no—
251C4⋊#6923—42no—
252C4⋊#6923—42no—
253C4⋊#6923—42no—
254C4×#6923—21no—
255C4×#6923—21no—
256C4×#6923—21no—
257C4×#6923—21no—
258C4×#6923—21no—
259C4×#6923—21no—
260C4×#6923—21no—
261C4×#6923—42no—
262C4×#6923—42no—
263C4×#6923C2×Q812yescomplemented
264#11758213—21no—
265#11758213—21no—
266#11758213—21no—
267#11758213—21no—
268#11758213—21no—
269#11758213—21no—
270#11758213—21no—
271#11758213C2×Q812yescomplemented
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C22⋊C411yescharacteristic
281C4⋊C4×C61C22⋊C411yescharacteristic
282C4⋊C4×C61C22⋊C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C4⋊C4×C61C22×C411yescharacteristic
285C4⋊C4×C61C22×C411yescharacteristic
286C42×C61—21no—
287C42×C61—21no—
288C42×C61—21no—
289C42×C61C22×C411yescharacteristic
290C42×C61C22×C411yescharacteristic
291C42×C61C22×C411yescharacteristic
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61C22⋊C411yescharacteristic
308C4⋊Dic61C22⋊C411yescharacteristic
309C4⋊Dic61C22⋊C411yescharacteristic
310C4⋊Dic61C22×C411yescharacteristic
311C4⋊Dic61C22×C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196C22⋊C411yescharacteristic
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327#11758196C22⋊C411yescharacteristic
328#11758196C22⋊C411yescharacteristic
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61—21no—
334C4×Dic61—21no—
335C4×Dic61C22×C411yescharacteristic
336C4×Dic61C22×C411yescharacteristic
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C4×Dic61C2×D411yescharacteristic
341C4×Dic61C2×D411yescharacteristic
342C4×Dic61C2×D411yescharacteristic
343C4×Dic61C2×D411yescharacteristic
344C22×D61—21no—
345C22×D61C22×D411yescharacteristic
346C2×#6923—22no—
347C2×#6923—22no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358Q8×C61—21no—
359Q8×C61—41no—
360Q8×C61—42no—
361Q8×C61C4×Q812yes—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C2×C22⋊C411yescharacteristic
372C2×C4×C61C23×C411yescharacteristic
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C22×D411yescharacteristic
383D244—22no—
384D244—22no—
385D244—21no—
386D244C4×Q812yes—
387C4×D61—22no—
388C4×D61—22no—
389C4×D61—22no—
390C4×D61—41no—
391C4×D61—41no—
392C4×D61—41no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61—42no—
396C4×D61—42no—
397C4×D61—42no—
398C4×D61—81no—
399C4×D61—81no—
400C4×D61—81no—
401C4×D61C22×Q811yescharacteristic
402C4×D61C2×#4111yescharacteristic
403C4×D612−1+411yescharacteristic
404C4×D612−1+411yescharacteristic
405Dic122—22no—
406Dic122—22no—
407Dic122—41no—
408Dic122—42no—
409Dic122—42no—
410Dic122—81no—
411Dic122—81no—
412Dic122—81no—
413#92420—22no—
414#92420—41no—
415#92420—41no—
416#92420—41no—
417#22529—611nomaximal, Sylow
418C22×C61C22×C22⋊C411yescharacteristic
419C2×D61—21no—
420C2×D61—21no—
421C2×D61—22no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61#54811yescharacteristic
425C2×D61D4×Q811yescharacteristic
426#6923—42no—
427#6923—42no—
428#6923—81no—
429#6923—81no—
430C4×C61—22no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—21no—
434C4×C61—21no—
435C4×C61—21no—
436C4×C61—21no—
437C4×C61—41no—
438C4×C61—41no—
439C4×C61—41no—
440C4×C61C2×C4×Q811yescharacteristic
441C4×C61#51911yescharacteristic
442Dic61—21no—
443Dic61—21no—
444Dic61—21no—
445Dic61—21no—
446Dic61—21no—
447Dic61—41no—
448Dic61—41no—
449Dic61—41no—
450Dic61#42112yes—
451Dic61#54811yescharacteristic
452Dic61D4×Q811yescharacteristic
453Q8×#41—611no—
454Q8×M16—611no—
455#2295—611no—
456#1995—611no—
457#1995—611no—
458#1994—611no—
459#1986—611no—
460#1986—611no—
461#1986—611no—
462#1806—611no—
463#1806—611no—
464#1806—611no—
465#1759—611no—
466#1759—611no—
467C4×#104—611no—
468C2×C61Q8×C22⋊C411yescharacteristic
