Finite Group Databasebeta

← #13170490

Subgroups — #13170490

Order 1728.

1426 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11724578C211yesmaximal, characteristic
2#11723657C211yesmaximal, characteristic, complemented
3#11723358C211yesmaximal, characteristic, complemented
4C2×#88785C211yesmaximal, characteristic, complemented
5C3×#63817C211yesmaximal, characteristic, complemented
6C3×#63815C211yesmaximal, characteristic, complemented
7C3×#63814C211yesmaximal, characteristic, complemented
8#11722825C212yesmaximal, complemented
9#11722824C212yesmaximal, complemented
10#11722819C212yesmaximal, complemented
11D3×#3710C212yesmaximal, complemented
12#10595442—31nomaximal
13#10594707—31nomaximal
14#10594669—31nomaximal
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C3×#3828C2211yescharacteristic
17C32×#235C2211yescharacteristic
18#89039C412yes—
19#89029C412yes—
20#89026C411yescharacteristic
21C4×D3×C3⋊D3C2212yes—
22#89020C2212yes—
23#89019C411yescharacteristic
24#89017C411yescharacteristic
25#89015C411yescharacteristic
26C3×#3748C2211yescharacteristic, complemented
27C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C32×#208C2211yescharacteristic, complemented
29C2×C32×C3⋊C8C2211yescharacteristic, complemented
30#88809C2212yescomplemented
31#88808C2212yescomplemented
32#88788C2212yescomplemented
33#88785C2211yescharacteristic
34#88785C2212yes—
35#88785C2211yescharacteristic
36#88785C2211yescharacteristic, complemented
37#88785C2211yescharacteristic, complemented
38C3×#3712C2212yescomplemented
39C3×#3711C2212yescomplemented
40C3×#3711C2212yescomplemented
41C3×#3710C2212yescomplemented
42C3×D3×C3⋊C8C2212yescomplemented
43C3×D3×C3⋊C8C2212yescomplemented
44#41×C3⋊D3—31no—
45#64306—31no—
46#64306—31no—
47#64306—61no—
48M16×C3⋊D3—31no—
49C2×C8×C3⋊D3—31no—
50C3×#948—31no—
51C3×#948—31no—
52C3×#907—31no—
53C3×#907—31no—
54C3×#901—31no—
55C3×#901—31no—
56#63818—31no—
57#63818—31no—
58#63818—32no—
59#63818—61no—
60#63817—31no—
61#63817—32no—
62#63817—32no—
63#63817D311yescharacteristic, complemented
64C2×#3710—31no—
65C2×#3710—31no—
66C2×#3710—32no—
67C2×#3710—61no—
68#63815—31no—
69#63815D311yescharacteristic, complemented
70#63814—31no—
71#63814D311yescharacteristic, complemented
72#63805—32no—
73#63804—32no—
74#63804—32no—
75#63803—32no—
76#63791—32no—
77#63791—32no—
78D32×C8—32no—
79D32×C8—32no—
80C22×C3⋊(C3⋊D3)C2×C411yescharacteristic
81C2×D3×C3⋊D3C2×C412yes—
82C2×C33×C4C2311yescharacteristic
83C2×C3⋊(C3⋊Dic3)C2×C411yescharacteristic
84C4×C3⋊(C3⋊D3)C2×C411yescharacteristic
85C4×C3⋊(C3⋊D3)C2×C411yescharacteristic
86C4×C3⋊(C3⋊D3)C2311yescharacteristic
