Finite Group Databasebeta

← #11864052

Subgroups — #11864052

Order 1152.

1597 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3C2×#63801C211yesmaximal, characteristic, complemented
4#10594627C211yesmaximal, characteristic, complemented
5#10592480C211yesmaximal, characteristic, complemented
6C3×#4783C211yesmaximal, characteristic, complemented
7C3×#4770C211yesmaximal, characteristic, complemented
8#10591466C211yesmaximal, characteristic, complemented
9#10591452C211yesmaximal, characteristic, complemented
10#10590968C211yesmaximal, characteristic, complemented
11#10590965C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590614C211yesmaximal, characteristic, complemented
15#10590600C211yesmaximal, characteristic, complemented
16#80227—31nomaximal
17#78927—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3805—21no—
23C2×#3804—21no—
24C22×D3×Dic3—21no—
25D3×#237—24no—
26D3×#237—24no—
27C2×C4×D32C2211yescharacteristic
28C2×#3799C2211yescharacteristic
29C2×#3796C2211yescharacteristic
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×#3753C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
38C3×#897C2211yescharacteristic, complemented
39C3×#892C2211yescharacteristic
40#63934—24no—
41#63923—21no—
42#63909C2211yescharacteristic, complemented
43#63894—21no—
44#63890—21no—
45#63880—21no—
46#63871C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic
52#63801—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C2×#932—31no—
68C2×#918—31no—
69C2×#914—31no—
70C2×#909—31no—
71#5627—31no—
72#5524—31no—
73C3×#452—31no—
74C3×#418—31no—
75#5238—31no—
76#5187—31no—
77#5173—31no—
78#5126—31no—
79#5047—31no—
80#5004—31no—
81#4810—31no—
82#4802—31no—
83#4783—31no—
84#4783—31no—
85#4783—31no—
86#4783D311yescharacteristic, complemented
87#4781—31no—
88#4781—31no—
89#4781—31no—
90#4781—31no—
91#4781—31no—
92#4781—61no—
93#4770D311yescharacteristic, complemented
94#4734—31no—
95#4726—31no—
96C23×C3×D3—21no—
97C22×D32D411yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×#638—21no—
100C22×C3⋊Dic3—21no—
101#3830—22no—
102#3830—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C3×#237—22no—
111C3×#237—22no—
112C3×D3×D4—22no—
113C3×D3×D4D414yescomplemented
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119D3×#67—28no—
120C2×#627—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#625—21no—
125C2×#624—21no—
126C2×#624D411yescharacteristic
127#3805—28no—
128#3804—28no—
129C2×D3×Dic3—28no—
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3—21no—
133C2×D3×Dic3D411yescharacteristic
134C2×D3×Dic3D411yescharacteristic
135C4×D32—22no—
136C4×D32—22no—
137#3799—22no—
138#3799—22no—
139#3796—22no—
140#3796—22no—
141#3795—22no—
142#3795—22no—
143D3×Dic6—22no—
144D3×Dic6D414yescomplemented
145C2×C32×C8C2311yescharacteristic
146C32×C4⋊C4C2311yescharacteristic
147#3753—22no—
148#3752—21no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150#3744—22no—
151C3×#214—22no—
152C3×(C2×D3)⋊C4—21no—
153C3×(C2×D3)⋊C4—21no—
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4×Dic3—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×Dic12—22no—
