Finite Group Databasebeta

← #10804997

Subgroups — #10804997

Order 768.

1158 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5538C211yesmaximal, characteristic
2#73864C211yesmaximal, characteristic, complemented
3#73863C211yesmaximal, characteristic, complemented
4C3×#1799C211yesmaximal, characteristic, complemented
5#71619C211yesmaximal, characteristic, complemented
6#70030C212yesmaximal
7#70029C212yesmaximal, complemented
8#69530C211yesmaximal, characteristic, complemented
9#69530C211yesmaximal, characteristic, complemented
10#68955C212yesmaximal, complemented
11#68954C212yesmaximal, complemented
12#21875—31nomaximal, Sylow
13C2×C3×C4×D4C2211yescharacteristic
14C2×#939C2211yescharacteristic
15C2×#935C2211yescharacteristic
16C2×C4×#67C411yescharacteristic, complemented
17C2×C4×#67C2211yescharacteristic
18C2×#926C411yescharacteristic, complemented
19C22×C4×Dic3C2211yescharacteristic
20#5538—21no—
21#5538—21no—
22#5538—21no—
23#5538—21no—
24#5538—21no—
25#5538—21no—
26#5538—21no—
27#5538—21no—
28C2×#898C411yescharacteristic, complemented
29C2×#889C411yescharacteristic, complemented
30C2×#886C2211yescharacteristic
31C2×#885C411yescharacteristic, complemented
32C2×#879C411yescharacteristic, complemented
33C2×#878C2211yescharacteristic
34C2×#877C2212yes—
35C2×#872C411yescharacteristic, complemented
36C2×C4×Dic6C411yescharacteristic, complemented
37C2×C3×#99C2212yes—
38C3×#380C2211yescharacteristic
39C3×#380C2211yescharacteristic
40C2×#834C2212yes—
41#5212C2211yescharacteristic
42#5212C2211yescharacteristic
43#4977—21no—
44#4975—21no—
45Dic3×C4⋊C4—21no—
46Dic3×C4⋊C4—21no—
47C2×#806C2212yes—
48C2×#806C2212yes—
49#4943C2212yes—
50#4942C2212yes—
51Dic3×C22⋊C4C2212yes—
52#4651—21no—
53#4650—21no—
54#4649—21no—
55#4648—21no—
56C3×#342C2212yes—
57#4527C2212yes—
58#4527C2212yes—
59#4526C2212yes—
60C2×#529—31no—
61#2285—31no—
62#2283—31no—
63#1996—32no—
64#1964—32no—
65#1899—32no—
66#1899—32no—
67#1799—31no—
68#1799—31no—
69#1799—31no—
70#1799D311yescharacteristic, complemented
71C22×C3×D4C2311yescharacteristic
72C23×C3×C4C2×C411yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C22×#67C2×C411yescharacteristic
75C22×#67C2311yescharacteristic
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C22×C4×D3C2×C411yescharacteristic
79C22×Dic6C2×C411yescharacteristic
80C3×C4×D4—21no—
81C3×C4×D4—21no—
82C3×C4×D4—21no—
83C3×C4×D4—21no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4C2×C411yescharacteristic
87C2×C3×C22⋊C4C2×C411yescharacteristic
88C2×C3×C22⋊C4C2312yes—
89C2×C3×C22⋊C4C2312yes—
90C2×C3×C22⋊C4C2311yescharacteristic
91C2×C3×C42C2×C411yescharacteristic
92C2×#217C2×C411yescharacteristic
93C2×#217C2×C411yescharacteristic
94C2×#217C2×C411yescharacteristic
95C2×#217C2312yes—
96C2×#217C2312yes—
97C2×#217C2311yescharacteristic
98#939—21no—
99#939—21no—
100#939—21no—
101#939—21no—
102#935—21no—
103#935—21no—
104#935—21no—
105#935—21no—
106C4×#67—21no—
107C4×#67—21no—
108C4×#67—21no—
109C4×#67—21no—
110C4×#67—21no—
111C4×#67—21no—
112C4×#67—21no—
113C4×#67—21no—
114C2×(C2×D3)⋊C4C2×C411yescharacteristic
115C2×(C2×D3)⋊C4C2×C411yescharacteristic
