Finite Group Databasebeta

← #11889091

Subgroups — #11889091

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5513C211yesmaximal, characteristic, complemented
2#10595074C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic, complemented
5#10591183C211yesmaximal, characteristic, complemented
6#10591179C211yesmaximal, characteristic, complemented
7#10591158C211yesmaximal, characteristic, complemented
8#10590596C211yesmaximal, characteristic, complemented
9#10590592C211yesmaximal, characteristic, complemented
10#10590585C211yesmaximal, characteristic, complemented
11#10590550C211yesmaximal, characteristic, complemented
12#10590549C211yesmaximal, characteristic, complemented
13#10590468C211yesmaximal, characteristic, complemented
14#10590457C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic, complemented
16#83599—31nomaximal
17#81303—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×#930C2211yescharacteristic
24C3×#929—21no—
25C3×C4×#67C2211yescharacteristic
26C3×#926—21no—
27C3×#924C2211yescharacteristic, complemented
28C3×#898—21no—
29C3×#897C2211yescharacteristic, complemented
30C3×#892C2211yescharacteristic, complemented
31C3×#890C2211yescharacteristic, complemented
32C3×#889—21no—
33C3×#887C2211yescharacteristic, complemented
34#63981—21no—
35#63923—21no—
36#63911C2211yescharacteristic
37#63910—21no—
38#63909C2211yescharacteristic
39#63894C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3717C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic, complemented
43C2×#3711C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic, complemented
47#63636C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×#809C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#552—31no—
62#5609—31no—
63D4×D12—31no—
64#5513D311yescharacteristic, complemented
65C3×#480—31no—
66#5067—31no—
67#5066—31no—
68#5049—31no—
69#5048—31no—
70#5046—31no—
71#5046—31no—
72#5041—31no—
73#5027—31no—
74#5026—31no—
75#5011—31no—
76#5003—31no—
77#5001—31no—
78#4967D311yescharacteristic, complemented
79C2×#809—31no—
80C2×#809—31no—
81C2×#809—61no—
82#4891—31no—
83#4889—31no—
84#4886—31no—
85#4885—31no—
86#4776—31no—
87#4770—31no—
88#4764—31no—
89#4762—31no—
90#4731—31no—
91#4730—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C22×C32×C4—21no—
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
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
117C2×C3⋊(C3⋊C8)—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3722—21no—
140#3722—21no—
141#3717—22no—
142#3717—41no—
143#3715—41no—
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—
153C3×#126—61no—
154C3×#125—31no—
155C3×#125—61no—
156C3×#123—61no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×#121—31no—
160C3×C4×Q8—31no—
161C3×C4×D4—31no—
162C3×#117—31no—
163C3×#117—61no—
164C2×C3×C4⋊C4—21no—
165C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
166C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
167C2×#215—31no—
168C2×#215—31no—
169C2×#215—31no—
170#940—31no—
171#937—61no—
172C2×#214—31no—
173#930—31no—
174#930C2×D311yescharacteristic
175#929—21no—
176C4×#67C2×D311yescharacteristic
177#926—21no—
178#924C2×D311yescharacteristic, complemented
179C2×#208—31no—
180C22×C3⋊C8—31no—
181C22×C3⋊C8—31no—
182C22×C3⋊C8—61no—
183C2×#204—31no—
184C2×#204—31no—
185C2×ΓL(1,𝔽25)—31no—
186#898—21no—
187#897C2×D311yescharacteristic, complemented
188#895—31no—
189#895—61no—
190#893—31no—
191#892C2×D311yescharacteristic, complemented
192#890C2×D311yescharacteristic, complemented
193#889—21no—
194#887C2×D311yescharacteristic, complemented
195#884—61no—
196#882—61no—
197#882—61no—
198#882—61no—
199#874—31no—
200C4×D12—31no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206#835—31no—
207#832—31no—
208#830—31no—
209#830C2×D311yescharacteristic, complemented
210#821—31no—
211#821—31no—
212(C2×D3)⋊C8—31no—
213#815—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#809—31no—
217#809—31no—
218#809—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#809—61no—
229#809—61no—
230#809—61no—
231#809C2×D311yescharacteristic, complemented
232#809C2×D311yescharacteristic, complemented
233#808—31no—
234#808—31no—
235#807C2×D311yescharacteristic, complemented
236#807C2×D311yescharacteristic, complemented
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—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—42no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—42no—
261C4⋊(C3⋊D3)#4112yes—
262C3×#67—22no—
263C3×#67—42no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×Dic6—21no—
275C3×Dic6—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—31no—
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—
