Finite Group Databasebeta

← #11889101

Subgroups — #11889101

Order 1152.

962 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5642C211yesmaximal, characteristic, complemented
2D12×#67C211yesmaximal, characteristic
3#10592747C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic, complemented
6#10591617C211yesmaximal, characteristic, complemented
7#10591587C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591158C211yesmaximal, characteristic, complemented
10#10591133C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12#10590592C211yesmaximal, characteristic, complemented
13#10590550C211yesmaximal, characteristic, complemented
14#10590505C211yesmaximal, characteristic, complemented
15#10590469C211yesmaximal, characteristic, complemented
16#83599—31nomaximal
17#80160—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
25C3×#946C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic, complemented
29C3×C4×#67C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
31C3×#898—21no—
32C3×#892C2211yescharacteristic, complemented
33C3×#890—21no—
34C3×#890C2211yescharacteristic, complemented
35C3×#886—21no—
36C3×#877—21no—
37#63977—21no—
38#63922—21no—
39#63911C2211yescharacteristic
40#63908C2211yescharacteristic
41Dic3×D12C2211yescharacteristic
42#63886—21no—
43C2×#3711C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63564C2211yescharacteristic, complemented
54#63564C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#552—31no—
62D4×#67—31no—
63#5642D311yescharacteristic, complemented
64D4×D12—31no—
65C3×#450—31no—
66C2×#832—31no—
67#5174—31no—
68#5169—31no—
69#5164—31no—
70#5163—31no—
71#5067—31no—
72#5066—31no—
73#5049—31no—
74#5048—31no—
75#5048—31no—
76#5048—61no—
77#5046—31no—
78#5046D311yescharacteristic, complemented
79#5027—31no—
80#5026—31no—
81#5011—31no—
82#5003—31no—
83#5001—31no—
84#4967—31no—
85C2×#809—31no—
86#4784—31no—
87#4770—31no—
88#4766—31no—
89#4764—31no—
90#4736—31no—
91#4730—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106D3×#67—44no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—41no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117#3755—41no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)—41no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217D411yescharacteristic
124C3×#215—22no—
125C3×#215—41no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144#3711—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×#126—61no—
155C3×#125—31no—
156C3×#125—61no—
157C3×#123—61no—
158C3×C22⋊Q8—21no—
159C3×C22⋊Q8—31no—
160C3×C22⋊Q8C2×D311yescharacteristic, complemented
161C3×C22⋊Q8C2×D311yescharacteristic, complemented
162C3×C4×Q8—31no—
163C3×C4×D4—31no—
164C3×#117—31no—
165C3×#117—61no—
166C2×C3×C4⋊C4—31no—
167#953—61no—
168#946C2×D311yescharacteristic, complemented
169Q8×Dic3C2×D311yescharacteristic, complemented
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—61no—
173C2×#215C2×D311yescharacteristic
174C2×#215C2×D311yescharacteristic, complemented
175#940—31no—
176#939—61no—
177#938—31no—
178#937—61no—
179D4×Dic3—31no—
180#930—31no—
181#930—31no—
182#930—31no—
183#930—61no—
184C4×#67C2×D311yescharacteristic
185C2×C4⋊Dic3C2×D311yescharacteristic, complemented
186C2×#208—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—61no—
190C2×ΓL(1,𝔽25)—31no—
191#898—21no—
192#895—61no—
193#892C2×D311yescharacteristic, complemented
194#890—21no—
195#890C2×D311yescharacteristic, complemented
196#886—21no—
197#882—61no—
198#882—61no—
199#877—21no—
200#874—31no—
201C4×D12—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205#835—31no—
206#835—31no—
207#835—61no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#830—31no—
213#830C2×D311yescharacteristic, complemented
214#821—31no—
215#821—31no—
216(C2×D3)⋊C8—31no—
217#818—31no—
218#818—31no—
219#815—31no—
220Dic3⋊C8—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#809C2×D311yescharacteristic
231#809C2×D311yescharacteristic, complemented
232#808—31no—
233#808—31no—
234#808—61no—
235#807—31no—
236#807—31no—
237C4⋊(C3⋊C8)—31no—
238#803—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×Q8—21no—
251C32×Q8—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258#638—42no—
259C2×C3⋊Dic3—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—21no—
262C3×#67—22no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—42no—
273C3×D12#4112yes—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276#626—42no—
277#626—42no—
278#626—81no—
279#625—42no—
280D3×Dic3—42no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—31no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—31no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—21no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—62no—
