Finite Group Databasebeta

← #11864197

Subgroups — #11864197

Order 1152.

1602 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64312C211yesmaximal, characteristic
2C2×#63929C211yesmaximal, characteristic, complemented
3C2×#63801C211yesmaximal, characteristic, complemented
4D3×#897C211yesmaximal, characteristic, complemented
5#10592475C211yesmaximal, characteristic, complemented
6C3×#4783C211yesmaximal, characteristic, complemented
7C3×#4771C211yesmaximal, characteristic, complemented
8#10591467C211yesmaximal, characteristic, complemented
9#10591463C211yesmaximal, characteristic, complemented
10#10590970C211yesmaximal, characteristic, complemented
11#10590950C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590616C211yesmaximal, characteristic, complemented
14#10590609C211yesmaximal, characteristic, complemented
15#10590605C211yesmaximal, characteristic, complemented
16#80228—31nomaximal
17#78885—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×#3811—21no—
22C22×#624—21no—
23C2×#3804—21no—
24C2×#3804—21no—
25#64312—24no—
26#64312—24no—
27C2×C4×D32C2211yescharacteristic
28C2×#3799C2211yescharacteristic
29C2×#3799C2211yescharacteristic
30C2×#3797C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic, complemented
32C2×#3754C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64106C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
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
46#63857C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3719C2211yescharacteristic, complemented
49C2×#3718C2211yescharacteristic, complemented
50C2×#3717C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63801—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic
55#63636C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63557C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C2×D3×#41—31no—
67C2×#951—31no—
68C2×#918—31no—
69C2×#915—31no—
70C2×#909—31no—
71D3×C22⋊Q8—31no—
72C2×#897—31no—
73C3×#452—31no—
74C3×#417—31no—
75#5239—31no—
76#5186—31no—
77#5169—31no—
78#5126—31no—
79#5047—31no—
80#4966—31no—
81#4809—31no—
82#4809—31no—
83#4809—31no—
84#4808—31no—
85#4808—31no—
86#4803—31no—
87#4783—31no—
88#4783D311yescharacteristic, complemented
89#4776—31no—
90#4776—31no—
91#4776—31no—
92#4776—61no—
93#4771D311yescharacteristic, complemented
94#4733—31no—
95#4726—31no—
96C23×C3⋊D3—21no—
97C22×D32D411yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×#638—21no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3—22no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237—22no—
111C3×#237—22no—
112C3×#237D414yes—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119#3811—28no—
120C2×#627—21no—
121C2×#627—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#624—28no—
125C2×#624—21no—
126C2×#624—21no—
127C2×#624—21no—
128C2×#624D411yescharacteristic
129#3804—28no—
130#3804—28no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3D411yescharacteristic
133C2×D3×Dic3D411yescharacteristic
134C4×D32—22no—
135C4×D32—22no—
136#3799—22no—
137#3799—22no—
138#3799—22no—
139#3799D414yes—
140#3797—22no—
141#3797—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#3744—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×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#3719—22no—
166#3718—22no—
167#3717—22no—
168#3711—22no—
169#3007—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172D3×#41—64no—
173D3×#41—64no—
174D3×#41—64no—
175D3×#41—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×D3×Q8—31no—
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×#237—61no—
182C2×#237—61no—
183C2×#237C2×D311yescharacteristic
184C2×#237C2×D311yescharacteristic
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—61no—
193C2×#235—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×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×#215—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#918—64no—
220#915—64no—
221#909—64no—
222C2×Dic12—31no—
223C2×Dic12—31no—
224C2×Dic12C2×D311yescharacteristic, complemented
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, complemented