160C3×ΓL(1,𝔽25)—22no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163#3722—21no—
164#3719—22no—
165#3717—22no—
166#3715—22no—
167#3714—22no—
168#3711—22no—
169#3005—91noSylow
170C2×C3×#41—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C23×Dic3—61no—
174D3×#41—64no—
175D3×#41—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×D3×Q8—31no—
179C2×#237—31no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—61no—
184C2×#237—64no—
185C2×#237—61no—
186C2×#237—61no—
187C2×#237—64no—
188C2×#237—61no—
189C2×#237C2×D311yescharacteristic
190C2×D3×D4—61no—
191C2×D3×D4C2×D311yescharacteristic
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×M16—31no—
202C3×C22⋊Q8—31no—
203C3×#117—31no—
204#946—31no—
205C2×#216—31no—
206C2×#215—31no—
207C2×#215—31no—
208C2×#214—31no—
209C2×#214C2×D311yescharacteristic, complemented
210#932—64no—
211C2×#213—31no—
212C2×#213—31no—
213C2×#213—31no—
214C2×#213—61no—
215#930—31no—
216C2×#208—31no—
217#918—64no—
218#914—64no—
219#909—64no—
220C2×Dic12—31no—
221C2×Dic12C2×D311yescharacteristic, complemented
222C2×D24—31no—
223C2×#204—31no—
224C2×#204—31no—
225C2×#204—31no—
226C2×#204—61no—
227C2×ΓL(1,𝔽25)—31no—
228C2×ΓL(1,𝔽25)C2×D311yescharacteristic
229#897—31no—
230#897C2×D311yescharacteristic, complemented
231#895—31no—
232#895—31no—
233#895—31no—
234#895—61no—
235#894—61no—
236#893—61no—
237#892C2×D311yescharacteristic
238#886—61no—
239#882—61no—
240#882—61no—
241#67⋊C4—61no—
242C4×D12—61no—
243C4×D12—61no—
244C3×#103—31no—
245C3×#102—21no—
246C3×#102—31no—
247C3×#102—31no—
248C3×#102—31no—
249C3×#102C2×D311yescharacteristic, complemented
250C3×#102C2×D311yescharacteristic, complemented
251C3×C22⋊C8—31no—
252#835—31no—
253#832C2×D311yescharacteristic, complemented
254#830—31no—
255#821C2×D311yescharacteristic, complemented
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816—31no—
264#810—31no—
265#810—31no—
266#810—31no—
267#810—31no—
268#810—61no—
269#810C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
271C23×C32—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3—24no—
276C22×C3×D3—42no—
277C22×C3×D3—42no—
278C22×C3×D3C2×D411yescharacteristic
279C22×C3×D3C2×D411yescharacteristic
280C2×D32—22no—
281C2×D32—41no—
282C2×D32—41no—
283C32×D4—21no—
284C32×D4C2×D412yes—
285C2×C32×C4—21no—
286C2×C32×C4C2411yescharacteristic
287#638—24no—
288C2×C3⋊Dic3—24no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3C2×D411yescharacteristic
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)—21no—
293C4⋊(C3⋊D3)—42no—
294C4×C3⋊D3—21no—
295C4×C3⋊D3—21no—
296#634—21no—
297#634C2×D412yes—
298C3×#67—24no—
299C3×#67—24no—
300C2×C3×Dic3—24no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3C2×D411yescharacteristic
305C2×C3×Dic3C2×D411yescharacteristic
306C3×D12—21no—
307C3×D12C2×D412yes—
308C3×C4×D3—21no—
309C3×C4×D3—21no—
310C3×C4×D3C2×D412yes—
311C3×C4×D3C2×D412yes—
312C3×Dic6—21no—
313C3×Dic6—21no—
314C3×Dic6—21no—
315C3×Dic6C2×D412yes—
316#627—24no—
317#626—24no—
318#626—42no—
319#626—42no—
320#625—24no—
321#624—22no—
322#624—42no—
323D3×Dic3—24no—
324D3×Dic3—24no—
325D3×Dic3—24no—
326D3×Dic3—22no—
327D3×Dic3—22no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#137—91no—
