Finite Group Databasebeta

← #11864228

Subgroups — #11864228

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×#239C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic, complemented
3C2×#63801C211yesmaximal, characteristic, complemented
4D3×#897C211yesmaximal, characteristic, complemented
5#10592507C211yesmaximal, characteristic, complemented
6C3×#4809C211yesmaximal, characteristic, complemented
7C3×#4803C211yesmaximal, characteristic, complemented
8#10591602C211yesmaximal, characteristic, complemented
9#10591595C211yesmaximal, characteristic, complemented
10#10590965C211yesmaximal, characteristic, complemented
11#10590946C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590618C211yesmaximal, characteristic, complemented
14#10590609C211yesmaximal, characteristic, complemented
15#10590596C211yesmaximal, characteristic, complemented
16#80184—31nomaximal
17#78885—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21D3×#239—24no—
22D3×#239—24no—
23C2×D3×D12—21no—
24C2×D3×D12C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32C2211yescharacteristic
27C2×#3799—21no—
28C2×#3799C2211yescharacteristic
29C2×#3796—21no—
30C2×#3796C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic, complemented
32C2×#3756C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic
39C3×D3×C4⋊C4C2211yescharacteristic, complemented
40#63943—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×#3717C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63801—24no—
53C32×#103C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×#951—31no—
68C2×#918—31no—
69C2×#918—31no—
70C2×#909—31no—
71D3×C22⋊Q8—31no—
72C2×#897—31no—
73C3×#451—31no—
74C3×#417—31no—
75#5228—31no—
76#5187—31no—
77#5187—31no—
78#5126—31no—
79#5046—31no—
80#4966—31no—
81#4809—31no—
82#4809D311yescharacteristic, complemented
83#4808—31no—
84#4808—31no—
85#4808—31no—
86#4808—31no—
87#4808—61no—
88#4803—31no—
89#4803D311yescharacteristic, complemented
90#4783—31no—
91#4783—31no—
92#4776—31no—
93#4776—31no—
94#4731—31no—
95#4726—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99#3832—22no—
100#3832—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C3×#239—22no—
107C3×#239D414yes—
108C3×D3×Q8—22no—
109C3×D3×Q8—22no—
110C2×C3×D12—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×#627—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#624—21no—
125C2×#624D411yescharacteristic
126C2×D3×Dic3—21no—
127C2×D3×Dic3—21no—
128C2×D3×Dic3D411yescharacteristic
129C2×D3×Dic3D411yescharacteristic
130D3×D12—28no—
131D3×D12—22no—
132D3×D12—22no—
133C4×D32—28no—
134C4×D32—22no—
135C4×D32—22no—
136#3799—28no—
137#3799—22no—
138#3799D414yes—
139#3796—28no—
140#3796—22no—
141#3796—22no—
142D3×Dic6—22no—
143D3×Dic6—22no—
144C2×C32×C8C2311yescharacteristic
145C32×C4⋊C4C2311yescharacteristic
146#3756—22no—
147#3752—21no—
148C4⋊(C3⋊Dic3)—21no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150#3744—22no—
151C3×#216—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×Dic12—22no—
159C3×ΓL(1,𝔽25)—22no—
160Dic3⋊Dic3—21no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164#3719—22no—
165#3717—22no—
166#3716—22no—
167#3715—22no—
168#3711—22no—
169#3007—91noSylow
170C2×C3×#41—31no—
171C22×C3×Q8—31no—
172D3×#41—64no—
173D3×#41—64no—
174C2×#239—31no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—61no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—64no—
