Finite Group Databasebeta

← #11858014

Subgroups — #11858014

Order 1152.

1657 conjugacy classes of subgroups.

The subgroup lattice has 981 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C211yesmaximal, characteristic
2C2×#63805C211yesmaximal, characteristic, complemented
3#10594510C211yesmaximal, characteristic, complemented
4C3⋊D3×#102C211yesmaximal, characteristic, complemented
5C3×#4771C211yesmaximal, characteristic, complemented
6C3×#4770C211yesmaximal, characteristic, complemented
7#10591426C211yesmaximal, characteristic, complemented
8#10591420C211yesmaximal, characteristic, complemented
9D3×#832C211yesmaximal, characteristic, complemented
10#10590956C211yesmaximal, characteristic, complemented
11#10590939C211yesmaximal, characteristic, complemented
12#10590671C211yesmaximal, characteristic, complemented
13#10590612C211yesmaximal, characteristic, complemented
14#10590610C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16#78925—31nomaximal
17#78882—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3811—21no—
22C2×D3×#67—21no—
23C22×#626—21no—
24C2×#3804—21no—
25#64314—24no—
26#64314C418yescomplemented
27C2×D3×D12C2211yescharacteristic
28C2×#3799C2211yescharacteristic
29C2×#3798C2211yescharacteristic
30C2×#3796C2211yescharacteristic
31C2×C8×C3⋊D3C2211yescharacteristic, complemented
32C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
34C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
35C3×#892C2211yescharacteristic, complemented
36C3×D3×C4⋊C4C2211yescharacteristic, complemented
37C4×#626—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63881—21no—
40#63879—21no—
41#63849C2211yescharacteristic, complemented
42#63841C2211yescharacteristic, complemented
43#63837—21no—
44C2×#3712C2211yescharacteristic, complemented
45C2×D3×C3⋊C8C2211yescharacteristic, complemented
46C2×D3×C3⋊C8C2211yescharacteristic, complemented
47#63805—24no—
48C32×#102C2211yescharacteristic, complemented
49#63659C2211yescharacteristic, complemented
50#63648C2211yescharacteristic, complemented
51#63636C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, complemented
64C2×#1009—31no—
65C2×#1004—31no—
66C2×#907—31no—
67C2×#907—31no—
68#5523—31no—
69#5504—31no—
70C3×#418—31no—
71C3×#417—31no—
72#5233—31no—
73C2×#832—31no—
74#5133—31no—
75#5131—31no—
76#5002—31no—
77C2×#809—31no—
78#4804—31no—
79#4804—31no—
80#4803—31no—
81#4803—31no—
82#4772—31no—
83#4772—31no—
84#4771—31no—
85#4771D311yescharacteristic, complemented
86#4770—31no—
87#4770—31no—
88#4770—31no—
89#4770D311yescharacteristic, complemented
90D3×#102—31no—
91D3×#102—31no—
92D3×#102—31no—
93D3×#102—31no—
94D3×#102—61no—
95C23×C3⋊D3—21no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C2×C32×D4C2311yescharacteristic
99C2×#638—21no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3C2×C414yescomplemented
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C22×C3×Dic3—21no—
108C3×#237—22no—
109C3×#237C2×C414yescomplemented
110C3×D3×D4—22no—
111C3×D3×D4C2×C414yescomplemented
