Finite Group Databasebeta

← #11864195

Subgroups — #11864195

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 1007 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic
2C2×#64124C211yesmaximal, characteristic, complemented
3#10595429C211yesmaximal, characteristic, complemented
4C2×#63951C211yesmaximal, characteristic, complemented
5C3×#5173C211yesmaximal, characteristic, complemented
6C3×#5169C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591653C211yesmaximal, characteristic, complemented
9#10591463C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591418C211yesmaximal, characteristic, complemented
12#10590969C211yesmaximal, characteristic, complemented
13#10590957C211yesmaximal, characteristic, complemented
14#10590952C211yesmaximal, characteristic, complemented
15#10590937C211yesmaximal, characteristic, complemented
16#80228—31nomaximal
17#80147—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×#3830C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×D3×#67—21no—
23C2×#3805—21no—
24C2×#3804—21no—
25C22×D3×Dic3—21no—
26D3×#237—24no—
27D3×#237—24no—
28C2×C4×D32C2211yescharacteristic
29C2×#3796C2211yescharacteristic
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33C2×#3756C2211yescharacteristic, complemented
34C2×#3754C2211yescharacteristic, complemented
35#64124—24no—
36C2×#3746C2211yescharacteristic, complemented
37C2×#3743C2211yescharacteristic, complemented
38C3×#946C2211yescharacteristic
39C3×#946C2211yescharacteristic, complemented
40C2×C3×#216C2211yescharacteristic, complemented
41C2×C3×#215C2211yescharacteristic, complemented
42#63951—24no—
43#63921—21no—
44#63900C2211yescharacteristic, complemented
45#63896—21no—
46#63896—21no—
47#63883—21no—
48#63857C2211yescharacteristic
49#63857C2211yescharacteristic, complemented
50C2×#3719C2211yescharacteristic, complemented
51C2×#3716C2211yescharacteristic, complemented
52C2×#3712C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C2×#918—31no—
68C2×#915—31no—
69C2×#915—31no—
70C2×#915—31no—
71C2×#915—61no—
72D3×C22⋊Q8—31no—
73D3×C22⋊Q8—31no—
74C3×#452—31no—
75C3×#450—31no—
76#5239—31no—
77#5218—31no—
78#5186—31no—
79#5173—31no—
80#5173D311yescharacteristic, complemented
81#5169D311yescharacteristic, complemented
82#5050—31no—
83#5047—31no—
84#4809—31no—
85#4803—31no—
86#4783—31no—
87#4783—31no—
88#4776—31no—
89#4771—31no—
90#4771—31no—
91#4771—31no—
92#4739—31no—
93#4733—31no—
94#4726—31no—
95#4726—31no—
96C23×C3×D3—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101C22×C3⋊Dic3—21no—
102Q8×C3⋊D3—22no—
103Q8×C3⋊D3—22no—
104#3830—22no—
105#3830D414yes—
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×#634—21no—
109C2×#634C2311yescharacteristic
110C2×#634C2311yescharacteristic
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C22×C3×Dic3—21no—
114C3×#237—22no—
115C3×#237—22no—
116C3×D3×D4—22no—
117C3×D3×D4—22no—
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122D3×#67—28no—
123C2×#627—21no—
124C2×#626—21no—
125C2×#625—21no—
126C2×#624—21no—
127C2×#624D411yescharacteristic
128#3805—28no—
129#3804—28no—
130C2×D3×Dic3—28no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3—21no—
133C2×D3×Dic3—21no—
134C2×D3×Dic3D411yescharacteristic
135C2×D3×Dic3D411yescharacteristic
136C4×D32—22no—
137C4×D32—22no—