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×#103—31no—
247C3×#102—21no—
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#821—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—31no—
261(C2×D3)⋊C8—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816C2×D311yescharacteristic, complemented
264#810—31no—
265#810C2×D311yescharacteristic, complemented
266#810C2×D311yescharacteristic, complemented
267#809—31no—
268#809—31no—
269#809—31no—
270#809—61no—
271C23×C32—21no—
272C22×C3⋊D3—24no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3—42no—
275C22×C3⋊D3—42no—
276C22×C3⋊D3C2×D411yescharacteristic
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—21no—
288C2×C3⋊Dic3C2×D411yescharacteristic
289C4⋊(C3⋊D3)—21no—
290C4⋊(C3⋊D3)C2×D412yes—
291C4×C3⋊D3—21no—
292C4×C3⋊D3—21no—
293#634—21no—
294#634—21no—
295C3×#67—24no—
296C3×#67—24no—
297C2×C3×Dic3—24no—
298C2×C3×Dic3—21no—
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×C4×D3—21no—
306C3×C4×D3—21no—
307C3×C4×D3—42no—
308C3×C4×D3C2×D412yes—
309C3×C4×D3C2×D412yes—
310C3×Dic6—21no—
311C3×Dic6—21no—
312C3×Dic6—21no—
313C3×Dic6—21no—
314C3×Dic6C2×D412yes—
315C3×Dic6C2×D412yes—
316#627—24no—
317#627—42no—
318#626—24no—
319#626—24no—
320#624—24no—
321#624—24no—
322#624—24no—
323#624—22no—
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—31no—
336#452—91no—
337#452—91no—
338#452—91no—
339#451—91no—
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—
350C23×D3—121no—
351C3×#41—34no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C2×C3×Q8—31no—
356C2×C3×Q8—31no—
357C2×C3×Q8—31no—
358C2×C3×D4—21no—
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—
366C22×C3×C4—61no—
367C22×C3×C4—61no—
368C2×#67—21no—
369C2×#67—21no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—121no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—61no—
380#239—34no—
381#239—62no—
382#239—62no—
383#239—62no—
384D3×Q8—62no—
385D3×Q8—62no—
386D3×Q8—62no—
387D3×Q8—62no—
388D3×Q8—62no—
389D3×Q8—62no—
390#237—22no—
391#237—22no—
392#237—22no—
393#237—68no—
394#237—68no—
395#237D1214yes—
396D3×D4—62no—
397D3×D4—62no—
398D3×D4—68no—
399D3×D4—68no—
400D3×D4—62no—
401D3×D4—62no—
402D3×D4—122no—
403D3×D4—122no—
404#235—34no—
405#235—62no—
406#235—62no—
407#235—68no—
408#235—68no—
409#235—62no—
410C2×D12—31no—
411C2×D12—31no—
412C2×D12—61no—
413C2×D12—61no—
414C2×D12—61no—
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—61no—
428C2×C4×D3—61no—
429C2×C4×D3—68no—
430C2×C4×D3—68no—
431C2×C4×D3—61no—
432C2×C4×D3—61no—
433C2×C4×D3—62no—
434C2×C4×D3—62no—
435C2×C4×D3—61no—
436C2×C4×D3C22×D311yescharacteristic
437C2×C4×D3C22×D311yescharacteristic
438C2×Dic6—31no—
439C2×Dic6—31no—
440C2×Dic6—61no—
441C2×Dic6—62no—
442C2×Dic6—62no—
443C2×Dic6—61no—
444C2×Dic6—61no—
445C2×Dic6—61no—
446C2×Dic6—61no—
447C2×Dic6C22×D311yescharacteristic
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—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#215—62no—
471#214—22no—
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—22no—
499Dic12—62no—
500Dic12—62no—
501#204—62no—
502#204—62no—
503#204—62no—
504#204—122no—
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—22no—
514C2×C3⋊D3—48no—
515C2×C3⋊D3—41no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3#13712yescomplemented
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3#12012yes—
524D32—44no—
525C32×C4—41no—
526C32×C4C22×D411yescharacteristic
527C32×C4C22×D411yescharacteristic
528C3⋊Dic3—21no—
529C3⋊Dic3—41no—
530C3×Dic3—21no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C3×Dic3#12012yes—
536C2×#41—31no—
537C2×#41—31no—
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—91no—
547C22×D4—181no—
548C23×C4—91no—
549C23×C4—181no—
550#137—184no—
551#137—184no—
552C2×Q16—31no—
553C2×Q16—91no—
554C2×Q16—91no—
555C2×Q16—91no—
556C2×SD16—31no—
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—31no—
574#103—91no—
575#102—31no—
576#102—91no—
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—
588C22×D3—31no—
589C22×D3—31no—
590C22×D3—61no—
591C22×D3—62no—
