Finite Group Databasebeta

← #11909799

Subgroups — #11909799

Order 1152.

2326 conjugacy classes of subgroups.

The subgroup lattice has 951 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596056C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
4#10595402C212yesmaximal, complemented
5#10595346C212yesmaximal, complemented
6#10594516C214yesmaximal, complemented
7#10594512C212yesmaximal, complemented
8#10594330C214yesmaximal, complemented
9#10594327C212yesmaximal, complemented
10#10593978C212yesmaximal, complemented
11#10593976C212yesmaximal, complemented
12#10593974C211yesmaximal, characteristic, complemented
13#10593970C211yesmaximal, characteristic, complemented
14#10593968C212yesmaximal, complemented
15#10593938C212yesmaximal, complemented
16#10593902C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#86936—31nomaximal
19#85821—31nomaximal
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3799C2212yes—
22C2×#3799C2212yes—
23C2×#3798C2214yes—
24C32×C4×Q8C2211yescharacteristic
25#64156C2212yes—
26#64103C2214yes—
27#64102C2212yes—
28#64084C2212yes—
29#64083C2211yescharacteristic
30C4×C4⋊(C3⋊D3)C2212yes—
31C4×#634C2211yescharacteristic
32C3×#946C2212yes—
33C3×Q8×Dic3C2211yescharacteristic
34C3×#896C2214yes—
35C3×D3×C4⋊C4C2212yes—
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×D3×C4⋊C4C2212yes—
38C3×#887C2211yescharacteristic
39C3×#887C2212yes—
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2212yes—
42C3×C42×D3C2212yes—
43C3×C42×D3C2211yescharacteristic
44C3×#870C2212yes—
45C3×#869C2211yescharacteristic
46C3×C4×Dic6C2211yescharacteristic
47C3×C4×Dic6C2212yes—
48#63919C2212yes—
49#63918C2212yes—
50#63911C2212yes—
51#63910C2214yes—
52#63909C2212yes—
53#63909C2212yes—
54#63909C2212yes—
55#63908C2211yescharacteristic
56#63907C2214yes—
57#63906C2214yes—
58#63905C2212yes—
59#63904C2214yes—
60#63904C2214yes—
61C4×#626C2214yes—
62C4×#625C2212yes—
63#63895C2214yes—
64#63894C2212yes—
65#63894C2212yes—
66#63894C2212yes—
67#63888C2214yes—
68#63883C2214yes—
69#63869C2211yescharacteristic
70#63868C2214yes—
71#63865C2214yes—
72#63864C2212yes—
73#63860C2211yescharacteristic
74#63859C2212yes—
75#63857C2211yescharacteristic
76#63855C2212yes—
77#63854C2214yes—
78#63852C2214yes—
79#63850C2214yes—
80#63850C2214yes—
81#63844C2212yes—
82#63843C2212yes—
83#63839C2214yes—
84#63836C2214yes—
85C3×#554—31no—
86C2×C3×C4×Q8—31no—
87#5817—32no—
88#5725—31no—
89#5722—31no—
90#5691—32no—
91#5690—32no—
92#5643—32no—
93#5640—34no—
94#5633—32no—
95#5631—34no—
96#5585—31no—
97#5585—31no—
98#5585—32no—
99#5585—61no—
100#5582—32no—
101#5582—34no—
102#5579—32no—
103#5579D311yescharacteristic, complemented
104#5577—31no—
105#5574—32no—
106C4×D3×Q8D311yescharacteristic, complemented
107Q8×Dic6—31no—
108#5559—32no—
109#5557—31no—
110#5553—31no—
111#5548—32no—
112#5507—34no—
113#5507—32no—
114#5507—32no—
115#5504—32no—
116#5479—31no—
117#5479—32no—
118#5477—32no—
119#5477—31no—
120C2×C32×Q8C2311yescharacteristic
121C2×C4⋊(C3⋊D3)C2312yes—
122C2×C4⋊(C3⋊D3)C2312yes—
