Finite Group Databasebeta

← #11889103

Subgroups — #11889103

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
1#10595074C211yesmaximal, characteristic
2#10594853C211yesmaximal, characteristic, complemented
3C2×#63648C211yesmaximal, characteristic, complemented
4C3×#5114C211yesmaximal, characteristic, complemented
5C3×#5111C211yesmaximal, characteristic, complemented
6#10591183C211yesmaximal, characteristic, complemented
7#10591094C211yesmaximal, characteristic, complemented
8#10590942C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590882C211yesmaximal, characteristic, complemented
11#10590850C211yesmaximal, characteristic, complemented
12#10590799C211yesmaximal, characteristic, complemented
13#10590795C211yesmaximal, characteristic, complemented
14#10590769C211yesmaximal, characteristic, complemented
15#10590704C211yesmaximal, characteristic, complemented
16#80685—31nomaximal
17#79501—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
23C3×#930C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#924C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic, complemented
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
28#63981—21no—
29#63962—21no—
30#63957—21no—
31#63923—21no—
32#63911C2211yescharacteristic
33#63910—21no—
34#63909C2211yescharacteristic
35#63894C2211yescharacteristic
36#63869C2211yescharacteristic, complemented
37#63861—21no—
38#63856C2211yescharacteristic, complemented
39#63845—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41#63841C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3717C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic, complemented
47#63648C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#5642—31no—
62#5609—31no—
63D4×D12—31no—
64#5541—31no—
65C3×#465—31no—
66C3×#435—31no—
67#5169—31no—
68#5163—31no—
69#5134—31no—
70#5131—31no—
71#5114D311yescharacteristic, complemented
72C2×#821—31no—
73C2×#821—31no—
74C2×#821—61no—
75#5111D311yescharacteristic, complemented
76#5046—31no—
77#5033—31no—
78#4871—31no—
79#4866—31no—
80#4848—31no—
81#4847—31no—
82#4817—31no—
83#4812—31no—
84#4770—31no—
85#4764—31no—
86#4737—31no—
87#4736—31no—
88#4731—31no—
89#4731—31no—
90#4713—31no—
91#4710—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
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—
114C2×C32×C8—41no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132C3×ΓL(1,𝔽25)—41no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143#3717—22no—
144#3717—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—
154C2×C3×M16—31no—
155C22×C3×C8—21no—
156C22×C3×C8C2×D311yescharacteristic, complemented
157C22×C3×C8C2×D311yescharacteristic, complemented
158C3×C22⋊Q8—31no—
159C3×#121—31no—
160C3×C4×D4—31no—
161#946—31no—
162Q8×Dic3—31no—
163C2×#215—31no—
164C2×#215—31no—
165#940—31no—
166#937—61no—
167#935—61no—
168#930—31no—
169#930C2×D311yescharacteristic
170C4×#67C2×D311yescharacteristic
171#926—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—61no—
175#924—31no—
176#924C2×D311yescharacteristic, complemented
177C2×#204—31no—
178C2×#204—31no—
179C2×#204C2×D311yescharacteristic, complemented
180C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
181#898—61no—
182#895—31no—
183#895—61no—
184#893—31no—
185#892—31no—
186#890—31no—
187#890—61no—
188#889—61no—
189#886—61no—
190#884—61no—
191#882—61no—
192#882—61no—
193#882—61no—
194#879—61no—
195#877—61no—
196#877—61no—
197#874—31no—
198C4×D12—31no—
199#870—31no—
200C4×Dic6—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
207C3×#97—31no—
208#832—31no—
209#832—31no—
210#830C2×D311yescharacteristic, complemented
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223#821—61no—
224#821—61no—
225#821—61no—
226#821—61no—
227#821C2×D311yescharacteristic, complemented
228(C2×D3)⋊C8C2×D311yescharacteristic, complemented
229#818—31no—
230#818—31no—
231#817C2×D311yescharacteristic, complemented
232#816C2×D311yescharacteristic, complemented
233#815C2×D311yescharacteristic, complemented
234Dic3⋊C8C2×D311yescharacteristic, complemented
235#809—31no—
236#809—31no—
237#807—31no—
238#807—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×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—42no—
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—
281C32×C8—21no—
282C32×C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
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—31no—
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—31no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C2×#67—21no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67D1211yescharacteristic
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
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
352C3×SD16—121no—
353C3×M16—121no—
354C2×C3×C8—21no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—41no—
359C2×C3×C8—41no—
360C2×C3×C8—42no—
361C2×C3×C8C22×D311yescharacteristic
362C2×C3×C8C22×D311yescharacteristic
363C2×C3×C8C22×D311yescharacteristic
364C2×C3×C8C22×D311yescharacteristic
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—61no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C42—31no—
374#217—21no—
375#217—61no—
376#217—61no—
377#217D1211yescharacteristic
378#215—62no—
379#215—121no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4D1211yescharacteristic
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—121no—
399C4⋊Dic3C22×D311yescharacteristic
400C4⋊Dic3C22×D311yescharacteristic
401Dic3⋊C4—21no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4D1211yescharacteristic
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416#204—41no—
417#204—62no—
418#204—121no—
419ΓL(1,𝔽25)—41no—