138#3796—22no—
139#3796D414yes—
140#3795—22no—
141#3795—22no—
142D3×Dic6—22no—
143D3×Dic6—22no—
144C32×SD16—22no—
145C2×C32×C8C2311yescharacteristic
146#3756—22no—
147#3754—22no—
148C2×C3⋊(C3⋊C8)C2311yescharacteristic
149#3746—22no—
150#3743—22no—
151C3×#216—22no—
152C3×#215—22no—
153C3×(C2×D3)⋊C4—21no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4⋊Dic3C2311yescharacteristic
157C3×Dic3⋊C4—21no—
158C3×Dic3⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161#3724—21no—
162Dic3⋊Dic3—21no—
163Dic3⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165(C2×D3)⋊Dic3—21no—
166#3719—22no—
167#3716—22no—
168#3712—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×D3×Q8—31no—
180C2×D3×Q8—61no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—31no—
185C2×#237—61no—
186C2×#237—61no—
187C2×#237—61no—
188C2×#237—64no—
189C2×#237—64no—
190C2×#237—61no—
191C2×#237C2×D311yescharacteristic
192C2×D3×D4—61no—
193C2×D3×D4C2×D311yescharacteristic
194C2×#235—31no—
195C2×#235—61no—
196C22×C4×D3—31no—
197C22×C4×D3—31no—
198C22×C4×D3—61no—
199C22×Dic6—31no—
200C2×C3×Q16—31no—
201C2×C3×SD16—21no—
202C2×C3×SD16—31no—
203C2×C3×SD16C2×D311yescharacteristic, complemented
204C2×C3×SD16C2×D311yescharacteristic, complemented
205C3×C22⋊Q8—31no—
206C3×C22⋊Q8—31no—
207#946C2×D311yescharacteristic
208#946C2×D311yescharacteristic, complemented
209C2×#216—31no—
210C2×#216—31no—
211C2×#216—31no—
212C2×#216—61no—
213C2×#216C2×D311yescharacteristic, complemented
214C2×#215C2×D311yescharacteristic, complemented
215C2×#214—31no—
216C2×#214—31no—
217C2×#214—31no—
218C2×#214—61no—
219#924—31no—
220#924—31no—
221#918—64no—
222#915—64no—
223#915—64no—
224#915—64no—
225#915—68no—
226C2×Dic12—31no—
227C2×Dic12—31no—
228C2×Dic12—31no—
229C2×Dic12—61no—
230C2×#204—31no—
231C2×ΓL(1,𝔽25)—31no—
232C2×ΓL(1,𝔽25)—31no—
233C2×ΓL(1,𝔽25)—31no—
234C2×ΓL(1,𝔽25)—31no—
235C2×ΓL(1,𝔽25)—61no—
236#897—31no—
237#897—31no—
238#896—61no—
239#896—61no—
240D3×C4⋊C4—31no—
241D3×C4⋊C4—31no—
242D3×C4⋊C4—61no—
243D3×C4⋊C4—61no—
244D3×C22⋊C4—61no—
245D3×C22⋊C4—61no—
246#878—61no—
247#878—61no—
248C3×#103—31no—
249C3×#102—31no—
250C3×#102—31no—
251C3×#102—31no—
252C3×C22⋊C8—31no—
253C3×C22⋊C8—31no—
254#835—31no—
255#832—31no—
256#832C2×D311yescharacteristic, complemented
257#832C2×D311yescharacteristic, complemented
258#830—31no—
259#830—31no—
260#821C2×D311yescharacteristic, complemented
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8C2×D311yescharacteristic
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265#816—31no—
266#816—31no—
267#816C2×D311yescharacteristic, complemented
268#810—31no—
269#810—31no—
270#810—31no—
271#809—31no—
272C23×C32—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—24no—
275C22×C3×D3—21no—
276C22×C3×D3—42no—
277C22×C3×D3—42no—
278C22×C3×D3C2×D411yescharacteristic
279C22×C3×D3C2×D411yescharacteristic
280C2×D32—22no—
281C2×D32—22no—
282C2×D32—41no—
283C32×Q8—21no—
284C32×Q8—21no—
285C32×D4—21no—
286C32×D4C2×D412yes—
287C2×C32×C4—21no—
288C2×C32×C4C2411yescharacteristic
289#638—24no—
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3—24no—
292C2×C3⋊Dic3—21no—
293C2×C3⋊Dic3C2×D411yescharacteristic
294C4×C3⋊D3—42no—
295C4×C3⋊D3C2×D412yes—
296C4×C3⋊D3C2×D412yes—
297#634—21no—
298#634—21no—
299#634—21no—
300#634—42no—
301#634C2×D412yes—