182C2×#239—64no—
183C2×#239C2×D311yescharacteristic
184C2×D3×Q8—31no—
185C2×D3×Q8C2×D311yescharacteristic
186C2×#237—31no—
187C2×#237—61no—
188C2×D3×D4—31no—
189C2×D3×D4—61no—
190C2×#235—31no—
191C2×#235—61no—
192C22×D12—31no—
193C22×D12—61no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—61no—
197C22×C4×D3—61no—
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×Q16—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—61no—
210C2×#216C2×D311yescharacteristic, complemented
211C2×#215—31no—
212C2×#215—31no—
213C2×#214—31no—
214C2×#214—31no—
215C2×(C2×D3)⋊C4—61no—
216C2×C4⋊Dic3—61no—
217#924—31no—
218C2×#208—31no—
219#918—64no—
220#918—64no—
221#909—64no—
222C2×Dic12—31no—
223C2×Dic12C2×D311yescharacteristic, complemented
224C2×#204—31no—
225C2×#204—31no—
226C2×#204—31no—
227C2×#204—31no—
228C2×#204—61no—
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—21no—
245C3×#103—31no—
246C3×#103—31no—
247C3×#103C2×D311yescharacteristic, complemented
248C3×#103C2×D311yescharacteristic, complemented
249C3×#102—31no—
250C3×#102—31no—
251C3×C22⋊C8—31no—
252#835—31no—
253#835C2×D311yescharacteristic, complemented
254#830—31no—
255#821—31no—
256#821C2×D311yescharacteristic, complemented
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—61no—
263(C2×D3)⋊C8C2×D311yescharacteristic
264#810—31no—
265#810C2×D311yescharacteristic, complemented
266#809—31no—
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C22×C3⋊D3—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3C2×D411yescharacteristic
275C22×C3×D3C2×D411yescharacteristic
276C2×D32—24no—
277C2×D32—22no—
278C2×D32—22no—
279C2×D32—41no—
280C2×D32—42no—
281C2×D32—42no—
282C32×Q8—21no—
283C32×Q8C2×D412yes—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4C2411yescharacteristic
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3C2×D411yescharacteristic
289C4⋊(C3⋊D3)—24no—
290C4⋊(C3⋊D3)—21no—
291C4⋊(C3⋊D3)C2×D412yes—
292C4×C3⋊D3—24no—
293C4×C3⋊D3—21no—
294C4×C3⋊D3—21no—
295#634—21no—
296#634—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3C2×D411yescharacteristic
301C2×C3×Dic3C2×D411yescharacteristic
302C3×D12—24no—
303C3×D12—21no—
304C3×D12C2×D412yes—
305C3×C4×D3—24no—
306C3×C4×D3—21no—
307C3×C4×D3—21no—
308C3×C4×D3—24no—
309C3×C4×D3—42no—
310C3×C4×D3C2×D412yes—
311C3×C4×D3C2×D412yes—
312C3×Dic6—24no—
313C3×Dic6—21no—
314C3×Dic6—21no—
315C3×Dic6—21no—
316C3×Dic6C2×D412yes—
317#627—42no—
318#626—24no—
319#626—24no—
320#626—24no—
321#624—22no—
322#624—24no—
323D3×Dic3—24no—
324D3×Dic3—22no—
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—31no—
340#451—91no—
341#450—91no—
342#450—91no—
343#417—31no—
344#417—91no—
345#407—91no—
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—61no—
349C23×D3—61no—
350C3×#41—34no—
351C3×#41—62no—
352C2×C3×Q8—21no—
353C2×C3×Q8—31no—
354C2×C3×Q8—31no—
355C2×C3×Q8—61no—
356C2×C3×Q8—62no—
357C2×C3×Q8—62no—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×D4—31no—
361C2×C3×D4—61no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—61no—
365C22×C3×C4—61no—
366C22×C3×C4—61no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—61no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374#239—22no—
375#239—34no—
376#239—68no—
377#239—62no—
378#239—68no—
379#239—62no—
380#239—62no—
381#239—62no—
382#239—62no—
383#239—62no—
384#239—62no—
385#239—122no—
386#239—122no—
387#239D1214yes—