123C2×C4⋊(C3⋊D3)C2312yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634C2311yescharacteristic
126C3×D3×Q8—24no—
127C2×C3×D12C2311yescharacteristic
128C2×C3×C4×D3C2312yes—
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2314yes—
135C2×C3×Dic6C2312yes—
136C2×C3×Dic6C2312yes—
137C2×C3×Dic6C2311yescharacteristic
138C2×#627C2314yes—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#626C2314yes—
142C2×#625C2312yes—
143C2×#624C2314yes—
144C2×#624C2314yes—
145#3799—28no—
146#3799—44no—
147#3798—48no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151C32×C42C2312yes—
152#3752C2314yes—
153#3752C2314yes—
154#3752C2314yes—
155C4⋊(C3⋊Dic3)C2311yescharacteristic
156#3750C2312yes—
157C4×C3⋊Dic3C2312yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2314yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2312yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2311yescharacteristic
176#3724C2314yes—
177#3724C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181#3722C2314yes—
182#3722C2314yes—
183#3722C2314yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2312yes—
187(C2×D3)⋊Dic3C2312yes—
188Dic32C2314yes—
189#3522—91noSylow
190C22×C3×Q8—31no—
191C2×#239—32no—
192C2×#239—32no—
193C2×D3×Q8C2×D311yescharacteristic
194C2×#235—34no—
195C2×#235—34no—
196C2×#235—32no—
197C2×#235—32no—
198C3×C4⋊Q8—31no—
199C3×#125—32no—
200C3×C22⋊Q8—32no—
201C3×C22⋊Q8—34no—
202C3×C4×Q8—21no—
203C3×C4×Q8—31no—
204C3×C4×Q8—31no—
205C3×C4×Q8—32no—
206C3×C4×Q8—31no—
207C3×C4×Q8—32no—
208C3×C4×Q8C2×D311yescharacteristic
209C3×C4×Q8C2×D311yescharacteristic
210C3×C4×D4—32no—
211C3×C4×D4—31no—
212C2×C3×C4⋊C4—32no—
213C2×C3×C4⋊C4—32no—
214C2×C3×C4⋊C4—31no—
215C2×C3×C42—32no—
216C2×C3×C42—31no—
217#947—32no—
218#947—32no—
219#947—34no—
220#947—32no—
221#947—62no—
222#946—34no—
223#946C2×D312yes—
224Q8×Dic3—32no—
225Q8×Dic3C2×D311yescharacteristic
226#944—34no—
227#940—32no—
228#938—31no—
229#936—31no—
230#930—31no—
231#930—34no—
232#930—32no—
233#930—32no—
234#930—32no—
235#929—32no—
236#929—34no—
237#929—34no—
238C4×#67—32no—
239C4×#67—32no—
240C4×#67—34no—
241C4×#67—34no—
242C4×#67—34no—
243#926—32no—
244#924—31no—
245#898—34no—
246#897—31no—
247#897—34no—
248#896—34no—
249#896—34no—
250#896—34no—
251#896—34no—
252#896C2×D314yes—
253#895—32no—
254#895—32no—
255#895—32no—
256#895—34no—
257#894—34no—
258#894—34no—
259#894—34no—
260#894—34no—
261#894—34no—
262#894—64no—
263#893—34no—
264#893—34no—
265#893—32no—
266#893—32no—
267#893—32no—
268#893—32no—
269#893—32no—
270#893—62no—
271#892—34no—
272D3×C4⋊C4—34no—
273D3×C4⋊C4—34no—
274D3×C4⋊C4C2×D311yescharacteristic
275D3×C4⋊C4C2×D312yes—
276D3×C4⋊C4C2×D312yes—
277#890—31no—
278#888—34no—
279#888—32no—
280#888—32no—
281#888—32no—
282#887—32no—
283#887—32no—
284#887C2×D312yes—
285#887C2×D311yescharacteristic
286#885—34no—
287#885—34no—
288#884—34no—
289#884—34no—
290#883—32no—
291#883—34no—
292#879—32no—
293#876—32no—
294#876—34no—
295#875—31no—
296#875—32no—
297#875—32no—
298#875—32no—
299#875—34no—
300#875—62no—
301#874—32no—