311C2×C3×D4—61no—
312C2×C3×D4—121no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—121no—
326C2×#67—124no—
327C2×#67#6711yescharacteristic
328C22×Dic3—21no—
329C22×Dic3—61no—
330D3×D4—62no—
331D3×D4—121no—
332D3×D4—124no—
333C2×D12—22no—
334C2×D12—21no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—41no—
338C2×D12—61no—
339C2×D12—62no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—121no—
344C2×D12C22×D311yescharacteristic
345C2×D12C22×D311yescharacteristic
346C2×C4×D3—61no—
347C2×C4×D3C22×D311yescharacteristic
348C3×SD16—62no—
349C3×SD16—121no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—41no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—41no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C42—31no—
374C3×C42—61no—
375C3×C42—61no—
376#217—61no—
377#217—61no—
378#217#6711yescharacteristic
379#215—22no—
380#215—41no—
381#215—121no—
382#215—121no—
383#215—122no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—121no—
391(C2×D3)⋊C4#6711yescharacteristic
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3—21no—
395C4⋊Dic3—31no—
396C4⋊Dic3—31no—
397C4⋊Dic3—61no—
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4#6711yescharacteristic
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3C22×D311yescharacteristic
406#208—121no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—121no—
414C2×C3⋊C8—121no—
415C2×C3⋊C8—122no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418ΓL(1,𝔽25)—121no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32AGL(1,ℤ/8)12yes—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—22no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—84no—
436D32—84no—
437C32×C4—21no—
438C32×C4—41no—
439C32×C4—41no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—31no—
453C2×SD16—91no—
454C2×M16—91no—
455C22×C8—91no—
456#127—91no—
457#126—61no—
458#125—31no—
459#125—61no—
460#123—61no—
461C22⋊Q8—31no—
462C22⋊Q8D3211yescharacteristic, complemented
463#121—91no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—31no—
469C4×D4—31no—
470C4×D4—91no—
471#117—31no—
472#117—61no—
473C2×C4⋊C4—31no—
474#107—91no—
475#107—91no—
476#106—91no—
477C4⋊C8—91no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—31no—
489C22⋊C8—91no—
490#97—91no—
491C23×C3—21no—
492C23×C3—31no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—122no—
496C23×C3—122no—
497C23×C3—241no—
498C23×C3D3×D411yescharacteristic
499C23×C3C2×#6711yescharacteristic
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—42no—
503C22×D3—42no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—81no—
507C22×D3—121no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3C2×#6711yescharacteristic
515C3×Q8—21no—
516C3×Q8—21no—
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—41no—
520C3×Q8—41no—
521C3×D4—32no—
522C3×D4—62no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—61no—
526C3×D4—122no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—122no—
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—22no—
554#67—122no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—122no—
559#67—122no—
560#67—242no—
561#67—241no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—42no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—121no—
568C2×Dic3—122no—
569C2×Dic3C2×#6711yescharacteristic
570C2×Dic3C2×#6711yescharacteristic
571C2×Dic3C2×#6711yescharacteristic
572D12—21no—
573D12—21no—
574D12—21no—
575D12—42no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12—121no—
582D12—122no—
583D12—122no—
584D12—241no—
585D12#23712yes—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—122no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—62no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—121no—
599C2×C32—22no—
600C2×C32#54611yescharacteristic
601C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
602C2×C32#57711yescharacteristic
603C3⋊D3—81no—
604C3×D3—41no—
605C3×D3—42no—
606C3×D3—81no—
607C24—61no—
608C24—181no—
609C2×Q8C2×D3211yescharacteristic
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—62no—
614C2×D4—61no—
615C2×D4—91no—
616C2×D4—121no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—181no—
620C2×D4—182no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—361no—
624C2×D4—364no—
625C22×C4—31no—
626C22×C4—61no—
627C22×C4—181no—
628C22×C4C2×D3211yescharacteristic
629SD16—62no—
630SD16—121no—
631SD16—361no—
632M16—361no—
633C2×C8—31no—
634C2×C8—31no—
635C2×C8—91no—
636C2×C8—91no—
637C2×C8—361no—
