Finite Group Databasebeta

← #11858096

Subgroups — #11858096

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64309C211yesmaximal, characteristic
2C2×#63804C211yesmaximal, characteristic, complemented
3#10594510C211yesmaximal, characteristic, complemented
4#10592470C211yesmaximal, characteristic, complemented
5C3×#4772C211yesmaximal, characteristic, complemented
6C3×#4771C211yesmaximal, characteristic, complemented
7#10591424C211yesmaximal, characteristic, complemented
8#10591420C211yesmaximal, characteristic, complemented
9#10591414C211yesmaximal, characteristic, complemented
10#10590948C211yesmaximal, characteristic, complemented
11#10590691C211yesmaximal, characteristic, complemented
12D3×#816C211yesmaximal, characteristic, complemented
13#10590601C211yesmaximal, characteristic, complemented
14#10590600C211yesmaximal, characteristic, complemented
15D3×#810C211yesmaximal, characteristic, complemented
16#78883—31nomaximal
17#78832—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C22×#627—21no—
22C2×#3805—21no—
23C2×#3804—21no—
24C2×#3804—21no—
25#64309—24no—
26#64309C418yescomplemented
27C2×#3798C2211yescharacteristic
28C2×#3797C2211yescharacteristic
29C2×D3×Dic6C2211yescharacteristic
30C2×D3×Dic6C2211yescharacteristic
31C2×#3743C2211yescharacteristic
32C4⋊C4×C3⋊D3C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34C2×C3×D3×C8C2211yescharacteristic
35C3×#892C2211yescharacteristic
36C3×D3×C4⋊C4C2211yescharacteristic
37C4×#626—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63881—21no—
40#63879—21no—
41#63849C2211yescharacteristic
42#63841C2211yescharacteristic
43#63837—21no—
44C2×#3711C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C2×D3×C3⋊C8C2211yescharacteristic
47#63804—24no—
48C32×#102C2211yescharacteristic
49#63659C2211yescharacteristic
50#63643C2211yescharacteristic
51#63637C2211yescharacteristic
52C3×#832C2211yescharacteristic
53C3×#832C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58#63567C2211yescharacteristic
59#63567C2211yescharacteristic
60#63566C2211yescharacteristic
61#63566C2211yescharacteristic
62#63565C2211yescharacteristic
63#63565C2211yescharacteristic
64C2×#1010—31no—
65C2×#1010—31no—
66C2×#907—31no—
67C2×#901—31no—
68#5523—31no—
69#5504—31no—
70C3×#417—31no—
71C3×#416—31no—
72#5233—31no—
73#5232—31no—
74#5120—31no—
75C2×#816—31no—
76#5004—31no—
77C2×#810—31no—
78#4802—31no—
79#4802—31no—
80#4802—31no—
81#4802—31no—
82D3×#103—31no—
83D3×#103—31no—
84D3×#103—31no—
85D3×#103—31no—
86#4772—31no—
87#4772—31no—
88#4772—31no—
89#4772D311yescharacteristic, complemented
90#4771—31no—
91#4771—31no—
92#4771—31no—
93#4771—61no—
94#4771D311yescharacteristic, complemented
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98#3830—22no—
99#3830C2×C414yescomplemented
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C22×C3×Dic3—21no—
106C22×C3×Dic3—21no—
107C3×#237—22no—
108C3×#237—22no—
109C3×#237C2×C414yescomplemented
110C3×#237C2×C414yescomplemented
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#627—21no—
117C2×#627—21no—
118C2×#627—21no—
119C2×#627—28no—
120C2×#627D411yescharacteristic
121C2×#626D411yescharacteristic
122C2×#626D411yescharacteristic
123C2×#625D411yescharacteristic
124C2×#624—21no—
125#3805—28no—
126#3804—28no—
127#3804—28no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3—21no—
131#3798C2×C414yes—
132#3798D414yes—
133#3797—22no—