302#874—31no—
303#874—31no—
304#874—61no—
305C4×D12—34no—
306C4×D12—32no—
307C4×D12—32no—
308C4×D12—32no—
309C4×D12—32no—
310C4×D12—32no—
311C4×D12—62no—
312C4×D12C2×D312yes—
313C4×D12C2×D311yescharacteristic
314#872—32no—
315#872—34no—
316C42×D3C2×D312yes—
317C42×D3C2×D311yescharacteristic
318#870—31no—
319#870C2×D312yes—
320#869—32no—
321#869C2×D311yescharacteristic
322C4×Dic6—31no—
323C4×Dic6—31no—
324C4×Dic6—32no—
325C4×Dic6—61no—
326C4×Dic6C2×D312yes—
327C4×Dic6C2×D311yescharacteristic
328C22×C3⋊D3C2414yes—
329C22×C3×D3C2412yes—
330C22×C3×D3C2411yescharacteristic
331C32×Q8—22no—
332C2×C32×C4C2412yes—
333C2×C32×C4C2412yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2412yes—
339C4⋊(C3⋊D3)—24no—
340C4⋊(C3⋊D3)—24no—
341C4⋊(C3⋊D3)—42no—
342C4×C3⋊D3—44no—
343#634—22no—
344C2×C3×Dic3C2414yes—
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C3×D12—22no—
352C3×C4×D3—24no—
353C3×C4×D3—22no—
354C3×C4×D3—24no—
355C3×C4×D3—22no—
356C3×C4×D3—22no—
357C3×C4×D3—24no—
358C3×C4×D3—44no—
359C3×Dic6—24no—
360C3×Dic6—42no—
361C3×Dic6#4114yescomplemented
362#627—44no—
363#626—28no—
364#626—28no—
365#626—44no—
366#625—24no—
367#624—28no—
368#624—44no—
369#559—92no—
370#559—91no—
371Q82—91no—
372#554—31no—
373#554—92no—
374#550—91no—
375#548—92no—
376#547—92no—
377#547—94no—
378#542—94no—
379#542—92no—
380#532—92no—
381#532—91no—
382#529—91no—
383#529—92no—
384#520—92no—
385C2×C4×Q8—31no—
386C2×C3×Q8—21no—
387C2×C3×Q8—31no—
388C2×C3×Q8—32no—
389C2×C3×Q8—32no—
390C2×C3×Q8—64no—
391C2×C3×Q8C22×D311yescharacteristic
392C2×C3×Q8C22×D311yescharacteristic
393C2×C3×D4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—32no—
396C22×C3×C4—32no—
397C22×C3×C4—31no—
398C22×C3×C4—32no—
399C22×C3×C4—31no—
400C22×C3×C4—34no—
401C2×#67—32no—
402C2×#67—32no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406#239—68no—
407#239—124no—
408D3×Q8—24no—
409#235—68no—
410#235—124no—
411#235—128no—
412#235—128no—
413C2×D12—34no—
414C2×D12—34no—
415C2×D12—32no—
416C2×D12—32no—
417C2×D12—32no—
418C2×D12—32no—
419C2×D12—34no—
420C2×D12—32no—
421C2×D12—32no—
422C2×D12—62no—
423C2×D12—62no—
424C2×D12—62no—
425C2×D12C22×D311yescharacteristic
426C2×C4×D3—34no—
427C2×C4×D3—34no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—64no—
433C2×C4×D3C22×D311yescharacteristic
434C2×C4×D3C22×D311yescharacteristic
435C2×C4×D3C22×D312yes—
436C2×C4×D3C22×D312yes—
437C2×C4×D3C22×D311yescharacteristic
438C2×C4×D3C22×D312yes—
439C2×C4×D3C22×D314yes—
440C2×Dic6—31no—
441C2×Dic6—31no—
442C2×Dic6—34no—
443C2×Dic6—34no—
444C2×Dic6—61no—
445C2×Dic6C22×D312yes—
446C2×Dic6C22×D312yes—
447C2×Dic6C22×D311yescharacteristic
448C3×C4⋊C4—21no—
449C3×C4⋊C4—22no—
450C3×C4⋊C4—32no—
451C3×C4⋊C4—32no—
452C3×C4⋊C4—32no—
453C3×C4⋊C4—31no—
454C3×C4⋊C4—31no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4—34no—
457C3×C4⋊C4—34no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4C22×D311yescharacteristic
461C3×C4⋊C4C22×D312yes—
462C3×C4⋊C4C22×D311yescharacteristic
463C3×C4⋊C4C22×D312yes—
464C3×C22⋊C4—32no—