334C2×AGL(1,ℤ/8)—91no—
335#525—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#449—91no—
341#449—91no—
342#449—91no—
343#449—91no—
344#419—91no—
345#418—31no—
346#407—91no—
347C24×C3—61no—
348C23×D3—21no—
349C23×D3—31no—
350C23×D3—31no—
351C3×#41—62no—
352C3×#41—62no—
353C2×C3×Q8—31no—
354C2×C3×Q8—31no—
355C2×C3×D4—21no—
356C2×C3×D4—34no—
357C2×C3×D4—31no—
358C2×C3×D4—62no—
359C2×C3×D4—61no—
360C2×C3×D4—61no—
361C2×C3×D4C22×D311yescharacteristic
362C2×C3×D4C22×D311yescharacteristic
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—61no—
366C2×#67—21no—
367C2×#67—21no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—68no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—121no—
377C22×Dic3—21no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—68no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—121no—
387#239—62no—
388#239—62no—
389#239—62no—
390#239—62no—
391D3×Q8—34no—
392D3×Q8—62no—
393#237—22no—
394#237—22no—
395#237—62no—
396#237—62no—
397#237—62no—
398#237—62no—
399#237—62no—
400#237—68no—
401#237—68no—
402#237—68no—
403#237—62no—
404#237—62no—
405#237—62no—
406#237—122no—
407#237—122no—
408D3×D4—22no—
409D3×D4—68no—
410D3×D4D1214yescomplemented
411#235—62no—
412#235—62no—
413#235—62no—
414#235—68no—
415#235—62no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12—121no—
425C2×D12C22×D311yescharacteristic
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—61no—
433C2×C4×D3—62no—
434C2×C4×D3—62no—
435C2×C4×D3—61no—
436C2×C4×D3—61no—
437C2×C4×D3—68no—
438C2×C4×D3—61no—
439C2×C4×D3—62no—
440C2×C4×D3—62no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3C22×D311yescharacteristic
444C2×C4×D3C22×D311yescharacteristic
445C2×Dic6—31no—
446C2×Dic6—31no—
447C2×Dic6—34no—
448C2×Dic6—61no—
449C2×Dic6—62no—
450C2×Dic6—61no—
451C2×Dic6—61no—
452C2×Dic6C22×D311yescharacteristic
453C2×Dic6C22×D311yescharacteristic
454C3×Q16—62no—
455C3×SD16—62no—
456C3×M16—62no—
457C2×C3×C8—21no—
458C2×C3×C8—31no—
459C2×C3×C8—31no—
460C2×C3×C8C22×D311yescharacteristic
461C2×C3×C8C22×D311yescharacteristic
462C3×C4⋊C4—21no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—61no—
465C3×C4⋊C4C22×D311yescharacteristic
466C3×C4⋊C4C22×D311yescharacteristic
467C3×C22⋊C4—61no—
468C3×C22⋊C4—61no—
469C3×C42—61no—
470#216—62no—
471#215—62no—
472#215—62no—
473#214—22no—
474#214—62no—
475#213—62no—
476#213—62no—
477#213—62no—
478#213—122no—
479(C2×D3)⋊C4—21no—
480(C2×D3)⋊C4—21no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—121no—
488C4⋊Dic3—21no—
489C4⋊Dic3—61no—
490C4⋊Dic3C22×D311yescharacteristic
491Dic3⋊C4—61no—
492C4×Dic3—21no—
493#208—62no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—61no—
497C2×C3⋊C8C22×D311yescharacteristic
498C2×C3⋊C8C22×D311yescharacteristic
499Dic12—22no—
500Dic12—62no—
501D24—62no—
502#204—62no—
503#204—62no—
504#204—62no—
505#204—122no—
506ΓL(1,𝔽25)—22no—
507ΓL(1,𝔽25)—62no—
508C22×C32—22no—
509C22×C32—41no—
510C22×C32—41no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—41no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—22no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—48no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3#12012yes—
