Finite Group Databasebeta

← #11889100

Subgroups — #11889100

Order 1152.

994 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5642C211yesmaximal, characteristic, complemented
2#10595074C211yesmaximal, characteristic
3#10592745C211yesmaximal, characteristic, complemented
4C3×#5048C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic, complemented
6#10591617C211yesmaximal, characteristic, complemented
7#10591589C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591155C211yesmaximal, characteristic, complemented
10C2×#63564C211yesmaximal, characteristic, complemented
11#10591089C211yesmaximal, characteristic, complemented
12#10590592C211yesmaximal, characteristic, complemented
13#10590550C211yesmaximal, characteristic, complemented
14#10590470C211yesmaximal, characteristic, complemented
15#10590425C211yesmaximal, characteristic, complemented
16#83599—31nomaximal
17#80685—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C2×#3755C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic, complemented
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C3×#930C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
30C22×C3×C3⋊C8C2211yescharacteristic, complemented
31C3×#898—21no—
32C3×#892C2211yescharacteristic, complemented
33C3×#890—21no—
34C3×#890C2211yescharacteristic, complemented
35C3×#886—21no—
36C3×#877—21no—
37#63981—21no—
38#63923—21no—
39#63911C2211yescharacteristic
40#63910—21no—
41#63909C2211yescharacteristic
42#63894C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44#63657C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50#63576C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#552—31no—
62#5642D311yescharacteristic, complemented
63#5609—31no—
64D4×D12—31no—
65C3×#465—31no—
66#5169—31no—
67#5163—31no—
68C2×#821—31no—
69#5111—31no—
70#5067—31no—
71#5066—31no—
72#5049—31no—
73#5048D311yescharacteristic, complemented
74#5046—31no—
75#5046—31no—
76#5046—31no—
77#5046—61no—
78#5033—31no—
79#5027—31no—
80#5026—31no—
81#5011—31no—
82#5003—31no—
83#5001—31no—
84#4967—31no—
85C2×#809—31no—
86#4871—31no—
87#4866—31no—
88#4817—31no—
89#4812—31no—
90#4770—31no—
91#4764—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106#3811—44no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#624—21no—
112D3×D12—22no—
113D3×D12—41no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117#3755—22no—
118#3755—41no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217D411yescharacteristic
122C3×#215—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8—41no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142#3722—21no—
143#3722—21no—
144#3711—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—61no—
148C2×D3×D4—61no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—61no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×#126—61no—
156C3×#125—31no—
157C3×#125—61no—
158C3×#123—61no—
159C3×C22⋊Q8—21no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8C2×D311yescharacteristic, complemented
162C3×C22⋊Q8C2×D311yescharacteristic, complemented
163C3×#121—31no—
164C3×C4×Q8—31no—
165C3×C4×D4—31no—
166C3×#117—31no—
167C3×#117—61no—
168C2×C3×C4⋊C4—31no—
169#946C2×D311yescharacteristic, complemented
170Q8×Dic3C2×D311yescharacteristic, complemented
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—31no—
175C2×#215—61no—
176C2×#215—61no—
177C2×#215C2×D311yescharacteristic, complemented
178#940—31no—
179#937—61no—
180#930—31no—
181#930C2×D311yescharacteristic
182C4×#67C2×D311yescharacteristic
183C2×C4⋊Dic3C2×D311yescharacteristic, complemented
184C2×#208—31no—
185C22×C3⋊C8C2×D311yescharacteristic, complemented
186C2×ΓL(1,𝔽25)—31no—
187#898—21no—
188#895—31no—
189#895—61no—
190#893—31no—
191#892C2×D311yescharacteristic, complemented
192#890—21no—
193#890C2×D311yescharacteristic, complemented
194#886—21no—
195#884—61no—
196#882—61no—
197#882—61no—
198#882—61no—
199#877—21no—
200#874—31no—
201C4×D12—31no—
202C3×#106—31no—
203C3×#103—31no—
204C3×#102—31no—
205#835C2×D311yescharacteristic, complemented
206#832—31no—
207#832—31no—
208#830—31no—
209#830—31no—
210#830—31no—
211#830—61no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216(C2×D3)⋊C8—31no—
217#815—31no—
218Dic3⋊C8—31no—
219#809—31no—
220#809—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#809—61no—
231#809C2×D311yescharacteristic, complemented
232#808C2×D311yescharacteristic, complemented
233#807—31no—
234#807—31no—
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—42no—
243C22×C3⋊D3—42no—
244C22×C3⋊D3—81no—
245C22×C3×D3—21no—
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
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—42no—
262C4⋊(C3⋊D3)#4112yes—
263C3×#67—22no—
264C3×#67—42no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—42no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276#626—42no—
277#626—42no—
278#626—42no—