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117#3811—28no—
118D3×#67—28no—
119C2×#627D411yescharacteristic
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—28no—
124C2×#626D411yescharacteristic
125C2×#626D411yescharacteristic
126C2×#625D411yescharacteristic
127C2×#624—21no—
128#3804—28no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3—21no—
131D3×D12—22no—
132D3×D12C2×C414yescomplemented
133#3799—22no—
134#3799C2×C414yescomplemented
135#3798C2×C414yes—
136#3798D414yes—
137#3796—22no—
138#3796C2×C414yescomplemented
139C2×C32×C8C2311yescharacteristic
140C32×C4⋊C4C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142#3750—21no—
143C2×C3⋊(C3⋊C8)C2311yescharacteristic
144C8×C3⋊D3—22no—
145C3×(C2×D3)⋊C4—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×ΓL(1,𝔽25)—22no—
153C3×ΓL(1,𝔽25)—22no—
154Dic3⋊Dic3—21no—
155#3722—21no—
156(C2×D3)⋊Dic3—21no—
157Dic32—21no—
158Dic32—21no—
159#3712—22no—
160D3×C3⋊C8—22no—
161D3×C3⋊C8—22no—
162#2897—91noSylow
163C2×C3×#41—31no—
164C22×C3×D4—31no—
165C22×#67—61no—
166C22×#67—61no—
167#1009—38no—
168#1009—64no—
169C2×#239—31no—
170C2×#239—31no—
171#1004—38no—
172#1004—64no—
173C2×#237—31no—
174C2×#237—61no—
175C2×#237C2×D311yescharacteristic
176C2×D3×D4—31no—
177C2×D3×D4—31no—
178C2×D3×D4—31no—
179C2×D3×D4—61no—
180C2×D3×D4—61no—
181C2×D3×D4—61no—
182C2×D3×D4—61no—
183C2×D3×D4C2×D311yescharacteristic
184C2×#235—31no—
185C2×#235—31no—
186C2×#235—31no—
187C2×#235—61no—
188C22×D12—31no—
189C22×D12—61no—
190C2×C3×M16—31no—
191C2×C3×M16—31no—
192C3×#117—31no—
193C2×C3×C4⋊C4—31no—
194C4×#67—61no—
195C4×#67—61no—
196#926—31no—
197C2×C4⋊Dic3—31no—
198C22×C3⋊C8—31no—
199C22×C3⋊C8—31no—
200#907—64no—
201#907—64no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
205C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
206C2×D3×C8—31no—
207C2×D3×C8—31no—
208C2×D3×C8—31no—
209C2×D3×C8—31no—
210C2×D3×C8—61no—
211#893—61no—
212#892—31no—
213#892—31no—
214#892—31no—
215#892C2×D311yescharacteristic, complemented
216D3×C4⋊C4—31no—
217D3×C4⋊C4—31no—
218D3×C4⋊C4—31no—
219D3×C4⋊C4—61no—
220D3×C4⋊C4C2×D311yescharacteristic, complemented
221#887—61no—
222#67⋊C4—61no—
223#67⋊C4—61no—
224C4×D12—61no—
225C4×Dic6—61no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#102—21no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic, complemented
234C3×#102C2×D311yescharacteristic, complemented
235#835—31no—
236#835—31no—
237#832—31no—
238#832—31no—
239#832—31no—
240#832—31no—
241#832—61no—
242#832C2×D311yescharacteristic, complemented
243#832C2×D311yescharacteristic, complemented
244#821—31no—
245#821—31no—
246#821—31no—
247#821—31no—
248#821—31no—
249#821—61no—
250#821C2×D311yescharacteristic, complemented
251#816—31no—
252#816C2×D311yescharacteristic, complemented
253#810—31no—
254#810C2×D311yescharacteristic, complemented
255#809—31no—
256#809—31no—
257#809—31no—
258#809—31no—
259#809—31no—
260#809—61no—
261#809C2×D311yescharacteristic, complemented
262C23×C32—21no—
