Finite Group Databasebeta

← #11859540

Subgroups — #11859540

Order 1152.

1030 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63804C211yesmaximal, characteristic, complemented
2C2×#63803C211yesmaximal, characteristic, complemented
3#10593968C211yesmaximal, characteristic
4#10592405C211yesmaximal, characteristic, complemented
5C3×#4706C211yesmaximal, characteristic, complemented
6C3×D3×#97C211yesmaximal, characteristic, complemented
7#10590953C211yesmaximal, characteristic, complemented
8#10590953C211yesmaximal, characteristic, complemented
9#10590739C211yesmaximal, characteristic, complemented
10#10590736C211yesmaximal, characteristic, complemented
11#10590728C211yesmaximal, characteristic, complemented
12#10590726C211yesmaximal, characteristic, complemented
13#10590336C211yesmaximal, characteristic, complemented
14#10590328C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#79480—31nomaximal
17#78491—31nomaximal
18C2×#3798C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29#63918C411yescharacteristic
30#63911C411yescharacteristic
31#63909C411yescharacteristic
32#63908C411yescharacteristic
33#63906C411yescharacteristic
34#63906C411yescharacteristic
35C4×#626C2211yescharacteristic
36C4×#626C2211yescharacteristic
37#63852C411yescharacteristic
38#63852C411yescharacteristic
39C2×#3712C2211yescharacteristic
40C2×#3711C2211yescharacteristic
41C2×#3711C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63804—24no—
46#63803—24no—
47C32×#97C2211yescharacteristic
48#63647C2211yescharacteristic
49#63647C2211yescharacteristic
50C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×#815C2211yescharacteristic
55C3×C4⋊(C3⋊C8)C2211yescharacteristic
56C3×#803C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C2×#907—31no—
64C2×#901—31no—
65C2×#901—31no—
66C2×#901—31no—
67#5548—31no—
68#5477—31no—
69C3×#435—31no—
70C2×C3×#97—31no—
71#5127—31no—
72#5111—31no—
73#5110—31no—
74#5110—31no—
75#5011—31no—
76#4924—31no—
77#4837—31no—
78#4836—31no—
79#4730—31no—
80#4728—31no—
81#4727—31no—
82#4727—31no—
83#4706—31no—
84#4706—31no—
85#4706—31no—
86#4706—31no—
87#4706—31no—
88#4706—31no—
89#4706—31no—
90#4706—31no—
91#4706—61no—
92#4706D311yescharacteristic, complemented
93D3×#97D311yescharacteristic, complemented
94C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×D12C2×C411yescharacteristic
98C2×C3×C4×D3C2×C411yescharacteristic
99C2×C3×C4×D3C2×C411yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×#627C2×C411yescharacteristic
104C2×#627C2×C411yescharacteristic
105C2×#626C2×C411yescharacteristic
106C2×#626C2×C411yescharacteristic
107C2×#626C2×C411yescharacteristic
108C2×#626C2×C411yescharacteristic
109C2×#626C2×C411yescharacteristic
110C2×#626C2×C411yescharacteristic
111C2×#625C2×C411yescharacteristic
112C2×#625C2×C411yescharacteristic
113#3798—22no—
114#3798—22no—
115#3798—22no—
116#3798—22no—
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C42C2311yescharacteristic
120#3752C2×C411yescharacteristic
121#3752C2×C411yescharacteristic
122C4⋊(C3⋊Dic3)C2×C411yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3743—22no—
126C8×C3⋊D3—22no—
127C3×(C2×D3)⋊C4C2×C411yescharacteristic
128C3×(C2×D3)⋊C4C2×C411yescharacteristic
129C3×C4⋊Dic3C2×C411yescharacteristic
130C3×C4×Dic3C2×C411yescharacteristic