302C3×#67—24no—
303C3×#67—24no—
304C2×C3×Dic3—24no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3C2×D411yescharacteristic
309C2×C3×Dic3C2×D411yescharacteristic
310C3×D12—21no—
311C3×D12C2×D412yes—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×Dic6—21no—
317C3×Dic6C2×D412yes—
318#627—24no—
319#626—24no—
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×#137—91no—
335C2×C22⋊Q8—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#451—91no—
341#451—91no—
342#450—31no—
343#450—91no—
344#417—91no—
345#417—91no—
346#407—91no—
347C24×C3—61no—
348C23×D3—21no—
349C23×D3—31no—
350C23×D3—31no—
351C3×#41—62no—
352C3×#41—62no—
353C2×C3×Q8—21no—
354C2×C3×Q8—31no—
355C2×C3×Q8C22×D311yescharacteristic
356C2×C3×Q8C22×D311yescharacteristic
357C2×C3×D4—21no—
358C2×C3×D4—31no—
359C2×C3×D4—61no—
360C2×C3×D4—62no—
361C2×C3×D4—61no—
362C2×C3×D4—62no—
363C2×C3×D4C22×D311yescharacteristic
364C2×C3×D4C22×D311yescharacteristic
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—61no—
368C2×#67—21no—
369C2×#67—21no—
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—34no—
388#239—62no—
389D3×Q8—62no—
390D3×Q8—62no—
391D3×Q8—62no—
392D3×Q8—62no—
393D3×Q8—62no—
394D3×Q8—62no—
395D3×Q8—64no—
396D3×Q8—122no—
397#237—22no—
398#237—22no—
399#237—34no—
400#237—34no—
401#237—34no—
402#237—64no—
403#237—62no—
404#237—62no—
405#237—62no—
406#237—62no—
407#237—62no—
408#237—68no—
409#237—68no—
410#237—68no—
411#237—122no—
412D3×D4—22no—
413D3×D4—22no—
414D3×D4—68no—
415#235—62no—
416#235—68no—
417#235—62no—
418C2×D12—61no—
419C2×D12C22×D311yescharacteristic
420C2×C4×D3—31no—
421C2×C4×D3—31no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—61no—
427C2×C4×D3—62no—
428C2×C4×D3—62no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—61no—
432C2×C4×D3—61no—
433C2×C4×D3—68no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—121no—
440C2×C4×D3C22×D311yescharacteristic
441C2×C4×D3C22×D311yescharacteristic
442C2×Dic6—31no—
443C2×Dic6—31no—
444C2×Dic6—31no—
445C2×Dic6—31no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6—62no—
449C2×Dic6—61no—
450C2×Dic6—61no—
451C2×Dic6—62no—
452C2×Dic6—61no—
453C2×Dic6—61no—
454C2×Dic6—121no—
455C2×Dic6C22×D311yescharacteristic
456C3×Q16—62no—
457C3×SD16—24no—
458C3×SD16—22no—
459C3×SD16—22no—
460C3×SD16—62no—
461C2×C3×C8—21no—
462C2×C3×C8—31no—
463C2×C3×C8—31no—
464C2×C3×C8C22×D311yescharacteristic
465C2×C3×C8C22×D311yescharacteristic
466C3×C4⋊C4—31no—
467C3×C4⋊C4—31no—
468C3×C4⋊C4—61no—
469C3×C4⋊C4—61no—
470C3×C22⋊C4—61no—
471C3×C22⋊C4—61no—
472#217—61no—
473#217—61no—
474#216—22no—
475#216—62no—
476#216—62no—
477#216—62no—
478#216—64no—
479#215—22no—
480#214—62no—
481#214—64no—
482#214—62no—
483#214—62no—
484(C2×D3)⋊C4—21no—
485(C2×D3)⋊C4—21no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—61no—
488C4⋊Dic3—61no—
489C4⋊Dic3—61no—
490C4⋊Dic3C22×D311yescharacteristic
491C4⋊Dic3C22×D311yescharacteristic
492Dic3⋊C4—21no—
493Dic3⋊C4—21no—
494Dic3⋊C4—61no—
495Dic3⋊C4—61no—
496Dic3⋊C4—61no—
497Dic3⋊C4—61no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8C22×D311yescharacteristic
502C2×C3⋊C8C22×D311yescharacteristic
503Dic12—62no—
504Dic12—62no—
505Dic12—64no—
506Dic12—62no—
507#204—62no—
508ΓL(1,𝔽25)—62no—
509ΓL(1,𝔽25)—62no—
510ΓL(1,𝔽25)—62no—
511ΓL(1,𝔽25)—62no—