388D3×Q8—22no—
389D3×Q8—22no—
390D3×Q8—62no—
391D3×Q8—62no—
392#237—62no—
393#237—68no—
394#237—62no—
395D3×D4—62no—
396D3×D4—62no—
397D3×D4—68no—
398#235—34no—
399#235—62no—
400#235—68no—
401C2×D12—21no—
402C2×D12—31no—
403C2×D12—31no—
404C2×D12—61no—
405C2×D12—62no—
406C2×D12—68no—
407C2×D12—61no—
408C2×D12—61no—
409C2×D12—61no—
410C2×D12—61no—
411C2×D12—61no—
412C2×D12—62no—
413C2×D12—121no—
414C2×D12C22×D311yescharacteristic
415C2×C4×D3—21no—
416C2×C4×D3—21no—
417C2×C4×D3—21no—
418C2×C4×D3—31no—
419C2×C4×D3—31no—
420C2×C4×D3—31no—
421C2×C4×D3—31no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—61no—
425C2×C4×D3—62no—
426C2×C4×D3—62no—
427C2×C4×D3—68no—
428C2×C4×D3—68no—
429C2×C4×D3—61no—
430C2×C4×D3—61no—
431C2×C4×D3—61no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
434C2×C4×D3—62no—
435C2×C4×D3—62no—
436C2×C4×D3—61no—
437C2×C4×D3—121no—
438C2×C4×D3C22×D311yescharacteristic
439C2×C4×D3C22×D311yescharacteristic
440C2×Dic6—21no—
441C2×Dic6—31no—
442C2×Dic6—31no—
443C2×Dic6—61no—
444C2×Dic6—62no—
445C2×Dic6—62no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—62no—
451C3×Q16—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—22no—
467#216—62no—
468#216—62no—
469#216—62no—
470#216—122no—
471#215—62no—
472#215—62no—
473#214—62no—
474#214—62no—
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—22no—
499Dic12—62no—
500#204—62no—
501#204—62no—
502#204—62no—
503#204—62no—
504#204—122no—
505ΓL(1,𝔽25)—22no—
506ΓL(1,𝔽25)—62no—
507C22×C32C22×D411yescharacteristic
508C2×C3⋊D3—21no—
509C2×C3⋊D3—22no—
510C2×C3⋊D3—21no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—41no—
513C2×C3⋊D3—41no—
514C2×C3×D3—21no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
519C2×C3×D3—41no—
520C2×C3×D3—41no—
521C2×C3×D3#12012yes—
522C2×C3×D3#13712yescomplemented
523D32—44no—
524D32—48no—
525C32×C4—22no—
526C32×C4—41no—
527C32×C4C22×D411yescharacteristic
528C32×C4C22×D411yescharacteristic
529C3⋊Dic3—21no—
530C3⋊Dic3—41no—
531C3×Dic3—21no—
532C3×Dic3—22no—
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—31no—
545C22×Q8—91no—
546C22×D4—91no—
547C22×D4—181no—
548C23×C4—91no—
549C23×C4—181no—
550#137—184no—
551#137—184no—
552C2×Q16—31no—
553C2×Q16—31no—
554C2×Q16—91no—
555C2×Q16—91no—
556C2×SD16—91no—
557C2×SD16—91no—
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#103D3211yescharacteristic, complemented
575#102—31no—
576#102—31no—
577#102—91no—
578#102—91no—
579C22⋊C8—31no—
580C22⋊C8—91no—
581C22⋊C8—91no—
582C22⋊C8—91no—
583C23×C3—31no—
584C23×C3—31no—
585C23×C3—61no—
586C22×D3—21no—
587C22×D3—31no—
588C22×D3—31no—
589C22×D3—61no—
590C22×D3—62no—
591C22×D3—62no—
592C22×D3—64no—
593C22×D3—64no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—121no—
599C22×D3—121no—
600C22×D3—121no—
601C22×D3—122no—
602C22×D3—122no—
603C22×D3—122no—
604C22×D3—122no—
605C22×D3D3×D411yescharacteristic
606C22×D3D3×D411yescharacteristic
607C3×Q8—21no—
608C3×Q8—21no—
609C3×Q8—22no—
610C3×Q8—32no—
611C3×Q8—41no—
612C3×Q8—64no—
613C3×Q8—61no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8C2×D1212yes—
617C3×Q8D3×D412yes—
618C3×D4—32no—
619C3×D4—64no—
620C3×D4—61no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—31no—
627C2×C3×C4—32no—
628C2×C3×C4—32no—
629C2×C3×C4—31no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—64no—
633C2×C3×C4—64no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—122no—