131C3×C4×Dic3C2×C411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×ΓL(1,𝔽25)—22no—
138C3×D3×C8—22no—
139C3×D3×C8—22no—
140C3×D3×C8D414yescomplemented
141Dic3⋊Dic3C2×C411yescharacteristic
142Dic3⋊Dic3C2×C411yescharacteristic
143#3722C2×C411yescharacteristic
144#3722C2×C411yescharacteristic
145(C2×D3)⋊Dic3C2×C411yescharacteristic
146(C2×D3)⋊Dic3C2×C411yescharacteristic
147#3712—22no—
148#3711—22no—
149#3711—22no—
150#3711—22no—
151#3710—22no—
152D3×C3⋊C8—22no—
153#2932—91noSylow
154C2×#235—31no—
155C2×#235—31no—
156C2×#235—31no—
157C2×#235—31no—
158C2×C3×M16—31no—
159C22×C3×C8—31no—
160C22×C3×C8—31no—
161C22×C3×C8—31no—
162C3×C4×D4—31no—
163C2×C3×C42—31no—
164#940—31no—
165#938—31no—
166#930—31no—
167#930—31no—
168#930—31no—
169#930—31no—
170C4×#67—31no—
171C4×#67—31no—
172C2×#208—31no—
173C2×#208—31no—
174C2×#208—31no—
175C22×C3⋊C8—31no—
176#907—64no—
177#901—64no—
178#901—64no—
179#901—64no—
180C2×ΓL(1,𝔽25)—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×ΓL(1,𝔽25)—31no—
186C2×ΓL(1,𝔽25)—31no—
187C2×ΓL(1,𝔽25)—61no—
188C2×ΓL(1,𝔽25)C2×D311yescharacteristic
189C2×D3×C8—31no—
190C2×D3×C8—31no—
191C2×D3×C8—31no—
192C2×D3×C8—31no—
193C2×D3×C8—31no—
194C2×D3×C8—61no—
195C2×D3×C8C2×D311yescharacteristic
196C2×D3×C8C2×D311yescharacteristic
197C2×D3×C8C2×D311yescharacteristic
198#895—31no—
199#888—31no—
200#885—31no—
201#885—31no—
202#884—31no—
203#884—31no—
204#875—31no—
205#875—31no—
206#874—31no—
207C4×D12—31no—
208C4×D12—31no—
209C4×D12—31no—
210C4×D12—31no—
211C4×D12—61no—
212C4×D12C2×D311yescharacteristic
213C42×D3C2×D311yescharacteristic
214#869—31no—
215C3×C4⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×#97—21no—
219C3×#97—31no—
220C3×#97—31no—
221C3×#97—31no—
222C3×#97C2×D311yescharacteristic
223C3×#97C2×D311yescharacteristic
224#830—31no—
225#830—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8—31no—
234(C2×D3)⋊C8—31no—
235(C2×D3)⋊C8—31no—
236(C2×D3)⋊C8—61no—
237(C2×D3)⋊C8—61no—
238(C2×D3)⋊C8C2×D311yescharacteristic
239(C2×D3)⋊C8C2×D311yescharacteristic
240#815C2×D311yescharacteristic
241#815C2×D311yescharacteristic
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244C4⋊(C3⋊C8)—31no—
245C4⋊(C3⋊C8)—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—61no—
249C4⋊(C3⋊C8)C2×D311yescharacteristic
250#803C2×D311yescharacteristic
251C22×C3⋊D3C22×C411yescharacteristic
252C22×C3⋊D3C22×C411yescharacteristic
253C22×C3×D3C22×C411yescharacteristic
254C22×C3×D3C22×C411yescharacteristic
255C22×C3×D3C22×C411yescharacteristic
256C2×C32×C4C22×C411yescharacteristic
257C2×C32×C4C22×C411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3C22×C411yescharacteristic
260C2×C3⋊Dic3C22×C411yescharacteristic
261C4⋊(C3⋊D3)—41no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264C4×C3⋊D3—21no—
265C4×C3⋊D3—21no—
266C2×C3×Dic3C22×C411yescharacteristic
267C2×C3×Dic3C22×C411yescharacteristic
268C2×C3×Dic3C22×C411yescharacteristic
269C2×C3×Dic3C22×C411yescharacteristic
270C2×C3×Dic3C22×C411yescharacteristic
271C3×D12—41no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—41no—
277C3×C4×D3—41no—
278C3×C4×D3C2×D412yes—
279C3×C4×D3#4112yes—
280#627—22no—
281#627—22no—
282#626—22no—
283#626—22no—
284#626—22no—
285#626—22no—
286#626—41no—
287#626—41no—
288#625—22no—
289#625—22no—
290C32×C8—21no—