279#626—81no—
280#624—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—31no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—121no—
305C2×C3×Q8—21no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—61no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C2×#67—21no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67#6711yescharacteristic
322C22×Dic3—21no—
323D3×D4—62no—
324D3×D4—121no—
325D3×D4—124no—
326D3×D4—124no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—62no—
334C2×D12—62no—
335C2×D12—62no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—122no—
343C2×D12—121no—
344C2×D12—121no—
345C2×D12—121no—
346C2×D12—121no—
347C2×D12—122no—
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3C22×D311yescharacteristic
352C3×SD16—121no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—121no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—41no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—41no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C42—31no—
380C3×C42—61no—
381C3×C42—61no—
382#217#6711yescharacteristic
383#215—41no—
384#215—62no—
385#215—62no—
386#215—122no—
387#215—121no—
388#215—121no—
389#215—122no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4#6711yescharacteristic
398C4⋊Dic3—21no—
399C4⋊Dic3—21no—
400C4⋊Dic3—21no—
401C4⋊Dic3C22×D311yescharacteristic
402C4⋊Dic3C22×D311yescharacteristic
403C4⋊Dic3C22×D311yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4#6711yescharacteristic
407C4×Dic3—21no—
408C4×Dic3—21no—
409C4×Dic3C22×D311yescharacteristic
410#208—121no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—41no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420ΓL(1,𝔽25)—121no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32AGL(1,ℤ/8)12yes—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—22no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—84no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438D32—84no—
439C32×C4—21no—
440C32×C4—41no—
441C32×C4—41no—
442C32×C4C2×#4111yescharacteristic
443C32×C4H(5,𝔽2)11yescharacteristic
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—91no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—31no—
454C2×SD16—91no—
455C2×SD16—91no—
456C2×M16—91no—
457C22×C8—31no—
458#127—91no—
459#126—61no—
460#125—31no—
461#125—61no—
462#123—61no—
463C22⋊Q8—31no—
464C22⋊Q8D3211yescharacteristic, complemented
465#121—31no—
466#121—91no—
467#121—181no—
468#120—181no—
469#120—181no—
470C4×Q8—31no—
471C4×D4—31no—
472C4×D4—91no—
473#117—31no—
474#117—61no—
475C2×C4⋊C4—31no—
476#107—91no—
477#107—91no—
478#106—31no—
479C4⋊C8—91no—
480#103—31no—
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—91no—
491C22⋊C8—91no—
492#97—91no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—61no—
496C23×C3D3×D411yescharacteristic
497C23×C3C2×#6711yescharacteristic
498C22×D3—21no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—124no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—242no—
515C22×D3—241no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—241no—
519C22×D3—242no—
520C22×D3C2×#6711yescharacteristic
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—41no—
526C3×Q8—41no—
527C3×D4—62no—
528C3×D4—61no—
529C3×D4—61no—
530C3×D4—122no—
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—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—122no—
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4C2×#6711yescharacteristic
556C2×C3×C4C23×D311yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558#67—22no—
559#67—42no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—241no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—42no—
568C2×Dic3C2×#6711yescharacteristic
569C2×Dic3C2×#6711yescharacteristic
570C2×Dic3C2×#6711yescharacteristic
571D12—21no—
572D12—21no—
573D12—32no—
574D12—32no—
575D12—62no—
576D12—62no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—61no—
581D12—61no—
582D12—61no—
583D12—121no—
584D12—121no—
585D12—122no—
586D12—122no—
587D12—124no—
588D12—122no—
589D12—122no—
590D12—122no—
591D12—241no—
592C4×D3—21no—
593C4×D3—21no—
594C4×D3—122no—
595C4×D3—122no—
596C3×C8—61no—
597C3×C8—61no—
598C3⋊C8—21no—
599C3⋊C8—21no—
600C3⋊C8—61no—
601C3⋊C8—61no—
602C3⋊C8—61no—
603C3⋊C8—61no—
604C3⋊C8—121no—
605C3⋊C8—121no—
606C2×C32—22no—
607C2×C32#54611yescharacteristic
608C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
609C2×C32#57711yescharacteristic
610C3⋊D3—42no—
611C3⋊D3—81no—
612C3×D3—41no—
613C3×D3—81no—
614C24—181no—
615C24—181no—
616C2×Q8C2×D3211yescharacteristic
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—61no—
620C2×D4—91no—
621C2×D4—91no—
622C2×D4—182no—
623C2×D4—181no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—182no—
627C2×D4—181no—
628C2×D4—181no—
629C2×D4—361no—
630C2×D4—361no—
631C2×D4—364no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—181no—
