Finite Group Databasebeta

← #11889129

Subgroups — #11889129

Order 1152.

960 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5581C211yesmaximal, characteristic, complemented
2#10594004C211yesmaximal, characteristic
3#10592725C211yesmaximal, characteristic, complemented
4C3×#5027C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591634C211yesmaximal, characteristic, complemented
8#10591587C211yesmaximal, characteristic, complemented
9#10590592C211yesmaximal, characteristic, complemented
10D3×#809C211yesmaximal, characteristic, complemented
11#10590502C211yesmaximal, characteristic, complemented
12#10590498C211yesmaximal, characteristic, complemented
13#10590330C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590279C211yesmaximal, characteristic, complemented
16#83599—31nomaximal
17#80397—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C3×#946C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#894—21no—
29C3×#892C2211yescharacteristic, complemented
30C3×D3×C4⋊C4C2211yescharacteristic, complemented
31C3×#889—21no—
32C3×#876—21no—
33C3×#874C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×#872—21no—
36C3×#870C2211yescharacteristic, complemented
37#63922—21no—
38#63922—21no—
39#63916—21no—
40#63908C2211yescharacteristic
41#63908C2211yescharacteristic
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46#63634C2211yescharacteristic, complemented
47#63630C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63562C2211yescharacteristic, complemented
56#63562C2211yescharacteristic, complemented
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#5581D311yescharacteristic, complemented
64D4×D12—31no—
65C3×#460—31no—
66#5174—31no—
67#5171—31no—
68#5169—31no—
69#5169—31no—
70#5071—31no—
71#5067—31no—
72#5066—31no—
73#5049—31no—
74#5048—31no—
75#5046—31no—
76#5046—31no—
77#5027D311yescharacteristic, complemented
78#5026—31no—
79#5026—31no—
80#5026—61no—
81#5011—31no—
82#5003—31no—
83#5001—31no—
84#4967—31no—
85C2×#809—31no—
86#4847—31no—
87#4836—31no—
88#4779—31no—
89#4774—31no—
90#4770—31no—
91D3×#102—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12D411yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
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⋊C4C2311yescharacteristic
116C32×C42—21no—
117C32×C42C2311yescharacteristic
118#3755—22no—
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#215—41no—
124C3×#215—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
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—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×#127—31no—
155C3×#126—61no—
156C3×#125—31no—
157C3×#125—61no—
158C3×#123—61no—
159C3×C22⋊Q8—31no—
160C3×C22⋊Q8—31no—
161C3×C4×Q8—21no—
162C3×C4×Q8C2×D311yescharacteristic, complemented
163C3×C4×Q8C2×D311yescharacteristic, complemented
164C3×C4×D4—31no—
165C3×#117—31no—
166C3×#117—61no—
167C2×C3×C4⋊C4—31no—
168#946C2×D311yescharacteristic, complemented
169#946C2×D311yescharacteristic, complemented
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—61no—
173C2×#215C2×D311yescharacteristic, complemented
174C2×#215C2×D311yescharacteristic, complemented
175#938—31no—
176#938—31no—
177#938—61no—
178#937—61no—
179#937—61no—
180#930—31no—
181#930—31no—
182C2×#208—31no—
183C22×C3⋊C8—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×D3×C8—31no—
186#895—61no—
187#894—21no—
188#892C2×D311yescharacteristic, complemented
189D3×C4⋊C4C2×D311yescharacteristic, complemented
190#889—21no—
191#882—61no—
192#882—61no—
193#876—21no—
194#874C2×D311yescharacteristic
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199#872—21no—
200#870C2×D311yescharacteristic, complemented
201C3×C4⋊C8—31no—
202C3×#102—31no—
203C3×#102—31no—
204#835—31no—
205#835—31no—
206#835—61no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#830—31no—
212#830—31no—
213#821—31no—
214#821—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217#818—31no—
218#817—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—61no—
228#809C2×D311yescharacteristic, complemented
229#809C2×D311yescharacteristic, complemented
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
236#803—31no—
237#803—31no—
238#803—61no—
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—
250C32×Q8—21no—
251C32×Q8—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C2×C3⋊Dic3—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)#4112yes—