640C2×C3×C4C23×D311yescharacteristic
641C2×C3×C4C23×D311yescharacteristic
642#67—64no—
643#67—64no—
644#67—64no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—31no—
649C2×Dic3—31no—
650C2×Dic3—61no—
651C2×Dic3—62no—
652C2×Dic3—64no—
653C2×Dic3—62no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—121no—
657C2×Dic3—122no—
658C2×Dic3D3×D411yescharacteristic
659C2×Dic3D3×D411yescharacteristic
660D12—24no—
661D12—21no—
662D12—32no—
663D12—32no—
664D12—62no—
665D12—64no—
666D12—64no—
667D12—64no—
668D12—64no—
669D12—64no—
670D12—61no—
671D12—61no—
672D12—121no—
673D12—124no—
674D12C2×D1212yes—
675C4×D3—24no—
676C4×D3—21no—
677C4×D3—21no—
678C4×D3—24no—
679C4×D3—42no—
680C4×D3—62no—
681C4×D3—64no—
682C4×D3—64no—
683C4×D3—64no—
684C4×D3—62no—
685C4×D3—64no—
686C4×D3—62no—
687C4×D3—61no—
688C4×D3—61no—
689C4×D3—61no—
690C4×D3—61no—
691C4×D3—62no—
692C4×D3—64no—
693C4×D3—121no—
694C4×D3—121no—
695C4×D3—124no—
696C4×D3—122no—
697C4×D3C2×D1212yes—
698C4×D3D3×D412yes—
699Dic6—24no—
700Dic6—21no—
701Dic6—21no—
702Dic6—21no—
703Dic6—61no—
704Dic6—61no—
705Dic6—61no—
706Dic6—61no—
707Dic6—121no—
708Dic6—121no—
709Dic6—122no—
710Dic6—122no—
711Dic6D3×D412yes—
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×C32C2×#12011yescharacteristic
723C2×C32C2×#13711yescharacteristic
724C2×C32#57511yescharacteristic
725C3⋊D3—41no—
726C3⋊D3—42no—
727C3×D3—22no—
728C3×D3—22no—
729C3×D3—42no—
730C24—91no—
731C24—181no—
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—61no—
745C2×Q8—62no—
746C2×Q8—62no—
747C2×Q8—91no—
748C2×Q8—181no—
749C2×Q8—182no—
750C2×Q8—182no—
751C2×Q8C2×D3211yescharacteristic
752C2×D4—31no—
753C2×D4—61no—
754C2×D4—91no—
755C2×D4—181no—
756C2×D4—181no—
757C2×D4—182no—
758C2×D4—182no—
759C2×D4—188no—
760C2×D4—181no—
761C2×D4—181no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—181no—
772C22×C4—182no—
773C22×C4—182no—
774C22×C4—181no—
775C22×C4—188no—
776C22×C4—181no—
777C22×C4—181no—
778Q16—62no—
779Q16—62no—
780Q16—182no—
781Q16—182no—
782SD16—182no—
783SD16—182no—
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—21no—
804C22×C3—32no—
805C22×C3—32no—
806C22×C3—61no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—62no—
811C22×C3—121no—
812C22×C3—121no—
813C22×C3C2×D3×D411yescharacteristic
814C22×C3C2×D3×D411yescharacteristic
815C2×D3—21no—
816C2×D3—21no—
817C2×D3—21no—
818C2×D3—21no—
819C2×D3—22no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—62no—
823C2×D3—61no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—62no—
829C2×D3—61no—
830C2×D3—122no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—124no—
835C2×D3—124no—
836C2×D3—128no—
837C2×D3—128no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—241no—
843C2×D3—241no—
844C2×D3#88212yes—
845C2×D3#91812yescomplemented
846C3×C4—22no—
847C3×C4—22no—
848C3×C4—21no—
849C3×C4—21no—
850C3×C4—32no—
851C3×C4—42no—
852C3×C4—41no—
853C3×C4—41no—
854C3×C4—61no—
855C3×C4—62no—
856C3×C4—81no—
857C3×C4—121no—
858C3×C4—121no—
859C3×C4C22×D1211yescharacteristic
860C3×C4C2×D3×D411yescharacteristic
861C3×C4C2×D3×D411yescharacteristic
862C3×C4C2×D3×D411yescharacteristic
863Dic3—21no—
864Dic3—22no—
865Dic3—41no—
866Dic3—41no—
867Dic3—61no—
868Dic3—61no—
869Dic3—121no—
870Dic3—121no—
871Dic3—121no—
872Dic3—241no—
873Dic3#88212yes—
874C32#300711yescharacteristic, complemented, Sylow
875C23—31no—
876C23—31no—
877C23—61no—