291C32×C8C2×D412yes—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8—21no—
297C3×C3⋊C8C2×D412yes—
298C2×#131—91no—
299C2×#131—91no—
300#532—91no—
301#435—31no—
302#435—91no—
303#435—91no—
304#435—91no—
305#435—91no—
306#435—91no—
307#435—91no—
308#435—91no—
309#423—91no—
310#408—91no—
311#408—91no—
312C2×#97—31no—
313C2×C3×D4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C2×#67—31no—
320C2×#67—31no—
321C2×#67—31no—
322C2×#67—31no—
323C2×#67—31no—
324C2×#67—31no—
325C2×#67—31no—
326C2×#67—31no—
327C2×#67—31no—
328C2×#67—31no—
329#235—62no—
330#235—62no—
331#235—62no—
332#235—62no—
333#235—62no—
334#235—62no—
335#235—62no—
336#235—62no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—61no—
346C2×D12C4×D311yescharacteristic
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3C4×D311yescharacteristic
354C2×C4×D3C4×D311yescharacteristic
355C2×C4×D3C22×D311yescharacteristic
356C2×C4×D3C22×D311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6—31no—
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6—31no—
362C3×M16—62no—
363C2×C3×C8—21no—
364C2×C3×C8—21no—
365C2×C3×C8—31no—
366C2×C3×C8—34no—
367C2×C3×C8—31no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8—62no—
371C2×C3×C8—62no—
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C22×D311yescharacteristic
374C2×C3×C8C22×D311yescharacteristic
375C2×C3×C8C22×D311yescharacteristic
376C3×C4⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C42—21no—
380C3×C42—31no—
381C3×C42—31no—
382C3×C42—31no—
383C3×C42C22×D311yescharacteristic
384C3×C42C22×D311yescharacteristic
385#217—31no—
386#217—31no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—31no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4C4×D311yescharacteristic
400(C2×D3)⋊C4C4×D311yescharacteristic
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3C4×D311yescharacteristic
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409C4×Dic3C4×D311yescharacteristic
410C4×Dic3C4×D311yescharacteristic
411C4×Dic3C22×D311yescharacteristic
412#208—62no—
413#208—62no—
414#208—62no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8—62no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426ΓL(1,𝔽25)—22no—
427ΓL(1,𝔽25)—62no—
428ΓL(1,𝔽25)—62no—
429ΓL(1,𝔽25)—62no—
430ΓL(1,𝔽25)—62no—
431ΓL(1,𝔽25)—62no—
432ΓL(1,𝔽25)—62no—
433ΓL(1,𝔽25)—62no—
434ΓL(1,𝔽25)—122no—
435D3×C8—22no—
436D3×C8—22no—
437D3×C8—62no—
438D3×C8—62no—
439D3×C8—62no—
440D3×C8—62no—
441D3×C8—62no—
442D3×C8—122no—
443D3×C8D1214yescomplemented
444C22×C32C23×C411yescharacteristic
445C2×C3⋊D3—21no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3C4×D412yes—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4C22×D411yescharacteristic
463C32×C4C2×#4111yescharacteristic
464C3⋊Dic3—21no—
465C3⋊Dic3—21no—
466C3×Dic3—21no—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3C4×D412yes—
471C2×#41—91no—
472C2×#41—91no—
473#131—184no—
474#131—184no—
475C2×M16—31no—
476C2×M16—91no—
477C2×M16—91no—
478C2×M16—91no—
479C2×M16—91no—
480C2×M16—91no—
481C22×C8—31no—
482C22×C8—31no—
483C22×C8—31no—
484C22×C8—91no—
485C22×C8—91no—
486C22×C8—91no—
487C4⋊Q8—91no—
488#127—91no—
489#124—91no—
490#124—91no—
491#121—91no—
492#121—91no—
493#121—91no—
494#121—91no—
495C4×D4—31no—
496C4×D4—91no—
497C4×D4—91no—
498C4×D4—91no—
