Finite Group Databasebeta

← #11889123

Subgroups — #11889123

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5694C211yesmaximal, characteristic, complemented
2#10594004C211yesmaximal, characteristic
3#10592765C211yesmaximal, characteristic, complemented
4C3×#5067C211yesmaximal, characteristic, complemented
5#10590596C211yesmaximal, characteristic, complemented
6#10590596C211yesmaximal, characteristic, complemented
7#10590592C211yesmaximal, characteristic, complemented
8D3×#809C211yesmaximal, characteristic, complemented
9#10590505C211yesmaximal, characteristic, complemented
10#10590503C211yesmaximal, characteristic, complemented
11#10590501C211yesmaximal, characteristic, complemented
12#10590498C211yesmaximal, characteristic, complemented
13#10590364C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83599—31nomaximal
17#81725—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C32×#125C2211yescharacteristic, complemented
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#898—21no—
24C3×#897C2211yescharacteristic, complemented
25C3×#897C2211yescharacteristic, complemented
26C3×#894—21no—
27C3×#892—21no—
28C3×#892C2211yescharacteristic, complemented
29C3×D3×C4⋊C4C2211yescharacteristic, complemented
30C3×#890—21no—
31C3×#874C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic, complemented
34#63922—21no—
35#63922—21no—
36#63916—21no—
37#63908C2211yescharacteristic
38#63908C2211yescharacteristic
39C2×#3717C2211yescharacteristic
40C2×#3715C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic, complemented
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46#63635C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×#809C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#552—31no—
62#5717—31no—
63#5694D311yescharacteristic, complemented
64D4×D12—31no—
65C3×#490—31no—
66#5075—31no—
67#5067D311yescharacteristic, complemented
68#5066—31no—
69#5066—31no—
70#5066—61no—
71#5049—31no—
72#5048—31no—
73#5046—31no—
74#5046—31no—
75#5027—31no—
76#5026—31no—
77#5011—31no—
78#5003—31no—
79#5001—31no—
80#4967—31no—
81C2×#809—31no—
82#4784—31no—
83#4780—31no—
84#4778—31no—
85#4776—31no—
86#4776—31no—
87#4774—31no—
88#4770—31no—
89D3×#102—31no—
90#4710—31no—
91#4706—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12—21no—
97C2×C3×D12—21no—
98C2×C3×D12D411yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#625—21no—
109#3802—44no—
110D3×D12—22no—
111D3×D12—22no—
112D3×D12—41no—
113D3×D12—41no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C42C2311yescharacteristic
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3717—22no—
141#3715—41no—
142#3715—41no—
143#3711—41no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12—31no—
152C3×#127—31no—
153C3×#126—61no—
154C3×#125—21no—
155C3×#125—61no—
156C3×#125C2×D311yescharacteristic, complemented
157C3×#125C2×D311yescharacteristic, complemented
158C3×#123—61no—
159C3×C22⋊Q8—31no—
160C3×C22⋊Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×D4—31no—
163C3×#117—31no—
164C3×#117—61no—
165C2×C3×C4⋊C4—31no—
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—31no—
169#938—31no—
170#938—31no—
171#938—61no—
172#937—61no—
173#937—61no—
174C2×#214—31no—
175C2×#214—31no—
176#930—31no—
177#930—31no—
178C2×#208—31no—
179C22×C3⋊C8—31no—
180C2×#204—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×D3×C8—31no—
183#898—21no—
184#897C2×D311yescharacteristic, complemented
185#897C2×D311yescharacteristic, complemented
186#895—61no—
187#894—21no—
188#892—21no—
189#892C2×D311yescharacteristic, complemented
190D3×C4⋊C4C2×D311yescharacteristic, complemented
191#890—21no—
192#882—61no—
193#882—61no—
194#874C2×D311yescharacteristic
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199C4×Dic6C2×D311yescharacteristic, complemented
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#97—31no—
205#835—31no—
206#832—31no—
207#832—31no—
208#830—31no—
209#830—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213#818—31no—
214#816—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—61no—
223#809—61no—
224#809C2×D311yescharacteristic, complemented
225#809C2×D311yescharacteristic, complemented
226#809C2×D311yescharacteristic, complemented
227#809C2×D311yescharacteristic, complemented
228#808—31no—
229#808—31no—
230#808—61no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—31no—
237C4⋊(C3⋊C8)—61no—
238#803C2×D311yescharacteristic, complemented
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)#4112yes—