512ΓL(1,𝔽25)—64no—
513C22×C32—22no—
514C22×C32—41no—
515C22×C32—41no—
516C22×C32C22×D411yescharacteristic
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3#12012yes—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—22no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—21no—
526C2×C3×D3—48no—
527C2×C3×D3—41no—
528C2×C3×D3—41no—
529C2×C3×D3#13712yescomplemented
530D32—44no—
531C32×C4—41no—
532C32×C4C22×D411yescharacteristic
533C32×C4C22×D411yescharacteristic
534C3⋊Dic3—22no—
535C3⋊Dic3—41no—
536C3⋊Dic3#12012yes—
537C3×Dic3—21no—
538C3×Dic3—22no—
539C3×Dic3—21no—
540C3×Dic3—41no—
541C3×Dic3—41no—
542C2×#41—31no—
543C2×#41—91no—
544C2×#41—91no—
545C2×#41—91no—
546C2×#41—181no—
547C2×#41—181no—
548C2×#41—184no—
549C2×#41—184no—
550C22×Q8—91no—
551C22×Q8—91no—
552C22×D4—31no—
553C22×D4—181no—
554C23×C4—91no—
555C23×C4—181no—
556#137—184no—
557#137—184no—
558C2×Q16—31no—
559C2×Q16—91no—
560C2×Q16—91no—
561C2×Q16—91no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16D3211yescharacteristic, complemented
566C2×M16—91no—
567C2×M16—91no—
568C22⋊Q8—31no—
569C22⋊Q8—31no—
570C22⋊Q8—91no—
571C22⋊Q8—91no—
572C22⋊Q8—181no—
573C22⋊Q8—181no—
574C2×C4⋊C4—91no—
575C2×C4⋊C4—181no—
576C2×C22⋊C4—181no—
577#103—31no—
578#103—91no—
579#103—91no—
580#103—91no—
581#102—31no—
582#102—31no—
583#102—31no—
584#102—91no—
585C22⋊C8—31no—
586C22⋊C8—31no—
587C22⋊C8—91no—
588C22⋊C8—91no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—31no—
592C23×C3—31no—
593C23×C3—41no—
594C23×C3—64no—
595C23×C3—61no—
596C23×C3—122no—
597C23×C3—122no—
598C22×D3—24no—
599C22×D3—21no—
600C22×D3—31no—
601C22×D3—31no—
602C22×D3—42no—
603C22×D3—42no—
604C22×D3—61no—
605C22×D3—62no—
606C22×D3—62no—
607C22×D3—62no—
608C22×D3—62no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3D3×D411yescharacteristic
612C22×D3D3×D411yescharacteristic
613C3×Q8—22no—
614C3×Q8—21no—
615C3×Q8—21no—
616C3×Q8—21no—
617C3×Q8—21no—
618C3×Q8—32no—
619C3×Q8—41no—
620C3×Q8—61no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—22no—
624C3×D4—32no—
625C3×D4—41no—
626C3×D4—64no—
627C3×D4—64no—
628C3×D4—61no—
629C3×D4D3×D412yes—
630C3×D4D3×D412yes—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—41no—
637C2×C3×C4—64no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647#67—24no—
648#67—24no—
649#67—64no—
650#67—64no—
651#67—64no—
652#67—64no—
653#67—64no—
654#67—124no—
655C2×Dic3—24no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—31no—
660C2×Dic3—31no—
661C2×Dic3—61no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—64no—
665C2×Dic3—64no—
666C2×Dic3—64no—
667C2×Dic3—64no—
668C2×Dic3—64no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—124no—
674C2×Dic3—121no—
675C2×Dic3—121no—
676C2×Dic3D3×D411yescharacteristic
677C2×Dic3D3×D411yescharacteristic
678D12—21no—
679D12—64no—
680D12D3×D412yes—
681C4×D3—21no—
682C4×D3—21no—
683C4×D3—21no—
684C4×D3—21no—
685C4×D3—32no—
686C4×D3—32no—
687C4×D3—32no—
688C4×D3—32no—
689C4×D3—62no—
690C4×D3—62no—
691C4×D3—62no—
692C4×D3—62no—
693C4×D3—62no—
694C4×D3—62no—
695C4×D3—64no—
696C4×D3—64no—
697C4×D3—64no—
698C4×D3—122no—
699C4×D3—122no—
700C4×D3—122no—
701C4×D3—122no—
702C4×D3—124no—
703Dic6—21no—
704Dic6—32no—
705Dic6—32no—
706Dic6—62no—
707Dic6—64no—
708Dic6—64no—
709Dic6—61no—
710Dic6—61no—
711Dic6—62no—
