Finite Group Databasebeta

← #11864199

Subgroups — #11864199

Order 1152.

1584 conjugacy classes of subgroups.

The subgroup lattice has 997 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic
2C2×#63929C211yesmaximal, characteristic, complemented
3C2×#63800C211yesmaximal, characteristic, complemented
4D3×#897C211yesmaximal, characteristic, complemented
5#10592482C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×#4771C211yesmaximal, characteristic, complemented
8#10591466C211yesmaximal, characteristic, complemented
9#10591459C211yesmaximal, characteristic, complemented
10#10590961C211yesmaximal, characteristic, complemented
11#10590952C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590618C211yesmaximal, characteristic, complemented
14#10590607C211yesmaximal, characteristic, complemented
15#10590604C211yesmaximal, characteristic, complemented
16#80147—31nomaximal
17#78885—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×#3796C2211yescharacteristic
29C2×#3795C2211yescharacteristic
30C2×D3×Dic6C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic, complemented
32C2×#3754C2211yescharacteristic, complemented
33C2×#3746C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic
39C3×D3×C4⋊C4C2211yescharacteristic, complemented
40#63929—24no—
41D3×(C2×D3)⋊C4—21no—
42#63895—21no—
43#63893—21no—
44D3×C4⋊Dic3—21no—
45#63871C2211yescharacteristic, complemented
46#63857C2211yescharacteristic
47C2×#3719C2211yescharacteristic, complemented
48C2×#3719C2211yescharacteristic, complemented
49C2×#3718C2211yescharacteristic, complemented
50C2×#3716C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63800—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
65C2×D3×#41—31no—
66C22×#237—31no—
67C2×#951—31no—
68C2×#915—31no—
69C2×#915—31no—
70C2×#909—31no—
71D3×C22⋊Q8—31no—
72C2×#897—31no—
73C3×#450—31no—
74C3×#417—31no—
75#5218—31no—
76#5173—31no—
77#5173—31no—
78#5126—31no—
79#5050—31no—
80#4966—31no—
81#4809—31no—
82#4809—31no—
83#4808—31no—
84#4808—31no—
85#4783—31no—
86#4783—31no—
87#4783—31no—
88#4783—31no—
89#4783—61no—
90#4776—31no—
91#4776D311yescharacteristic, complemented
92#4771—31no—
93#4771D311yescharacteristic, complemented
94#4739—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⋊D3C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237D414yes—
111C3×D3×D4—22no—
112C3×D3×D4—22no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119D3×#67—28no—
120C2×#627—21no—
121C2×#627—21no—
122C2×#626—21no—
123C2×#625—21no—
124C2×#624D411yescharacteristic
125#3805—28no—
126#3804—28no—
127C2×D3×Dic3—28no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3D411yescharacteristic
133C2×D3×Dic3D411yescharacteristic
134C4×D32—22no—
135C4×D32—22no—
136#3796—22no—
137#3796—22no—
138#3795—22no—
139#3795D414yes—
140D3×Dic6—22no—
141D3×Dic6—22no—
142D3×Dic6—22no—
143D3×Dic6—22no—
144C2×C32×C8C2311yescharacteristic
145C32×C4⋊C4C2311yescharacteristic
146#3754—22no—
147#3752—21no—
148C4⋊(C3⋊Dic3)—21no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150#3746—22no—
151C3×#214—22no—
152C3×(C2×D3)⋊C4—21no—
153C3×C4⋊Dic3—21no—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×Dic3⋊C4—21no—
156C2×C3×C3⋊C8C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C3×#204—22no—