258C4×C3⋊D3—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—22no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12—81no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—42no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277#626—42no—
278#626—42no—
279#625—42no—
280#625—42no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—31no—
286D42—91no—
287#490—31no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
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—
304C2×C3×Q8—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—121no—
322D3×D4—121no—
323D3×D4—124no—
324D3×D4—124no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—62no—
331C2×D12—62no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—121no—
335C2×D12—121no—
336C2×D12#6711yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—21no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—121no—
343C2×C4×D3C22×D311yescharacteristic
344C2×C4×D3C22×D311yescharacteristic
345C2×Dic6C22×D311yescharacteristic
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—41no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42—61no—
373C3×C42—61no—
374C3×C42C22×D311yescharacteristic
375C3×C42C22×D311yescharacteristic
376#217—61no—
377#217—61no—
378#215—62no—
379#215—121no—
380#215—121no—
381#214—121no—
382#214—121no—
383(C2×D3)⋊C4—21no—
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
392(C2×D3)⋊C4#6711yescharacteristic
393C4⋊Dic3—21no—
394C4⋊Dic3—21no—
395C4⋊Dic3—31no—
396C4⋊Dic3—31no—
397C4⋊Dic3—61no—
398C4⋊Dic3#6711yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404#208—121no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—121no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414#204—62no—
415ΓL(1,𝔽25)—121no—
416D3×C8—121no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3AGL(1,ℤ/8)12yes—
433D32—84no—
434D32—84no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4—41no—
438C32×C4—41no—
439C32×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—41no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—91no—
447C22×D4—91no—
448C22×D4—181no—
449C2×SD16—91no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×M16—91no—
453C22×C8—91no—
454#127—31no—
455#126—61no—
456#125—61no—
457#125D3211yescharacteristic, complemented
458#123—61no—
459C22⋊Q8—31no—
460C22⋊Q8—31no—
461#121—91no—
462#121—91no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—31no—
467C4×D4—31no—
468C4×D4—91no—
469#117—31no—
470#117—61no—
471C2×C4⋊C4—31no—
472#107—91no—
473#107—91no—
474#106—91no—
475C4⋊C8—91no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486C22⋊C8—91no—
487C22⋊C8—91no—
488#97—31no—
489C23×C3—31no—
490C23×C3—31no—
491C23×C3—61no—
492C23×C3—61no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—121no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—241no—
507C22×D3—241no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3C2×#6711yescharacteristic
511C22×D3C2×#6711yescharacteristic
512C3×Q8—61no—
513C3×Q8—61no—
514C3×D4—62no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—122no—
520C3×D4—241no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—122no—
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4D3×D411yescharacteristic
541C2×C3×C4C2×#6711yescharacteristic
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—122no—
546#67—122no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—122no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—121no—
556C2×Dic3C2×#6711yescharacteristic
557C2×Dic3C2×#6711yescharacteristic
558D12—22no—
559D12—21no—
560D12—21no—
561D12—21no—
562D12—21no—
563D12—32no—
564D12—32no—
565D12—42no—
566D12—62no—
567D12—61no—
568D12—61no—
569D12—81no—
570D12—121no—
571D12—122no—
572D12—122no—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—42no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—242no—
581Dic6—21no—
582Dic6—21no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C3⋊C8—61no—
588C3⋊C8—61no—
589C3⋊C8—61no—
590C3⋊C8—61no—
591C3⋊C8—121no—
592C3⋊C8—121no—
593C2×C32#54611yescharacteristic
594C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
595C2×C32#57711yescharacteristic
596C3⋊D3—42no—
597C3×D3—22no—
598C3×D3—41no—
599C3×D3—81no—
600C3×D3—81no—
601C24—181no—
602C24—181no—
603C2×Q8—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—31no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—91no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4—182no—
613C2×D4—182no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—361no—
617C2×D4—361no—