528D32—44no—
529C32×C4—41no—
530C32×C4C22×D411yescharacteristic
531C32×C4C22×D411yescharacteristic
532C3⋊Dic3—21no—
533C3⋊Dic3—22no—
534C3×Dic3—21no—
535C3×Dic3—22no—
536C3×Dic3—41no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—91no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—91no—
544C2×#41—181no—
545C2×#41—181no—
546C2×#41—184no—
547C2×#41—184no—
548C22×Q8—91no—
549C22×D4—31no—
550C22×D4—181no—
551C23×C4—91no—
552C23×C4—181no—
553#137—184no—
554AGL(1,ℤ/8)—184no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—91no—
562C2×D8—91no—
563C2×M16—31no—
564C2×M16—91no—
565#123—181no—
566C22⋊Q8—31no—
567C22⋊Q8—91no—
568#121—91no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—31no—
574#103—31no—
575#103—91no—
576#103—91no—
577#103—91no—
578#102—31no—
579#102—31no—
580#102—31no—
581#102D3211yescharacteristic, complemented
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—31no—
589C23×C3—31no—
590C23×C3—41no—
591C23×C3—64no—
592C23×C3—61no—
593C23×C3—122no—
594C23×C3—122no—
595C22×D3—21no—
596C22×D3—24no—
597C22×D3—31no—
598C22×D3—31no—
599C22×D3—42no—
600C22×D3—42no—
601C22×D3—61no—
602C22×D3—62no—
603C22×D3—62no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—121no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3D3×D411yescharacteristic
612C22×D3D3×D411yescharacteristic
613C3×Q8—32no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8—61no—
617C3×D4—21no—
618C3×D4—21no—
619C3×D4—22no—
620C3×D4—32no—
621C3×D4—41no—
622C3×D4—64no—
623C3×D4—64no—
624C3×D4—61no—
625C3×D4C2×D1212yes—
626C3×D4D3×D412yes—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—31no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—31no—
634C2×C3×C4—41no—
635C2×C3×C4—64no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4C23×D311yescharacteristic
642C2×C3×C4C23×D311yescharacteristic
643#67—24no—
644#67—24no—
645#67—64no—
646#67—64no—
647#67—64no—
648#67—64no—
649#67—64no—
650#67—124no—
651#67—122no—
652#67—122no—
653C2×Dic3—24no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—61no—
660C2×Dic3—64no—
661C2×Dic3—62no—
662C2×Dic3—64no—
663C2×Dic3—64no—
664C2×Dic3—64no—
665C2×Dic3—64no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—62no—
669C2×Dic3—121no—
670C2×Dic3—124no—
671C2×Dic3D3×D411yescharacteristic
672C2×Dic3D3×D411yescharacteristic
673D12—21no—
674D12—64no—
675D12—61no—
676D12—61no—
677D12—61no—
678D12—61no—
679D12—121no—
680D12—121no—
681D12—122no—
682D12—122no—
683D12—122no—
684D12—122no—
685D12—242no—
686D12C2×D1212yes—
687C4×D3—21no—
688C4×D3—21no—
689C4×D3—62no—
690C4×D3—62no—
691C4×D3—64no—
692C4×D3—64no—
693C4×D3—62no—
694C4×D3—64no—
695C4×D3—61no—
696C4×D3—61no—
697C4×D3—61no—
698C4×D3—61no—
699C4×D3—62no—
700C4×D3—121no—
701C4×D3—121no—
702C4×D3—122no—
703C4×D3—122no—
704C4×D3C2×D1212yes—
705C4×D3D3×D412yes—
706Dic6—21no—
707Dic6—21no—
708Dic6—21no—
709Dic6—32no—
710Dic6—32no—
711Dic6—62no—
712Dic6—64no—
713Dic6—61no—
714Dic6—61no—
715Dic6—64no—
716Dic6—121no—
717Dic6D3×D412yes—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—41no—
721C3×C8—61no—
722C3×C8—61no—
723C3⋊C8—21no—
724C3⋊C8—21no—
