Finite Group Databasebeta

← #11858073

Subgroups — #11858073

Order 1152.

1527 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64315C211yesmaximal, characteristic
2C2×#63804C211yesmaximal, characteristic, complemented
3#10594511C211yesmaximal, characteristic, complemented
4#10592501C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6C3×#4802C211yesmaximal, characteristic, complemented
7#10591552C211yesmaximal, characteristic, complemented
8#10591550C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10590957C211yesmaximal, characteristic, complemented
11#10590670C211yesmaximal, characteristic, complemented
12D3×#816C211yesmaximal, characteristic, complemented
13#10590611C211yesmaximal, characteristic, complemented
14#10590608C211yesmaximal, characteristic, complemented
15#10590600C211yesmaximal, characteristic, complemented
16#78957—31nomaximal
17#78832—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21#64315—24no—
22#64315C418yescomplemented
23C2×#3798—21no—
24C2×#3798C2211yescharacteristic
25C2×#3796—21no—
26C2×#3796C2211yescharacteristic
27C2×#3795—21no—
28C2×#3795C2211yescharacteristic
29C2×D3×Dic6—21no—
30C2×D3×Dic6C2211yescharacteristic
31C2×#3743C2211yescharacteristic
32#64101C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34C2×C3×D3×C8C2211yescharacteristic
35C3×#892C2211yescharacteristic
36C3×#892C2211yescharacteristic
37C4×#627—21no—
38#63902—21no—
39#63900C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic
41D3×C4⋊Dic3C2211yescharacteristic
42#63880—21no—
43#63880—21no—
44C2×#3711C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C2×D3×C3⋊C8C2211yescharacteristic
47#63804—24no—
48C32×#103C2211yescharacteristic
49#63662C2211yescharacteristic
50#63643C2211yescharacteristic
51#63637C2211yescharacteristic
52C3×#835C2211yescharacteristic
53C3×#835C2211yescharacteristic
54C3×#821C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58#63567C2211yescharacteristic
59#63567C2211yescharacteristic
60#63566C2211yescharacteristic
61#63565C2211yescharacteristic
62#63563C2211yescharacteristic
63#63562C2211yescharacteristic
64C2×#1010—31no—
65C2×#1007—31no—
66C2×#907—31no—
67C2×#901—31no—
68#5523—31no—
69#5523—31no—
70C3×#419—31no—
71C3×#416—31no—
72#5232—31no—
73C2×#835—31no—
74#5133—31no—
75C2×#816—31no—
76#5004—31no—
77#5002—31no—
78#4804—31no—
79#4804D311yescharacteristic, complemented
80#4803—31no—
81#4803—31no—
82#4802—31no—
83#4802—31no—
84#4802—31no—
85#4802—61no—
86#4802D311yescharacteristic, complemented
87D3×#103—31no—
88D3×#103—31no—
89D3×#103—31no—
90D3×#103—31no—
91#4772—31no—
92#4772—31no—
93#4771—31no—
94#4771—31no—
95C2×C32×Q8C2311yescharacteristic
96Q8×C3⋊D3—22no—
97Q8×C3⋊D3C2×C414yescomplemented
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634—21no—
101C2×#634C2311yescharacteristic
102C3×#239—22no—
103C3×#239C2×C414yescomplemented
104C3×D3×Q8—22no—
105C3×D3×Q8C2×C414yescomplemented
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6C2311yescharacteristic
114C2×#627—21no—
115C2×#627D411yescharacteristic
