Finite Group Databasebeta

← #11817839

Subgroups — #11817839

Order 1152.

1165 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63955C211yesmaximal, characteristic, complemented
2C2×#63848C211yesmaximal, characteristic, complemented
3#10592656C211yesmaximal, characteristic
4C3×#4950C211yesmaximal, characteristic, complemented
5C3×#4949C211yesmaximal, characteristic, complemented
6#10591712C211yesmaximal, characteristic
7#10591711C211yesmaximal, characteristic
8#10591702C211yesmaximal, characteristic, complemented
9#10591350C211yesmaximal, characteristic, complemented
10#10591342C211yesmaximal, characteristic, complemented
11#10591335C211yesmaximal, characteristic, complemented
12#10591274C211yesmaximal, characteristic, complemented
13#10591266C211yesmaximal, characteristic, complemented
14#10591258C211yesmaximal, characteristic, complemented
15#10591234C211yesmaximal, characteristic, complemented
16#78028—31nomaximal
17#74451—31nomaximal
18C22×#638C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42#63955—24no—
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46#63848—24no—
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#926—31no—
56C2×#898—31no—
57C2×#898—31no—
58C2×#877—31no—
59C3×#399—31no—
60C3×#385—31no—
61#5213—31no—
62#4993—31no—
63#4990—31no—
64#4990—31no—
65#4982—31no—
66#4981—31no—
67Dic3×C4⋊C4—31no—
68Dic3×C4⋊C4—31no—
69#4972—31no—
70#4961—31no—
71#4959—31no—
72#4958—31no—
73#4957—31no—
74#4957—31no—
75#4957—61no—
76#4951—31no—
77#4950D311yescharacteristic, complemented
78#4949D311yescharacteristic, complemented
79#4945—31no—
80#4677—31no—
81#4670—31no—
82#4669—31no—
83#4655—31no—
84#4654—31no—
85#4647—31no—
86C24×C32C2311yescharacteristic
87C23×C3⋊D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C2×#638—22no—
91C2×#638—22no—
92C2×#638—41no—
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3×Dic3—22no—
97C22×C3×Dic3—22no—
98C22×C3×Dic3—22no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C32×C22⋊C4—22no—
108#3757—22no—
109#3752—22no—
110#3752—22no—
111#3750—41no—
112C4×C3⋊Dic3—22no—
113C3×#217—22no—
114C3×#217—22no—
115C3×#217—41no—
116C3×C4⋊Dic3—22no—
117C3×C4⋊Dic3—22no—
118C3×C4⋊Dic3—22no—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4—41no—
121Dic3⋊Dic3—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3D414yescomplemented
125#3722—22no—
126#3722—22no—
127#3722—22no—
128#3722—41no—
129Dic32—22no—
130Dic32—22no—
131Dic32—22no—
132#2479—91noSylow
133C23×C3×C4—31no—
134C22×#67—31no—
135C22×#67—31no—
136C22×#67—61no—
137C23×Dic3C2×D311yescharacteristic
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4C2×D311yescharacteristic
148C2×C3×C22⋊C4C2×D311yescharacteristic
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—61no—
152C2×#217C2×D311yescharacteristic
153C2×#217C2×D311yescharacteristic
154C2×#217C2×D311yescharacteristic
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—61no—
168C2×(C2×D3)⋊C4—61no—
169#926—64no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3C2×D311yescharacteristic
175C2×C4⋊Dic3C2×D311yescharacteristic
176C2×C4⋊Dic3C2×D311yescharacteristic
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—61no—
184C2×Dic3⋊C4C2×D311yescharacteristic
185C2×Dic3⋊C4C2×D311yescharacteristic
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—61no—
195#898—64no—
196#898—64no—
197#877—64no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32#4112yes—
221C23×C32C2411yescharacteristic
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4#4112yes—
235#638—44no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C2×D412yes—
244C2×C3⋊Dic3#4112yes—
245C2×C3×Dic3—28no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D412yes—
268C2×C3×Dic3C2×D412yes—
269C2×C3×Dic3#4112yes—
270C2×#126—91no—
271C2×#117—91no—
272#399—31no—
273#399—91no—
274#398—91no—
275#394—91no—
276#390—91no—
277#389—91no—
278#388—91no—
279#388—91no—
280#388—91no—