635C22×C4C2×D3211yescharacteristic
636SD16—121no—
637SD16—182no—
638SD16—361no—
639M16—361no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—91no—
643C2×C8—91no—
644C2×C8—121no—
645C4⋊C4—21no—
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—31no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—61no—
654C4⋊C4—61no—
655C4⋊C4C2×D3211yescharacteristic
656C22⋊C4—21no—
657C22⋊C4—31no—
658C22⋊C4—31no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4—61no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—31no—
665C42—61no—
666C42—61no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—22no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3#91412yes—
682C22×C3#94912yes—
683C22×C3C2×D3×D411yescharacteristic
684C22×C3C22×#6711yescharacteristic
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—122no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—122no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—241no—
708C2×D3—241no—
709C2×D3—244no—
710C2×D3—244no—
711C2×D3—244no—
712C2×D3—244no—
713C2×D3—248no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—61no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—81no—
727C3×C4—81no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4#100411yescharacteristic
732C3×C4D3×#4111yescharacteristic
733C3×C4D3×#4111yescharacteristic
734C3×C4#100911yescharacteristic
735Dic3—21no—
736Dic3—21no—
737Dic3—21no—
738Dic3—41no—
739Dic3—41no—
740Dic3—41no—
741C32#331011yescharacteristic, complemented, Sylow
742C23—31no—
743C23—61no—
744C23—181no—
745C23—181no—
746C23—362no—
747C23—362no—
748C23—362no—
749C23—362no—
750C23—721no—
751C23—721no—
752C23D3×#6711yescharacteristic
753Q8—21no—
754Q8—21no—
755D4—62no—
756D4—61no—
757D4—61no—
758D4—92no—
759D4—122no—
760D4—181no—
761D4—181no—
762D4—181no—
763D4—362no—
764D4—362no—
765D4—362no—
766D4—362no—
767D4—721no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—31no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—122no—
781C2×C4—362no—
782C2×C4D3×#6711yescharacteristic
783C2×C4C22×D3211yescharacteristic
784C8—61no—
785C8—61no—
786C8—181no—
787C8—181no—
788C2×C3—22no—
789C2×C3—22no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—42no—
794C2×C3—121no—
795C2×C3—241no—
796C2×C3#561011yescharacteristic
797C2×C3C2×#91411yescharacteristic
798C2×C3#577011yescharacteristic
799C2×C3C2×#94911yescharacteristic
800C2×C3#582911yescharacteristic
801C2×C3#583711yescharacteristic
802D3—41no—
803D3—81no—
804D3—122no—
805D3—122no—
806D3—242no—
807D3—242no—
808D3—241no—
809D3—241no—
810C22—21no—
811C22—21no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—182no—
819C22—361no—
820C22—361no—
821C22—361no—
822C22—361no—
823C22—361no—
824C22—724no—
825C22—724no—
826C22#6393912yes—
827C22C2×D3×#6711yescharacteristic
828C4—21no—
829C4—41no—
830C4—41no—
831C4—61no—
832C4—61no—
833C4—61no—
834C4—121no—
835C4—121no—
836C4—121no—
837C4#6431211yescharacteristic
838C4#6431411yescharacteristic
839C3—21no—
840C3#8068511yescharacteristic, complemented
841C3#8359911yescharacteristic, complemented
842C2—22no—
843C2—121no—
844C2—241no—
845C2—362no—
846C2—721no—
847C2#1059530511yescharacteristic
848C2C2×#6393911yescharacteristic
849C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595074C2
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. #10592745C2semidirect
4. C3×#5048C2semidirect
5. #10591651C2semidirect
6. #10591617C2semidirect
7. #10591589C2semidirect
8. #10591540C2semidirect
9. #10591155C2semidirect
10. C2×#63564C2semidirect
11. #10591089C2semidirect
12. #10590592C2semidirect
13. #10590550C2semidirect
14. #10590470C2semidirect
15. #10590425C2semidirect
21. C32×C22⋊Q8C22semidirect
23. C2×#3755C22semidirect
24. C3×#946C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#215C22semidirect
29. C2×C3×C4⋊Dic3C22semidirect
30. C22×C3×C3⋊C8C22semidirect
32. C3×#892C22semidirect
34. C3×#890C22semidirect
43. C2×#3711C22semidirect
44. #63657C22semidirect
46. #63636C22semidirect
47. C3×#835C22semidirect
48. C3×#809C22semidirect
49. C3×#808C22semidirect
50. #63576C22semidirect
51. #63576C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
62. #5642D3semidirect
73. #5048D3semidirect
161. C3×C22⋊Q8C2×D3semidirect
162. C3×C22⋊Q8C2×D3semidirect
169. #946C2×D3semidirect
170. Q8×Dic3C2×D3semidirect
177. C2×#215C2×D3semidirect
183. C2×C4⋊Dic3C2×D3semidirect
185. C22×C3⋊C8C2×D3semidirect
191. #892C2×D3semidirect
193. #890C2×D3semidirect
205. #835C2×D3semidirect
231. #809C2×D3semidirect
232. #808C2×D3semidirect
464. C22⋊Q8D32semidirect
741. C32#3310semidirect
840. C3#80685semidirect
841. C3#83599semidirect

Maximal subgroups

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

subgroupindex
C3×#56422
#105950742
#105927452
C3×#50482
#105916512
#105916172
#105915892
#105915402
#105911552
C2×#635642
#105910892
#105905922
#105905502
#105904702
#105904252
#835993
#806853