116C2×#626—21no—
117C2×#626D411yescharacteristic
118C2×#626D411yescharacteristic
119C2×#625—21no—
120C2×#625D411yescharacteristic
121C2×#624—21no—
122C2×D3×Dic3—21no—
123C2×D3×Dic3—21no—
124C2×D3×Dic3—21no—
125C2×D3×Dic3—21no—
126C2×D3×Dic3—21no—
127#3798—28no—
128#3798C2×C414yes—
129#3798D414yes—
130#3796—22no—
131#3796—28no—
132#3796C2×C414yescomplemented
133#3795—22no—
134#3795—28no—
135#3795C2×C414yescomplemented
136D3×Dic6—22no—
137D3×Dic6—28no—
138D3×Dic6C2×C414yescomplemented
139C2×C32×C8C2311yescharacteristic
140C32×C4⋊C4C2311yescharacteristic
141#3752—21no—
142C4⋊(C3⋊Dic3)C2311yescharacteristic
143C4×C3⋊Dic3—21no—
144C2×C3⋊(C3⋊C8)C2311yescharacteristic
145#3743—22no—
146C3×(C2×D3)⋊C4—21no—
147C3×(C2×D3)⋊C4—21no—
148C3×C4⋊Dic3C2311yescharacteristic
149C3×C4⋊Dic3C2311yescharacteristic
150C3×C4×Dic3—21no—
151C3×C4×Dic3—21no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C3×ΓL(1,𝔽25)—22no—
155C3×D3×C8—22no—
156#3724—21no—
157Dic3⋊Dic3—21no—
158Dic3⋊Dic3—21no—
159#3711—22no—
160#3710—22no—
161D3×C3⋊C8—22no—
162#2898—91noSylow
163C2×C3×#41—31no—
164C22×C3×Q8—31no—
165#1010—38no—
166#1010—64no—
167#1007—38no—
168#1007—64no—
169C2×#239—31no—
170C2×#239—61no—
171C2×#239C2×D311yescharacteristic
172C2×D3×Q8—31no—
173C2×D3×Q8—31no—
174C2×D3×Q8—31no—
175C2×D3×Q8—61no—
176C2×D3×Q8—61no—
177C2×D3×Q8C2×D311yescharacteristic
178C2×#237—31no—
179C2×#237—31no—
180C2×#237—61no—
181C2×#237—61no—
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—31no—
185C2×#235—61no—
186C2×#235—61no—
187C2×#235—61no—
188C22×Dic6—31no—
189C22×Dic6—61no—
190C2×C3×M16—31no—
191C22×C3×C8—31no—
192C3×#117—31no—
193C3×#117—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×#208—31no—
197C22×C3⋊C8—31no—
198#907—64no—
199#901—64no—
200C2×ΓL(1,𝔽25)—31no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—61no—
204C2×ΓL(1,𝔽25)C2×D311yescharacteristic
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207C2×D3×C8—31no—
208C2×D3×C8C2×D311yescharacteristic
209#892—31no—
210#892—31no—
211#892—61no—
212#892C2×D311yescharacteristic
213#892C2×D311yescharacteristic
214D3×C4⋊C4—31no—
215D3×C4⋊C4—31no—
216D3×C4⋊C4—31no—
217D3×C4⋊C4—31no—
218#67⋊C4—61no—
219#67⋊C4—61no—
220#67⋊C4—61no—
221#67⋊C4—61no—
222C4×D12—61no—
223C4×D12—61no—
224C4×Dic6—61no—
225C4×Dic6—61no—
226C3×#103—21no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#103—31no—
231C3×#103C2×D311yescharacteristic
232C3×#103C2×D311yescharacteristic
233C3×#102—31no—
234C3×#102—31no—
235#835—31no—
236#835—31no—
237#835—31no—
238#835—31no—
239#835—61no—
240#835C2×D311yescharacteristic
241#835C2×D311yescharacteristic
242#832—31no—
243#832—31no—
244#821—31no—
245#821C2×D311yescharacteristic
246#816—31no—
247#816—31no—
248#816—31no—
249#816—31no—
250#816—31no—
251#816—61no—
252#816C2×D311yescharacteristic
253#810—31no—
254#810—31no—
255#810—31no—
256#810—31no—
257#810—31no—
258#810—61no—
259#810C2×D311yescharacteristic
260#809—31no—
261#809C2×D311yescharacteristic
262C22×C3⋊D3C2×D411yescharacteristic
263C22×C3×D3—21no—