260C4×C3⋊D3—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—22no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—42no—
271C3×D12—81no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—42no—
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—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—31no—
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—21no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321D3×D4—62no—
322D3×D4—62no—
323D3×D4—121no—
324D3×D4—121no—
325D3×D4—124no—
326D3×D4—124no—
327C2×D12—21no—
328C2×D12—21no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—61no—
332C2×D12—62no—
333C2×D12—62no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—121no—
337C2×D12—121no—
338C2×D12#6711yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—121no—
345C2×C4×D3C22×D311yescharacteristic
346C2×C4×D3C22×D311yescharacteristic
347C3×SD16—121no—
348C3×SD16—121no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—41no—
374C3×C42—61no—
375C3×C42C22×D311yescharacteristic
376C3×C42C22×D311yescharacteristic
377#217—61no—
378#217—61no—
379#215—41no—
380#215—41no—
381#215—62no—
382#215—62no—
383#215—64no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—121no—
392(C2×D3)⋊C4#6711yescharacteristic
393(C2×D3)⋊C4#6711yescharacteristic
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3#6711yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405C4×Dic3—21no—
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⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416ΓL(1,𝔽25)—121no—
417D3×C8—121no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3AGL(1,ℤ/8)12yes—
434D32—84no—
435D32—84no—
436C32×C4—21no—
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—41no—
446C3×Dic3—41no—
447C22×D4—91no—
448C22×D4—91no—
449C22×D4—181no—
450C2×SD16—31no—
451C2×SD16—31no—
452C2×SD16—91no—
453C2×M16—91no—
454C22×C8—91no—
455#127—31no—
456#126—61no—
457#125—31no—
458#125—61no—
459#123—61no—
460C22⋊Q8—31no—
461C22⋊Q8—31no—
462#121—91no—
463#121—91no—
464#121—181no—
465#120—181no—
466#120—181no—
467C4×Q8D3211yescharacteristic, complemented
468C4×D4—31no—
469C4×D4—91no—
470#117—31no—
471#117—61no—
472C2×C4⋊C4—31no—
473#107—91no—
474#107—91no—
475#106—91no—
476C4⋊C8—31no—
477#103—91no—
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487C22⋊C8—91no—
488C22⋊C8—91no—
489#97—91no—
490C23×C3—31no—
491C23×C3—31no—
492C23×C3—61no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—121no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—241no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3C2×#6711yescharacteristic
512C22×D3C2×#6711yescharacteristic
513C3×Q8—22no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—21no—
517C3×Q8—21no—
518C3×Q8—41no—
519C3×D4—62no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—122no—
525C3×D4—241no—
526C2×C3×C4—21no—
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—31no—
534C2×C3×C4—31no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—122no—
544C2×C3×C4D3×D411yescharacteristic
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C2×#6711yescharacteristic
547C2×C3×C4C2×#6711yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—122no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—122no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—121no—
561C2×Dic3C2×#6711yescharacteristic
562C2×Dic3C2×#6711yescharacteristic
563D12—22no—
564D12—21no—
565D12—21no—
566D12—21no—
567D12—21no—
568D12—32no—
569D12—32no—
570D12—42no—
571D12—62no—
572D12—61no—
573D12—61no—
574D12—81no—
575D12—121no—
576D12—122no—
577D12—122no—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—42no—
583C4×D3—122no—
584C4×D3—122no—
585C4×D3—242no—
586C3×C8—61no—
587C3×C8—61no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—62no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—61no—
595C3⋊C8—121no—
596C2×C32#54611yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C2×C32#57711yescharacteristic
599C3⋊D3—42no—
600C3×D3—22no—
601C3×D3—41no—
602C3×D3—81no—
603C3×D3—81no—
604C24—181no—
605C24—181no—
606C2×Q8C2×D3211yescharacteristic
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—91no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—182no—
616C2×D4—182no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—361no—
620C2×D4—361no—
621C2×D4—364no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—61no—
625C22×C4—181no—
626SD16—121no—
627SD16—121no—
628SD16—182no—