465C3×C22⋊C4—34no—
466C3×C42—21no—
467C3×C42—22no—
468C3×C42—32no—
469C3×C42—31no—
470C3×C42—32no—
471C3×C42—31no—
472C3×C42—31no—
473C3×C42—32no—
474C3×C42C22×D311yescharacteristic
475C3×C42C22×D311yescharacteristic
476C3×C42C22×D312yes—
477C3×C42C22×D312yes—
478#217—32no—
479#217—32no—
480#217—32no—
481#217—32no—
482(C2×D3)⋊C4—32no—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—64no—
499(C2×D3)⋊C4—64no—
500(C2×D3)⋊C4—64no—
501(C2×D3)⋊C4C22×D314yes—
502(C2×D3)⋊C4C22×D312yes—
503C4⋊Dic3—31no—
504C4⋊Dic3—31no—
505C4⋊Dic3—34no—
506C4⋊Dic3—32no—
507C4⋊Dic3—32no—
508C4⋊Dic3—61no—
509C4⋊Dic3C22×D312yes—
510C4⋊Dic3C22×D312yes—
511C4⋊Dic3C22×D311yescharacteristic
512C4⋊Dic3C22×D312yes—
513C4⋊Dic3C22×D311yescharacteristic
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—34no—
517Dic3⋊C4—32no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—62no—
524Dic3⋊C4C22×D312yes—
525Dic3⋊C4C22×D312yes—
526Dic3⋊C4C22×D312yes—
527Dic3⋊C4C22×D314yes—
528Dic3⋊C4C22×D314yes—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—34no—
532C4×Dic3—34no—
533C4×Dic3—62no—
534C4×Dic3C22×D312yes—
535C4×Dic3C22×D311yescharacteristic
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D312yes—
539C4×Dic3C22×D311yescharacteristic
540C22×C32C2511yescharacteristic
541C2×C3⋊D3—24no—
542C2×C3⋊D3—24no—
543C2×C3⋊D3—24no—
544C2×C3×D3—21no—
545C2×C3×D3—21no—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3—22no—
549C2×C3×D3H(5,𝔽2)12yes—
550C32×C4—22no—
551C32×C4—21no—
552C32×C4—22no—
553C32×C4C2×#4112yes—
554C32×C42−1+412yes—
555C3⋊Dic3—22no—
556C3⋊Dic3—22no—
557C3×Dic3—22no—
558C3×Dic3—21no—
559C3×Dic3—21no—
560C3×Dic3—24no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3C2×#4114yes—
564C2×#41—94no—
565C2×#41—92no—
566C2×#41—92no—
567C22×Q8—31no—
568C4⋊Q8—31no—
569C4⋊Q8—92no—
570C4⋊Q8—92no—
571C4⋊Q8—94no—
572#127—92no—
573#127—91no—
574#126—92no—
575#126—94no—
576#125—32no—
577#125—91no—
578#124—94no—
579#124—91no—
580#124—92no—
581#124—94no—
582#124—92no—
583#124—92no—
584#123—94no—
585#123—92no—
586#123—94no—
587#123—94no—
588#123—94no—
589C22⋊Q8—32no—
590C22⋊Q8—34no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—91no—
594C22⋊Q8—94no—
595#121—94no—
596#121—94no—
597#121—92no—
598#121—92no—
599#121—92no—
600#121—91no—
601C4×Q8—31no—
602C4×Q8—31no—
603C4×Q8—32no—
604C4×Q8—31no—
605C4×Q8—32no—
606C4×Q8—92no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×Q8D3211yescharacteristic
610C4×D4—31no—
611C4×D4—32no—
612C4×D4—92no—
613C4×D4—92no—
614C4×D4—92no—
615C4×D4—94no—
616C4×D4—94no—
617C4×D4—94no—
618C4×D4—92no—
619C4×D4—92no—
620C4×D4—92no—
621#117—94no—
622#117—92no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—31no—
625C2×C4⋊C4—32no—
626C2×C4⋊C4—94no—
627C2×C42—31no—
628C2×C42—32no—
629C23×C3—31no—
630C23×C3—32no—
631C22×D3—34no—
632C22×D3—34no—
633C22×D3—64no—
634C22×D3C23×D312yes—
635C22×D3C23×D311yescharacteristic
636C3×Q8—22no—
637C3×Q8—22no—
638C3×Q8—34no—
639C3×Q8—42no—
640C3×Q8—64no—
641C3×Q8—122no—
642C3×D4—62no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—32no—