264C22×C3×D3C2×D411yescharacteristic
265C22×C3×D3C2×D411yescharacteristic
266C32×Q8—21no—
267C32×Q8C22×C412yes—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4×C3⋊D3—24no—
275C4×C3⋊D3C22×C412yes—
276C4×C3⋊D3C2×D412yes—
277#634—21no—
278#634—24no—
279#634C22×C412yes—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—24no—
286C3×D12—21no—
287C3×D12C22×C412yes—
288C3×C4×D3—24no—
289C3×C4×D3—24no—
290C3×C4×D3C22×C412yes—
291C3×C4×D3C22×C412yes—
292C3×C4×D3C2×D412yes—
293C3×C4×D3C2×D412yes—
294C3×Dic6—21no—
295C3×Dic6—24no—
296C3×Dic6C22×C412yes—
297#627—24no—
298#627C22⋊C414yes—
299#626—24no—
300#626C22⋊C414yes—
301#626C22⋊C414yes—
302#625—24no—
303#625C22⋊C414yes—
304#624—81no—
305D3×Dic3—24no—
306D3×Dic3—24no—
307D3×Dic3—24no—
308D3×Dic3—81no—
309D3×Dic3—81no—
310C32×C8—21no—
311C3⋊(C3⋊C8)—21no—
312C3×C3⋊C8—21no—
313C3×C3⋊C8—21no—
314C2×2−1+4—91no—
315C2×#131—91no—
316#520—91no—
317#419—31no—
318#419—91no—
319#419—91no—
320#417—91no—
321#417—91no—
322#417—91no—
323#416—31no—
324#416—91no—
325#416—91no—
326C2×#103—91no—
327C2×#103—91no—
328C2×#103—91no—
329C3×#41—34no—
330C3×#41—62no—
331C2×C3×Q8—21no—
332C2×C3×Q8—34no—
333C2×C3×Q8—31no—
334C2×C3×Q8—61no—
335C2×C3×Q8—62no—
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×Q8C22×D311yescharacteristic
338C2×C3×D4—31no—
339C2×C3×D4—61no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C2×#67—31no—
345C2×#67—31no—
346C2×#67—31no—
347C2×#67—31no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356#239—22no—
357#239—34no—
358#239—62no—
359#239—68no—
360#239C4×D314yescomplemented
361D3×Q8—22no—
362D3×Q8—34no—
363D3×Q8—34no—
364D3×Q8—34no—
365D3×Q8—64no—
366D3×Q8—68no—
367D3×Q8—62no—
368D3×Q8—62no—
369D3×Q8—62no—
370D3×Q8—122no—
371D3×Q8C4×D314yescomplemented
372#237—34no—
373#237—34no—
374#237—62no—
375#237—68no—
376#237—68no—
377#237—62no—
378#235—34no—
379#235—34no—
380#235—34no—
381#235—34no—
382#235—34no—
383#235—68no—
384#235—68no—
385#235—68no—
386#235—62no—
387C2×D12—21no—
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—61no—
391C2×D12C22×D311yescharacteristic
392C2×C4×D3—21no—
393C2×C4×D3—21no—
394C2×C4×D3—31no—
395C2×C4×D3—31no—
396C2×C4×D3—61no—
397C2×C4×D3—61no—
398C2×C4×D3—61no—
399C2×C4×D3—61no—
400C2×C4×D3—61no—
401C2×C4×D3—61no—
402C2×C4×D3—61no—
403C2×C4×D3—61no—
404C2×C4×D3—61no—
405C2×C4×D3—61no—
406C2×C4×D3—121no—
407C2×C4×D3C22×D311yescharacteristic
408C2×C4×D3C22×D311yescharacteristic
409C2×Dic6—21no—
410C2×Dic6—31no—
411C2×Dic6—31no—
412C2×Dic6—31no—
413C2×Dic6—31no—
414C2×Dic6—34no—
415C2×Dic6—61no—
416C2×Dic6—68no—
417C2×Dic6—62no—
418C2×Dic6—61no—
419C2×Dic6—61no—
420C2×Dic6—61no—
421C2×Dic6—61no—
422C2×Dic6—121no—
423C2×Dic6C22×D311yescharacteristic
424C3×M16—62no—
425C2×C3×C8—21no—
426C2×C3×C8—31no—
427C2×C3×C8—31no—
428C2×C3×C8—62no—
429C2×C3×C8C22×D311yescharacteristic
430C2×C3×C8C22×D311yescharacteristic
431C3×C4⋊C4—21no—
432C3×C4⋊C4—31no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4C22×D311yescharacteristic
435C3×C4⋊C4C22×D311yescharacteristic
436C3×C22⋊C4—61no—