499C2×C42—31no—
500C4⋊C8—31no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C22⋊C8—31no—
505C22⋊C8—31no—
506C22⋊C8—91no—
507C22⋊C8—91no—
508C22⋊C8—91no—
509C22⋊C8—91no—
510C22⋊C8—91no—
511C22⋊C8—91no—
512#97—31no—
513#97—31no—
514#97—31no—
515#97D3211yescharacteristic
516C23×C3—31no—
517C23×C3—31no—
518C23×C3—31no—
519C22×D3—31no—
520C22×D3—31no—
521C22×D3—31no—
522C22×D3—31no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3C2×C4×D311yescharacteristic
526C22×D3C2×C4×D311yescharacteristic
527C22×D3C2×C4×D311yescharacteristic
528C3×D4—121no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—31no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—121no—
544C2×C3×C4—121no—
545C2×C3×C4C2×C4×D311yescharacteristic
546C2×C3×C4C2×C4×D311yescharacteristic
547C2×C3×C4C2×C4×D311yescharacteristic
548C2×C3×C4C2×C4×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551#67—62no—
552#67—62no—
553#67—62no—
554#67—62no—
555#67—62no—
556#67—62no—
557#67—62no—
558#67—62no—
559#67—121no—
560#67—121no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3C2×C4×D311yescharacteristic
568C2×Dic3C2×C4×D311yescharacteristic
569C2×Dic3C2×C4×D311yescharacteristic
570C2×Dic3C2×C4×D311yescharacteristic
571C2×Dic3C2×C4×D311yescharacteristic
572D12—41no—
573D12—62no—
574D12—62no—
575D12—62no—
576D12—62no—
577D12—121no—
578D12—121no—
579D12—122no—
580D12—121no—
581D12—121no—
582C4×D3—21no—
583C4×D3—21no—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—41no—
587C4×D3—41no—
588C4×D3—61no—
589C4×D3—61no—
590C4×D3—61no—
591C4×D3—61no—
592C4×D3—61no—
593C4×D3—61no—
594C4×D3—61no—
595C4×D3—61no—
596C4×D3—121no—
597C4×D3—121no—
598C4×D3—121no—
599C4×D3—121no—
600C4×D3C2×D1212yes—
601C4×D3#23512yes—
602Dic6—62no—
603Dic6—62no—
604Dic6—62no—
605Dic6—62no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—22no—
609C3×C8—32no—
610C3×C8—41no—
611C3×C8—61no—
612C3×C8—61no—
613C3×C8—61no—
614C3×C8C2×D1212yes—
615C3×C8D3×D412yes—
616C3⋊C8—21no—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C3⋊C8—61no—
620C3⋊C8—61no—
621C3⋊C8—61no—
622C3⋊C8—61no—
623C3⋊C8—121no—
624C3⋊C8—121no—
625C3⋊C8C2×D1212yes—
626C2×C32C2×C4×D411yescharacteristic
627C2×C32#56811yescharacteristic
628C2×C32#56811yescharacteristic
629C3⋊D3—41no—
630C3⋊D3—41no—
631C3×D3—22no—
632C3×D3—41no—
633C3×D3—41no—
634#41—182no—
635#41—182no—
636#41—182no—
637#41—182no—
638C2×Q8—91no—
639C2×Q8—91no—
640C2×D4—31no—
641C2×D4—91no—
642C2×D4—91no—
643C2×D4—91no—
644C2×D4—91no—
645C2×D4—91no—
646C2×D4—91no—
647C2×D4—91no—
648C2×D4—91no—
649C2×D4—91no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—91no—
656C22×C4—91no—
657M16—62no—
658M16—182no—
659M16—182no—
660M16—182no—
661M16—182no—
662M16—182no—
663C2×C8—31no—
664C2×C8—34no—
665C2×C8—31no—
666C2×C8—31no—
667C2×C8—31no—
668C2×C8—62no—
669C2×C8—62no—
670C2×C8—91no—
671C2×C8—91no—
672C2×C8—182no—
673C2×C8—182no—
674C2×C8—182no—
675C2×C8C2×D3211yescharacteristic
676C2×C8C2×D3211yescharacteristic
677C4⋊C4—31no—
678C4⋊C4—91no—
679C4⋊C4—91no—
680C4⋊C4—91no—
681C22⋊C4—31no—
682C22⋊C4—31no—
683C22⋊C4—91no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C42—31no—
690C42—31no—
691C42—31no—
692C42C2×D3211yescharacteristic
693C22×C3—21no—
694C22×C3—32no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3C22×C4×D311yescharacteristic