134#3797C2×C414yescomplemented
135D3×Dic6—22no—
136D3×Dic6—22no—
137D3×Dic6C2×C414yescomplemented
138D3×Dic6C2×C414yescomplemented
139C2×C32×C8C2311yescharacteristic
140C32×C4⋊C4C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142#3750—21no—
143C2×C3⋊(C3⋊C8)C2311yescharacteristic
144#3743—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×D3×C8—22no—
154Dic3⋊Dic3—21no—
155#3722—21no—
156(C2×D3)⋊Dic3—21no—
157Dic32—21no—
158Dic32—21no—
159#3711—22no—
160#3710—22no—
161D3×C3⋊C8—22no—
162#2898—91noSylow
163C2×C3×#41—31no—
164C2×C3×#41—31no—
165#1010—38no—
166#1010—38no—
167#1010—64no—
168#1010—64no—
169C2×D3×Q8—31no—
170C2×D3×Q8—31no—
171C2×D3×Q8—31no—
172C2×D3×Q8—31no—
173C2×#237—31no—
174C2×#237—31no—
175C2×#237—61no—
176C2×#237—61no—
177C2×#237—61no—
178C2×#237—61no—
179C2×#237—61no—
180C2×#237C2×D311yescharacteristic
181C2×#237C2×D311yescharacteristic
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—61no—
185C2×#235—61no—
186C22×Dic6—31no—
187C22×Dic6—31no—
188C22×Dic6—61no—
189C22×Dic6—61no—
190C2×C3×M16—31no—
191C22×C3×C8—31no—
192C3×#117—31no—
193C2×C3×C4⋊C4—31no—
194C4×#67—61no—
195C4×#67—61no—
196#926—31no—
197C2×C4⋊Dic3—31no—
198C2×#208—31no—
199C22×C3⋊C8—31no—
200#907—64no—
201#901—64no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×ΓL(1,𝔽25)—61no—
206C2×ΓL(1,𝔽25)C2×D311yescharacteristic
207C2×D3×C8—31no—
208C2×D3×C8—31no—
209C2×D3×C8—31no—
210C2×D3×C8C2×D311yescharacteristic
211#893—61no—
212#892—31no—
213#892—31no—
214#892—31no—
215#892C2×D311yescharacteristic
216D3×C4⋊C4—31no—
217D3×C4⋊C4—31no—
218D3×C4⋊C4—31no—
219D3×C4⋊C4—61no—
220D3×C4⋊C4C2×D311yescharacteristic
221#887—61no—
222#67⋊C4—61no—
223#67⋊C4—61no—
224C4×D12—61no—
225C4×Dic6—61no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#102—21no—
231C3×#102—31no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic
234C3×#102C2×D311yescharacteristic
235#835—31no—
236#835—31no—
237#835—31no—
238#835—31no—
239#832—31no—
240#832—31no—
241#832—61no—
242#832C2×D311yescharacteristic
243#832C2×D311yescharacteristic
244#816—31no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—31no—
249#816—31no—
250#816—61no—
251#816C2×D311yescharacteristic
252#816C2×D311yescharacteristic
253#810—31no—
254#810—31no—
255#810—31no—
256#810—31no—
257#810—31no—
258#810—31no—
259#810—61no—
260#810C2×D311yescharacteristic
261#810C2×D311yescharacteristic
262C23×C32—21no—
263C22×C3⋊D3C2×D411yescharacteristic
264C22×C3×D3C2×D411yescharacteristic
265C22×C3×D3C2×D411yescharacteristic
266C32×D4—21no—
267C32×D4C22×C412yes—
268C2×C32×C4—21no—
269C2×C32×C4C2411yescharacteristic
270#638—24no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—24no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C4×C3⋊D3—81no—
276C4×C3⋊D3C22×C412yes—
277C4×C3⋊D3C2×D412yes—
278#634—21no—
279#634C22×C412yes—
280C3×#67—24no—
281C3×#67—24no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—24no—
285C2×C3×Dic3—24no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×C4×D3—81no—
291C3×C4×D3C22×C412yes—
292C3×C4×D3C22×C412yes—
293C3×C4×D3C2×D412yes—
294C3×C4×D3C2×D412yes—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6C22×C412yes—
298C3×Dic6C22×C412yes—
299#627—24no—
300#627—24no—
301#627—24no—
302#627C22⋊C414yes—
303#626C22⋊C414yes—
304#626C22⋊C414yes—
305#625C22⋊C414yes—
306#624—24no—
307D3×Dic3—24no—
308D3×Dic3—24no—
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—91no—