437C3×C22⋊C4—61no—
438C3×C42—61no—
439C3×C42—61no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—121no—
445C4⋊Dic3—31no—
446C4⋊Dic3—31no—
447C4⋊Dic3—61no—
448C4⋊Dic3—61no—
449C4⋊Dic3—61no—
450C4⋊Dic3C22×D311yescharacteristic
451C4⋊Dic3C22×D311yescharacteristic
452Dic3⋊C4—61no—
453Dic3⋊C4—61no—
454Dic3⋊C4—61no—
455Dic3⋊C4—61no—
456C4×Dic3—21no—
457C4×Dic3—21no—
458C4×Dic3—61no—
459C4×Dic3—61no—
460C4×Dic3—121no—
461#208—62no—
462C2×C3⋊C8—31no—
463C2×C3⋊C8—31no—
464C2×C3⋊C8—61no—
465C2×C3⋊C8—62no—
466C2×C3⋊C8C22×D311yescharacteristic
467C2×C3⋊C8C22×D311yescharacteristic
468ΓL(1,𝔽25)—22no—
469ΓL(1,𝔽25)—62no—
470ΓL(1,𝔽25)—62no—
471ΓL(1,𝔽25)—62no—
472ΓL(1,𝔽25)—122no—
473D3×C8—22no—
474D3×C8—62no—
475D3×C8—62no—
476D3×C8—62no—
477C22×C32C22×D411yescharacteristic
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3C2×C22⋊C412yes—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—22no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3C2×C22⋊C412yes—
489C2×C3×D3C2×C22⋊C412yes—
490C32×C4—22no—
491C32×C4—41no—
492C32×C4C23×C411yescharacteristic
493C32×C4C22×D411yescharacteristic
494C3⋊Dic3—22no—
495C3⋊Dic3—41no—
496C3⋊Dic3C2×C22⋊C412yes—
497C3×Dic3—22no—
498C3×Dic3—41no—
499C3×Dic3—41no—
500C3×Dic3C2×C22⋊C412yes—
501C3×Dic3C2×C22⋊C412yes—
5022−1+4—98no—
5032−1+4—184no—
504C2×#41—31no—
505C2×#41—91no—
506C2×#41—91no—
507C2×#41—91no—
508C2×#41—181no—
509C2×#41—181no—
510C2×#41—181no—
511C22×Q8—31no—
512C22×Q8—91no—
513C22×Q8—91no—
514C22×Q8—181no—
515#131—184no—
516C2×M16—31no—
517C2×M16—91no—
518C2×M16—91no—
519C22×C8—31no—
520C22×C8—91no—
521C22×C8—91no—
522C4×Q8—181no—
523C4×D4—181no—
524C4×D4—181no—
525C4×D4—181no—
526#117—31no—
527#117—31no—
528#117—91no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C4⋊C4—91no—
532#103—31no—
533#103—31no—
534#103—31no—
535#103—31no—
536#103—91no—
537#103—91no—
538#103—91no—
539#103—91no—
540#103—91no—
541#103—91no—
542#103—91no—
543#103D3211yescharacteristic
544#102—31no—
545#102—31no—
546#102—91no—
547#102—91no—
548C23×C3—31no—
549C23×C3—31no—
550C23×C3—61no—
551C22×D3—21no—
552C22×D3—31no—
553C22×D3—31no—
554C22×D3—61no—
555C22×D3D3×D411yescharacteristic
556C22×D3D3×D411yescharacteristic
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—22no—
560C3×Q8—32no—
561C3×Q8—41no—
562C3×Q8—64no—
563C3×Q8—61no—
564C3×Q8C2×C4×D312yes—
565C3×Q8C2×C4×D312yes—
566C3×D4—32no—
567C3×D4—64no—
568C3×D4—61no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—64no—
583C2×C3×C4—64no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589#67—34no—
590#67—34no—
591#67—34no—
592#67—34no—
593#67—64no—
594#67—64no—
595#67—64no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—31no—
600C2×Dic3—31no—
601C2×Dic3—61no—
602C2×Dic3—64no—
603C2×Dic3—64no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—64no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3—241no—
612C2×Dic3—241no—
613C2×Dic3D3×D411yescharacteristic
614C2×Dic3D3×D411yescharacteristic
615D12—24no—
616D12—21no—
617D12—34no—
618D12—34no—
619D12—64no—