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×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
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—31no—
453C2×SD16—91no—
454C2×SD16—91no—
455C2×M16—31no—
456C22×C8D3211yescharacteristic, complemented
457#127—91no—
458#126—181no—
459#125—91no—
460#125—181no—
461#123—181no—
462C22⋊Q8—31no—
463C22⋊Q8—91no—
464#121—31no—
465#121—91no—
466#121—181no—
467#120—181no—
468#120—181no—
469C4×Q8—91no—
470C4×D4—31no—
471C4×D4—91no—
472#117—91no—
473#117—181no—
474C2×C4⋊C4—91no—
475#107—91no—
476#107—91no—
477#106—31no—
478C4⋊C8—31no—
479#103—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—
488#102—91no—
489C22⋊C8—31no—
490C22⋊C8—31no—
491#97—31no—
492C23×C3—21no—
493C23×C3—31no—
494C23×C3—61no—
495C23×C3C2×D1211yescharacteristic
496C23×C3D3×D411yescharacteristic
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×D1211yescharacteristic
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—31no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4C2×D1211yescharacteristic
543C2×C3×C4D3×D411yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—22no—
547#67—42no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—241no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—122no—
562C2×Dic3—122no—
563C2×Dic3—242no—
564C2×Dic3C2×D1211yescharacteristic
565C2×Dic3C2×D1211yescharacteristic
566C2×Dic3C2×D1211yescharacteristic
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—21no—
595C3×C8—21no—
596C3×C8—21no—
597C3×C8—21no—
598C3×C8—41no—
599C3×C8—41no—
600C3×C8—61no—
601C3×C8—61no—
602C3⋊C8—21no—
603C3⋊C8—21no—
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—31no—
631C22×C4—181no—
632C22×C4—181no—
633C22×C4C2×D3211yescharacteristic
634SD16—121no—
635SD16—182no—
636SD16—361no—
637M16—121no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—41no—
641C2×C8C2×D3211yescharacteristic
642C2×C8C2×D3211yescharacteristic
643C4⋊C4—31no—
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—61no—
647C4⋊C4—91no—
648C4⋊C4—91no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C22⋊C4—31no—
655C22⋊C4—31no—
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C42—31no—
663C42—181no—
664C42—181no—
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#90812yes—
680C22×C3#91412yes—
681C22×C3C22×D1211yescharacteristic
682C22×C3C2×D3×D411yescharacteristic
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—61no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4#100411yescharacteristic
724C3×C4#100411yescharacteristic
725C3×C4D3×#4111yescharacteristic
726C3×C4D3×#4111yescharacteristic
727Dic3—21no—
728Dic3—21no—
729Dic3—21no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—121no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—241no—
738Dic3—241no—
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×D1211yescharacteristic
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—31no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—362no—
779C2×C4—362no—
780C2×C4D3×D1211yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—21no—
783C8—21no—
784C8—61no—
785C8—61no—
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#555411yescharacteristic
795C2×C3#561011yescharacteristic
796C2×C3C2×#90811yescharacteristic
797C2×C3#575111yescharacteristic
798C2×C3C2×#91411yescharacteristic
799C2×C3#577011yescharacteristic
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#6379412yes—
825C22C2×D3×D1211yescharacteristic
826C4—21no—
827C4—61no—
828C4—61no—
829C4—61no—
830C4—121no—
831C4—121no—
832C4—121no—
833C4—361no—
834C4—361no—
835C4#6430611yescharacteristic
836C4#6433011yescharacteristic
837C3—21no—
838C3#7950111yescharacteristic, complemented
839C3#8068511yescharacteristic, complemented
840C2—22no—
841C2—121no—
842C2—241no—
843C2—362no—
844C2—721no—
845C2C2×#6379411yescharacteristic
846C2#1059467911yescharacteristic
847C2#1059507511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595074C2
hypercenterC22×C8D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594853C2semidirect
3. C2×#63648C2semidirect
4. C3×#5114C2semidirect
5. C3×#5111C2semidirect
6. #10591183C2semidirect
7. #10591094C2semidirect
8. #10590942C2semidirect
9. #10590939C2semidirect
10. #10590882C2semidirect
11. #10590850C2semidirect
12. #10590799C2semidirect
13. #10590795C2semidirect
14. #10590769C2semidirect
15. #10590704C2semidirect
21. C22×C32×C8C22semidirect
22. C2×C4⋊(C3⋊Dic3)C22semidirect
25. C3×#924C22semidirect
26. C2×C3×#204C22semidirect
27. C2×C3×ΓL(1,𝔽25)C22semidirect
36. #63869C22semidirect
38. #63856C22semidirect
40. Dic3×Dic6C22semidirect
41. #63841C22semidirect
43. C2×#3717C22semidirect
46. #63648C22semidirect
47. #63648C22semidirect
48. C3×#830C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#817C22semidirect
52. C3×#816C22semidirect
53. C3×#815C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
58. #63564C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
71. #5114D3semidirect
75. #5111D3semidirect
156. C22×C3×C8C2×D3semidirect
157. C22×C3×C8C2×D3semidirect
176. #924C2×D3semidirect
179. C2×#204C2×D3semidirect
180. C2×ΓL(1,𝔽25)C2×D3semidirect
210. #830C2×D3semidirect
227. #821C2×D3semidirect
228. (C2×D3)⋊C8C2×D3semidirect
231. #817C2×D3semidirect
232. #816C2×D3semidirect
233. #815C2×D3semidirect
234. Dic3⋊C8C2×D3semidirect
456. C22×C8D32semidirect
739. C32#3310semidirect
838. C3#79501semidirect
839. C3#80685semidirect

Maximal subgroups

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

subgroupindex
#105950742
#105948532
C2×#636482
C3×#51142
C3×#51112
#105911832
#105910942
#105909422
#105909392
#105908822
#105908502
#105907992
#105907952
#105907692
#105907042
#806853
#795013