712Dic6—61no—
713Dic6—61no—
714Dic6—61no—
715Dic6—61no—
716Dic6—121no—
717Dic6—121no—
718Dic6—122no—
719Dic6—122no—
720Dic6—124no—
721Dic6D3×D412yes—
722C3×C8—22no—
723C3×C8—21no—
724C3×C8—21no—
725C3×C8—61no—
726C3×C8—61no—
727C3⋊C8—21no—
728C3⋊C8—21no—
729C3⋊C8—62no—
730C3⋊C8—61no—
731C3⋊C8—61no—
732C2×C32—42no—
733C2×C32C2×#12011yescharacteristic
734C2×C32C2×#13711yescharacteristic
735C2×C32#57511yescharacteristic
736C3⋊D3—22no—
737C3×D3—22no—
738C3×D3—41no—
739C3×D3—42no—
740C24—61no—
741C24—91no—
742#41—62no—
743#41—62no—
744#41—94no—
745#41—94no—
746#41—182no—
747#41—182no—
748#41—188no—
749#41—182no—
750#41—182no—
751#41—188no—
752C2×Q8—31no—
753C2×Q8—91no—
754C2×Q8—91no—
755C2×Q8—181no—
756C2×Q8—181no—
757C2×Q8—182no—
758C2×Q8—182no—
759C2×Q8—182no—
760C2×Q8—182no—
761C2×Q8C2×D3211yescharacteristic
762C2×D4—31no—
763C2×D4—61no—
764C2×D4—62no—
765C2×D4—61no—
766C2×D4—62no—
767C2×D4—181no—
768C2×D4—188no—
769C2×D4—181no—
770C2×D4—181no—
771C2×D4C2×D3211yescharacteristic
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—61no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—91no—
779C22×C4—181no—
780C22×C4—181no—
781C22×C4—182no—
782C22×C4—182no—
783C22×C4—181no—
784C22×C4—181no—
785C22×C4—181no—
786C22×C4—188no—
787C22×C4—181no—
788Q16—62no—
789Q16—182no—
790Q16—182no—
791Q16—182no—
792SD16—22no—
793SD16—62no—
794SD16—182no—
795SD16—182no—
796M16—182no—
797M16—182no—
798C2×C8—31no—
799C2×C8—31no—
800C2×C8—91no—
801C2×C8C2×D3211yescharacteristic
802C4⋊C4—31no—
803C4⋊C4—31no—
804C4⋊C4—61no—
805C4⋊C4—61no—
806C4⋊C4—181no—
807C4⋊C4—181no—
808C4⋊C4—181no—
809C22⋊C4—61no—
810C22⋊C4—61no—
811C22⋊C4—181no—
812C22⋊C4—181no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—21no—
816C22×C3—32no—
817C22×C3—42no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—61no—
826C22×C3—62no—
827C22×C3—61no—
828C22×C3—81no—
829C22×C3—81no—
830C22×C3—128no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3C2×D3×D411yescharacteristic
834C22×C3C2×D3×D411yescharacteristic
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—21no—
839C2×D3—21no—
840C2×D3—22no—
841C2×D3—32no—
842C2×D3—32no—
843C2×D3—48no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—62no—
847C2×D3—61no—
848C2×D3—61no—
849C2×D3—61no—
850C2×D3—61no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—124no—
854C2×D3—124no—
855C2×D3#91512yescomplemented
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—42no—
859C3×C4—41no—
860C3×C4—41no—
861C3×C4—61no—
862C3×C4—62no—
863C3×C4—61no—
864C3×C4—121no—
865C3×C4—121no—
866C3×C4C2×D3×D411yescharacteristic
867C3×C4C2×D3×D411yescharacteristic
868C3×C4C2×D3×D411yescharacteristic
869C3×C4C2×D3×D411yescharacteristic
870Dic3—22no—
871Dic3—21no—
872Dic3—21no—
873Dic3—32no—
874Dic3—32no—
875Dic3—41no—
876Dic3—41no—
877Dic3—62no—
878Dic3—62no—
879Dic3—62no—
880Dic3—122no—
881Dic3—122no—
882Dic3—121no—
883Dic3—121no—
884C32#300711yescharacteristic, complemented, Sylow
885C23—21no—
886C23—31no—
887C23—31no—
888C23—64no—
889C23—61no—
890C23—91no—
891C23—122no—
892C23—122no—
893C23—182no—
894C23—182no—
895C23—361no—
896Q8—21no—
897Q8—21no—
898Q8—32no—
899Q8—61no—
900Q8—92no—
901Q8—184no—
902Q8—181no—
903Q8—181no—
904Q8—181no—
905Q8—362no—
906D4—21no—
907D4—32no—
908D4—64no—
909D4—64no—
910D4—61no—
911D4—184no—