159C3×ΓL(1,𝔽25)—22no—
160Dic3⋊Dic3—21no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164#3719—22no—
165#3719—22no—
166#3718—22no—
167#3716—22no—
168#3711—22no—
169#3007—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×D3×Q8—31no—
178C2×D3×Q8—31no—
179C2×#237—31no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—61no—
184C2×#237—61no—
185C2×#237—61no—
186C2×#237—64no—
187C2×#237—61no—
188C2×#237—64no—
189C2×#237C2×D311yescharacteristic
190C2×D3×D4—61no—
191C2×D3×D4C2×D311yescharacteristic
192C2×#235—31no—
193C2×#235—61no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—61no—
197C22×Dic6—31no—
198C22×Dic6—31no—
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C2×C3×M16—31no—
202C3×C22⋊Q8—31no—
203C2×C3×C4⋊C4—31no—
204#951—64no—
205#946—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#216—31no—
209C2×#216—31no—
210C2×#214—31no—
211C2×#214—31no—
212C2×#214—31no—
213C2×#214—61no—
214C2×#214C2×D311yescharacteristic, complemented
215C2×(C2×D3)⋊C4—61no—
216C2×C4⋊Dic3—61no—
217#924—31no—
218C2×#208—31no—
219#915—64no—
220#915—64no—
221#909—64no—
222C2×Dic12—31no—
223C2×Dic12—31no—
224C2×Dic12—31no—
225C2×Dic12—31no—
226C2×Dic12—61no—
227C2×#204—31no—
228C2×#204C2×D311yescharacteristic, complemented
229C2×ΓL(1,𝔽25)—31no—
230C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
231#897—31no—
232#897—31no—
233#897—31no—
234#897—31no—
235#897—61no—
236#897—61no—
237#897—61no—
238#897C2×D311yescharacteristic
239#896—61no—
240D3×C4⋊C4—61no—
241D3×C4⋊C4C2×D311yescharacteristic, complemented
242D3×C22⋊C4—61no—
243#878—61no—
244C3×#103—31no—
245C3×#103—31no—
246C3×#102—21no—
247C3×#102—31no—
248C3×#102—31no—
249C3×#102C2×D311yescharacteristic, complemented
250C3×#102C2×D311yescharacteristic, complemented
251C3×C22⋊C8—31no—
252#832—31no—
253#832C2×D311yescharacteristic, complemented
254#830—31no—
255(C2×D3)⋊C8—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—61no—
261(C2×D3)⋊C8C2×D311yescharacteristic
262#816—31no—
263#816C2×D311yescharacteristic, complemented
264#810—31no—
265#810—31no—
266#810—31no—
267#810—61no—
268#810C2×D311yescharacteristic, complemented
269#809—31no—
270#809C2×D311yescharacteristic, complemented
271C23×C32—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—24no—
274C22×C3×D3—21no—
275C22×C3×D3—42no—
276C22×C3×D3—42no—
277C22×C3×D3C2×D411yescharacteristic
278C22×C3×D3C2×D411yescharacteristic
279C2×D32—22no—
280C2×D32—22no—
281C2×D32—41no—
282C32×D4—21no—
283C32×D4C2×D412yes—
284C2×C32×C4—21no—
285C2×C32×C4C2411yescharacteristic
286#638—24no—
287C2×C3⋊Dic3—24no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3C2×D411yescharacteristic
291C4×C3⋊D3—21no—
292C4×C3⋊D3—21no—
293#634—21no—
294#634—21no—
295#634—21no—
296#634C2×D412yes—
297C3×#67—24no—
298C3×#67—24no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—24no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×D12—21no—
306C3×D12C2×D412yes—
307C3×C4×D3—21no—
308C3×C4×D3—21no—
309C3×C4×D3—42no—
310C3×C4×D3C2×D412yes—
311C3×C4×D3C2×D412yes—
312C3×Dic6—21no—
313C3×Dic6—21no—
314C3×Dic6—21no—
315C3×Dic6C2×D412yes—
316#627—24no—
317#627—42no—
318#626—24no—
319#625—24no—
320#624—22no—
321D3×Dic3—24no—
322D3×Dic3—24no—
323D3×Dic3—22no—