87C4×C3⋊(C3⋊D3)C2311yescharacteristic
88C3×#638C2×C412yes—
89C3×C4⋊(C3⋊D3)C2×C411yescharacteristic
90C3×C4×C3⋊D3C2312yes—
91C3×#634C2×C411yescharacteristic
92C32×#67C2×C412yes—
93C32×D12C2×C411yescharacteristic
94C32×C4×D3C2312yes—
95C32×Dic6C2×C411yescharacteristic
96#6293C2×C412yes—
97#6292C2×C412yes—
98#6291C2×C412yes—
99#6290C2×C412yes—
100#6289C2×C412yes—
101Dic3×C3⋊D3C2×C412yes—
102D3×C3⋊Dic3C2×C412yes—
103C3×C3⋊(C3⋊C8)C2311yescharacteristic
104C3×C3⋊(C3⋊C8)C2311yescharacteristic
105C3×C3⋊(C3⋊C8)C2312yes—
106C32×C3⋊C8C2311yescharacteristic
107C32×C3⋊C8C2312yes—
108C32×C3⋊C8C2311yescharacteristic
109D3×#131—91no—
110D3×#131—91no—
111D3×#131—91no—
112C32×#41—31no—
113#3832—31no—
114Q8×C3⋊D3—31no—
115#3830—32no—
116#3830—31no—
117D4×C3⋊D3—32no—
118D4×C3⋊D3—31no—
119#3828—32no—
120#3828C2×D311yescharacteristic
121C2×C4×C3⋊D3—31no—
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—32no—
125C2×C4×C3⋊D3—61no—
126C2×C4×C3⋊D3—61no—
127C2×C4×C3⋊D3—61no—
128C2×C4×C3⋊D3—121no—
129C3×#235—21no—
130C3×#235—31no—
131C3×#235—31no—
132C3×#235—61no—
133C3×#235C2×D311yescharacteristic
134C3×#235C2×D311yescharacteristic
135#3811—32no—
136#3811—32no—
137#3811—62no—
138#3805—32no—
139#3805—32no—
140#3805—62no—
141#3802—31no—
142#3802—31no—
143#3802—61no—
144C4×D32—32no—
145C4×D32—32no—
146C4×D32—62no—
147#3798—32no—
148#3798—32no—
149#3798—62no—
150#3797—31no—
151#3797—31no—
152#3797—61no—
153#3796—31no—
154#3796—31no—
155#3796—31no—
156#3796—31no—
157#3796—61no—
158#3796—61no—
159C32×M16—31no—
160C2×C32×C8—31no—
161#3748C2×D311yescharacteristic, complemented
162C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
163#3743—32no—
164C8×C3⋊D3—31no—
165C8×C3⋊D3—32no—
166C8×C3⋊D3—31no—
167C8×C3⋊D3—31no—
168C8×C3⋊D3—31no—
169C3×#208—21no—
170C3×#208—31no—
171C3×#208—31no—
172C3×#208—32no—
173C3×#208—32no—
174C3×#208—61no—
175C3×#208C2×D311yescharacteristic, complemented
176C3×#208C2×D311yescharacteristic, complemented
177C2×C3×C3⋊C8—21no—
178C2×C3×C3⋊C8—31no—
179C2×C3×C3⋊C8—31no—
180C2×C3×C3⋊C8—32no—
181C2×C3×C3⋊C8—32no—
182C2×C3×C3⋊C8—61no—
183C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
184C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
185C3×ΓL(1,𝔽25)—32no—
186C3×ΓL(1,𝔽25)—32no—
187C3×ΓL(1,𝔽25)—32no—
188C3×ΓL(1,𝔽25)—32no—
189C3×D3×C8—32no—
190C3×D3×C8—32no—
191C3×D3×C8—32no—
192C3×D3×C8—32no—
193#3712—32no—
194#3712—32no—
195#3712—32no—
196#3712—62no—
197#3712C2×D312yescomplemented
198#3711—32no—
199#3711—32no—
200#3711C2×D312yescomplemented
201#3711C2×D312yescomplemented
202#3710—32no—
203#3710—31no—
204#3710—32no—
205#3710—31no—
206#3710—31no—
207#3710—31no—