116C2×(C2×D3)⋊C4C2×C411yescharacteristic
117C2×(C2×D3)⋊C4C2×C411yescharacteristic
118#926—21no—
119#926—21no—
120#926—21no—
121#926—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2×C411yescharacteristic
125C2×C4⋊Dic3C2×C411yescharacteristic
126C2×C4⋊Dic3C2×C411yescharacteristic
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4C2×C411yescharacteristic
130C2×Dic3⋊C4C2×C411yescharacteristic
131C2×Dic3⋊C4C2×C411yescharacteristic
132C2×Dic3⋊C4C2×C411yescharacteristic
133C2×Dic3⋊C4C2×C411yescharacteristic
134C2×Dic3⋊C4C2×C411yescharacteristic
135C2×C4×Dic3—22no—
136C2×C4×Dic3—22no—
137C2×C4×Dic3C2×C411yescharacteristic
138C2×C4×Dic3C2×C411yescharacteristic
139C2×C4×Dic3C2×C411yescharacteristic
140C2×C4×Dic3C2×C411yescharacteristic
141C2×C4×Dic3C2×C411yescharacteristic
142C2×C4×Dic3D411yescharacteristic
143C2×C4×Dic3D411yescharacteristic
144C2×C4×Dic3D411yescharacteristic
145C2×C4×Dic3D411yescharacteristic
146C2×C4×Dic3D411yescharacteristic
147C2×C4×Dic3D411yescharacteristic
148C2×C4×Dic3D411yescharacteristic
149C2×C4×Dic3D411yescharacteristic
150#898—21no—
151#898—21no—
152#898—21no—
153#898—21no—
154#889—21no—
155#889—21no—
156#889—21no—
157#889—21no—
158#886—21no—
159#886—21no—
160#886—21no—
161#886—21no—
162#885—21no—
163#885—21no—
164#885—21no—
165#885—21no—
166#879—21no—
167#879—21no—
168#879—21no—
169#879—21no—
170#878—21no—
171#878—21no—
172#878—21no—
173#878—21no—
174#877—42no—
175#877—42no—
176#872—21no—
177#872—21no—
178#872—21no—
179#872—21no—
180C4×Dic6—21no—
181C4×Dic6—21no—
182C4×Dic6—21no—
183C4×Dic6—21no—
184C3×#99—42no—
185C3×#95—21no—
186C3×#95—21no—
187#834—42no—
188C3⋊#95—21no—
189C3⋊#95—21no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—22no—
193C3⋊#95—22no—
194#806—42no—
195#806—42no—
196#529—61no—
197#529—61no—
198#529—61no—
199#529—61no—
200#529—61no—
201#529—61no—
202#529—61no—
203#529—61no—
204C2×#126—31no—
205C2×#126—31no—
206C2×#125—31no—
207C2×#124—31no—
208C2×#123—31no—
209C2×#123—31no—
210C2×C22⋊Q8—31no—
211C2×#121—31no—
212C2×C4×Q8—31no—
213C2×C4×D4—31no—
214C2×C4×D4—31no—
215C2×C4×D4C2×D311yescharacteristic
216C2×#117—31no—
217C2×#117—31no—
218C2×#117—32no—
219C22×C42—31no—
220C2×#99—32no—
221C2×#99—32no—
222C2×#99—32no—
223C2×#99C2×D312yes—
224#384—61no—
225#383—61no—
226#382—61no—
227#382—61no—
228#381—32no—
229#380—31no—
230#380—31no—
231#380—32no—
232#380C2×D311yescharacteristic
233#380C2×D311yescharacteristic
234C4×C4⋊C4—61no—
235C4×C4⋊C4—61no—
236C4×C4⋊C4—61no—
237C4×C22⋊C4—32no—
238#376—61no—
239#342—32no—
240#342—32no—
241#342—32no—
242#342C2×D312yes—
243C24×C3C22×C411yescharacteristic
244C24×C3C2411yescharacteristic
245C23×D3C22×C411yescharacteristic
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4C22×C411yescharacteristic
259C22×C3×C4C22×C411yescharacteristic
260C22×C3×C4C22×C411yescharacteristic
261C22×C3×C4C22×C411yescharacteristic
262C22×C3×C4C22×C411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C2×#67—21no—
268C2×#67—21no—
269C2×#67—21no—
270C2×#67—21no—
271C2×#67—21no—
272C2×#67—21no—
273C2×#67—21no—
274C2×#67—21no—
275C2×#67—42no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—42no—