638C4⋊C4—21no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—91no—
648C4⋊C4C2×D3211yescharacteristic
649C22⋊C4—21no—
650C22⋊C4—31no—
651C22⋊C4—31no—
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C42—31no—
658C42—61no—
659C42—61no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—22no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—62no—
671C22×C3—61no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—244no—
678C22×C3#91412yes—
679C22×C3#94912yes—
680C22×C3C2×D3×D411yescharacteristic
681C22×C3C22×#6711yescharacteristic
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—22no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—84no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—241no—
699C2×D3—241no—
700C2×D3—241no—
701C2×D3—244no—
702C2×D3—244no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—81no—
716C3×C4—81no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4C2×#23711yescharacteristic
720C3×C4#100411yescharacteristic
721C3×C4D3×#4111yescharacteristic
722C3×C4#100911yescharacteristic
723Dic3—21no—
724Dic3—21no—
725Dic3—21no—
726Dic3—41no—
727Dic3—41no—
728Dic3—121no—
729Dic3—121no—
730Dic3—241no—
731C32#331011yescharacteristic, complemented, Sylow
732C23—31no—
733C23—61no—
734C23—61no—
735C23—122no—
736C23—122no—
737C23—181no—
738C23—241no—
739C23—362no—
740C23—362no—
741C23—721no—
742C23D3×#6711yescharacteristic
743Q8—21no—
744Q8—21no—
745D4—32no—
746D4—62no—
747D4—61no—
748D4—61no—
749D4—61no—
750D4—122no—
751D4—181no—
752D4—181no—
753D4—362no—
754D4—362no—
755D4—362no—
756D4—362no—
757D4—721no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—122no—
770C2×C4—181no—
771C2×C4—362no—
772C2×C4D3×#6711yescharacteristic
773C2×C4C22×D3211yescharacteristic
774C8—61no—
775C8—61no—
776C8—181no—
777C8—181no—
778C2×C3—22no—
779C2×C3—22no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—42no—
784C2×C3—121no—
785C2×C3—122no—
786C2×C3—241no—
787C2×C3#559111yescharacteristic
788C2×C3C2×#91411yescharacteristic
789C2×C3#577511yescharacteristic
790C2×C3C2×#94911yescharacteristic
791C2×C3#582911yescharacteristic
792C2×C3#583711yescharacteristic
793D3—42no—
794D3—41no—
795D3—81no—
796D3—241no—
797D3—241no—
798D3—481no—
799C22—21no—
800C22—21no—
801C22—61no—
802C22—61no—
803C22—62no—
804C22—61no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—244no—
811C22—361no—
812C22—361no—
813C22—361no—
814C22—724no—
815C22#6393912yes—
816C22C2×D3×#6711yescharacteristic
817C4—21no—
818C4—41no—
819C4—41no—
820C4—61no—
821C4—61no—
822C4—61no—
823C4—121no—
824C4—121no—
825C4—361no—
826C4D3×#23711yescharacteristic
827C4#6431411yescharacteristic
828C3—21no—
829C3#8016011yescharacteristic, complemented
830C3#8359911yescharacteristic, complemented
831C2—22no—
832C2—121no—
833C2—122no—
834C2—241no—
835C2—721no—
836C2#1059530411yescharacteristic
837C2C2×#6393911yescharacteristic
838C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalD12×#67C2
hypercenterC22⋊Q8D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5642C2semidirect
3. #10592747C2semidirect
4. C3×#5046C2semidirect
5. #10591651C2semidirect
6. #10591617C2semidirect
7. #10591587C2semidirect
8. #10591566C2semidirect
9. #10591158C2semidirect
10. #10591133C2semidirect
11. C2×#63562C2semidirect
12. #10590592C2semidirect
13. #10590550C2semidirect
14. #10590505C2semidirect
15. #10590469C2semidirect
21. C32×C22⋊Q8C22semidirect
22. C2×#3755C22semidirect
24. C22×C3⋊(C3⋊C8)C22semidirect
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
28. C2×C3×#215C22semidirect
30. C2×C3×C4⋊Dic3C22semidirect
32. C3×#892C22semidirect
34. C3×#890C22semidirect
43. C2×#3711C22semidirect
44. #63662C22semidirect
45. #63636C22semidirect
46. #63635C22semidirect
47. C3×#830C22semidirect
49. C3×#809C22semidirect
50. #63575C22semidirect
51. #63575C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63564C22semidirect
54. #63564C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
63. #5642D3semidirect
78. #5046D3semidirect
160. C3×C22⋊Q8C2×D3semidirect
161. C3×C22⋊Q8C2×D3semidirect
168. #946C2×D3semidirect
169. Q8×Dic3C2×D3semidirect
174. C2×#215C2×D3semidirect
185. C2×C4⋊Dic3C2×D3semidirect
193. #892C2×D3semidirect
195. #890C2×D3semidirect
213. #830C2×D3semidirect
231. #809C2×D3semidirect
462. C22⋊Q8D32semidirect
731. C32#3310semidirect
829. C3#80160semidirect
830. C3#83599semidirect

Maximal subgroups

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

subgroupindex
C3×#56422
D12×#672
#105927472
C3×#50462
#105916512
#105916172
#105915872
#105915662
#105911582
#105911332
C2×#635622
#105905922
#105905502
#105905052
#105904692
#835993
#801603