208#3710—31no—
209#3710—31no—
210#3710—31no—
211#3710—31no—
212#3710—32no—
213#3710—61no—
214#3710—61no—
215#3710—61no—
216#3710—61no—
217#3710—62no—
218#3710C2×D312yescomplemented
219D3×C3⋊C8—32no—
220D3×C3⋊C8—32no—
221D3×C3⋊C8C2×D312yescomplemented
222D3×C3⋊C8C2×D312yescomplemented
223C22×C33C22×C411yescharacteristic
224C2×C3⋊(C3⋊D3)—22no—
225C2×C3⋊(C3⋊D3)C22×C411yescharacteristic
226C2×C3⋊(C3⋊D3)C22×C411yescharacteristic
227C2×C3×C3⋊D3C22×C412yes—
228C2×C32×D3C22×C412yes—
229D3×C3⋊D3—24no—
230C33×C4C22×C411yescharacteristic
231C33×C4C2411yescharacteristic
232C3⋊(C3⋊Dic3)C22×C411yescharacteristic
233C3⋊(C3⋊Dic3)C22×C411yescharacteristic
234C3×C3⋊Dic3C22×C412yes—
235C32×Dic3C22×C412yes—
236D3×#41—91no—
237D3×#41—91no—
238D3×#41—91no—
239D3×#41—181no—
240C3×#131—91no—
241C3×#131—91no—
242C3×#131—91no—
243#948—31no—
244#948—31no—
245#948—91no—
246#907—31no—
247#907—31no—
248#907—92no—
249#907—92no—
250#907—92no—
251#907—91no—
252D3×M16—92no—
253D3×M16—92no—
254D3×M16—92no—
255D3×M16—91no—
256D3×M16—91no—
257D3×M16—91no—
258D3×M16—181no—
259#901—31no—
260#901—31no—
261#901—92no—
262#901—92no—
263#901—92no—
264#901—91no—
265C2×D3×C8—92no—
266C2×D3×C8—92no—
267C2×D3×C8—92no—
268C2×D3×C8—91no—
269C2×D3×C8—91no—
270C2×D3×C8—91no—
271C2×D3×C8—181no—
272C22×C3⋊D3—31no—
273C22×C3⋊D3—31no—
274C22×C3⋊D3—31no—
275C22×C3⋊D3—32no—
276C22×C3⋊D3—61no—
277C22×C3⋊D3—61no—
278C22×C3⋊D3—61no—
279C22×C3⋊D3—121no—
280C2×D32—32no—
281C2×D32—32no—
282C2×D32—62no—
283C32×Q8—31no—
284C32×D4—32no—
285C32×D4—31no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—32no—
290C2×C32×C4—41no—
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294#638—32no—
295#638—32no—
296#638C4×D312yes—
297C2×C3⋊Dic3—31no—
298C2×C3⋊Dic3—31no—
299C2×C3⋊Dic3—31no—
300C2×C3⋊Dic3—32no—
301C2×C3⋊Dic3—61no—
302C2×C3⋊Dic3—61no—
303C2×C3⋊Dic3—61no—
304C2×C3⋊Dic3—121no—
305C4⋊(C3⋊D3)—32no—
306C4⋊(C3⋊D3)C4×D311yescharacteristic
307C4×C3⋊D3—32no—
308C4×C3⋊D3—31no—
309C4×C3⋊D3—31no—
310C4×C3⋊D3—31no—
311C4×C3⋊D3—31no—
312C4×C3⋊D3—31no—
313C4×C3⋊D3—31no—
314C4×C3⋊D3—31no—
315C4×C3⋊D3—31no—
316C4×C3⋊D3—31no—
317C4×C3⋊D3—31no—
318C4×C3⋊D3—31no—
319C4×C3⋊D3—31no—
320C4×C3⋊D3—32no—
321C4×C3⋊D3—61no—
322C4×C3⋊D3—61no—
323C4×C3⋊D3—61no—
324C4×C3⋊D3—61no—
325C4×C3⋊D3—61no—
326C4×C3⋊D3—61no—
327C4×C3⋊D3—61no—
328C4×C3⋊D3—61no—
329C4×C3⋊D3—61no—
330C4×C3⋊D3—61no—
331C4×C3⋊D3—61no—
332C4×C3⋊D3—61no—
333C4×C3⋊D3—121no—
334C4×C3⋊D3—121no—
335C4×C3⋊D3—121no—
336C4×C3⋊D3—121no—
337C4×C3⋊D3C22×D312yes—
338#634—32no—
339#634C4×D311yescharacteristic
340C3×#67—22no—
341C3×#67—32no—
342C3×#67—32no—
343C3×#67—62no—
344C3×#67C4×D312yes—