318#419—91no—
319#419—91no—
320#417—31no—
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—34no—
331C3×#41—62no—
332C3×#41—62no—
333C2×C3×Q8—31no—
334C2×C3×Q8—31no—
335C2×C3×D4—21no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C2×#67—21no—
346C2×#67—21no—
347C2×#67—31no—
348C2×#67—31no—
349C2×#67—31no—
350C2×#67—31no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—121no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—121no—
362D3×Q8—34no—
363D3×Q8—34no—
364D3×Q8—34no—
365D3×Q8—34no—
366D3×Q8—62no—
367D3×Q8—62no—
368D3×Q8—62no—
369D3×Q8—62no—
370#237—22no—
371#237—22no—
372#237—34no—
373#237—34no—
374#237—64no—
375#237—62no—
376#237—62no—
377#237—68no—
378#237—68no—
379#237—68no—
380#237—68no—
381#237—122no—
382#237C4×D314yescomplemented
383#237C4×D314yescomplemented
384#235—34no—
385#235—34no—
386#235—34no—
387#235—34no—
388#235—68no—
389#235—68no—
390C2×D12—31no—
391C2×D12—31no—
392C2×C4×D3—21no—
393C2×C4×D3—31no—
394C2×C4×D3—31no—
395C2×C4×D3—61no—
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—121no—
404C2×C4×D3C22×D311yescharacteristic
405C2×C4×D3C22×D311yescharacteristic
406C2×Dic6—31no—
407C2×Dic6—31no—
408C2×Dic6—31no—
409C2×Dic6—31no—
410C2×Dic6—34no—
411C2×Dic6—34no—
412C2×Dic6—61no—
413C2×Dic6—62no—
414C2×Dic6—62no—
415C2×Dic6—68no—
416C2×Dic6—68no—
417C2×Dic6—61no—
418C2×Dic6—61no—
419C2×Dic6—61no—
420C2×Dic6—61no—
421C2×Dic6—61no—
422C2×Dic6—61no—
423C2×Dic6C22×D311yescharacteristic
424C2×Dic6C22×D311yescharacteristic
425C3×M16—62no—
426C2×C3×C8—21no—
427C2×C3×C8—31no—
428C2×C3×C8—31no—
429C2×C3×C8—62no—
430C2×C3×C8C22×D311yescharacteristic
431C2×C3×C8C22×D311yescharacteristic
432C3×C4⋊C4—21no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—31no—
435C3×C4⋊C4—61no—
436C3×C4⋊C4C22×D311yescharacteristic
437C3×C4⋊C4C22×D311yescharacteristic
438C3×C22⋊C4—61no—
439C3×C42—61no—
440#217—61no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445C4⋊Dic3—31no—
446C4⋊Dic3—31no—
447C4⋊Dic3—61no—
448C4⋊Dic3—61no—
449C4⋊Dic3C22×D311yescharacteristic
450C4⋊Dic3C22×D311yescharacteristic
451Dic3⋊C4—21no—
452Dic3⋊C4—61no—
453Dic3⋊C4—61no—
454Dic3⋊C4—61no—
455Dic3⋊C4—121no—
456C4×Dic3—21no—
457C4×Dic3—61no—
458C4×Dic3—61no—
459C4×Dic3—61no—
460C4×Dic3—61no—
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×C32—22no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32C22×D411yescharacteristic
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3C2×C22⋊C412yes—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—21no—
488C2×C3×D3C2×C22⋊C412yes—
489C2×C3×D3C2×C22⋊C412yes—
490C32×C4—41no—
491C32×C4C23×C411yescharacteristic
492C32×C4C22×D411yescharacteristic
493C3⋊Dic3—22no—
494C3⋊Dic3—41no—
495C3⋊Dic3C2×C22⋊C412yes—
496C3×Dic3—22no—
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—31no—
506C2×#41—91no—
507C2×#41—91no—
508C2×#41—181no—
509C2×#41—181no—
510C2×#41—181no—
511C22×Q8—91no—
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—91no—
528#117—91no—
529C2×C4⋊C4—31no—
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#103—91no—
544#102—31no—
545#102—31no—
546#102—91no—
547#102D3211yescharacteristic
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—31no—
551C23×C3—31no—
552C23×C3—41no—
553C22×D3—31no—
554C22×D3—31no—
555C22×D3—61no—
556C22×D3D3×D411yescharacteristic
557C22×D3D3×D411yescharacteristic
558C3×Q8—32no—