649C2×C3×C4—34no—
650C2×C3×C4—31no—
651C2×C3×C4—31no—
652C2×C3×C4—32no—
653C2×C3×C4—31no—
654C2×C3×C4—32no—
655C2×C3×C4—64no—
656C2×C3×C4—62no—
657C2×C3×C4—64no—
658C2×C3×C4—64no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—124no—
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D312yes—
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672#67—68no—
673#67—64no—
674#67—64no—
675#67—68no—
676#67—124no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3C23×D314yes—
684C2×Dic3C23×D311yescharacteristic
685C2×Dic3C23×D312yes—
686C2×Dic3C23×D311yescharacteristic
687C2×Dic3C23×D311yescharacteristic
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D312yes—
690D12—22no—
691D12—68no—
692D12—68no—
693D12—64no—
694D12—64no—
695D12—64no—
696D12—64no—
697D12—124no—
698D12—124no—
699D12—122no—
700D12—122no—
701D12—124no—
702D12—242no—
703C4×D3—24no—
704C4×D3—22no—
705C4×D3—22no—
706C4×D3—22no—
707C4×D3—24no—
708C4×D3—24no—
709C4×D3—44no—
710C4×D3—68no—
711C4×D3—68no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3—124no—
715C4×D3—124no—
716C4×D3—244no—
717Dic6—24no—
718Dic6—42no—
719Dic6—62no—
720Dic6—62no—
721Dic6—122no—
722Dic6—124no—
723Dic6—124no—
724Dic6#23514yescomplemented
725C2×C32C22×#4111yescharacteristic
726C2×C32C2×H(5,𝔽2)11yescharacteristic
727C2×C32C2×2−1+411yescharacteristic
728C3⋊D3—44no—
729C3×D3—22no—
730C3×D3—42no—
731#41—188no—
732#41—368no—
733#41—364no—
734C2×Q8—31no—
735C2×Q8—32no—
736C2×Q8—32no—
737C2×Q8—64no—
738C2×Q8—94no—
739C2×Q8—91no—
740C2×Q8C2×D3211yescharacteristic
741C2×D4—31no—
742C2×D4—94no—
743C2×D4—94no—
744C2×D4—94no—
745C2×D4—92no—
746C2×D4—92no—
747C2×D4—92no—
748C2×D4—92no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—31no—
754C22×C4—32no—
755C22×C4—34no—
756C22×C4—94no—
757C22×C4—94no—
758C22×C4—94no—
759C4⋊C4—32no—
760C4⋊C4—34no—
761C4⋊C4—32no—
762C4⋊C4—32no—
763C4⋊C4—31no—
764C4⋊C4—32no—
765C4⋊C4—32no—
766C4⋊C4—31no—
767C4⋊C4—32no—
768C4⋊C4—34no—
769C4⋊C4—92no—
770C4⋊C4—94no—
771C4⋊C4—92no—
772C4⋊C4—92no—
773C4⋊C4—94no—
774C4⋊C4—91no—
775C4⋊C4—92no—
776C4⋊C4C2×D3211yescharacteristic
777C4⋊C4C2×D3212yes—
778C22⋊C4—32no—
779C22⋊C4—34no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4—92no—
784C22⋊C4—92no—
785C22⋊C4—92no—
786C22⋊C4—92no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C42—32no—
791C42—31no—
792C42—31no—
793C42—32no—
794C42—31no—
795C42—32no—
796C42—94no—
797C42—92no—
798C42C2×D3212yes—
799C42C2×D3211yescharacteristic
800C22×C3—21no—
801C22×C3—32no—
802C22×C3—61no—
803C22×C3—61no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—62no—
807C22×C3C24×D311yescharacteristic
808C22×C3C24×D311yescharacteristic
809C2×D3—21no—
810C2×D3—21no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—64no—
815C2×D3—64no—
816C2×D3—64no—
817C2×D3—64no—
818C2×D3—64no—
819C2×D3—64no—
820C2×D3—124no—
821C2×D3—124no—
822C2×D3—124no—
823C2×D3#100912yes—
824C3×C4—22no—
825C3×C4—22no—
826C3×C4—22no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—22no—
830C3×C4—22no—