283C22×Dic3C22×C411yescharacteristic
284C22×Dic3C22×C411yescharacteristic
285C22×Dic3C22×C411yescharacteristic
286C22×Dic3C22×C411yescharacteristic
287C22×Dic3C22×C411yescharacteristic
288C22×Dic3C22×C411yescharacteristic
289C22×Dic3C22×C411yescharacteristic
290C22×Dic3C2×D411yescharacteristic
291C22×Dic3C2×D411yescharacteristic
292C22×Dic3C2×D411yescharacteristic
293C22×Dic3C2×D411yescharacteristic
294C22×Dic3C2×D411yescharacteristic
295C22×Dic3C2×D411yescharacteristic
296C22×Dic3C2×D411yescharacteristic
297C22×Dic3C2×D411yescharacteristic
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—42no—
301C2×Dic6—21no—
302C2×Dic6—21no—
303C2×Dic6—42no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—42no—
307C3×C4⋊C4—42no—
308C3×C22⋊C4—21no—
309C3×C22⋊C4—21no—
310C3×C22⋊C4—21no—
311C3×C22⋊C4—21no—
312C3×C22⋊C4—22no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—22no—
315C3×C22⋊C4—22no—
316C3×C42—21no—
317C3×C42—21no—
318#217—21no—
319#217—21no—
320#217—21no—
321#217—21no—
322#217—21no—
323#217—21no—
324#217—21no—
325#217—21no—
326#217—22no—
327#217—22no—
328#217—22no—
329#217—22no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—21no—
333(C2×D3)⋊C4—21no—
334(C2×D3)⋊C4—21no—
335(C2×D3)⋊C4—21no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—42no—
345C4⋊Dic3—42no—
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—44no—
359Dic3⋊C4—44no—
360C4×Dic3—21no—
361C4×Dic3—21no—
362C4×Dic3—44no—
363C4×Dic3—44no—
364C4×Dic3C22⋊C411yescharacteristic
365C4×Dic3C22⋊C411yescharacteristic
366C4×Dic3C22⋊C411yescharacteristic
367C4×Dic3C22⋊C411yescharacteristic
368C4×Dic3C22⋊C411yescharacteristic
369C4×Dic3C22⋊C411yescharacteristic
370C4×Dic3C22⋊C411yescharacteristic
371C4×Dic3C22⋊C411yescharacteristic
372C4×Dic3C22⋊C411yescharacteristic
373C4×Dic3C22⋊C411yescharacteristic
374C4×Dic3C22⋊C411yescharacteristic
375C4×Dic3C22⋊C411yescharacteristic
376C4×Dic3C22⋊C411yescharacteristic
377C4×Dic3C22⋊C411yescharacteristic
378C4×Dic3C22⋊C411yescharacteristic
379C4×Dic3C22⋊C411yescharacteristic
380C22×Q8—31no—
381C22×D4—31no—
382C22×D4—31no—
383C22×D4C22×D311yescharacteristic
384C23×C4—31no—
385C23×C4—31no—
386C23×C4—31no—
387C23×C4C4×D311yescharacteristic
388C23×C4C22×D311yescharacteristic
389#126—61no—
390#126—61no—
391#126—61no—
392#126—61no—
393#126—61no—
394#126—61no—
395#126—61no—
396#126—61no—
397#125—61no—
398#125—61no—
399#125—61no—
400#125—61no—
401#124—61no—
402#124—61no—
403#124—61no—
404#124—61no—
405#123—61no—
406#123—61no—
407#123—61no—
408#123—61no—
409#123—61no—
410#123—61no—
411#123—61no—
412#123—61no—
413C22⋊Q8—61no—
414C22⋊Q8—61no—
415C22⋊Q8—61no—
416C22⋊Q8—61no—
417#121—61no—
418#121—61no—
419#121—61no—
420#121—61no—
421C4×Q8—61no—
422C4×Q8—61no—
423C4×Q8—61no—
424C4×Q8—61no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—61no—
430C4×D4—61no—
431C4×D4—61no—
432C4×D4—61no—
433C4×D4—61no—
434C4×D4—61no—
435C4×D4—61no—
436C4×D4—61no—
437#117—61no—
438#117—61no—
439#117—61no—
440#117—61no—
441#117—61no—
442#117—61no—
443#117—61no—
444#117—61no—
445#117—122no—