324D3×Dic3—24no—
325D3×Dic3—22no—
326D3×Dic3—42no—
327C32×C8—21no—
328C3⋊(C3⋊C8)—21no—
329C3×C3⋊C8—21no—
330C3×C3⋊C8—21no—
331C22×#41—91no—
332C2×#137—91no—
333C2×#137—91no—
334C2×C22⋊Q8—91no—
335#452—91no—
336#452—91no—
337#452—91no—
338#452—91no—
339#451—91no—
340#451—91no—
341#450—31no—
342#450—91no—
343#417—31no—
344#417—91no—
345#407—91no—
346C24×C3—61no—
347C23×D3—21no—
348C23×D3—31no—
349C23×D3—31no—
350C3×#41—34no—
351C3×#41—62no—
352C2×C3×Q8—31no—
353C2×C3×Q8—31no—
354C2×C3×D4—21no—
355C2×C3×D4—31no—
356C2×C3×D4—61no—
357C2×C3×D4—62no—
358C2×C3×D4—61no—
359C2×C3×D4—62no—
360C2×C3×D4C22×D311yescharacteristic
361C2×C3×D4C22×D311yescharacteristic
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—61no—
365C22×C3×C4—61no—
366C2×#67—21no—
367C2×#67—21no—
368C2×#67—61no—
369C2×#67—68no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—121no—
375C22×Dic3—21no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—68no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—121no—
386#239—62no—
387#239—62no—
388D3×Q8—62no—
389D3×Q8—62no—
390D3×Q8—62no—
391D3×Q8—62no—
392#237—22no—
393#237—34no—
394#237—62no—
395#237—62no—
396#237—62no—
397#237—68no—
398#237—68no—
399#237—68no—
400#237—62no—
401#237—62no—
402#237—62no—
403#237—62no—
404#237—122no—
405#237—122no—
406#237D1214yes—
407D3×D4—22no—
408D3×D4—22no—
409D3×D4—68no—
410#235—34no—
411#235—62no—
412#235—68no—
413C2×D12—61no—
414C2×D12C22×D311yescharacteristic
415C2×C4×D3—21no—
416C2×C4×D3—31no—
417C2×C4×D3—31no—
418C2×C4×D3—31no—
419C2×C4×D3—31no—
420C2×C4×D3—31no—
421C2×C4×D3—31no—
422C2×C4×D3—61no—
423C2×C4×D3—62no—
424C2×C4×D3—62no—
425C2×C4×D3—61no—
426C2×C4×D3—61no—
427C2×C4×D3—68no—
428C2×C4×D3—61no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—61no—
432C2×C4×D3C22×D311yescharacteristic
433C2×C4×D3C22×D311yescharacteristic
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6—31no—
438C2×Dic6—61no—
439C2×Dic6—61no—
440C2×Dic6—62no—
441C2×Dic6—62no—
442C2×Dic6—62no—
443C2×Dic6—61no—
444C2×Dic6—61no—
445C2×Dic6—62no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×SD16—62no—
451C3×SD16—62no—
452C3×M16—62no—
453C2×C3×C8—21no—
454C2×C3×C8—31no—
455C2×C3×C8—31no—
456C2×C3×C8C22×D311yescharacteristic
457C2×C3×C8C22×D311yescharacteristic
458C3×C4⋊C4—21no—
459C3×C4⋊C4—31no—
460C3×C4⋊C4—61no—
461C3×C4⋊C4—61no—
462C3×C4⋊C4C22×D311yescharacteristic
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C22⋊C4—61no—
465#217—61no—
466#216—62no—
467#216—62no—
468#216—62no—
469#216—62no—
470#214—22no—
471#214—62no—
472#214—62no—
473#214—62no—
474#214—122no—
475(C2×D3)⋊C4—21no—
476(C2×D3)⋊C4—61no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—121no—
482C4⋊Dic3—21no—
483C4⋊Dic3—61no—
484C4⋊Dic3—61no—
485C4⋊Dic3—61no—
486C4⋊Dic3—61no—
487C4⋊Dic3—121no—
488C4⋊Dic3C22×D311yescharacteristic
489Dic3⋊C4—21no—
490Dic3⋊C4—61no—
491Dic3⋊C4—61no—
492#208—62no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—61no—
496C2×C3⋊C8C22×D311yescharacteristic
497C2×C3⋊C8C22×D311yescharacteristic
498Dic12—62no—
499Dic12—62no—
500Dic12—62no—
501Dic12—62no—
502Dic12—122no—
503#204—22no—
504#204—62no—
505ΓL(1,𝔽25)—22no—
506ΓL(1,𝔽25)—62no—
507C22×C32—22no—
508C22×C32—41no—
509C22×C32—41no—