345C3×#67C4×D312yes—
346C3×D12—21no—
347C3×D12—31no—
348C3×D12—31no—
349C3×D12—61no—
350C3×D12C4×D311yescharacteristic
351C3×D12C4×D311yescharacteristic
352C3×C4×D3—22no—
353C3×C4×D3—32no—
354C3×C4×D3—32no—
355C3×C4×D3—62no—
356C3×C4×D3C22×D312yes—
357C3×C4×D3C22×D312yes—
358C3×Dic6—21no—
359C3×Dic6—31no—
360C3×Dic6—31no—
361C3×Dic6—61no—
362C3×Dic6C4×D311yescharacteristic
363C3×Dic6C4×D311yescharacteristic
364#627—32no—
365#627—32no—
366#627—62no—
367#626—32no—
368#626—32no—
369#626—32no—
370#626—32no—
371#626—62no—
372#626—62no—
373#625—32no—
374#625—32no—
375#625—62no—
376#624—32no—
377#624—32no—
378#624—62no—
379D3×Dic3—32no—
380D3×Dic3—32no—
381D3×Dic3—32no—
382D3×Dic3—32no—
383D3×Dic3—62no—
384D3×Dic3—62no—
385C32×C8—31no—
386C32×C8—32no—
387C32×C8—31no—
388C3⋊(C3⋊C8)C22×D311yescharacteristic
389C3⋊(C3⋊C8)C22×D312yes—
390C3⋊(C3⋊C8)C22×D311yescharacteristic
391C3×C3⋊C8—21no—
392C3×C3⋊C8—21no—
393C3×C3⋊C8—22no—
394C3×C3⋊C8—31no—
395C3×C3⋊C8—32no—
396C3×C3⋊C8—31no—
397C3×C3⋊C8—31no—
398C3×C3⋊C8—31no—
399C3×C3⋊C8—32no—
400C3×C3⋊C8—61no—
401C3×C3⋊C8—61no—
402C3×C3⋊C8—62no—
403C3×C3⋊C8C22×D311yescharacteristic
404C3×C3⋊C8C22×D312yes—
405C3×C3⋊C8C22×D311yescharacteristic
406C3×C3⋊C8C22×D311yescharacteristic
407C3×C3⋊C8C22×D311yescharacteristic
408C3×C3⋊C8C22×D312yes—
409C2×#131—271noSylow
410C2×C33—21no—
411C2×C33C23×C411yescharacteristic
412C3⋊(C3⋊D3)—21no—
413C3⋊(C3⋊D3)#13112yescomplemented
414C3×C3⋊D3—22no—
415C32×D3—22no—
416C3×#41—31no—
417C3×#41—31no—
418C3×#41—61no—
419C3×#41—91no—
420#239—91no—
421#239—91no—
422#239—91no—
423#239—181no—
424D3×Q8—91no—
425D3×Q8—91no—
426D3×Q8—91no—
427D3×Q8—181no—
428#237—91no—
429#237—91no—
430#237—92no—
431#237—92no—
432#237—92no—
433#237—91no—
434#237—181no—
435#237—182no—
436D3×D4—91no—
437D3×D4—91no—
438D3×D4—92no—
439D3×D4—92no—
440D3×D4—92no—
441D3×D4—91no—
442D3×D4—181no—
443D3×D4—182no—
444#235—31no—
445#235—31no—
446#235—61no—
447#235—92no—
448#235—92no—
449#235—92no—
450#235—182no—
451#235D3211yescharacteristic
452C2×C4×D3—92no—
453C2×C4×D3—92no—
454C2×C4×D3—91no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—92no—
458C2×C4×D3—182no—
459C2×C4×D3—181no—
460C2×C4×D3—181no—
461C2×C4×D3—181no—
462C2×C4×D3—361no—
463C3×M16—31no—
464C3×M16—31no—
465C3×M16—61no—
466C3×M16—92no—
467C3×M16—92no—
468C3×M16—92no—
469C3×M16—91no—
470C2×C3×C8—31no—
471C2×C3×C8—31no—
472C2×C3×C8—61no—
473C2×C3×C8—92no—
474C2×C3×C8—92no—
475C2×C3×C8—92no—
476C2×C3×C8—91no—
477#208—31no—
478#208—31no—
479#208—32no—
480#208—32no—
481#208—61no—
482#208—92no—
483#208D3211yescharacteristic, complemented
484C2×C3⋊C8—31no—
485C2×C3⋊C8—31no—
486C2×C3⋊C8—32no—