263C22×C3⋊D3—21no—
264C22×C3⋊D3—24no—
265C22×C3⋊D3—81no—
266C22×C3⋊D3—81no—
267C22×C3⋊D3C2×D411yescharacteristic
268C22×C3×D3—21no—
269C22×C3×D3—24no—
270C22×C3×D3—81no—
271C22×C3×D3—81no—
272C22×C3×D3C2×D411yescharacteristic
273C22×C3×D3C2×D411yescharacteristic
274C2×D32—24no—
275C2×D32—81no—
276C2×D32—81no—
277C32×D4—21no—
278C32×D4C22×C412yes—
279C2×C32×C4—21no—
280C2×C32×C4C2411yescharacteristic
281#638—24no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3C2×D411yescharacteristic
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)C22×C412yes—
286C4×C3⋊D3—81no—
287C4×C3⋊D3C22×C412yes—
288C4×C3⋊D3C2×D412yes—
289C3×#67—24no—
290C3×#67—24no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—24no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3C2×D411yescharacteristic
296C2×C3×Dic3C2×D411yescharacteristic
297C3×D12—21no—
298C3×D12C22×C412yes—
299C3×C4×D3—81no—
300C3×C4×D3C22×C412yes—
301C3×C4×D3C22×C412yes—
302C3×C4×D3C2×D412yes—
303C3×C4×D3C2×D412yes—
304C3×Dic6—21no—
305C3×Dic6C22×C412yes—
306#627C22⋊C414yes—
307#626—24no—
308#626—24no—
309#626—24no—
310#626C22⋊C414yes—
311#626C22⋊C414yes—
312#625C22⋊C414yes—
313#624—24no—
314D3×Dic3—24no—
315D3×Dic3—81no—
316C32×C8—21no—
317C3⋊(C3⋊C8)—21no—
318C3×C3⋊C8—21no—
319C3×C3⋊C8—21no—
320C2×H(5,𝔽2)—91no—
321C2×#131—91no—
322#520—91no—
323#418—31no—
324#418—91no—
325#418—91no—
326#417—31no—
327#417—91no—
328#417—91no—
329#416—91no—
330#416—91no—
331#416—91no—
332C2×#102—91no—
333C2×#102—91no—
334C2×#102—91no—
335C24×C3—61no—
336C23×D3—21no—
337C23×D3—61no—
338C23×D3—61no—
339C23×D3—61no—
340C23×D3—61no—
341C23×D3—121no—
342C3×#41—34no—
343C3×#41—62no—
344C2×C3×Q8—31no—
345C2×C3×D4—21no—
346C2×C3×D4—34no—
347C2×C3×D4—31no—
348C2×C3×D4—62no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4C22×D311yescharacteristic
352C2×C3×D4C22×D311yescharacteristic
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C2×#67—21no—
358C2×#67—21no—
359C2×#67—31no—
360C2×#67—31no—
361C2×#67—31no—
362C2×#67—31no—
363C2×#67—68no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—61no—
368C2×#67—68no—
369C2×#67—61no—
370C2×#67—121no—
371C22×Dic3—21no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374#239—34no—
375#239—34no—
376#239—62no—
377#239—62no—
378#237—22no—
379#237—34no—
380#237—62no—
381#237—68no—
382#237C4×D314yescomplemented
383D3×D4—22no—
384D3×D4—34no—
385D3×D4—34no—
386D3×D4—34no—
387D3×D4—64no—
388D3×D4—62no—
389D3×D4—62no—
390D3×D4—68no—
391D3×D4—68no—
392D3×D4—68no—
393D3×D4—62no—
394D3×D4—122no—
395D3×D4C4×D314yescomplemented
396#235—34no—
397#235—34no—
398#235—34no—
399#235—34no—
400#235—34no—
401#235—62no—
402#235—68no—
403C2×D12—31no—
404C2×D12—31no—
405C2×D12—31no—
406C2×D12—31no—
407C2×D12—34no—
408C2×D12—61no—
409C2×D12—62no—
410C2×D12—68no—
411C2×D12—61no—
412C2×D12—61no—
413C2×D12—61no—
414C2×D12C22×D311yescharacteristic
415C2×C4×D3—21no—
416C2×C4×D3—31no—
417C2×C4×D3—31no—
418C2×C4×D3—61no—
419C2×C4×D3—61no—
420C2×C4×D3—61no—
421C2×C4×D3—61no—
422C2×C4×D3—61no—