592C22×D3—62no—
593C22×D3—62no—
594C22×D3—64no—
595C22×D3—64no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—62no—
599C22×D3—121no—
600C22×D3—124no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—122no—
604C22×D3—122no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—242no—
608C22×D3—242no—
609C22×D3D3×D411yescharacteristic
610C22×D3D3×D411yescharacteristic
611C3×Q8—32no—
612C3×Q8—32no—
613C3×Q8—61no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8—61no—
617C3×D4—21no—
618C3×D4—21no—
619C3×D4—22no—
620C3×D4—41no—
621C3×D4—64no—
622C3×D4—64no—
623C3×D4C2×D1212yes—
624C3×D4D3×D412yes—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—31no—
629C2×C3×C4—32no—
630C2×C3×C4—32no—
631C2×C3×C4—31no—
632C2×C3×C4—41no—
633C2×C3×C4—64no—
634C2×C3×C4—64no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—122no—
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C23×D311yescharacteristic
644#67—24no—
645#67—24no—
646#67—64no—
647#67—64no—
648#67—64no—
649#67—64no—
650#67—124no—
651C2×Dic3—24no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—24no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—61no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—121no—
665C2×Dic3—122no—
666C2×Dic3D3×D411yescharacteristic
667C2×Dic3D3×D411yescharacteristic
668D12—32no—
669D12—32no—
670D12—62no—
671D12—64no—
672D12—64no—
673D12—61no—
674D12—61no—
675D12—121no—
676C4×D3—21no—
677C4×D3—21no—
678C4×D3—42no—
679C4×D3—62no—
680C4×D3—64no—
681C4×D3—64no—
682C4×D3—64no—
683C4×D3—64no—
684C4×D3—64no—
685C4×D3—62no—
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—122no—
696C4×D3C2×D1212yes—
697C4×D3D3×D412yes—
698Dic6—21no—
699Dic6—21no—
700Dic6—21no—
701Dic6—21no—
702Dic6—64no—
703Dic6—64no—
704Dic6—61no—
705Dic6—61no—
706Dic6—61no—
707Dic6—61no—
708Dic6—121no—
709Dic6—121no—
710Dic6—122no—
711Dic6—122no—
712Dic6C2×D1212yes—
713Dic6D3×D412yes—
714C3×C8—21no—
715C3×C8—21no—
716C3×C8—41no—
717C3×C8—61no—
718C3×C8—61no—
719C3⋊C8—21no—
720C3⋊C8—21no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—121no—
724C2×C32—42no—
725C2×C32C2×#12011yescharacteristic
726C2×C32C2×#13711yescharacteristic
727C2×C32#57511yescharacteristic
728C3⋊D3—22no—
729C3⋊D3—42no—
730C3×D3—22no—
731C3×D3—41no—
732C24—91no—
733C24—181no—
734#41—34no—
735#41—62no—
736#41—62no—
737#41—62no—
738#41—94no—
739#41—182no—
740#41—188no—
741#41—188no—
742#41—182no—
743#41—182no—
744C2×Q8—31no—
745C2×Q8—31no—
746C2×Q8—31no—
747C2×Q8—91no—
748C2×Q8—181no—
749C2×Q8—182no—
750C2×Q8—182no—
751C2×Q8—181no—
752C2×Q8—182no—
753C2×Q8—182no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—91no—
757C2×D4—181no—
758C2×D4—181no—
759C2×D4—181no—
760C2×D4—182no—
761C2×D4—188no—
762C2×D4—182no—
763C2×D4C2×D3211yescharacteristic
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—182no—
774C22×C4—182no—
775C22×C4—181no—
776C22×C4—181no—
777C22×C4—181no—
778C22×C4—188no—
779C22×C4—181no—
780Q16—62no—
781Q16—182no—
782Q16—182no—
783Q16—182no—
784SD16—62no—
785SD16—182no—
786SD16—182no—
787SD16—182no—
788M16—62no—
789M16—182no—
790C2×C8—31no—
791C2×C8—31no—
792C2×C8—91no—
793C2×C8C2×D3211yescharacteristic
794C4⋊C4—31no—
795C4⋊C4—61no—
796C4⋊C4—61no—
797C4⋊C4—181no—
798C4⋊C4—181no—
799C4⋊C4—181no—
800C4⋊C4C2×D3211yescharacteristic
801C22⋊C4—61no—
802C22⋊C4—181no—
803C22⋊C4—181no—
804C22⋊C4—181no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—21no—
808C22×C3—32no—
809C22×C3—42no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—81no—
820C22×C3—81no—
821C22×C3C2×D3×D411yescharacteristic
822C22×C3C2×D3×D411yescharacteristic
823C2×D3—21no—
824C2×D3—21no—
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—32no—
829C2×D3—32no—
830C2×D3—62no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—122no—
840C2×D3—124no—
841C2×D3—124no—
842C2×D3—128no—
843C2×D3—128no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—248no—
849C2×D3—241no—
850C2×D3—241no—
851C2×D3#88212yes—
852C3×C4—21no—
853C3×C4—21no—
854C3×C4—32no—
855C3×C4—41no—
856C3×C4—41no—
857C3×C4—62no—
858C3×C4—61no—
859C3×C4—62no—
860C3×C4—81no—