304C23×D3—121no—
305C2×C3×Q8—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—41no—
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
322D3×D4—62no—
323D3×D4—121no—
324D3×D4—124no—
325D3×D4—124no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—62no—
333C2×D12—62no—
334C2×D12—62no—
335C2×D12—64no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—121no—
343C2×D12—121no—
344C2×D12—121no—
345C2×D12—121no—
346C2×D12—122no—
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6C22×D311yescharacteristic
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—41no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C22⋊C4—31no—
372C3×C22⋊C4—31no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C42—31no—
378C3×C42—61no—
379C3×C42—61no—
380#217—21no—
381#217#6711yescharacteristic
382#215—62no—
383#215—121no—
384#215—121no—
385#214—121no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4#6711yescharacteristic
394C4⋊Dic3—21no—
395C4⋊Dic3—21no—
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4#6711yescharacteristic
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3C22×D311yescharacteristic
405#208—121no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—121no—
413C2×C3⋊C8—121no—
414C2×C3⋊C8—122no—
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417#204—62no—
418#204—121no—
419ΓL(1,𝔽25)—121no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32AGL(1,ℤ/8)12yes—
423C22×C32C22×D411yescharacteristic
424C2×C3⋊D3—22no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—84no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437D32—84no—
438C32×C4—21no—
439C32×C4—41no—
440C32×C4—41no—
441C32×C4C2×#4111yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C22×D4—91no—
450C22×D4—91no—
451C22×D4—181no—
452C2×SD16—91no—
453C2×SD16—91no—
454C2×SD16—91no—
455C2×M16—91no—
456C22×C8—91no—
457#127—91no—
458#126—61no—
459#125—31no—
460#125—61no—
461#123—61no—
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464#121—31no—
465#121—91no—
466#121—181no—
467#120—181no—
468#120—181no—
469C4×Q8—31no—
470C4×D4—31no—
471C4×D4—91no—
472#117—31no—
473#117—61no—
474C2×C4⋊C4D3211yescharacteristic, complemented
475#107—31no—
476#107—31no—
477#106—91no—
478C4⋊C8—91no—
479#103—91no—
480#102—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—
489C22⋊C8—31no—
490C22⋊C8—91no—
491#97—91no—
492C23×C3—21no—
493C23×C3—31no—
494C23×C3—61no—
495C23×C3D3×D411yescharacteristic
496C23×C3C2×#6711yescharacteristic
497C22×D3—21no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—121no—
503C22×D3—121no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—124no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—242no—
514C22×D3—241no—
515C22×D3—241no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—242no—
519C22×D3C2×#6711yescharacteristic
520C3×Q8—61no—
521C3×Q8—61no—
522C3×D4—62no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—122no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
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—21no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—42no—
544C2×C3×C4—42no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—82no—
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—22no—
556#67—42no—
557#67—122no—
558#67—122no—
559#67—122no—
560#67—241no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3C2×#6711yescharacteristic
565C2×Dic3C2×#6711yescharacteristic
566C2×Dic3C2×#6711yescharacteristic
567D12—21no—
568D12—21no—
569D12—32no—
570D12—32no—
571D12—62no—
572D12—62no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—121no—
580D12—121no—
581D12—122no—
582D12—122no—
583D12—124no—
584D12—122no—
585D12—122no—
586D12—122no—
587D12—241no—
588C4×D3—21no—
589C4×D3—21no—
590C4×D3—122no—
591C4×D3—122no—
592Dic6—21no—
593Dic6—21no—
594C3×C8—61no—
595C3×C8—61no—
596C3⋊C8—21no—
597C3⋊C8—21no—
598C3⋊C8—61no—
599C3⋊C8—61no—
600C3⋊C8—61no—
601C3⋊C8—61no—
602C3⋊C8—121no—
603C3⋊C8—121no—
604C2×C32—22no—
605C2×C32#54611yescharacteristic
606C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
607C2×C32#57711yescharacteristic
608C3⋊D3—42no—
609C3⋊D3—81no—
610C3×D3—41no—
611C3×D3—81no—
612C24—181no—
613C24—181no—
614C2×Q8—31no—
615C2×D4—31no—
616C2×D4—31no—
617C2×D4—61no—
618C2×D4—91no—
619C2×D4—91no—
620C2×D4—182no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—181no—
624C2×D4—182no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—361no—
628C2×D4—361no—
629C2×D4—364no—
630C22×C4—21no—
631C22×C4—31no—
632C22×C4—181no—
633C22×C4C2×D3211yescharacteristic
634SD16—182no—
635SD16—361no—
636SD16—361no—
637M16—361no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—91no—
641C2×C8—91no—
642C2×C8—361no—
643C4⋊C4—21no—