487C2×C3⋊C8—32no—
488C2×C3⋊C8—61no—
489C2×C3⋊C8—92no—
490C2×C3⋊C8D3211yescharacteristic, complemented
491ΓL(1,𝔽25)—32no—
492ΓL(1,𝔽25)—32no—
493ΓL(1,𝔽25)—32no—
494ΓL(1,𝔽25)—32no—
495ΓL(1,𝔽25)—92no—
496ΓL(1,𝔽25)—92no—
497ΓL(1,𝔽25)—92no—
498ΓL(1,𝔽25)—92no—
499ΓL(1,𝔽25)—92no—
500ΓL(1,𝔽25)—182no—
501D3×C8—32no—
502D3×C8—32no—
503D3×C8—32no—
504D3×C8—32no—
505D3×C8—91no—
506D3×C8—91no—
507D3×C8—91no—
508D3×C8—91no—
509D3×C8—92no—
510D3×C8—91no—
511D3×C8—92no—
512D3×C8—91no—
513D3×C8—91no—
514D3×C8—91no—
515D3×C8—92no—
516D3×C8—92no—
517D3×C8—91no—
518D3×C8—91no—
519D3×C8—92no—
520D3×C8—91no—
521D3×C8—91no—
522D3×C8—181no—
523D3×C8—181no—
524D3×C8—181no—
525D3×C8—181no—
526D3×C8—182no—
527C22×C32—21no—
528C22×C32—21no—
529C22×C32—21no—
530C22×C32—32no—
531C22×C32—41no—
532C22×C32C2×C4×D311yescharacteristic
533C22×C32C2×C4×D311yescharacteristic
534C22×C32C2×C4×D311yescharacteristic
535C2×C3⋊D3—31no—
536C2×C3⋊D3—31no—
537C2×C3⋊D3—31no—
538C2×C3⋊D3—31no—
539C2×C3⋊D3—31no—
540C2×C3⋊D3—31no—
541C2×C3⋊D3—61no—
542C2×C3⋊D3—61no—
543C2×C3⋊D3—61no—
544C2×C3⋊D3—61no—
545C2×C3⋊D3—61no—
546C2×C3⋊D3—61no—
547C2×C3⋊D3—62no—
548C2×C3⋊D3—64no—
549C2×C3⋊D3—62no—
550C2×C3⋊D3—62no—
551C2×C3⋊D3—64no—
552C2×C3⋊D3—121no—
553C2×C3⋊D3—121no—
554C2×C3⋊D3—122no—
555C2×C3⋊D3—122no—
556C2×C3⋊D3—124no—
557C2×C3⋊D3C2×C4×D312yes—
558C2×C3×D3—22no—
559C2×C3×D3—32no—
560C2×C3×D3—32no—
561C2×C3×D3—62no—
562C2×C3×D3C2×C4×D312yes—
563C2×C3×D3C2×C4×D312yes—
564D32—64no—
565D32—64no—
566D32—124no—
567C32×C4—21no—
568C32×C4—21no—
569C32×C4—21no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—21no—
573C32×C4—32no—
574C32×C4—41no—
575C32×C4—41no—
576C32×C4C2×C4×D311yescharacteristic
577C32×C4C2×C4×D311yescharacteristic
578C32×C4C2×C4×D311yescharacteristic
579C32×C4C23×D311yescharacteristic
580C32×C4C23×D311yescharacteristic
581C32×C4C23×D311yescharacteristic
582C3⋊Dic3—31no—
583C3⋊Dic3—31no—
584C3⋊Dic3—31no—
585C3⋊Dic3—31no—
586C3⋊Dic3—31no—
587C3⋊Dic3—31no—
588C3⋊Dic3—61no—
589C3⋊Dic3—61no—
590C3⋊Dic3—61no—
591C3⋊Dic3—61no—
592C3⋊Dic3—61no—
593C3⋊Dic3—61no—
594C3⋊Dic3—121no—
595C3⋊Dic3—121no—
596C3⋊Dic3C2×C4×D312yes—
597C3×Dic3—22no—
598C3×Dic3—32no—
599C3×Dic3—32no—
600C3×Dic3—62no—
601C3×Dic3C2×C4×D312yes—
602C3×Dic3C2×C4×D312yes—
603C2×#41—271no—
604#131—91no—
605#131—91no—
606#131—91no—
607#131—272no—
608#131—272no—
609#131—271no—
610C2×M16—271no—
611C2×M16—272no—
612C22×C8—271no—
613C22×C8—272no—
614C33C2×#13111yescharacteristic, complemented, Sylow
615C22×D3—92no—
616C22×D3—92no—
617C22×D3—91no—
618C22×D3—91no—
619C22×D3—91no—
620C22×D3—92no—
621C22×D3—182no—
622C22×D3—181no—
623C22×D3—181no—