446#117—122no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—31no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—62no—
459C2×C4⋊C4—62no—
460C2×C4⋊C4—61no—
461C2×C4⋊C4—61no—
462C2×C4⋊C4C4×D311yescharacteristic
463C2×C22⋊C4—31no—
464C2×C22⋊C4—31no—
465C2×C22⋊C4—31no—
466C2×C22⋊C4—31no—
467C2×C22⋊C4—31no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—32no—
472C2×C22⋊C4—32no—
473C2×C22⋊C4C4×D311yescharacteristic
474C2×C22⋊C4C22×D312yes—
475C2×C22⋊C4C22×D312yes—
476C2×C22⋊C4C22×D311yescharacteristic
477C2×C42—31no—
478C2×C42—31no—
479C2×C42—31no—
480C2×C42—31no—
481C2×C42—31no—
482C2×C42—31no—
483C2×C42—31no—
484C2×C42—31no—
485C2×C42—31no—
486C2×C42—31no—
487C2×C42—31no—
488C2×C42—31no—
489C2×C42—31no—
490C2×C42—62no—
491C2×C42—62no—
492C2×C42C4×D311yescharacteristic
493#99—42no—
494#99—122no—
495#99—122no—
496#99—122no—
497#95—21no—
498#95—21no—
499#95—62no—
500#95—62no—
501#95—62no—
502#95—62no—
503#95—61no—
504#95—61no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3C23×C411yescharacteristic
513C23×C3C22×D411yescharacteristic
514C23×C3C22×D411yescharacteristic
515C23×C3H(5,𝔽2)11yescharacteristic
516C23×C3H(5,𝔽2)11yescharacteristic
517C23×C32−1+411yescharacteristic
518C23×C32−1+411yescharacteristic
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—41no—
523C22×D3—41no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—41no—
527C3×D4—41no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—42no—
540C2×C3×C4—42no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—42no—
544C2×C3×C4—42no—
545C2×C3×C4—42no—
546C2×C3×C4—42no—
547C2×C3×C4—42no—
548C2×C3×C4—42no—
549C2×C3×C4C2×C22⋊C411yescharacteristic
550C2×C3×C4C2×C22⋊C411yescharacteristic
551C2×C3×C4C2×C22⋊C411yescharacteristic
552C2×C3×C4C2×C22⋊C411yescharacteristic
553#67—42no—
554#67—41no—
555#67—41no—
556#67—41no—
557#67—41no—
558#67—42no—
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—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—42no—
585C2×Dic3—42no—
586C2×Dic3—42no—
587C2×Dic3—42no—
588C2×Dic3—42no—
589C2×Dic3—42no—
590C2×Dic3C2×C22⋊C411yescharacteristic
591C2×Dic3C2×C22⋊C411yescharacteristic
592C2×Dic3C2×C22⋊C411yescharacteristic
593C2×Dic3C2×C22⋊C411yescharacteristic
594C2×Dic3C2×C22⋊C411yescharacteristic
595C2×Dic3C2×C22⋊C411yescharacteristic
596C2×Dic3C2×C22⋊C411yescharacteristic
597C2×Dic3C2×C22⋊C411yescharacteristic
598C4×D3—42no—
599C4×D3—42no—
600Dic6—42no—
601Dic6—42no—
602C24—31no—
603C24C2×C4×D311yescharacteristic
604C24C23×D311yescharacteristic
605C2×Q8—61no—
606C2×Q8—61no—
607C2×Q8—122no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—122no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—122no—
653C22×C4—122no—
654C22×C4C2×C4×D311yescharacteristic
655C22×C4C2×C4×D311yescharacteristic
656C22×C4C2×C4×D311yescharacteristic
657C22×C4C2×C4×D311yescharacteristic
658C22×C4C2×C4×D311yescharacteristic
659C22×C4D3×D411yescharacteristic
660C22×C4D3×D411yescharacteristic
661C22×C4D3×D411yescharacteristic
662C22×C4D3×D411yescharacteristic
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—61no—
673C4⋊C4—61no—
674C4⋊C4—61no—
675C4⋊C4—61no—