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4C2×D3211yescharacteristic
653C4⋊C4C2×D3211yescharacteristic
654C22⋊C4—31no—
655C22⋊C4—31no—
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C42—31no—
663C42—61no—
664C42—61no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—22no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3#91112yes—
680C22×C3#94912yes—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C22×#6711yescharacteristic
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—62no—
690C2×D3—62no—
691C2×D3—122no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—122no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—241no—
704C2×D3—241no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—244no—
708C2×D3—244no—
709C2×D3—244no—
710C2×D3—244no—
711C2×D3—248no—
712C3×C4—22no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—61no—
724C3×C4—81no—
725C3×C4—81no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4D3×#4111yescharacteristic
730C3×C4D3×#4111yescharacteristic
731C3×C4#100911yescharacteristic
732C3×C4#100911yescharacteristic
733Dic3—21no—
734Dic3—21no—
735Dic3—21no—
736Dic3—41no—
737Dic3—41no—
738Dic3—41no—
739C32#331011yescharacteristic, complemented, Sylow
740C23—31no—
741C23—61no—
742C23—181no—
743C23—181no—
744C23—362no—
745C23—362no—
746C23—362no—
747C23—362no—
748C23—721no—
749C23—721no—
750C23D3×#6711yescharacteristic
751Q8—61no—
752Q8—61no—
753D4—62no—
754D4—61no—
755D4—61no—
756D4—92no—
757D4—122no—
758D4—181no—
759D4—181no—
760D4—181no—
761D4—362no—
762D4—362no—
763D4—362no—
764D4—362no—
765D4—721no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—42no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—362no—
780C2×C4D3×#6711yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—61no—
783C8—61no—
784C8—181no—
785C8—181no—
786C2×C3—24no—
787C2×C3—22no—
788C2×C3—22no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—121no—
793C2×C3—241no—
794C2×C3#565411yescharacteristic
795C2×C3C2×#91111yescharacteristic
796C2×C3#577811yescharacteristic
797C2×C3C2×#94911yescharacteristic
798C2×C3#582911yescharacteristic
799C2×C3#583711yescharacteristic
800D3—41no—
801D3—81no—
802D3—122no—
803D3—122no—
804D3—242no—
805D3—242no—
806D3—241no—
807D3—241no—
808C22—21no—
809C22—21no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—182no—
817C22—361no—
818C22—361no—
819C22—361no—
820C22—361no—
821C22—361no—
822C22—724no—
823C22—724no—
824C22#6392512yes—
825C22C2×D3×#6711yescharacteristic
826C4—21no—
827C4—41no—
828C4—41no—
829C4—61no—
830C4—61no—
831C4—61no—
832C4—121no—
833C4—121no—
834C4—121no—
835C4#6430611yescharacteristic
836C4#6430811yescharacteristic
837C3—21no—
838C3#8130311yescharacteristic, complemented
839C3#8359911yescharacteristic, complemented
840C2—22no—
841C2—121no—
842C2—241no—
843C2—362no—
844C2—721no—
845C2#1059506811yescharacteristic
846C2C2×#6392511yescharacteristic
847C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10595074C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5513C2semidirect
3. C2×#63636C2semidirect
4. C3×#4967C2semidirect
5. #10591183C2semidirect
6. #10591179C2semidirect
7. #10591158C2semidirect
8. #10590596C2semidirect
9. #10590592C2semidirect
10. #10590585C2semidirect
11. #10590550C2semidirect
12. #10590549C2semidirect
13. #10590468C2semidirect
14. #10590457C2semidirect
15. #10590424C2semidirect
21. C2×C32×C4⋊C4C22semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
27. C3×#924C22semidirect
29. C3×#897C22semidirect
30. C3×#892C22semidirect
31. C3×#890C22semidirect
33. C3×#887C22semidirect
41. C2×#3717C22semidirect
42. C2×#3715C22semidirect
43. C2×#3711C22semidirect
46. #63636C22semidirect
47. #63636C22semidirect
48. C3×#830C22semidirect
49. C3×#809C22semidirect
50. C3×#809C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63574C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
57. #63564C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
64. #5513D3semidirect
78. #4967D3semidirect
165. C2×C3×C4⋊C4C2×D3semidirect
166. C2×C3×C4⋊C4C2×D3semidirect
178. #924C2×D3semidirect
187. #897C2×D3semidirect
191. #892C2×D3semidirect
192. #890C2×D3semidirect
194. #887C2×D3semidirect
209. #830C2×D3semidirect
231. #809C2×D3semidirect
232. #809C2×D3semidirect
235. #807C2×D3semidirect
236. #807C2×D3semidirect
474. C2×C4⋊C4D32semidirect
739. C32#3310semidirect
838. C3#81303semidirect
839. C3#83599semidirect

Maximal subgroups

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

subgroupindex
C3×#55132
#105950742
C2×#636362
C3×#49672
#105911832
#105911792
#105911582
#105905962
#105905922
#105905852
#105905502
#105905492
#105904682
#105904572
#105904242
#835993
#813033