423C2×C4×D3—61no—
424C2×C4×D3—61no—
425C2×C4×D3—121no—
426C2×C4×D3C22×D311yescharacteristic
427C2×C4×D3C22×D311yescharacteristic
428C2×Dic6—31no—
429C2×Dic6—31no—
430C2×Dic6C22×D311yescharacteristic
431C3×M16—62no—
432C3×M16—62no—
433C2×C3×C8—21no—
434C2×C3×C8—31no—
435C2×C3×C8—31no—
436C2×C3×C8C22×D311yescharacteristic
437C2×C3×C8C22×D311yescharacteristic
438C3×C4⋊C4—21no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—61no—
442C3×C4⋊C4C22×D311yescharacteristic
443C3×C4⋊C4C22×D311yescharacteristic
444C3×C22⋊C4—61no—
445C3×C42—61no—
446#217—61no—
447(C2×D3)⋊C4—21no—
448(C2×D3)⋊C4—61no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451C4⋊Dic3—31no—
452C4⋊Dic3—31no—
453C4⋊Dic3—61no—
454C4⋊Dic3—61no—
455C4⋊Dic3C22×D311yescharacteristic
456C4⋊Dic3C22×D311yescharacteristic
457Dic3⋊C4—21no—
458Dic3⋊C4—61no—
459Dic3⋊C4—61no—
460Dic3⋊C4—61no—
461Dic3⋊C4—121no—
462C4×Dic3—21no—
463C4×Dic3—61no—
464C4×Dic3—61no—
465C4×Dic3—61no—
466C4×Dic3—61no—
467C2×C3⋊C8—31no—
468C2×C3⋊C8—31no—
469C2×C3⋊C8—61no—
470C2×C3⋊C8—62no—
471C2×C3⋊C8—62no—
472C2×C3⋊C8C22×D311yescharacteristic
473C2×C3⋊C8C22×D311yescharacteristic
474ΓL(1,𝔽25)—22no—
475ΓL(1,𝔽25)—22no—
476ΓL(1,𝔽25)—62no—
477ΓL(1,𝔽25)—62no—
478D3×C8—62no—
479D3×C8—62no—
480D3×C8—62no—
481D3×C8—62no—
482D3×C8—122no—
483C22×C32—22no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32C22×D411yescharacteristic
487C2×C3⋊D3—21no—
488C2×C3⋊D3—21no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3—41no—
491C2×C3⋊D3—41no—
492C2×C3⋊D3—84no—
493C2×C3⋊D3C2×C22⋊C412yes—
494C2×C3×D3—21no—
495C2×C3×D3—21no—
496C2×C3×D3—21no—
497C2×C3×D3—21no—
498C2×C3×D3—22no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—84no—
502C2×C3×D3C2×C22⋊C412yes—
503C2×C3×D3C2×C22⋊C412yes—
504D32—84no—
505C32×C4—41no—
506C32×C4C23×C411yescharacteristic
507C32×C4C22×D411yescharacteristic
508C3⋊Dic3—41no—
509C3⋊Dic3C2×C22⋊C412yes—
510C3×Dic3—22no—
511C3×Dic3—41no—
512C3×Dic3—41no—
513C3×Dic3C2×C22⋊C412yes—
514C3×Dic3C2×C22⋊C412yes—
515H(5,𝔽2)—98no—
516H(5,𝔽2)—184no—
517C2×#41—31no—
518C2×#41—91no—
519C2×#41—91no—
520C2×#41—91no—
521C2×#41—181no—
522C22×D4—31no—
523C22×D4—91no—
524C22×D4—91no—
525C22×D4—181no—
526C22×D4—181no—
527C22×D4—181no—
528#131—184no—
529C2×M16—31no—
530C2×M16—31no—
531C2×M16—91no—
532C22×C8—91no—
533C22×C8—91no—
534C22×C8—91no—
535C4×Q8—181no—
536C4×D4—181no—
537C4×D4—181no—
538C4×D4—181no—
539#117—31no—
540#117—91no—
541#117—91no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545#103—31no—
546#103—31no—
547#103—91no—
548#103—91no—
549#102—31no—
550#102—31no—
551#102—31no—
552#102—31no—
553#102—91no—
554#102—91no—
555#102—91no—
556#102—91no—
557#102—91no—
558#102—91no—
559#102—91no—
560#102D3211yescharacteristic, complemented
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—31no—
564C23×C3—31no—
565C23×C3—41no—
566C23×C3—64no—
567C23×C3—61no—
568C23×C3—241no—
569C23×C3—241no—
570C22×D3—21no—
571C22×D3—24no—
572C22×D3—31no—
573C22×D3—31no—
574C22×D3—61no—
575C22×D3—64no—