620D12C2×C4×D312yes—
621C4×D3—24no—
622C4×D3—24no—
623C4×D3—32no—
624C4×D3—32no—
625C4×D3—32no—
626C4×D3—32no—
627C4×D3—62no—
628C4×D3—62no—
629C4×D3—64no—
630C4×D3—64no—
631C4×D3—64no—
632C4×D3—64no—
633C4×D3—64no—
634C4×D3—124no—
635C4×D3—241no—
636C4×D3—241no—
637C4×D3—241no—
638C4×D3—241no—
639C4×D3C2×C4×D312yes—
640C4×D3C2×C4×D312yes—
641C4×D3D3×D412yes—
642C4×D3D3×D412yes—
643Dic6—21no—
644Dic6—24no—
645Dic6—34no—
646Dic6—34no—
647Dic6—32no—
648Dic6—32no—
649Dic6—62no—
650Dic6—64no—
651Dic6—64no—
652Dic6—64no—
653Dic6—61no—
654Dic6—61no—
655Dic6—64no—
656Dic6—124no—
657Dic6—121no—
658Dic6C2×C4×D312yes—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—41no—
662C3×C8—61no—
663C3×C8—61no—
664C3⋊C8—21no—
665C3⋊C8—21no—
666C3⋊C8—61no—
667C3⋊C8—61no—
668C3⋊C8—121no—
669C2×C32C22×C22⋊C411yescharacteristic
670C2×C32#57711yescharacteristic
671C2×C32#57811yescharacteristic
672C3⋊D3—22no—
673C3×D3—22no—
674C3×D3—22no—
675C3×D3—42no—
676#41—34no—
677#41—62no—
678#41—94no—
679#41—94no—
680#41—94no—
681#41—94no—
682#41—182no—
683#41—188no—
684#41—188no—
685#41—182no—
686#41—188no—
687C2×Q8—34no—
688C2×Q8—31no—
689C2×Q8—61no—
690C2×Q8—62no—
691C2×Q8—91no—
692C2×Q8—94no—
693C2×Q8—94no—
694C2×Q8—91no—
695C2×Q8—181no—
696C2×Q8—181no—
697C2×Q8—182no—
698C2×Q8—188no—
699C2×Q8—182no—
700C2×Q8C2×D3211yescharacteristic
701C2×D4—31no—
702C2×D4—61no—
703C2×D4—91no—
704C2×D4—91no—
705C2×D4—91no—
706C2×D4—181no—
707C2×D4—181no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—91no—
713C22×C4—181no—
714C22×C4—181no—
715C22×C4—181no—
716C22×C4—181no—
717C22×C4—181no—
718C22×C4—181no—
719C22×C4—181no—
720M16—62no—
721M16—182no—
722M16—182no—
723C2×C8—31no—
724C2×C8—31no—
725C2×C8—62no—
726C2×C8—91no—
727C2×C8—182no—
728C2×C8—182no—
729C2×C8C2×D3211yescharacteristic
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—91no—
733C4⋊C4—181no—
734C4⋊C4—181no—
735C4⋊C4—181no—
736C4⋊C4C2×D3211yescharacteristic
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—181no—
740C42—61no—
741C42—61no—
742C42—181no—
743C22×C3—21no—
744C22×C3—32no—
745C22×C3—32no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—61no—
750C22×C3—62no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3C2×D3×D411yescharacteristic
754C22×C3C2×D3×D411yescharacteristic
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—22no—
760C2×D3—32no—
761C2×D3—32no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—62no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—61no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3D3×C22⋊C412yes—
772C2×D3D3×C22⋊C412yes—
773C3×C4—22no—
774C3×C4—22no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—32no—
778C3×C4—32no—
779C3×C4—42no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—62no—
783C3×C4—81no—
784C3×C4—121no—
785C3×C4—121no—
786C3×C4C22×C4×D311yescharacteristic
787C3×C4C22×C4×D311yescharacteristic
788C3×C4C2×D3×D411yescharacteristic
789C3×C4C2×D3×D411yescharacteristic
790Dic3—22no—
791Dic3—32no—
792Dic3—32no—
793Dic3—41no—
794Dic3—41no—
795Dic3—62no—