861C3×C4—121no—
862C3×C4—121no—
863C3×C4C22×D1211yescharacteristic
864C3×C4C2×D3×D411yescharacteristic
865C3×C4C2×D3×D411yescharacteristic
866C3×C4C2×D3×D411yescharacteristic
867Dic3—22no—
868Dic3—22no—
869Dic3—21no—
870Dic3—41no—
871Dic3—41no—
872Dic3—61no—
873Dic3—61no—
874Dic3—121no—
875Dic3—121no—
876Dic3—121no—
877Dic3—241no—
878Dic3#88212yes—
879C32#300711yescharacteristic, complemented, Sylow
880C23—21no—
881C23—31no—
882C23—31no—
883C23—91no—
884C23—184no—
885C23—182no—
886C23—182no—
887C23—181no—
888C23—362no—
889C23—362no—
890C23—361no—
891Q8—32no—
892Q8—32no—
893Q8—61no—
894Q8—61no—
895Q8—61no—
896Q8—61no—
897Q8—184no—
898Q8—181no—
899Q8—181no—
900Q8—362no—
901D4—21no—
902D4—64no—
903D4—64no—
904D4—92no—
905D4—184no—
906D4—184no—
907D4—184no—
908D4—181no—
909D4D3×D1212yes—
910C2×C4—21no—
911C2×C4—31no—
912C2×C4—32no—
913C2×C4—32no—
914C2×C4—31no—
915C2×C4—64no—
916C2×C4—64no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—91no—
924C2×C4—122no—
925C2×C4—182no—
926C2×C4—184no—
927C2×C4—182no—
928C2×C4—184no—
929C2×C4—184no—
930C2×C4—182no—
931C2×C4—181no—
932C2×C4—181no—
933C2×C4—181no—
934C2×C4—362no—
935C2×C4C22×D3211yescharacteristic
936C8—21no—
937C8—61no—
938C8—61no—
939C8—181no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—42no—
944C2×C3—42no—
945C2×C3—62no—
946C2×C3—82no—
947C2×C3—121no—
948C2×C3C2×#88211yescharacteristic
949C2×C3D3×#12011yescharacteristic
950C2×C3#576811yescharacteristic
951C2×C3#577311yescharacteristic
952C2×C3D3×#13711yescharacteristic
953C2×C3D3×#13711yescharacteristic
954D3—22no—
955D3—41no—
956D3—62no—
957D3—62no—
958D3—122no—
959D3—122no—
960D3—122no—
961D3—242no—
962C22—22no—
963C22—32no—
964C22—41no—
965C22—41no—
966C22—61no—
967C22—61no—
968C22—61no—
969C22—61no—
970C22—61no—
971C22—92no—
972C22—181no—
973C22—181no—
974C22—182no—
975C22—368no—
976C22—364no—
977C22—361no—
978C22—361no—
979C22D32×D411yescharacteristic
980C4—32no—
981C4—41no—
982C4—61no—
983C4—62no—
984C4—62no—
985C4—121no—
986C4—121no—
987C4—181no—
988C4—361no—
989C4C2×D3×D1211yescharacteristic
990C4D32×D411yescharacteristic
991C3—21no—
992C3#7888511yescharacteristic, complemented
993C3#8022811yescharacteristic, complemented
994C2—42no—
995C2—62no—
996C2—121no—
997C2—182no—
998C2—362no—
999C2D3×#88211yescharacteristic
1000C2#1059472911yescharacteristic
1001C2#1059474211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#64312C2
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×#63801C2semidirect
4. D3×#897C2semidirect
5. #10592475C2semidirect
6. C3×#4783C2semidirect
7. C3×#4771C2semidirect
8. #10591467C2semidirect
9. #10591463C2semidirect
10. #10590970C2semidirect
11. #10590950C2semidirect
12. #10590936C2semidirect
13. #10590616C2semidirect
14. #10590609C2semidirect
15. #10590605C2semidirect
31. C2×D3×Dic6C22semidirect
32. C2×#3754C22semidirect
33. C2×#3744C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
38. C3×#897C22semidirect
39. C3×D3×C4⋊C4C22semidirect
46. #63857C22semidirect
47. C2×#3719C22semidirect
48. C2×#3719C22semidirect
49. C2×#3718C22semidirect
50. C2×#3717C22semidirect
51. C2×#3711C22semidirect
53. C32×#102C22semidirect
55. #63636C22semidirect
56. C3×#832C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#810C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
88. #4783D3semidirect
93. #4771D3semidirect
214. C2×#214C2×D3semidirect
224. C2×Dic12C2×D3semidirect
230. C2×ΓL(1,𝔽25)C2×D3semidirect
238. #897C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
249. C3×#102C2×D3semidirect
250. C3×#102C2×D3semidirect
253. #832C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
263. #816C2×D3semidirect
265. #810C2×D3semidirect
266. #810C2×D3semidirect
517. C2×C3⋊D3#137semidirect
578. #102D32semidirect
879. C32#3007semidirect
992. C3#78885semidirect
993. C3#80228semidirect

Maximal subgroups

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

subgroupindex
C2×#643122
C2×#639292
C2×#638012
D3×#8972
#105924752
C3×#47832
C3×#47712
#105914672
#105914632
#105909702
#105909502
#105909362
#105906162
#105906092
#105906052
#802283
#788853