576C22×D3—64no—
577C22×D3—64no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—64no—
581C22×D3—81no—
582C22×D3—81no—
583C22×D3—124no—
584C22×D3—121no—
585C22×D3—241no—
586C22×D3—241no—
587C22×D3—241no—
588C22×D3—241no—
589C22×D3—241no—
590C22×D3—241no—
591C22×D3—241no—
592C22×D3—241no—
593C22×D3—242no—
594C22×D3—242no—
595C22×D3D3×D411yescharacteristic
596C22×D3D3×D411yescharacteristic
597C3×Q8—32no—
598C3×Q8—61no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—22no—
602C3×D4—32no—
603C3×D4—41no—
604C3×D4—64no—
605C3×D4—64no—
606C3×D4—61no—
607C3×D4C2×C4×D312yes—
608C3×D4C2×C4×D312yes—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—31no—
613C2×C3×C4—31no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—41no—
619C2×C3×C4—64no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—241no—
624C2×C3×C4C23×D311yescharacteristic
625C2×C3×C4C23×D311yescharacteristic
626#67—24no—
627#67—24no—
628#67—34no—
629#67—34no—
630#67—34no—
631#67—34no—
632#67—64no—
633#67—64no—
634#67—64no—
635#67—64no—
636#67—64no—
637#67—124no—
638C2×Dic3—21no—
639C2×Dic3—24no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—31no—
643C2×Dic3—31no—
644C2×Dic3—61no—
645C2×Dic3—64no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—121no—
649C2×Dic3—241no—
650C2×Dic3D3×D411yescharacteristic
651C2×Dic3D3×D411yescharacteristic
652D12—21no—
653D12—34no—
654D12—34no—
655D12—32no—
656D12—32no—
657D12—62no—
658D12—64no—
659D12—64no—
660D12—64no—
661D12—61no—
662D12—61no—
663D12—121no—
664D12C2×C4×D312yes—
665C4×D3—32no—
666C4×D3—32no—
667C4×D3—32no—
668C4×D3—32no—
669C4×D3—62no—
670C4×D3—62no—
671C4×D3—64no—
672C4×D3—64no—
673C4×D3—64no—
674C4×D3—81no—
675C4×D3—241no—
676C4×D3—241no—
677C4×D3—241no—
678C4×D3—242no—
679C4×D3C2×C4×D312yes—
680C4×D3C2×C4×D312yes—
681C4×D3D3×D412yes—
682C4×D3D3×D412yes—
683Dic6—21no—
684Dic6—34no—
685Dic6—34no—
686Dic6C2×C4×D312yes—
687C3×C8—21no—
688C3×C8—21no—
689C3×C8—41no—
690C3×C8—61no—
691C3×C8—61no—
692C3⋊C8—21no—
693C3⋊C8—21no—
694C3⋊C8—61no—
695C3⋊C8—61no—
696C3⋊C8—121no—
697C2×C32—42no—
698C2×C32C22×C22⋊C411yescharacteristic
699C2×C32#57611yescharacteristic
700C2×C32#57711yescharacteristic
701C3⋊D3—22no—
702C3⋊D3—42no—
703C3×D3—22no—
704C3×D3—22no—
705C3×D3—42no—
706C24—61no—
707C24—181no—
708C24—181no—
709#41—34no—
710#41—62no—
711#41—94no—
712#41—94no—
713#41—94no—
714#41—94no—
715#41—182no—
716#41—188no—
717#41—182no—
718C2×Q8—31no—
719C2×Q8—91no—
720C2×D4—34no—
721C2×D4—31no—
722C2×D4—62no—
723C2×D4—61no—
724C2×D4—61no—
725C2×D4—94no—
726C2×D4—91no—
727C2×D4—91no—
728C2×D4—91no—
729C2×D4—94no—
730C2×D4—91no—
731C2×D4—182no—
732C2×D4—181no—
733C2×D4—188no—
734C2×D4—181no—
735C2×D4—181no—
736C2×D4—182no—
737C2×D4—181no—
738C2×D4—188no—
739C2×D4—188no—
740C2×D4C2×D3211yescharacteristic
741C22×C4—31no—
742C22×C4—31no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—91no—
746C22×C4—181no—
747C22×C4—181no—
748C22×C4—181no—
749C22×C4—181no—
750M16—62no—
751M16—62no—
752M16—182no—
753C2×C8—31no—
754C2×C8—31no—