469C2×C61C2×#42111yescharacteristic
470C2×C61#290111yescharacteristic
471D61—21no—
472D61—21no—
473D61—42no—
474Q82—611no—
475#557—611no—
476#557—611no—
477#557#692311yescharacteristic, complemented
478#554—611no—
479#554—611no—
480#554—611no—
481#554—1221no—
482#554—1221no—
483#554—1221no—
484D4×Q8—611no—
485D4×Q8—1221no—
486#533—611no—
487#533—611no—
488#533—611no—
489#533—1221no—
490#533—1221no—
491#533—1221no—
492C4×#41—611no—
493C4×#41—611no—
494C4×#41—611no—
495C2×C4×Q8—611no—
496C2×C4×Q8—1221no—
497#446—1221no—
498#446—1221no—
499#446—1221no—
500C8×Q8—1221no—
501#423—611no—
502#423—611no—
503#423—611no—
504C2×#104—611no—
505C2×#104—611no—
506C2×#104—611no—
507C2×#104—611no—
508C4×M16—611no—
509C4×M16—611no—
510C4×M16—611no—
511#391—1221no—
512#389—1221no—
513#387—1221no—
514#387—1221no—
515C4×C4⋊C4—611no—
516C4×C4⋊C4—611no—
517C4×C4⋊C4—611no—
518#376—611no—
519#376—611no—
520C43—611no—
521#339—611no—
522#339—611no—
523#339—611no—
524#339—611no—
525#339—611no—
526#339—611no—
527#339—611no—
528#339—611no—
529#339—611no—
530#339—611no—
531#339—611no—
532#339—611no—
533C61#2252911yescharacteristic, complemented, Sylow
534C2×#41—611no—
535C22×Q8—611no—
536C22×Q8—1221no—
537C2×M16—611no—
538C2×M16—611no—
539C2×M16—611no—
540C2×M16—611no—
541C4⋊Q8—21no—
542C4⋊Q8—611no—
543C4⋊Q8—611no—
544C4⋊Q8—611no—
545C4⋊Q8—611no—
546C4⋊Q8—611no—
547C4⋊Q8—1221no—
548C4⋊Q8—1221no—
549C4⋊Q8—1221no—
550C4⋊Q8—1221no—
551C4⋊Q8—1221no—
552C4⋊Q8C2×#692311yescharacteristic
553#125—21no—
554#125—21no—
555#125—611no—
556#125—611no—
557#125—611no—
558#125—611no—
559#125—1221no—
560#125—1221no—
561#125—1221no—
562#125—1221no—
563#125C2×#692311yescharacteristic
564#125C2×#692311yescharacteristic
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
577C22⋊Q8—1221no—
578C22⋊Q8—1221no—
579C22⋊Q8—1221no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C4×Q8—21no—
584C4×Q8—611no—
585C4×Q8—611no—
586C4×Q8—611no—
587C4×Q8—611no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—611no—
594C4×Q8—1221no—
595C4×Q8—1221no—
596C4×Q8—1221no—
597C4×Q8—1221no—
598C4×Q8—1221no—
599C4×Q8—1221no—
600C4×Q8—1221no—
601C4×Q8—1221no—
602C4×Q8—1221no—
603C4×Q8C2×#692311yescharacteristic
604C4×Q8C2×#692311yescharacteristic
605C4×Q8C2×#692311yescharacteristic
606C4×Q8C2×#692311yescharacteristic
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—611no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—611no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619#117—611no—
620#117—611no—
621#117—611no—
622#117—1221no—
623#117—1221no—
624#117—1221no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C4⋊C4—1221no—
633C2×C4⋊C4—1221no—
634C2×C42—611no—
635C2×C42—611no—
636C2×C42—611no—
637C2×C42—611no—
638C2×C42—611no—
639C2×C42—611no—
640C2×C42—611no—
641C2×C42—1221no—
642C2×C42—1221no—
643C2×C42—1221no—
644C2×C42—1221no—
645C2×C42—1221no—
646C4⋊C8—1221no—
647C4⋊C8—1221no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C4⋊C8—1221no—
652#104—614no—
653#104—1222no—
654#104—1222no—
655#104—1222no—
656#97—1221no—
657#97—1221no—
658#97—1221no—
659C4×C8—1221no—
660C4×C8—1221no—
661C4×C8—1221no—
662#95—1221no—
663#95—1221no—
664#95—1221no—
665#95—1221no—
666#95—1221no—
667#95—1221no—
668#95—1221no—
669#41—612no—
670#41—612no—
671#41—1221no—
672#41—1221no—
673C2×Q8—21no—
674C2×Q8—611no—
675C2×Q8—611no—
676C2×Q8—611no—
677C2×Q8—1221no—
678C2×Q8—1221no—
679C2×Q8—1221no—
680C2×Q8—1221no—
681C2×Q8—1221no—
682C2×Q8—2442no—
683C2×Q8—2444no—
684C2×Q8C22⋊#692311yescharacteristic
685C2×Q8C22×#692311yescharacteristic
686C2×D4—611no—
687C2×D4—1221no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706M16—612no—
707M16—1221no—
708M16—1221no—
709M16—1221no—
710M16—1221no—