831C3×C4—22no—
832C3×C4—34no—
833C3×C4—42no—
834C3×C4—41no—
835C3×C4—42no—
836C3×C4—62no—
837C3×C4—61no—
838C3×C4—61no—
839C3×C4—64no—
840C3×C4—62no—
841C3×C4—61no—
842C3×C4C2×#23512yes—
843C3×C4#100712yes—
844C3×C4#100712yes—
845C3×C4D3×#4112yes—
846Dic3—21no—
847Dic3—21no—
848Dic3—22no—
849Dic3—22no—
850Dic3—21no—
851Dic3—24no—
852Dic3—62no—
853Dic3—62no—
854Dic3—62no—
855Dic3—62no—
856Dic3—122no—
857Dic3—122no—
858Dic3C2×#23514yes—
859C32#352211yescharacteristic, complemented, Sylow
860C23—31no—
861C23—32no—
862C23—94no—
863Q8—22no—
864Q8—34no—
865Q8—64no—
866Q8—122no—
867Q8—182no—
868Q8—364no—
869D4—62no—
870D4—188no—
871D4—188no—
872D4—184no—
873D4—184no—
874D4—184no—
875D4—362no—
876D4—364no—
877C2×C4—32no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—32no—
882C2×C4—34no—
883C2×C4—32no—
884C2×C4—64no—
885C2×C4—64no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—64no—
889C2×C4—62no—
890C2×C4—92no—
891C2×C4—92no—
892C2×C4—124no—
893C2×C4—188no—
894C2×C4—364no—
895C2×C4—364no—
896C2×C4C22×D3212yes—
897C2×C4C22×D3211yescharacteristic
898C2×C4C22×D3212yes—
899C2×C4C22×D3211yescharacteristic
900C2×C4C22×D3211yescharacteristic
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—62no—
905C2×C3—122no—
906C2×C3C22×#23511yescharacteristic
907C2×C3C2×#100711yescharacteristic
908C2×C3C2×#100711yescharacteristic
909C2×C3C2×D3×#4111yescharacteristic
910C2×C3C2×#100911yescharacteristic
911C2×C3D3×H(5,𝔽2)11yescharacteristic
912D3—22no—
913D3—42no—
914D3—124no—
915D3—124no—
916D3—244no—
917C22—32no—
918C22—61no—
919C22—61no—
920C22—62no—
921C22—62no—
922C22—62no—
923C22—184no—
924C22—184no—
925C22—184no—
926C22C23×D3211yescharacteristic
927C4—22no—
928C4—22no—
929C4—21no—
930C4—34no—
931C4—62no—
932C4—61no—
933C4—61no—
934C4—61no—
935C4—62no—
936C4—64no—
937C4—182no—
938C4—182no—
939C4D3×#23512yes—
940C4#6431612yes—
941C3—21no—
942C3#8582111yescharacteristic, complemented
943C3#8693611yescharacteristic, complemented
944C2—62no—
945C2—122no—
946C2—364no—
947C2C2×D3×#23511yescharacteristic
948C2C2×#6431611yescharacteristic
949C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596056C2semidirect
2. C3×#5579C2semidirect
3. C3×C4×D3×Q8C2semidirect
4. #10595402C2semidirect
5. #10595346C2semidirect
6. #10594516C2semidirect
7. #10594512C2semidirect
8. #10594330C2semidirect
9. #10594327C2semidirect
10. #10593978C2semidirect
11. #10593976C2semidirect
12. #10593974C2semidirect
13. #10593970C2semidirect
14. #10593968C2semidirect
15. #10593938C2semidirect
16. #10593902C2semidirect
17. #10593856C2semidirect
103. #5579D3semidirect
106. C4×D3×Q8D3semidirect
361. C3×Dic6#41semidirect
724. Dic6#235semidirect
859. C32#3522semidirect
942. C3#85821semidirect
943. C3#86936semidirect

Maximal subgroups

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

subgroupindex
#105960562
C3×#55792
C3×C4×D3×Q82
#105954022
#105953462
#105945162
#105945122
#105943302
#105943272
#105939782
#105939762
#105939742
#105939702
#105939682
#105939382
#105939022
#105938562
#869363
#858213