796Dic3—62no—
797Dic3—62no—
798Dic3—122no—
799Dic3—121no—
800Dic3—121no—
801Dic3—241no—
802Dic3D3×C22⋊C412yes—
803Dic3D3×C22⋊C412yes—
804C32#289811yescharacteristic, complemented, Sylow
805C23—31no—
806C23—31no—
807C23—61no—
808C23—91no—
809Q8—21no—
810Q8—32no—
811Q8—64no—
812Q8—61no—
813Q8—94no—
814Q8—92no—
815Q8—184no—
816Q8—184no—
817Q8—181no—
818Q8C4×D3212yes—
819D4—32no—
820D4—64no—
821D4—61no—
822D4—94no—
823D4—94no—
824D4—94no—
825D4—184no—
826D4—184no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—32no—
834C2×C4—32no—
835C2×C4—64no—
836C2×C4—64no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—91no—
841C2×C4—92no—
842C2×C4—92no—
843C2×C4—184no—
844C2×C4—184no—
845C2×C4—184no—
846C2×C4—184no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—721no—
850C2×C4—721no—
851C2×C4—721no—
852C2×C4C22×D3211yescharacteristic
853C8—21no—
854C8—61no—
855C8—61no—
856C8—181no—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—62no—
861C2×C3—62no—
862C2×C3—122no—
863C2×C3C2×D3×C22⋊C411yescharacteristic
864C2×C3C2×D3×C22⋊C411yescharacteristic
865C2×C3#577011yescharacteristic
866C2×C3#577111yescharacteristic
867C2×C3#577811yescharacteristic
868C2×C3#577911yescharacteristic
869D3—22no—
870D3—22no—
871D3—42no—
872D3—62no—
873D3—62no—
874D3—122no—
875C22—32no—
876C22—32no—
877C22—61no—
878C22—61no—
879C22—61no—
880C22—61no—
881C22—62no—
882C22—92no—
883C22—121no—
884C22—121no—
885C22—181no—
886C22—181no—
887C22D32×D411yescharacteristic
888C4—22no—
889C4—32no—
890C4—32no—
891C4—41no—
892C4—62no—
893C4—92no—
894C4—121no—
895C4—121no—
896C4—182no—
897C4—361no—
898C4C2×C4×D3211yescharacteristic
899C4D32×D411yescharacteristic
900C3—21no—
901C3#7883211yescharacteristic, complemented
902C3#7895711yescharacteristic, complemented
903C2—62no—
904C2—62no—
905C2—122no—
906C2—182no—
907C2D32×C22⋊C411yescharacteristic
908C2#1059475611yescharacteristic
909C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#64315C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32#2898
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#63804C2semidirect
3. #10594511C2semidirect
4. #10592501C2semidirect
5. C3×#4804C2semidirect
6. C3×#4802C2semidirect
7. #10591552C2semidirect
8. #10591550C2semidirect
9. D3×#835C2semidirect
10. #10590957C2semidirect
11. #10590670C2semidirect
12. D3×#816C2semidirect
13. #10590611C2semidirect
14. #10590608C2semidirect
15. #10590600C2semidirect
22. #64315C4semidirect
79. #4804D3semidirect
86. #4802D3semidirect
97. Q8×C3⋊D3C2×C4semidirect
103. C3×#239C2×C4semidirect
105. C3×D3×Q8C2×C4semidirect
132. #3796C2×C4semidirect
135. #3795C2×C4semidirect
138. D3×Dic6C2×C4semidirect
360. #239C4×D3semidirect
371. D3×Q8C4×D3semidirect
804. C32#2898semidirect
901. C3#78832semidirect
902. C3#78957semidirect

Maximal subgroups

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

subgroupindex
C2×#643152
C2×#638042
#105945112
#105925012
C3×#48042
C3×#48022
#105915522
#105915502
D3×#8352
#105909572
#105906702
D3×#8162
#105906112
#105906082
#105906002
#789573
#788323