618C2×D4—364no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—61no—
622C22×C4—181no—
623SD16—182no—
624SD16—361no—
625SD16—361no—
626M16—361no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—91no—
630C2×C8—91no—
631C2×C8—361no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—91no—
641C4⋊C4C2×D3211yescharacteristic
642C4⋊C4C2×D3211yescharacteristic
643C22⋊C4—31no—
644C22⋊C4—31no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C42—61no—
652C42—61no—
653C42C2×D3211yescharacteristic
654C22×C3—21no—
655C22×C3—32no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C22×#6711yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—122no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—244no—
690C2×D3—244no—
691C2×D3—244no—
692C2×D3—244no—
693C2×D3#94912yes—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—81no—
709C3×C4—81no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4D3×#4111yescharacteristic
713C3×C4D3×#4111yescharacteristic
714C3×C4#100911yescharacteristic
715C3×C4#100911yescharacteristic
716Dic3—21no—
717Dic3—21no—
718Dic3—41no—
719Dic3—41no—
720Dic3—121no—
721Dic3—121no—
722Dic3—241no—
723C32#331011yescharacteristic, complemented, Sylow
724C23—31no—
725C23—31no—
726C23—61no—
727C23—61no—
728C23—181no—
729C23—362no—
730C23—362no—
731C23—362no—
732C23—362no—
733C23—721no—
734C23—721no—
735Q8—61no—
736Q8—61no—
737D4—62no—
738D4—61no—
739D4—61no—
740D4—61no—
741D4—61no—
742D4—92no—
743D4—122no—
744D4—181no—
745D4—241no—
746D4—362no—
747D4—362no—
748D4—362no—
749D4—362no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—122no—
761C2×C4—181no—
762C2×C4—362no—
763C2×C4D3×#6711yescharacteristic
764C2×C4D3×#6711yescharacteristic
765C2×C4C22×D3211yescharacteristic
766C8—61no—
767C8—61no—
768C8—181no—
769C8—181no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—62no—
774C2×C3—121no—
775C2×C3—241no—
776C2×C3—241no—
777C2×C3#567611yescharacteristic
778C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
779C2×C3#577511yescharacteristic
780C2×C3C2×#94911yescharacteristic
781C2×C3#582911yescharacteristic
782C2×C3#583711yescharacteristic
783D3—22no—
784D3—41no—
785D3—81no—
786D3—81no—
787D3—122no—
788D3—122no—
789D3—242no—
790C22—32no—
791C22—61no—
792C22—61no—
793C22—61no—
794C22—61no—
795C22—61no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—182no—
803C22—361no—
804C22—361no—
805C22—724no—
806C22—724no—
807C22C2×D3×#6711yescharacteristic
808C4—21no—
809C4—21no—
810C4—41no—
811C4—41no—
812C4—61no—
813C4—61no—
814C4—121no—
815C4—121no—
816C4—361no—
817C4#6431911yescharacteristic
818C4#6432011yescharacteristic
819C3—21no—
820C3#8172511yescharacteristic, complemented
821C3#8359911yescharacteristic, complemented
822C2—62no—
823C2—121no—
824C2—241no—
825C2—241no—
826C2—362no—
827C2#1059542811yescharacteristic
828C2D3×#94911yescharacteristic
829C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenter#125D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×#5694C2semidirect
3. #10592765C2semidirect
4. C3×#5067C2semidirect
5. #10590596C2semidirect
6. #10590596C2semidirect
7. #10590592C2semidirect
8. D3×#809C2semidirect
9. #10590505C2semidirect
10. #10590503C2semidirect
11. #10590501C2semidirect
12. #10590498C2semidirect
13. #10590364C2semidirect
14. #10590362C2semidirect
15. #10590326C2semidirect
21. C32×#125C22semidirect
24. C3×#897C22semidirect
25. C3×#897C22semidirect
28. C3×#892C22semidirect
29. C3×D3×C4⋊C4C22semidirect
33. C3×C4×Dic6C22semidirect
40. C2×#3715C22semidirect
41. C2×#3715C22semidirect
42. C2×#3711C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63635C22semidirect
47. #63634C22semidirect
48. C4⋊(C3⋊(C3⋊C8))C22semidirect
49. C3×#809C22semidirect
50. C3×#809C22semidirect
51. C3×#809C22semidirect
52. C3×#809C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
63. #5694D3semidirect
67. #5067D3semidirect
156. C3×#125C2×D3semidirect
157. C3×#125C2×D3semidirect
184. #897C2×D3semidirect
185. #897C2×D3semidirect
189. #892C2×D3semidirect
190. D3×C4⋊C4C2×D3semidirect
199. C4×Dic6C2×D3semidirect
224. #809C2×D3semidirect
225. #809C2×D3semidirect
226. #809C2×D3semidirect
227. #809C2×D3semidirect
238. #803C2×D3semidirect
457. #125D32semidirect
723. C32#3310semidirect
820. C3#81725semidirect
821. C3#83599semidirect

Maximal subgroups

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

subgroupindex
C3×#56942
#105940042
#105927652
C3×#50672
#105905962
#105905922
D3×#8092
#105905052
#105905032
#105905012
#105904982
#105903642
#105903622
#105903262
#835993
#817253