281#387—91no—
282#386—91no—
283#385—31no—
284C4×C4⋊C4—91no—
285C24×C3—21no—
286C24×C3C22×D311yescharacteristic
287C24×C3C22×D311yescharacteristic
288C23×D3—31no—
289C23×D3—31no—
290C23×D3—61no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—62no—
302C22×C3×C4—62no—
303C22×C3×C4—62no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—62no—
309C2×#67—62no—
310C2×#67—64no—
311C2×#67—62no—
312C2×#67—62no—
313C2×#67—122no—
314C2×#67—121no—
315C2×#67—121no—
316C2×#67—122no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C3×C4⋊C4—62no—
338C3×C4⋊C4—62no—
339C3×C4⋊C4—62no—
340C3×C4⋊C4—62no—
341C3×C4⋊C4—121no—
342C3×C22⋊C4—22no—
343C3×C22⋊C4—22no—
344C3×C22⋊C4—42no—
345C3×C22⋊C4—62no—
346C3×C22⋊C4—62no—
347C3×C22⋊C4—121no—
348#217—22no—
349#217—22no—
350#217—41no—
351#217—62no—
352#217—62no—
353#217—122no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—122no—
365(C2×D3)⋊C4—122no—
366(C2×D3)⋊C4—121no—
367(C2×D3)⋊C4—121no—
368C4⋊Dic3—22no—
369C4⋊Dic3—22no—
370C4⋊Dic3—22no—
371C4⋊Dic3—34no—
372C4⋊Dic3—62no—
373C4⋊Dic3—62no—
374C4⋊Dic3—121no—
375Dic3⋊C4—22no—
376Dic3⋊C4—34no—
377Dic3⋊C4—41no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380Dic3⋊C4—121no—
381Dic3⋊C4—121no—
382Dic3⋊C4—121no—
383Dic3⋊C4—122no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—62no—
389C4×Dic3—62no—
390C4×Dic3—62no—
391C4×Dic3—62no—
392C4×Dic3—122no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32C2×#4111yescharacteristic
404C22×C32C2×#4111yescharacteristic
405C22×C32H(5,𝔽2)11yescharacteristic
406C22×C322−1+411yescharacteristic
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C32×C4—22no—
415C32×C4—41no—
416C3⋊Dic3—22no—
417C3⋊Dic3—22no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4—91no—
428C23×C4—31no—
429#126—184no—
430#117—184no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—91no—
438C2×C4⋊C4—91no—
439C2×C4⋊C4—91no—
440C2×C4⋊C4—91no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C22⋊C4—91no—
448C2×C22⋊C4—91no—
449C2×C22⋊C4—91no—
450C2×C22⋊C4—91no—
451C2×C22⋊C4D3211yescharacteristic
452C2×C42—91no—
453C2×C42—91no—
454C2×C42—91no—
455C2×C42—91no—
456#95—31no—
457#95—31no—
458#95—31no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463#95—91no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—22no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3#23712yes—
485C23×C3#23912yes—
486C23×C3C23×D311yescharacteristic
487C23×C3C23×D311yescharacteristic
488C22×D3—62no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—121no—
506C22×D3—121no—
507C22×D3—121no—
508C22×D3—121no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—68no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4#23512yes—
551C2×C3×C4#23712yes—
552#67—124no—
553#67—124no—
554#67—128no—
555C2×Dic3—28no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—32no—
578C2×Dic3—32no—
579C2×Dic3—32no—
580C2×Dic3—32no—
581C2×Dic3—62no—
582C2×Dic3—62no—
583C2×Dic3—62no—
584C2×Dic3—62no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—121no—
604C2×Dic3D3×D412yes—
605C2×Dic3D3×D412yes—
606C2×Dic3#23712yes—
607C2×C32—42no—
608C2×C32#52511yescharacteristic
609C2×C32#52911yescharacteristic
610C2×C32#54211yescharacteristic
611C2×C32#54711yescharacteristic
612C2×C32#55011yescharacteristic
613C2×C32#55111yescharacteristic
614C2×C32#55211yescharacteristic
615C3⋊D3—81no—
616C24—91no—
617C24C2×D3211yescharacteristic
618C2×D4—182no—
619C2×D4—182no—
620C2×D4—361no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—91no—
635C22×C4C2×D3211yescharacteristic
636C22×C4C2×D3211yescharacteristic
637C4⋊C4—62no—
638C4⋊C4—62no—
639C4⋊C4—62no—
640C4⋊C4—62no—
641C4⋊C4—94no—
642C4⋊C4—121no—
643C4⋊C4—182no—
644C4⋊C4—182no—
645C4⋊C4—361no—
646C4⋊C4—361no—
647C22⋊C4—22no—
648C22⋊C4—62no—
649C22⋊C4—62no—
650C22⋊C4—121no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—182no—
654C22⋊C4—182no—
655C22⋊C4—182no—
656C22⋊C4—182no—