711M16—1221no—
712M16—1221no—
713M16—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—611no—
727C4⋊C4—611no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—611no—
735C4⋊C4—611no—
736C4⋊C4—611no—
737C4⋊C4—611no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—2442no—
755C4⋊C4—2442no—
756C4⋊C4—2442no—
757C4⋊C4C22⋊#692311yescharacteristic
758C4⋊C4C22⋊#692311yescharacteristic
759C4⋊C4C22⋊#692311yescharacteristic
760C4⋊C4C22×#692311yescharacteristic
761C4⋊C4C22×#692311yescharacteristic
762C4⋊C4C22×#692311yescharacteristic
763C22⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—611no—
776C42—611no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—611no—
782C42—611no—
783C42—611no—
784C42—612no—
785C42—1221no—
786C42—1221no—
787C42—1221no—
788C42—1221no—
789C42—1221no—
790C42—1221no—
791C42—1221no—
792C42—1221no—
793C42—1221no—
794C42—1221no—
795C42—1221no—
796C42—1221no—
797C42—1221no—
798C42—2442no—
799C42—2442no—
800C42C22×#692311yescharacteristic
801C42C22×#692311yescharacteristic
802C42C22×#692311yescharacteristic
803C23—611no—
804C23—1221no—
805Q8—21no—
806Q8—41no—
807Q8—42no—
808Q8—1222no—
809Q8—1222no—
810Q8—4881no—
811Q8—4881no—
812Q8—4881no—
813Q8—2441no—
814Q8—2442no—
815Q8—2442no—
816Q8Q8×#692312yes—
817D4—612no—
818D4—1222no—
819D4—1222no—
820D4—1221no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—611no—
826C2×C4—611no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—611no—
831C2×C4—611no—
832C2×C4—611no—
833C2×C4—611no—
834C2×C4—611no—
835C2×C4—611no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—4881no—
845C2×C4—4881no—
846C2×C4—4881no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2442no—
853C2×C4—2442no—
854C2×C4—2442no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4C2×C22⋊#692311yescharacteristic
866C2×C4C2×C22⋊#692311yescharacteristic
867C2×C4C2×C22⋊#692311yescharacteristic
868C2×C4C2×C22⋊#692311yescharacteristic
869C2×C4C2×C22⋊#692311yescharacteristic
870C2×C4C2×C22⋊#692311yescharacteristic
871C2×C4C23×#692311yescharacteristic
872C8—1222no—
873C8—2441no—
874C8—2441no—
875C8—2441no—
876C22—611no—
877C22—611no—
878C22—1221no—
879C22—1221no—
880C22—1222no—
881C22—2441no—
882C22—2441no—
883C22C22×C22⋊#692311yescharacteristic
884C4—22no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—611no—
895C4—611no—
896C4—612no—
897C4—1221no—
898C4—1221no—
899C4—1221no—
900C4—1221no—
901C4—1221no—
902C4—4881no—
903C4—4881no—
904C4—2442no—
905C4—2442no—
906C4—2441no—
907C4—2441no—
908C4—2441no—
909C4C2×Q8×#692311yescharacteristic
910C4#1684083011yescharacteristic
911C2—1221no—
912C2—1221no—
913C2—2442no—
914C2Q8×C22⋊#692311yescharacteristic
915C2D61⋊#42111yescharacteristic
916C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#557C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758226C23
cosocleC2×C4×D61C24
hypercenter#557#6923
hypocenterC61#22529
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #21462621C2semidirect
2. #21462278C2semidirect
3. #21462007C2semidirect
4. #21462006C2semidirect
5. #21462005C2semidirect
6. #21461996C2semidirect
7. #21461996C2semidirect
8. #21461994C2semidirect
52. Q8×Dic122C4semidirect
53. #16840488C4semidirect
54. #16840488C4semidirect
56. #16840472C4semidirect
59. #16840468C4semidirect
60. #16840468C4semidirect
62. #16840427C4semidirect
74. C61×#557C4semidirect
97. #14519842Q8semidirect
263. C4×#6923C2×Q8semidirect
271. #11758213C2×Q8semidirect
477. #557#6923semidirect
533. C61#22529semidirect

Maximal subgroups

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

subgroupindex
#214626212
#214622782
#214620072
#214620062
#214620052
#214619962
#214619942
#214616942
#214616922
#214615832
C4×#145198422
#214594012
#2252961