624C22×D3—181no—
625C22×D3—361no—
626C3×Q8—31no—
627C3×Q8—31no—
628C3×Q8—61no—
629C3×Q8—91no—
630C3×D4—32no—
631C3×D4—32no—
632C3×D4—31no—
633C3×D4—31no—
634C3×D4—61no—
635C3×D4—62no—
636C3×D4—92no—
637C3×D4—91no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—41no—
644C2×C3×C4—62no—
645C2×C3×C4—92no—
646C2×C3×C4C2×D3211yescharacteristic
647C2×C3×C4C2×D3211yescharacteristic
648C2×C3×C4C2×D3211yescharacteristic
649#67—32no—
650#67—32no—
651#67—62no—
652#67—92no—
653#67—92no—
654#67—92no—
655#67—92no—
656#67—92no—
657#67—92no—
658#67—182no—
659#67—182no—
660#67#62412yes—
661C2×Dic3—92no—
662C2×Dic3—92no—
663C2×Dic3—91no—
664C2×Dic3—91no—
665C2×Dic3—91no—
666C2×Dic3—92no—
667C2×Dic3—182no—
668C2×Dic3—181no—
669C2×Dic3—181no—
670C2×Dic3—181no—
671C2×Dic3—361no—
672D12—31no—
673D12—31no—
674D12—61no—
675D12—92no—
676D12—92no—
677D12—92no—
678D12—182no—
679D12#62411yescharacteristic
680C4×D3—32no—
681C4×D3—32no—
682C4×D3—62no—
683C4×D3—92no—
684C4×D3—92no—
685C4×D3—92no—
686C4×D3—92no—
687C4×D3—92no—
688C4×D3—91no—
689C4×D3—91no—
690C4×D3—91no—
691C4×D3—91no—
692C4×D3—91no—
693C4×D3—91no—
694C4×D3—91no—
695C4×D3—91no—
696C4×D3—91no—
697C4×D3—91no—
698C4×D3—91no—
699C4×D3—91no—
700C4×D3—92no—
701C4×D3—182no—
702C4×D3—181no—
703C4×D3—181no—
704C4×D3—181no—
705C4×D3—181no—
706C4×D3—181no—
707C4×D3—181no—
708C4×D3—181no—
709C4×D3—181no—
710C4×D3—181no—
711C4×D3—181no—
712C4×D3—181no—
713C4×D3—181no—
714C4×D3—182no—
715C4×D3—361no—
716C4×D3—361no—
717C4×D3—361no—
718C4×D3—361no—
719C4×D3C2×D3212yes—
720Dic6—31no—
721Dic6—31no—
722Dic6—61no—
723Dic6—92no—
724Dic6—92no—
725Dic6—92no—
726Dic6—182no—
727Dic6#62411yescharacteristic
728C3×C8—31no—
729C3×C8—31no—
730C3×C8—32no—
731C3×C8—32no—
732C3×C8—31no—
733C3×C8—31no—
734C3×C8—61no—
735C3×C8—61no—
736C3×C8—62no—
737C3×C8—91no—
738C3×C8—92no—
739C3×C8—91no—
740C3⋊C8—31no—
741C3⋊C8—32no—
742C3⋊C8—31no—
743C3⋊C8—31no—
744C3⋊C8—32no—
745C3⋊C8—31no—
746C3⋊C8—61no—
747C3⋊C8—61no—
748C3⋊C8—62no—
749C3⋊C8C2×D3211yescharacteristic
750C3⋊C8C2×D3212yes—
751C3⋊C8C2×D3211yescharacteristic
752C2×C32—21no—
753C2×C32—22no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—21no—
758C2×C32—21no—
759C2×C32—41no—
760C2×C32—41no—
761C2×C32—41no—
762C2×C32—42no—
763C2×C32—62no—
764C2×C32C22×C4×D311yescharacteristic
765C2×C32C22×C4×D311yescharacteristic
766C2×C32C22×C4×D311yescharacteristic
767C3⋊D3—22no—
768C3⋊D3—32no—
769C3⋊D3—32no—
770C3⋊D3—32no—
771C3⋊D3—62no—
772C3⋊D3—62no—
773C3⋊D3—62no—
774C3⋊D3—61no—
775C3⋊D3—62no—
776C3⋊D3—61no—
777C3⋊D3—61no—
778C3⋊D3—122no—
779C3⋊D3—121no—
780C3⋊D3—121no—
781C3⋊D3—122no—
782C3×D3—22no—
783C3×D3—22no—