657C22⋊C4—361no—
658C42—182no—
659C42—182no—
660C42—182no—
661C42—182no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3C2×#23511yescharacteristic
691C22×C3C2×D3×D411yescharacteristic
692C22×C3C2×D3×D411yescharacteristic
693C22×C3C2×#23711yescharacteristic
694C22×C3C2×#23711yescharacteristic
695C22×C3C2×#23711yescharacteristic
696C22×C3#100411yescharacteristic
697C22×C3C2×#23911yescharacteristic
698C22×C3#100711yescharacteristic
699C22×C3D3×#4111yescharacteristic
700C22×C3D3×#4111yescharacteristic
701C22×C3D3×#4111yescharacteristic
702C22×C3#100911yescharacteristic
703C22×C3#101011yescharacteristic
704C2×D3—122no—
705C2×D3—122no—
706C2×D3—122no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—241no—
722C2×D3—241no—
723C2×D3—241no—
724C2×D3—241no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—42no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—81no—
734C3×C4—121no—
735C3×C4—121no—
736C3×C4—121no—
737C3×C4—121no—
738C3×C4—121no—
739Dic3—22no—
740Dic3—22no—
741Dic3—22no—
742Dic3—41no—
743Dic3—41no—
744Dic3—41no—
745Dic3—41no—
746Dic3—41no—
747Dic3—64no—
748Dic3—62no—
749Dic3—62no—
750Dic3—62no—
751Dic3—62no—
752Dic3—122no—
753Dic3—121no—
754Dic3—121no—
755Dic3—241no—
756C32#247911yescharacteristic, complemented, Sylow
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—181no—
764C23—181no—
765C23—181no—
766C23—181no—
767C23—181no—
768C23—181no—
769C23—181no—
770C23#379612yes—
771C23C22×D3211yescharacteristic
772D4—364no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—68no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—92no—
804C2×C4—92no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4#380412yes—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—42no—
821C2×C3—42no—
822C2×C3—82no—
823C2×C3#551311yescharacteristic
824C2×C3#553811yescharacteristic
825C2×C3#555311yescharacteristic
826C2×C3#558611yescharacteristic
827C2×C3#562711yescharacteristic
828C2×C3#563111yescharacteristic
829C2×C3#563711yescharacteristic
830C2×C3#564211yescharacteristic
831C2×C3#564311yescharacteristic
832C2×C3#564911yescharacteristic
833C2×C3#565511yescharacteristic
834C2×C3#565811yescharacteristic
835C2×C3#566211yescharacteristic
836C2×C3#571811yescharacteristic
837D3—242no—
838D3—241no—
839D3—241no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—361no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22C2×#379611yescharacteristic
855C22#6429711yescharacteristic
856C22D32×D411yescharacteristic
857C22D3×#23711yescharacteristic
858C22#6431211yescharacteristic
859C22#6431411yescharacteristic
860C22C2×#380411yescharacteristic
861C4—22no—
862C4—41no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—121no—
867C4—121no—
868C4—121no—
869C4—121no—
870C4—121no—
871C4—182no—
872C4—182no—
873C4—361no—
874C3—21no—
875C3#7445111yescharacteristic, complemented
876C3#7802811yescharacteristic, complemented
877C2—42no—
878C2—721no—
879C2#1059403811yescharacteristic
880C2#1059405511yescharacteristic
881C2#1059406411yescharacteristic
882C2#1059416411yescharacteristic
883C2#1059482511yescharacteristic
884C2#1059511611yescharacteristic
885C2#1059514311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#63955C2semidirect
2. C2×#63848C2semidirect
4. C3×#4950C2semidirect
5. C3×#4949C2semidirect
8. #10591702C2semidirect
9. #10591350C2semidirect
10. #10591342C2semidirect
11. #10591335C2semidirect
12. #10591274C2semidirect
13. #10591266C2semidirect
14. #10591258C2semidirect
15. #10591234C2semidirect
77. #4950D3semidirect
78. #4949D3semidirect
124. Dic3⋊Dic3D4semidirect
756. C32#2479semidirect
875. C3#74451semidirect
876. C3#78028semidirect

Maximal subgroups

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

subgroupindex
C2×#639552
C2×#638482
#105926562
C3×#49502
C3×#49492
#105917122
#105917112
#105917022
#105913502
#105913422
#105913352
#105912742
#105912662
#105912582
#105912342
#780283
#744513