704C22×C3C22×C4×D311yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—62no—
714C2×D3—61no—
715C2×D3—61no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3C4×D1212yes—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—32no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—61no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4C22×D1211yescharacteristic
746C3×C4C2×#23511yescharacteristic
747C3×C4C2×D3×D411yescharacteristic
748C3×C4D3×#4111yescharacteristic
749Dic3—21no—
750Dic3—21no—
751Dic3—21no—
752Dic3—21no—
753Dic3—61no—
754Dic3—61no—
755Dic3—61no—
756Dic3—61no—
757Dic3—121no—
758Dic3—121no—
759Dic3C4×D1212yes—
760C32#293211yescharacteristic, complemented, Sylow
761C23—31no—
762C23—31no—
763C23—31no—
764C23—91no—
765C23—91no—
766Q8—182no—
767Q8—182no—
768D4—121no—
769D4—182no—
770D4—182no—
771D4—182no—
772D4—182no—
773D4—182no—
774D4—182no—
775D4—361no—
776D4—361no—
777D4—361no—
778C2×C4—31no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—31no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4C4×D3211yescharacteristic
798C2×C4C4×D3211yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C8—21no—
801C8—32no—
802C8—61no—
803C8—61no—
804C8—61no—
805C8—181no—
806C8—181no—
807C8D3×D1212yes—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—62no—
812C2×C3—121no—
813C2×C3—121no—
814C2×C3C2×C4×D1211yescharacteristic
815C2×C3C4×D3×D411yescharacteristic
816C2×C3#574511yescharacteristic
817C2×C3#574511yescharacteristic
818C2×C3#574511yescharacteristic
819C2×C3#575011yescharacteristic
820D3—22no—
821D3—41no—
822D3—41no—
823D3—122no—
824D3—121no—
825D3—121no—
826D3—121no—
827D3—121no—
828D3—241no—
829C22—32no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—61no—
838C22—181no—
839C22—181no—
840C22—181no—
841C22—181no—
842C22—181no—
843C22—181no—
844C22C2×C4×D3211yescharacteristic
845C4—21no—
846C4—21no—
847C4—32no—
848C4—61no—
849C4—61no—
850C4—61no—
851C4—61no—
852C4—181no—
853C4—181no—
854C4C2×D3×D1211yescharacteristic
855C4D3×#23511yescharacteristic
856C3—21no—
857C3#7849111yescharacteristic, complemented
858C3#7948011yescharacteristic, complemented
859C2—62no—
860C2—121no—
861C2—121no—
862C2—361no—
863C2—361no—
864C2C4×D3×D1211yescharacteristic
865C2#1059470611yescharacteristic
866C2#1059472211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×#97C22
prime radical#10593968C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2932
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#63804C2semidirect
2. C2×#63803C2semidirect
4. #10592405C2semidirect
5. C3×#4706C2semidirect
6. C3×D3×#97C2semidirect
7. #10590953C2semidirect
8. #10590953C2semidirect
9. #10590739C2semidirect
10. #10590736C2semidirect
11. #10590728C2semidirect
12. #10590726C2semidirect
13. #10590336C2semidirect
14. #10590328C2semidirect
15. #10590326C2semidirect
92. #4706D3semidirect
93. D3×#97D3semidirect
140. C3×D3×C8D4semidirect
443. D3×C8D12semidirect
760. C32#2932semidirect
857. C3#78491semidirect
858. C3#79480semidirect

Maximal subgroups

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

subgroupindex
C2×#638042
C2×#638032
#105939682
#105924052
C3×#47062
C3×D3×#972
#105909532
#105907392
#105907362
#105907282
#105907262
#105903362
#105903282
#105903262
#794803
#784913