912D4—184no—
913D4—184no—
914D4#381112yes—
915C2×C4—21no—
916C2×C4—31no—
917C2×C4—31no—
918C2×C4—64no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—91no—
927C2×C4—92no—
928C2×C4—92no—
929C2×C4—182no—
930C2×C4—182no—
931C2×C4—182no—
932C2×C4—184no—
933C2×C4—184no—
934C2×C4—184no—
935C2×C4—184no—
936C2×C4—181no—
937C2×C4—181no—
938C2×C4—362no—
939C2×C4—362no—
940C2×C4C22×D3211yescharacteristic
941C8—21no—
942C8—61no—
943C8—61no—
944C8—181no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—42no—
949C2×C3—42no—
950C2×C3—62no—
951C2×C3—82no—
952C2×C3—121no—
953C2×C3—122no—
954C2×C3D3×#12011yescharacteristic
955C2×C3D3×#12011yescharacteristic
956C2×C3C2×#91511yescharacteristic
957C2×C3#576811yescharacteristic
958C2×C3#577311yescharacteristic
959C2×C3D3×#13711yescharacteristic
960D3—22no—
961D3—42no—
962D3—41no—
963D3—62no—
964D3—62no—
965D3—122no—
966C22—22no—
967C22—32no—
968C22—41no—
969C22—41no—
970C22—61no—
971C22—61no—
972C22—61no—
973C22—61no—
974C22—61no—
975C22—62no—
976C22—92no—
977C22—128no—
978C22—121no—
979C22—121no—
980C22—181no—
981C22—181no—
982C22—364no—
983C22D32×D411yescharacteristic
984C4—41no—
985C4—61no—
986C4—61no—
987C4—62no—
988C4—92no—
989C4—121no—
990C4—121no—
991C4—182no—
992C4—361no—
993C4D32×D411yescharacteristic
994C4C2×#381111yescharacteristic
995C3—21no—
996C3#8014711yescharacteristic, complemented
997C3#8022811yescharacteristic, complemented
998C2—42no—
999C2—62no—
1000C2—121no—
1001C2—122no—
1002C2—182no—
1003C2D3×#91511yescharacteristic
1004C2#1059474511yescharacteristic
1005C2#1059527811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×D3×#237C2
hypercenterC2×SD16D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#64124C2semidirect
3. #10595429C2semidirect
4. C2×#63951C2semidirect
5. C3×#5173C2semidirect
6. C3×#5169C2semidirect
7. #10591655C2semidirect
8. #10591653C2semidirect
9. #10591463C2semidirect
10. #10591459C2semidirect
11. #10591418C2semidirect
12. #10590969C2semidirect
13. #10590957C2semidirect
14. #10590952C2semidirect
15. #10590937C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
32. C2×C32×SD16C22semidirect
33. C2×#3756C22semidirect
34. C2×#3754C22semidirect
36. C2×#3746C22semidirect
37. C2×#3743C22semidirect
39. C3×#946C22semidirect
40. C2×C3×#216C22semidirect
41. C2×C3×#215C22semidirect
44. #63900C22semidirect
49. #63857C22semidirect
50. C2×#3719C22semidirect
51. C2×#3716C22semidirect
52. C2×#3712C22semidirect
53. C3×#832C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
61. #63565C22semidirect
62. #63562C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
80. #5173D3semidirect
81. #5169D3semidirect
203. C2×C3×SD16C2×D3semidirect
204. C2×C3×SD16C2×D3semidirect
208. #946C2×D3semidirect
213. C2×#216C2×D3semidirect
214. C2×#215C2×D3semidirect
256. #832C2×D3semidirect
257. #832C2×D3semidirect
260. #821C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
267. #816C2×D3semidirect
529. C2×C3×D3#137semidirect
565. C2×SD16D32semidirect
855. C2×D3#915semidirect
884. C32#3007semidirect
996. C3#80147semidirect
997. C3#80228semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×#641242
#105954292
C2×#639512
C3×#51732
C3×#51692
#105916552
#105916532
#105914632
#105914592
#105914182
#105909692
#105909572
#105909522
#105909372
#802283
#801473