755C2×C8—91no—
756C2×C8—182no—
757C2×C8—182no—
758C2×C8—182no—
759C2×C8C2×D3211yescharacteristic
760C4⋊C4—31no—
761C4⋊C4—31no—
762C4⋊C4—61no—
763C4⋊C4—91no—
764C4⋊C4—181no—
765C4⋊C4—181no—
766C4⋊C4C2×D3211yescharacteristic
767C22⋊C4—61no—
768C22⋊C4—181no—
769C22⋊C4—181no—
770C42—61no—
771C42—181no—
772C42—181no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—21no—
776C22×C3—32no—
777C22×C3—32no—
778C22×C3—42no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—61no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3—61no—
787C22×C3—62no—
788C22×C3—81no—
789C22×C3—81no—
790C22×C3—121no—
791C22×C3—121no—
792C22×C3—244no—
793C22×C3C2×D3×D411yescharacteristic
794C22×C3C2×D3×D411yescharacteristic
795C2×D3—21no—
796C2×D3—21no—
797C2×D3—21no—
798C2×D3—21no—
799C2×D3—22no—
800C2×D3—32no—
801C2×D3—32no—
802C2×D3—41no—
803C2×D3—41no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—61no—
808C2×D3—61no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—62no—
812C2×D3—62no—
813C2×D3—84no—
814C2×D3—122no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—121no—
818C2×D3—121no—
819C2×D3—241no—
820C2×D3—241no—
821C2×D3—244no—
822C2×D3—244no—
823C2×D3—244no—
824C2×D3—244no—
825C2×D3—248no—
826C2×D3D3×C22⋊C412yes—
827C2×D3D3×C22⋊C412yes—
828C3×C4—21no—
829C3×C4—21no—
830C3×C4—32no—
831C3×C4—32no—
832C3×C4—41no—
833C3×C4—41no—
834C3×C4—62no—
835C3×C4—81no—
836C3×C4—121no—
837C3×C4—121no—
838C3×C4C22×C4×D311yescharacteristic
839C3×C4C22×C4×D311yescharacteristic
840C3×C4C2×D3×D411yescharacteristic
841C3×C4C2×D3×D411yescharacteristic
842Dic3—22no—
843Dic3—32no—
844Dic3—32no—
845Dic3—41no—
846Dic3—41no—
847Dic3—62no—
848Dic3—121no—
849Dic3—121no—
850Dic3—241no—
851Dic3D3×C22⋊C412yes—
852Dic3D3×C22⋊C412yes—
853C32#289711yescharacteristic, complemented, Sylow
854C23—21no—
855C23—31no—
856C23—31no—
857C23—64no—
858C23—61no—
859C23—91no—
860C23—184no—
861C23—184no—
862C23—181no—
863C23—241no—
864C23—241no—
865C23—721no—
866C23—721no—
867C23—721no—
868C23—721no—
869Q8—32no—
870Q8—61no—
871Q8—94no—
872D4—21no—
873D4—32no—
874D4—64no—
875D4—64no—
876D4—61no—
877D4—94no—
878D4—94no—
879D4—94no—
880D4—92no—
881D4—184no—
882D4—184no—
883D4—184no—
884D4—184no—
885D4—181no—
886D4C4×D3212yes—
887C2×C4—21no—
888C2×C4—31no—
889C2×C4—31no—
890C2×C4—32no—
891C2×C4—32no—
892C2×C4—32no—
893C2×C4—32no—
894C2×C4—64no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—91no—
899C2×C4—92no—
900C2×C4—92no—
901C2×C4—184no—
902C2×C4—184no—
903C2×C4—181no—
904C2×C4—241no—
905C2×C4—721no—
906C2×C4—721no—
907C2×C4C22×D3211yescharacteristic
908C8—21no—
909C8—61no—
910C8—61no—
911C8—181no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—42no—
916C2×C3—42no—
917C2×C3—62no—
918C2×C3—62no—
919C2×C3—82no—
920C2×C3—122no—
921C2×C3C2×D3×C22⋊C411yescharacteristic
922C2×C3C2×D3×C22⋊C411yescharacteristic
923C2×C3#577411yescharacteristic
924C2×C3#577411yescharacteristic
925C2×C3#577511yescharacteristic
926C2×C3#577811yescharacteristic
927D3—22no—
928D3—22no—