510C22×C32C22×D411yescharacteristic
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3×D3—21no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
519C2×C3×D3—48no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3#12012yes—
523C2×C3×D3#13712yescomplemented
524D32—44no—
525C32×C4—41no—
526C32×C4C22×D411yescharacteristic
527C32×C4C22×D411yescharacteristic
528C3⋊Dic3—21no—
529C3⋊Dic3—22no—
530C3⋊Dic3—41no—
531C3×Dic3—22no—
532C3×Dic3—21no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C3×Dic3#12012yes—
536C2×#41—31no—
537C2×#41—91no—
538C2×#41—91no—
539C2×#41—91no—
540C2×#41—181no—
541C2×#41—181no—
542C2×#41—184no—
543C2×#41—184no—
544C22×Q8—91no—
545C22×Q8—91no—
546C22×D4—31no—
547C22×D4—181no—
548C23×C4—91no—
549C23×C4—181no—
550#137—184no—
551#137—184no—
552C2×Q16—91no—
553C2×Q16—91no—
554C2×Q16—91no—
555C2×Q16—91no—
556C2×SD16—31no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×M16—31no—
561C2×M16—91no—
562C22⋊Q8—31no—
563C22⋊Q8—91no—
564C22⋊Q8—91no—
565C22⋊Q8—91no—
566C22⋊Q8—181no—
567C22⋊Q8—181no—
568C2×C4⋊C4—31no—
569C2×C4⋊C4—181no—
570C2×C22⋊C4—181no—
571#103—31no—
572#103—31no—
573#103—91no—
574#103—91no—
575#102—31no—
576#102—31no—
577#102—91no—
578#102D3211yescharacteristic, complemented
579C22⋊C8—31no—
580C22⋊C8—91no—
581C22⋊C8—91no—
582C22⋊C8—91no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—31no—
586C23×C3—31no—
587C23×C3—41no—
588C23×C3—64no—
589C23×C3—61no—
590C23×C3—122no—
591C23×C3—122no—
592C22×D3—24no—
593C22×D3—21no—
594C22×D3—31no—
595C22×D3—31no—
596C22×D3—42no—
597C22×D3—42no—
598C22×D3—61no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3D3×D411yescharacteristic
606C22×D3D3×D411yescharacteristic
607C3×Q8—32no—
608C3×Q8—61no—
609C3×Q8—61no—
610C3×Q8—61no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—22no—
614C3×D4—32no—
615C3×D4—41no—
616C3×D4—64no—
617C3×D4—64no—
618C3×D4—61no—
619C3×D4C2×D1212yes—
620C3×D4D3×D412yes—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—31no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—31no—
628C2×C3×C4—41no—
629C2×C3×C4—64no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—122no—
636C2×C3×C4C23×D311yescharacteristic
637C2×C3×C4C23×D311yescharacteristic
638#67—24no—
639#67—24no—
640#67—64no—
641#67—64no—
642#67—64no—
643#67—64no—
644#67—64no—
645#67—124no—
646C2×Dic3—21no—
647C2×Dic3—24no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—31no—
651C2×Dic3—31no—
652C2×Dic3—61no—
653C2×Dic3—62no—
654C2×Dic3—64no—
655C2×Dic3—64no—
656C2×Dic3—64no—
657C2×Dic3—64no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—62no—
661C2×Dic3—64no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—121no—
665C2×Dic3—124no—
666C2×Dic3—121no—
667C2×Dic3—122no—
668C2×Dic3D3×D411yescharacteristic
669C2×Dic3D3×D411yescharacteristic
670D12—21no—
671D12—64no—
672D12D3×D412yes—
673C4×D3—21no—
674C4×D3—21no—
675C4×D3—42no—
676C4×D3—62no—
677C4×D3—62no—
678C4×D3—64no—
679C4×D3—64no—
680C4×D3—64no—
681C4×D3—62no—
682C4×D3—61no—
683C4×D3—61no—
684C4×D3—61no—
685C4×D3—61no—
686C4×D3—62no—
687C4×D3—121no—
688C4×D3—121no—
689C4×D3—122no—
690C4×D3C2×D1212yes—
691C4×D3D3×D412yes—
692Dic6—21no—
693Dic6—21no—
694Dic6—21no—
695Dic6—32no—
696Dic6—32no—
697Dic6—62no—
698Dic6—64no—