784C3×D3—42no—
785C3×D3—62no—
786C3×D3—62no—
787C3×D3—122no—
788#41—31no—
789#41—91no—
790#41—272no—
791#41—272no—
792#41—271no—
793#41—271no—
794C2×Q8—271no—
795C2×D4—272no—
796C2×D4—271no—
797C22×C4—272no—
798C22×C4—271no—
799M16—31no—
800M16—92no—
801M16—92no—
802M16—92no—
803M16—91no—
804M16—272no—
805M16—272no—
806C2×C8—31no—
807C2×C8—92no—
808C2×C8—92no—
809C2×C8—92no—
810C2×C8—91no—
811C2×C8—271no—
812C2×C8—271no—
813C2×C8—272no—
814C2×C8—271no—
815C2×C8—271no—
816C2×C8—272no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—32no—
821C22×C3—32no—
822C22×C3—41no—
823C22×C3—62no—
824C22×C3—92no—
825C22×C3C4×D3211yescharacteristic
826C22×C3C4×D3211yescharacteristic
827C22×C3C2×#62411yescharacteristic
828C2×D3—32no—
829C2×D3—32no—
830C2×D3—62no—
831C2×D3—91no—
832C2×D3—91no—
833C2×D3—91no—
834C2×D3—91no—
835C2×D3—91no—
836C2×D3—91no—
837C2×D3—181no—
838C2×D3—181no—
839C2×D3—181no—
840C2×D3—181no—
841C2×D3—181no—
842C2×D3—181no—
843C2×D3—184no—
844C2×D3—184no—
845C2×D3—184no—
846C2×D3—182no—
847C2×D3—182no—
848C2×D3—182no—
849C2×D3—184no—
850C2×D3—361no—
851C2×D3—361no—
852C2×D3—364no—
853C2×D3—362no—
854C2×D3—362no—
855C2×D3—364no—
856C2×D3C2×#62412yes—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—32no—
864C3×C4—32no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—62no—
868C3×C4—92no—
869C3×C4C4×D3211yescharacteristic
870C3×C4C4×D3211yescharacteristic
871C3×C4C2×#62411yescharacteristic
872C3×C4C22×D3211yescharacteristic
873C3×C4C22×D3211yescharacteristic
874C3×C4C22×D3211yescharacteristic
875Dic3—32no—
876Dic3—32no—
877Dic3—62no—
878Dic3—91no—
879Dic3—91no—
880Dic3—91no—
881Dic3—91no—
882Dic3—91no—
883Dic3—91no—
884Dic3—181no—
885Dic3—181no—
886Dic3—181no—
887Dic3—181no—
888Dic3—181no—
889Dic3—181no—
890Dic3—361no—
891Dic3—361no—
892Dic3C2×#62412yes—
893C32—21no—
894C32—21no—
895C32—21no—
896C32—41no—
897C32D3×#13111yescharacteristic, complemented
898C32D3×#13111yescharacteristic, complemented
899C32D3×#13111yescharacteristic, complemented
900C23—272no—
901C23—271no—
902Q8—31no—
903Q8—91no—
904Q8—272no—
905D4—32no—
906D4—31no—
907D4—92no—
908D4—91no—
909D4—272no—
910D4—272no—
911D4—272no—
912C2×C4—32no—
913C2×C4—92no—
914C2×C4—272no—
915C2×C4—272no—
916C2×C4—272no—
917C2×C4—271no—
918C2×C4—271no—
919C2×C4—271no—
920C2×C4—271no—
921C2×C4—271no—
922C2×C4D3311yescharacteristic
923C8—31no—
924C8—31no—
925C8—32no—
926C8—91no—
927C8—92no—
928C8—91no—
929C2×C3—22no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—41no—
937C2×C3—41no—
938C2×C3—42no—
939C2×C3—41no—
940C2×C3—62no—
941C2×C3—62no—
942C2×C3—122no—
943C2×C3—182no—
944C2×C3C2×C4×D3211yescharacteristic