629M16—361no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—91no—
634C2×C8—361no—
635C4⋊C4—21no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—91no—
645C4⋊C4C2×D3211yescharacteristic
646C22⋊C4—31no—
647C22⋊C4—31no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C42—21no—
655C42—61no—
656C42C2×D3211yescharacteristic
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C22×#6711yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—62no—
684C2×D3—62no—
685C2×D3—122no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3—244no—
693C2×D3—244no—
694C2×D3—244no—
695C2×D3—244no—
696C2×D3#94912yes—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—42no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—41no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—81no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4#100411yescharacteristic
716C3×C4D3×#4111yescharacteristic
717C3×C4D3×#4111yescharacteristic
718C3×C4#100911yescharacteristic
719Dic3—21no—
720Dic3—21no—
721Dic3—41no—
722Dic3—41no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726C32#331011yescharacteristic, complemented, Sylow
727C23—31no—
728C23—31no—
729C23—61no—
730C23—61no—
731C23—181no—
732C23—362no—
733C23—362no—
734C23—362no—
735C23—362no—
736C23—721no—
737C23—721no—
738Q8—21no—
739Q8—21no—
740D4—62no—
741D4—61no—
742D4—61no—
743D4—61no—
744D4—61no—
745D4—92no—
746D4—122no—
747D4—181no—
748D4—241no—
749D4—362no—
750D4—362no—
751D4—362no—
752D4—362no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—122no—
764C2×C4—181no—
765C2×C4—362no—
766C2×C4D3×#6711yescharacteristic
767C2×C4D3×#6711yescharacteristic
768C2×C4C22×D3211yescharacteristic
769C8—61no—
770C8—61no—
771C8—181no—
772C8—181no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—62no—
777C2×C3—121no—
778C2×C3—241no—
779C2×C3—241no—
780C2×C3#561211yescharacteristic
781C2×C3#576211yescharacteristic
782C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
783C2×C3C2×#94911yescharacteristic
784C2×C3#582911yescharacteristic
785C2×C3#583711yescharacteristic
786D3—22no—
787D3—41no—
788D3—81no—
789D3—81no—
790D3—122no—
791D3—122no—
792D3—242no—
793C22—32no—
794C22—61no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—182no—
806C22—361no—
807C22—361no—
808C22—724no—
809C22—724no—
810C22C2×D3×#6711yescharacteristic
811C4—21no—
812C4—21no—
813C4—41no—
814C4—41no—
815C4—61no—
816C4—61no—
817C4—121no—
818C4—121no—
819C4—361no—
820C4#6430611yescharacteristic
821C4#6430711yescharacteristic
822C3—21no—
823C3#8039711yescharacteristic, complemented
824C3#8359911yescharacteristic, complemented
825C2—62no—
826C2—121no—
827C2—241no—
828C2—241no—
829C2—362no—
830C2#1059507011yescharacteristic
831C2#1059531811yescharacteristic
832C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenterC4×Q8D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5581C2semidirect
3. #10592725C2semidirect
4. C3×#5027C2semidirect
5. #10591651C2semidirect
6. #10591651C2semidirect
7. #10591634C2semidirect
8. #10591587C2semidirect
9. #10590592C2semidirect
10. D3×#809C2semidirect
11. #10590502C2semidirect
12. #10590498C2semidirect
13. #10590330C2semidirect
14. #10590308C2semidirect
15. #10590279C2semidirect
21. C32×C4×Q8C22semidirect
24. C3×#946C22semidirect
25. C3×#946C22semidirect
26. C2×C3×#215C22semidirect
27. C2×C3×#215C22semidirect
29. C3×#892C22semidirect
30. C3×D3×C4⋊C4C22semidirect
36. C3×#870C22semidirect
42. C2×#3711C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
46. #63634C22semidirect
47. #63630C22semidirect
48. C3×#809C22semidirect
49. C3×#809C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
55. #63562C22semidirect
56. #63562C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
63. #5581D3semidirect
77. #5027D3semidirect
162. C3×C4×Q8C2×D3semidirect
163. C3×C4×Q8C2×D3semidirect
168. #946C2×D3semidirect
169. #946C2×D3semidirect
173. C2×#215C2×D3semidirect
174. C2×#215C2×D3semidirect
188. #892C2×D3semidirect
189. D3×C4⋊C4C2×D3semidirect
200. #870C2×D3semidirect
228. #809C2×D3semidirect
229. #809C2×D3semidirect
235. C4⋊(C3⋊C8)C2×D3semidirect
467. C4×Q8D32semidirect
726. C32#3310semidirect
823. C3#80397semidirect
824. C3#83599semidirect

Maximal subgroups

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

subgroupindex
C3×#55812
#105940042
#105927252
C3×#50272
#105916512
#105916342
#105915872
#105905922
D3×#8092
#105905022
#105904982
#105903302
#105903082
#105902792
#835993
#803973