725C3⋊C8—61no—
726C3⋊C8—61no—
727C3⋊C8—121no—
728C2×C32—42no—
729C2×C32C2×#12011yescharacteristic
730C2×C32#57511yescharacteristic
731C2×C32#57511yescharacteristic
732C3⋊D3—41no—
733C3⋊D3—81no—
734C3×D3—22no—
735C3×D3—41no—
736C3×D3—42no—
737C24—61no—
738C24—91no—
739#41—62no—
740#41—62no—
741#41—182no—
742#41—182no—
743#41—182no—
744#41—182no—
745#41—188no—
746#41—182no—
747#41—182no—
748#41—188no—
749#41—182no—
750#41—182no—
751C2×Q8—31no—
752C2×Q8—31no—
753C2×Q8—94no—
754C2×Q8—91no—
755C2×Q8—181no—
756C2×Q8—182no—
757C2×D4—34no—
758C2×D4—31no—
759C2×D4—62no—
760C2×D4—61no—
761C2×D4—61no—
762C2×D4—91no—
763C2×D4—181no—
764C2×D4—181no—
765C2×D4—181no—
766C2×D4—181no—
767C2×D4—188no—
768C2×D4—181no—
769C2×D4—181no—
770C2×D4C2×D3211yescharacteristic
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—61no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—182no—
779C22×C4—182no—
780C22×C4—181no—
781C22×C4—181no—
782C22×C4—181no—
783C22×C4—181no—
784C22×C4—188no—
785C22×C4—181no—
786Q16—62no—
787Q16—182no—
788SD16—62no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792D8—182no—
793D8—182no—
794M16—62no—
795M16—182no—
796C2×C8—31no—
797C2×C8—31no—
798C2×C8—91no—
799C2×C8C2×D3211yescharacteristic
800C4⋊C4—31no—
801C4⋊C4—61no—
802C4⋊C4—181no—
803C4⋊C4C2×D3211yescharacteristic
804C22⋊C4—61no—
805C22⋊C4—61no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C22⋊C4—181no—
809C42—61no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—21no—
813C22×C3—32no—
814C22×C3—42no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—62no—
825C22×C3—81no—
826C22×C3—81no—
827C22×C3—128no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3C2×D3×D411yescharacteristic
831C22×C3C2×D3×D411yescharacteristic
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—22no—
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—48no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—61no—
842C2×D3—61no—
843C2×D3—61no—
844C2×D3—61no—
845C2×D3—61no—
846C2×D3—61no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—124no—
851C2×D3—124no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—241no—
859C2×D3—241no—
860C2×D3—241no—
861C2×D3#88212yes—
862C3×C4—21no—
863C3×C4—21no—
864C3×C4—32no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—62no—
868C3×C4—61no—
869C3×C4—81no—
870C3×C4—121no—
871C3×C4—121no—
872C3×C4C22×D1211yescharacteristic
873C3×C4C2×D3×D411yescharacteristic
874C3×C4C2×D3×D411yescharacteristic
875C3×C4C2×D3×D411yescharacteristic
876Dic3—22no—
877Dic3—21no—
878Dic3—41no—
879Dic3—41no—
880Dic3—62no—
881Dic3—61no—
882Dic3—62no—
883Dic3—61no—
884Dic3—122no—
885Dic3—121no—
886Dic3#88212yes—
887C32#300511yescharacteristic, complemented, Sylow
888C23—21no—
889C23—31no—
890C23—31no—
891C23—64no—
892C23—61no—
893C23—91no—
894C23—122no—
895C23—122no—
896C23—182no—
897C23—181no—
898C23—361no—
899C23—361no—
900Q8—32no—
901Q8—61no—
902Q8—61no—
903Q8—61no—
904Q8—92no—
905Q8—184no—
906Q8—181no—
907D4—21no—
908D4—32no—
909D4—64no—
910D4—64no—
911D4—61no—
912D4—184no—
913D4—184no—
914D4—184no—
915D4—181no—
916D4—181no—
917D4—362no—
918D4—362no—
919D4—362no—
920D4D3×D1212yes—
921C2×C4—21no—