699Dic6—64no—
700Dic6—61no—
701Dic6—61no—
702Dic6—61no—
703Dic6—61no—
704Dic6—61no—
705Dic6—61no—
706Dic6—121no—
707Dic6—121no—
708Dic6—121no—
709Dic6—122no—
710Dic6—122no—
711Dic6C2×D1212yes—
712C3×C8—21no—
713C3×C8—21no—
714C3×C8—41no—
715C3×C8—61no—
716C3×C8—61no—
717C3⋊C8—21no—
718C3⋊C8—21no—
719C3⋊C8—61no—
720C3⋊C8—61no—
721C3⋊C8—121no—
722C2×C32—42no—
723C2×C32C2×#12011yescharacteristic
724C2×C32C2×#13711yescharacteristic
725C2×C32#57511yescharacteristic
726C3⋊D3—41no—
727C3×D3—22no—
728C3×D3—22no—
729C3×D3—42no—
730C24—61no—
731C24—91no—
732#41—34no—
733#41—62no—
734#41—94no—
735#41—182no—
736#41—188no—
737#41—182no—
738#41—182no—
739#41—188no—
740#41—182no—
741#41—182no—
742C2×Q8—31no—
743C2×Q8—31no—
744C2×Q8—91no—
745C2×Q8—91no—
746C2×Q8—181no—
747C2×Q8—181no—
748C2×Q8—182no—
749C2×Q8—182no—
750C2×Q8—182no—
751C2×Q8—182no—
752C2×D4—31no—
753C2×D4—61no—
754C2×D4—62no—
755C2×D4—61no—
756C2×D4—62no—
757C2×D4—181no—
758C2×D4—188no—
759C2×D4—181no—
760C2×D4—181no—
761C2×D4C2×D3211yescharacteristic
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—91no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—182no—
771C22×C4—182no—
772C22×C4—181no—
773C22×C4—181no—
774C22×C4—181no—
775C22×C4—188no—
776C22×C4—181no—
777C22×C4—181no—
778Q16—182no—
779Q16—182no—
780Q16—182no—
781Q16—182no—
782SD16—62no—
783SD16—62no—
784SD16—182no—
785SD16—182no—
786M16—62no—
787M16—182no—
788C2×C8—31no—
789C2×C8—31no—
790C2×C8—91no—
791C2×C8C2×D3211yescharacteristic
792C4⋊C4—31no—
793C4⋊C4—61no—
794C4⋊C4—61no—
795C4⋊C4—181no—
796C4⋊C4—181no—
797C4⋊C4—181no—
798C4⋊C4C2×D3211yescharacteristic
799C22⋊C4—61no—
800C22⋊C4—181no—
801C22⋊C4—181no—
802C22⋊C4—181no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—21no—
806C22×C3—32no—
807C22×C3—32no—
808C22×C3—42no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—62no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3—128no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3C2×D3×D411yescharacteristic
824C22×C3C2×D3×D411yescharacteristic
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—22no—
830C2×D3—48no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—124no—
843C2×D3—124no—
844C2×D3#88212yes—
845C2×D3#91512yescomplemented
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—32no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—61no—
852C3×C4—62no—
853C3×C4—81no—
854C3×C4—121no—
855C3×C4—121no—
856C3×C4C22×D1211yescharacteristic
857C3×C4C2×D3×D411yescharacteristic
858C3×C4C2×D3×D411yescharacteristic
859C3×C4C2×D3×D411yescharacteristic
860Dic3—22no—
861Dic3—21no—
862Dic3—41no—
863Dic3—41no—
864Dic3—62no—
865Dic3—61no—
866Dic3—62no—
867Dic3—61no—
868Dic3—122no—
869Dic3—121no—
870Dic3—121no—
871Dic3—121no—
872Dic3—241no—
873Dic3#88212yes—
874C32#300711yescharacteristic, complemented, Sylow
875C23—21no—
876C23—31no—
877C23—31no—
878C23—64no—
879C23—61no—
880C23—91no—
881C23—122no—
882C23—122no—
883C23—182no—
884C23—182no—
885C23—361no—
886Q8—32no—
887Q8—61no—
888Q8—61no—
889Q8—61no—
890Q8—92no—
891Q8—184no—
892Q8—181no—
893Q8—181no—
894Q8—181no—
895Q8—362no—
896D4—21no—
897D4—32no—
898D4—64no—
899D4—64no—
900D4—61no—
901D4—184no—
902D4—184no—
903D4—184no—
904D4D3×D1212yes—
905C2×C4—21no—
906C2×C4—31no—