929D3—42no—
930D3—64no—
931D3—62no—
932D3—62no—
933D3—122no—
934D3—122no—
935D3—242no—
936C22—22no—
937C22—32no—
938C22—32no—
939C22—41no—
940C22—41no—
941C22—61no—
942C22—61no—
943C22—61no—
944C22—61no—
945C22—62no—
946C22—92no—
947C22—121no—
948C22—121no—
949C22—181no—
950C22—181no—
951C22—182no—
952C22—244no—
953C22—361no—
954C22—361no—
955C22—724no—
956C22—724no—
957C22D32×D411yescharacteristic
958C4—32no—
959C4—32no—
960C4—41no—
961C4—62no—
962C4—92no—
963C4—121no—
964C4—121no—
965C4—361no—
966C4C2×C4×D3211yescharacteristic
967C4D32×D411yescharacteristic
968C3—21no—
969C3#7888211yescharacteristic, complemented
970C3#7892511yescharacteristic, complemented
971C2—42no—
972C2—62no—
973C2—62no—
974C2—122no—
975C2—182no—
976C2—362no—
977C2D32×C22⋊C411yescharacteristic
978C2#1059473511yescharacteristic
979C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#64314C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2897
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#63805C2semidirect
3. #10594510C2semidirect
4. C3⋊D3×#102C2semidirect
5. C3×#4771C2semidirect
6. C3×#4770C2semidirect
7. #10591426C2semidirect
8. #10591420C2semidirect
9. D3×#832C2semidirect
10. #10590956C2semidirect
11. #10590939C2semidirect
12. #10590671C2semidirect
13. #10590612C2semidirect
14. #10590610C2semidirect
15. D3×#809C2semidirect
26. #64314C4semidirect
31. C2×C8×C3⋊D3C22semidirect
32. C4⋊C4×C3⋊D3C22semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
34. C2×C3×ΓL(1,𝔽25)C22semidirect
35. C3×#892C22semidirect
36. C3×D3×C4⋊C4C22semidirect
38. D3×C4⋊Dic3C22semidirect
41. #63849C22semidirect
42. #63841C22semidirect
44. C2×#3712C22semidirect
45. C2×D3×C3⋊C8C22semidirect
46. C2×D3×C3⋊C8C22semidirect
48. C32×#102C22semidirect
49. #63659C22semidirect
50. #63648C22semidirect
51. #63636C22semidirect
52. C3×#832C22semidirect
53. C3×#832C22semidirect
54. C3×#821C22semidirect
55. C3×#816C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. #63566C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
63. #63562C22semidirect
85. #4771D3semidirect
89. #4770D3semidirect
101. D4×C3⋊D3C2×C4semidirect
109. C3×#237C2×C4semidirect
111. C3×D3×D4C2×C4semidirect
132. D3×D12C2×C4semidirect
134. #3799C2×C4semidirect
138. #3796C2×C4semidirect
204. C2×ΓL(1,𝔽25)C2×D3semidirect
205. C2×ΓL(1,𝔽25)C2×D3semidirect
215. #892C2×D3semidirect
220. D3×C4⋊C4C2×D3semidirect
233. C3×#102C2×D3semidirect
234. C3×#102C2×D3semidirect
242. #832C2×D3semidirect
243. #832C2×D3semidirect
250. #821C2×D3semidirect
252. #816C2×D3semidirect
254. #810C2×D3semidirect
261. #809C2×D3semidirect
382. #237C4×D3semidirect
395. D3×D4C4×D3semidirect
560. #102D32semidirect
853. C32#2897semidirect
969. C3#78882semidirect
970. C3#78925semidirect

Maximal subgroups

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

subgroupindex
C2×#643142
C2×#638052
#105945102
C3⋊D3×#1022
C3×#47712
C3×#47702
#105914262
#105914202
D3×#8322
#105909562
#105909392
#105906712
#105906122
#105906102
D3×#8092
#789253
#788823