922C2×C4—31no—
923C2×C4—32no—
924C2×C4—32no—
925C2×C4—31no—
926C2×C4—64no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—91no—
933C2×C4—182no—
934C2×C4—182no—
935C2×C4—182no—
936C2×C4—184no—
937C2×C4—184no—
938C2×C4—184no—
939C2×C4—184no—
940C2×C4—181no—
941C2×C4—181no—
942C2×C4—181no—
943C2×C4—362no—
944C2×C4C22×D3211yescharacteristic
945C8—21no—
946C8—61no—
947C8—61no—
948C8—181no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—42no—
953C2×C3—42no—
954C2×C3—62no—
955C2×C3—82no—
956C2×C3—121no—
957C2×C3—122no—
958C2×C3C2×#88211yescharacteristic
959C2×C3D3×#12011yescharacteristic
960C2×C3#576811yescharacteristic
961C2×C3#577311yescharacteristic
962C2×C3#577311yescharacteristic
963C2×C3#577711yescharacteristic
964D3—22no—
965D3—42no—
966D3—41no—
967D3—121no—
968D3—121no—
969D3—241no—
970D3—241no—
971D3—241no—
972D3—481no—
973C22—22no—
974C22—32no—
975C22—41no—
976C22—41no—
977C22—61no—
978C22—61no—
979C22—61no—
980C22—61no—
981C22—61no—
982C22—62no—
983C22—128no—
984C22—121no—
985C22—121no—
986C22—181no—
987C22—181no—
988C22—181no—
989C22—364no—
990C22—361no—
991C22—361no—
992C22—361no—
993C22D32×D411yescharacteristic
994C4—32no—
995C4—41no—
996C4—61no—
997C4—62no—
998C4—121no—
999C4—121no—
1000C4—181no—
1001C4—182no—
1002C4C2×D3×D1211yescharacteristic
1003C4D32×D411yescharacteristic
1004C3—21no—
1005C3#7892711yescharacteristic, complemented
1006C3#8022711yescharacteristic, complemented
1007C2—42no—
1008C2—62no—
1009C2—121no—
1010C2—122no—
1011C2—361no—
1012C2—721no—
1013C2D3×#88211yescharacteristic
1014C2#1059472911yescharacteristic
1015C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×D3×#237C2semidirect
2. C2×#63934C2semidirect
3. C2×#63801C2semidirect
4. #10594627C2semidirect
5. #10592480C2semidirect
6. C3×#4783C2semidirect
7. C3×#4770C2semidirect
8. #10591466C2semidirect
9. #10591452C2semidirect
10. #10590968C2semidirect
11. #10590965C2semidirect
12. #10590936C2semidirect
13. #10590617C2semidirect
14. #10590614C2semidirect
15. #10590600C2semidirect
32. C2×#3753C22semidirect
33. C2×#3744C22semidirect
34. #64104C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×Dic12C22semidirect
38. C3×#897C22semidirect
42. #63909C22semidirect
46. #63871C22semidirect
47. C2×#3719C22semidirect
48. C2×#3717C22semidirect
49. C2×#3715C22semidirect
50. C2×#3714C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63637C22semidirect
56. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
86. #4783D3semidirect
93. #4770D3semidirect
113. C3×D3×D4D4semidirect
144. D3×Dic6D4semidirect
209. C2×#214C2×D3semidirect
221. C2×Dic12C2×D3semidirect
230. #897C2×D3semidirect
249. C3×#102C2×D3semidirect
250. C3×#102C2×D3semidirect
253. #832C2×D3semidirect
255. #821C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
269. #810C2×D3semidirect
270. #809C2×D3semidirect
410. D3×D4D12semidirect
581. #102D32semidirect
887. C32#3005semidirect
1005. C3#78927semidirect
1006. C3#80227semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×#639342
C2×#638012
#105946272
#105924802
C3×#47832
C3×#47702
#105914662
#105914522
#105909682
#105909652
#105909362
#105906172
#105906142
#105906002
#802273
#789273