559C3×Q8—32no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—22no—
565C3×D4—41no—
566C3×D4—64no—
567C3×D4—64no—
568C3×D4C2×C4×D312yes—
569C3×D4C2×C4×D312yes—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—41no—
580C2×C3×C4—64no—
581C2×C3×C4—64no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—241no—
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589#67—24no—
590#67—24no—
591#67—34no—
592#67—34no—
593#67—34no—
594#67—34no—
595#67—64no—
596#67—64no—
597#67—124no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—24no—
601C2×Dic3—24no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—61no—
607C2×Dic3—64no—
608C2×Dic3—64no—
609C2×Dic3—64no—
610C2×Dic3—64no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—124no—
616C2×Dic3—121no—
617C2×Dic3—121no—
618C2×Dic3—241no—
619C2×Dic3D3×D411yescharacteristic
620C2×Dic3D3×D411yescharacteristic
621D12—34no—
622D12—34no—
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—81no—
634C4×D3—241no—
635C4×D3—241no—
636C4×D3—241no—
637C4×D3—242no—
638C4×D3C2×C4×D312yes—
639C4×D3C2×C4×D312yes—
640C4×D3D3×D412yes—
641C4×D3D3×D412yes—
642Dic6—21no—
643Dic6—21no—
644Dic6—34no—
645Dic6—34no—
646Dic6—32no—
647Dic6—32no—
648Dic6—62no—
649Dic6—64no—
650Dic6—64no—
651Dic6—64no—
652Dic6—64no—
653Dic6—61no—
654Dic6—61no—
655Dic6—64no—
656Dic6—64no—
657Dic6—121no—
658Dic6C2×C4×D312yes—
659Dic6C2×C4×D312yes—
660C3×C8—21no—
661C3×C8—21no—
662C3×C8—41no—
663C3×C8—61no—
664C3×C8—61no—
665C3⋊C8—21no—
666C3⋊C8—21no—
667C3⋊C8—61no—
668C3⋊C8—61no—
669C3⋊C8—121no—
670C2×C32—42no—
671C2×C32C22×C22⋊C411yescharacteristic
672C2×C32#57711yescharacteristic
673C2×C32#57811yescharacteristic
674C3⋊D3—22no—
675C3×D3—22no—
676C3×D3—22no—
677#41—34no—
678#41—34no—
679#41—62no—
680#41—62no—
681#41—94no—
682#41—94no—
683#41—94no—
684#41—188no—
685#41—188no—
686#41—182no—
687#41—188no—
688C2×Q8—31no—
689C2×Q8—31no—
690C2×Q8—91no—
691C2×Q8—94no—
692C2×Q8—94no—
693C2×Q8—94no—
694C2×Q8—91no—
695C2×Q8—181no—
696C2×Q8—181no—
697C2×Q8—182no—
698C2×Q8—182no—
699C2×Q8—181no—
700C2×Q8—188no—
701C2×Q8—182no—
702C2×D4—61no—
703C2×D4—61no—
704C2×D4—91no—
705C2×D4—91no—
706C2×D4—91no—
707C2×D4—181no—
708C2×D4C2×D3211yescharacteristic
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—91no—
715C22×C4—181no—
716C22×C4—181no—
717C22×C4—181no—
718C22×C4—181no—
719C22×C4—181no—
720C22×C4—181no—
721M16—62no—
722M16—182no—
723M16—182no—
724C2×C8—31no—
725C2×C8—31no—
726C2×C8—62no—
727C2×C8—91no—
728C2×C8—182no—
729C2×C8—182no—
730C2×C8C2×D3211yescharacteristic
731C4⋊C4—31no—
732C4⋊C4—31no—
733C4⋊C4—61no—
734C4⋊C4—91no—
735C4⋊C4—181no—
736C4⋊C4—181no—
737C4⋊C4C2×D3211yescharacteristic
738C22⋊C4—61no—
739C22⋊C4—181no—
740C22⋊C4—181no—
741C42—61no—
742C42—181no—
743C42—181no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—21no—
747C22×C3—32no—
748C22×C3—32no—
749C22×C3—42no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—61no—
755C22×C3—61no—
756C22×C3—61no—
757C22×C3—61no—
758C22×C3—81no—
759C22×C3—81no—
760C22×C3C2×D3×D411yescharacteristic
761C22×C3C2×D3×D411yescharacteristic
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—32no—
767C2×D3—32no—
768C2×D3—62no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3D3×C22⋊C412yes—
776C2×D3D3×C22⋊C412yes—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—32no—
780C3×C4—32no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—62no—
784C3×C4—62no—