907C2×C4—32no—
908C2×C4—32no—
909C2×C4—31no—
910C2×C4—64no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—91no—
917C2×C4—122no—
918C2×C4—182no—
919C2×C4—182no—
920C2×C4—184no—
921C2×C4—182no—
922C2×C4—184no—
923C2×C4—184no—
924C2×C4—184no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4—181no—
928C2×C4—181no—
929C2×C4—362no—
930C2×C4C22×D3211yescharacteristic
931C8—21no—
932C8—61no—
933C8—61no—
934C8—181no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—42no—
939C2×C3—42no—
940C2×C3—62no—
941C2×C3—62no—
942C2×C3—82no—
943C2×C3—122no—
944C2×C3C2×#88211yescharacteristic
945C2×C3D3×#12011yescharacteristic
946C2×C3C2×#91511yescharacteristic
947C2×C3#577311yescharacteristic
948C2×C3#577311yescharacteristic
949C2×C3D3×#13711yescharacteristic
950D3—22no—
951D3—22no—
952D3—42no—
953D3—121no—
954D3—121no—
955D3—241no—
956C22—22no—
957C22—32no—
958C22—32no—
959C22—41no—
960C22—41no—
961C22—61no—
962C22—61no—
963C22—61no—
964C22—61no—
965C22—62no—
966C22—128no—
967C22—121no—
968C22—121no—
969C22—181no—
970C22—181no—
971C22—181no—
972C22—364no—
973C22D32×D411yescharacteristic
974C4—32no—
975C4—41no—
976C4—61no—
977C4—62no—
978C4—121no—
979C4—121no—
980C4—181no—
981C4—182no—
982C4—361no—
983C4C2×D3×D1211yescharacteristic
984C4D32×D411yescharacteristic
985C3—21no—
986C3#7888511yescharacteristic, complemented
987C3#8014711yescharacteristic, complemented
988C2—42no—
989C2—62no—
990C2—62no—
991C2—122no—
992C2—361no—
993C2D3×#88211yescharacteristic
994C2#1059472811yescharacteristic
995C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D3×#237C2
hypercenter#102D32
hypocenterC32#3007
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
2. C2×#63929C2semidirect
3. C2×#63800C2semidirect
4. D3×#897C2semidirect
5. #10592482C2semidirect
6. C3×#4776C2semidirect
7. C3×#4771C2semidirect
8. #10591466C2semidirect
9. #10591459C2semidirect
10. #10590961C2semidirect
11. #10590952C2semidirect
12. #10590936C2semidirect
13. #10590618C2semidirect
14. #10590607C2semidirect
15. #10590604C2semidirect
31. C2×D3×Dic6C22semidirect
32. C2×#3754C22semidirect
33. C2×#3746C22semidirect
34. #64106C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C3×D3×C4⋊C4C22semidirect
45. #63871C22semidirect
47. C2×#3719C22semidirect
48. C2×#3719C22semidirect
49. C2×#3718C22semidirect
50. C2×#3716C22semidirect
51. C2×#3711C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63637C22semidirect
56. C3×#832C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63567C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
91. #4776D3semidirect
93. #4771D3semidirect
214. C2×#214C2×D3semidirect
228. C2×#204C2×D3semidirect
230. C2×ΓL(1,𝔽25)C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
249. C3×#102C2×D3semidirect
250. C3×#102C2×D3semidirect
253. #832C2×D3semidirect
263. #816C2×D3semidirect
268. #810C2×D3semidirect
270. #809C2×D3semidirect
523. C2×C3×D3#137semidirect
578. #102D32semidirect
845. C2×D3#915semidirect
874. C32#3007semidirect
986. C3#78885semidirect
987. C3#80147semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×#639292
C2×#638002
D3×#8972
#105924822
C3×#47762
C3×#47712
#105914662
#105914592
#105909612
#105909522
#105909362
#105906182
#105906072
#105906042
#801473
#788853