945C2×C3C2×C4×D3211yescharacteristic
946C2×C3C22×#62411yescharacteristic
947D3—22no—
948D3—62no—
949D3—62no—
950D3—92no—
951D3—92no—
952D3—92no—
953D3—122no—
954D3—182no—
955D3—182no—
956D3—182no—
957D3—182no—
958D3—181no—
959D3—181no—
960D3—181no—
961D3—362no—
962D3—361no—
963D3—361no—
964D3—362no—
965C22—32no—
966C22—92no—
967C22—271no—
968C22—271no—
969C22—542no—
970C22—544no—
971C22D3×#62411yescharacteristic
972C4—32no—
973C4—92no—
974C4—271no—
975C4—271no—
976C4D3×#62411yescharacteristic
977C4C2×D3311yescharacteristic
978C3—21no—
979C3—21no—
980C3—21no—
981C3—41no—
982C3#1059466911yescharacteristic, complemented
983C3#1059470711yescharacteristic, complemented
984C3#1059544211yescharacteristic, complemented
985C2—21no—
986C2—62no—
987C2—182no—
988C2—272no—
989C2—541no—
990C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC4C2×D33
commutator, socleC2×C33C23×C4
FittingC2×C33×C4C23
prime radical#11724578C2
cosocleC33×C4C24
hypercenterC2×C4D33
hypocenterC33C2×#131
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723657C2semidirect
3. #11723358C2semidirect
4. C2×#88785C2semidirect
5. C3×#63817C2semidirect
6. C3×#63815C2semidirect
7. C3×#63814C2semidirect
8. #11722825C2semidirect
9. #11722824C2semidirect
10. #11722819C2semidirect
11. D3×#3710C2semidirect
26. C3×#3748C22semidirect
27. C2×C3×C3⋊(C3⋊C8)C22semidirect
28. C32×#208C22semidirect
29. C2×C32×C3⋊C8C22semidirect
30. #88809C22semidirect
31. #88808C22semidirect
32. #88788C22semidirect
36. #88785C22semidirect
37. #88785C22semidirect
38. C3×#3712C22semidirect
39. C3×#3711C22semidirect
40. C3×#3711C22semidirect
41. C3×#3710C22semidirect
42. C3×D3×C3⋊C8C22semidirect
43. C3×D3×C3⋊C8C22semidirect
63. #63817D3semidirect
69. #63815D3semidirect
71. #63814D3semidirect
161. #3748C2×D3semidirect
162. C2×C3⋊(C3⋊C8)C2×D3semidirect
175. C3×#208C2×D3semidirect
176. C3×#208C2×D3semidirect
183. C2×C3×C3⋊C8C2×D3semidirect
184. C2×C3×C3⋊C8C2×D3semidirect
197. #3712C2×D3semidirect
200. #3711C2×D3semidirect
201. #3711C2×D3semidirect
218. #3710C2×D3semidirect
221. D3×C3⋊C8C2×D3semidirect
222. D3×C3⋊C8C2×D3semidirect
413. C3⋊(C3⋊D3)#131semidirect
483. #208D32semidirect
490. C2×C3⋊C8D32semidirect
614. C33C2×#131semidirect
897. C32D3×#131semidirect
898. C32D3×#131semidirect
899. C32D3×#131semidirect
982. C3#10594669semidirect
983. C3#10594707semidirect
984. C3#10595442semidirect

Maximal subgroups

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

subgroupindex
#117245782
#117236572
#117233582
C2×#887852
C3×#638172
C3×#638152
C3×#638142
#117228252
#117228242
#117228192
D3×#37102
#105954423
#105947073
#105946693