785C3×C4—81no—
786C3×C4—121no—
787C3×C4—121no—
788C3×C4C22×C4×D311yescharacteristic
789C3×C4C22×C4×D311yescharacteristic
790C3×C4C2×D3×D411yescharacteristic
791C3×C4C2×D3×D411yescharacteristic
792Dic3—22no—
793Dic3—22no—
794Dic3—32no—
795Dic3—32no—
796Dic3—41no—
797Dic3—41no—
798Dic3—62no—
799Dic3—62no—
800Dic3—62no—
801Dic3—122no—
802Dic3—121no—
803Dic3—121no—
804Dic3—241no—
805Dic3D3×C22⋊C412yes—
806Dic3D3×C22⋊C412yes—
807C32#289811yescharacteristic, complemented, Sylow
808C23—21no—
809C23—31no—
810C23—31no—
811C23—91no—
812Q8—32no—
813Q8—32no—
814Q8—61no—
815Q8—61no—
816Q8—94no—
817Q8—92no—
818Q8—184no—
819Q8—184no—
820Q8—184no—
821Q8—181no—
822D4—21no—
823D4—64no—
824D4—64no—
825D4—94no—
826D4—94no—
827D4—94no—
828D4—184no—
829D4C4×D3212yes—
830C2×C4—21no—
831C2×C4—31no—
832C2×C4—31no—
833C2×C4—32no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—64no—
838C2×C4—64no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—91no—
844C2×C4—92no—
845C2×C4—92no—
846C2×C4—184no—
847C2×C4—184no—
848C2×C4—184no—
849C2×C4—184no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—241no—
853C2×C4—721no—
854C2×C4—721no—
855C2×C4C22×D3211yescharacteristic
856C8—21no—
857C8—61no—
858C8—61no—
859C8—181no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—42no—
864C2×C3—42no—
865C2×C3—62no—
866C2×C3—62no—
867C2×C3—82no—
868C2×C3C2×D3×C22⋊C411yescharacteristic
869C2×C3C2×D3×C22⋊C411yescharacteristic
870C2×C3#577011yescharacteristic
871C2×C3#577111yescharacteristic
872C2×C3#577511yescharacteristic
873C2×C3#577911yescharacteristic
874D3—22no—
875D3—22no—
876D3—62no—
877D3—62no—
878D3—122no—
879C22—22no—
880C22—32no—
881C22—32no—
882C22—41no—
883C22—41no—
884C22—61no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—92no—
889C22—181no—
890C22—181no—
891C22D32×D411yescharacteristic
892C4—32no—
893C4—32no—
894C4—41no—
895C4—62no—
896C4—62no—
897C4—92no—
898C4—121no—
899C4—121no—
900C4—182no—
901C4—361no—
902C4C2×C4×D3211yescharacteristic
903C4D32×D411yescharacteristic
904C3—21no—
905C3#7883211yescharacteristic, complemented
906C3#7888311yescharacteristic, complemented
907C2—42no—
908C2—62no—
909C2—62no—
910C2—182no—
911C2D32×C22⋊C411yescharacteristic
912C2#1059473611yescharacteristic
913C2#1059475611yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#64309C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2898
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×#63804C2semidirect
3. #10594510C2semidirect
4. #10592470C2semidirect
5. C3×#4772C2semidirect
6. C3×#4771C2semidirect
7. #10591424C2semidirect
8. #10591420C2semidirect
9. #10591414C2semidirect
10. #10590948C2semidirect
11. #10590691C2semidirect
12. D3×#816C2semidirect
13. #10590601C2semidirect
14. #10590600C2semidirect
15. D3×#810C2semidirect
26. #64309C4semidirect
89. #4772D3semidirect
94. #4771D3semidirect
99. #3830C2×C4semidirect
109. C3×#237C2×C4semidirect
110. C3×#237C2×C4semidirect
134. #3797C2×C4semidirect
137. D3×Dic6C2×C4semidirect
138. D3×Dic6C2×C4semidirect
382. #237C4×D3semidirect
383. #237C4×D3semidirect
807. C32#2898semidirect
905. C3#78832semidirect
906. C3#78883semidirect

Maximal subgroups

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

subgroupindex
C2×#643092
C2×#638042
#105945102
#105924702
C3×#47722
C3×#47712
#105914242
#105914202
#105914142
#105909482
#105906912
D3×#8162
#105906012
#105906002
D3×#8102
#788833
#788323