878C23—91no—
879C23—182no—
880C23—182no—
881C23—184no—
882C23—181no—
883C23—362no—
884C23—361no—
885C23—362no—
886Q8—21no—
887Q8—32no—
888Q8—64no—
889Q8—61no—
890Q8—61no—
891Q8—61no—
892Q8—181no—
893Q8—181no—
894Q8—362no—
895Q8D3×D1212yes—
896D4—32no—
897D4—64no—
898D4—61no—
899D4—92no—
900D4—184no—
901D4—184no—
902D4—184no—
903D4—184no—
904D4—181no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—31no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—31no—
911C2×C4—64no—
912C2×C4—64no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—91no—
919C2×C4—122no—
920C2×C4—184no—
921C2×C4—182no—
922C2×C4—184no—
923C2×C4—182no—
924C2×C4—182no—
925C2×C4—184no—
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—62no—
939C2×C3—62no—
940C2×C3—122no—
941C2×C3C2×#88211yescharacteristic
942C2×C3D3×#12011yescharacteristic
943C2×C3C2×#91811yescharacteristic
944C2×C3#577311yescharacteristic
945C2×C3D3×#13711yescharacteristic
946C2×C3#577711yescharacteristic
947D3—22no—
948D3—22no—
949D3—42no—
950D3—121no—
951D3—122no—
952D3—121no—
953D3—122no—
954D3—241no—
955D3—242no—
956C22—32no—
957C22—32no—
958C22—61no—
959C22—61no—
960C22—61no—
961C22—61no—
962C22—62no—
963C22—121no—
964C22—121no—
965C22—181no—
966C22—181no—
967C22—182no—
968C22—181no—
969C22—364no—
970C22—368no—
971C22—361no—
972C22—361no—
973C22D32×D411yescharacteristic
974C4—22no—
975C4—32no—
976C4—41no—
977C4—61no—
978C4—62no—
979C4—121no—
980C4—121no—
981C4—181no—
982C4—361no—
983C4C2×D3×D1211yescharacteristic
984C4D32×D411yescharacteristic
985C3—21no—
986C3#7888511yescharacteristic, complemented
987C3#8018411yescharacteristic, complemented
988C2—62no—
989C2—62no—
990C2—122no—
991C2—361no—
992C2—362no—
993C2D3×#88211yescharacteristic
994C2#1059474411yescharacteristic
995C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×D3×#239C2
hypercenter#103D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#63943C2semidirect
3. C2×#63801C2semidirect
4. D3×#897C2semidirect
5. #10592507C2semidirect
6. C3×#4809C2semidirect
7. C3×#4803C2semidirect
8. #10591602C2semidirect
9. #10591595C2semidirect
10. #10590965C2semidirect
11. #10590946C2semidirect
12. #10590936C2semidirect
13. #10590618C2semidirect
14. #10590609C2semidirect
15. #10590596C2semidirect
31. C2×D3×Dic6C22semidirect
32. C2×#3756C22semidirect
33. C2×#3744C22semidirect
34. #64106C22semidirect
35. C2×C3×#216C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C3×D3×C4⋊C4C22semidirect
45. #63871C22semidirect
47. C2×#3719C22semidirect
48. C2×#3717C22semidirect
49. C2×#3716C22semidirect
50. C2×#3715C22semidirect
51. C2×#3711C22semidirect
53. C32×#103C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
63. #63557C22semidirect
82. #4809D3semidirect
89. #4803D3semidirect
210. C2×#216C2×D3semidirect
223. C2×Dic12C2×D3semidirect
230. C2×ΓL(1,𝔽25)C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
247. C3×#103C2×D3semidirect
248. C3×#103C2×D3semidirect
253. #835C2×D3semidirect
256. #821C2×D3semidirect
265. #810C2×D3semidirect
270. #809C2×D3semidirect
522. C2×C3×D3#137semidirect
574. #103D32semidirect
845. C2×D3#918semidirect
874. C32#3007semidirect
986. C3#78885semidirect
987. C3#80184semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#639432
C2×#638012
D3×#8972
#105925072
C3×#48092
C3×#48032
#105916022
#105915952
#105909652
#105909462
#105909362
#105906182
#105906092
#105905962
#801843
#788853