676C4⋊C4—61no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—61no—
685C4⋊C4—122no—
686C4⋊C4—122no—
687C4⋊C4—124no—
688C4⋊C4—124no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—62no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—62no—
717C42—21no—
718C42—21no—
719C42—31no—
720C42—31no—
721C42—31no—
722C42—31no—
723C42—31no—
724C42—31no—
725C42—31no—
726C42—31no—
727C42—31no—
728C42—31no—
729C42—31no—
730C42—31no—
731C42—31no—
732C42—31no—
733C42—31no—
734C42—31no—
735C42—61no—
736C42—61no—
737C42—124no—
738C42—124no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—81no—
753C22×C3—81no—
754C22×C3C22×C22⋊C411yescharacteristic
755C22×C3#52011yescharacteristic
756C22×C3#52011yescharacteristic
757C22×C3#53511yescharacteristic
758C22×C3#53611yescharacteristic
759C22×C3#53711yescharacteristic
760C22×C3#53711yescharacteristic
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—81no—
765C2×D3—81no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4—82no—
773C3×C4—82no—
774C3×C4#41012yes—
775Dic3—21no—
776Dic3—21no—
777Dic3—21no—
778Dic3—21no—
779Dic3—21no—
780Dic3—21no—
781Dic3—21no—
782Dic3—41no—
783Dic3—41no—
784Dic3—41no—
785Dic3—82no—
786Dic3—82no—
787Dic3#41012yes—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—61no—
796C23—61no—
797C23—61no—
798C23—121no—
799C23—121no—
800C23C22×C4×D311yescharacteristic
801C23C2×D3×D411yescharacteristic
802C23C2×D3×D411yescharacteristic
803C23#100411yescharacteristic
804C23#100711yescharacteristic
805C23#100911yescharacteristic
806C23#101011yescharacteristic
807Q8—122no—
808Q8—122no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—122no—
814D4—122no—
815D4—121no—
816D4—121no—
817D4—121no—
818D4—121no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—31no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—31no—
832C2×C4—31no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—122no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—121no—
872C2×C4—122no—
873C2×C4—121no—
874C2×C4—121no—
875C2×C4—122no—
876C2×C4—122no—
877C2×C4—122no—
878C2×C4—122no—
879C2×C4—122no—
880C2×C4—122no—
881C2×C4D3×C22⋊C411yescharacteristic
882C2×C4D3×C22⋊C411yescharacteristic
883C2×C4D3×C22⋊C411yescharacteristic
884C2×C4D3×C22⋊C411yescharacteristic
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—81no—
892C2×C3#231111yescharacteristic
893C2×C3C2×#41011yescharacteristic
894C2×C3C2×#41011yescharacteristic
895D3—81no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—81no—
910C22—81no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—241no—
915C22—241no—
916C22C2×D3×C22⋊C411yescharacteristic
917C22#550411yescharacteristic
918C22#552311yescharacteristic
919C22#560711yescharacteristic
920C22#560811yescharacteristic
921C22#562811yescharacteristic
922C22#562911yescharacteristic
923C4—21no—
924C4—21no—
925C4—21no—
926C4—32no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—61no—
931C4—61no—
932C4—61no—
933C4—61no—
934C4—61no—
935C4—61no—
936C4—61no—
937C4—82no—
938C4—82no—
939C4—121no—
940C4—121no—
941C4—121no—
942C4—242no—
943C4—242no—
944C4#474012yes—
945C3#2187511yescharacteristic, complemented, Sylow
946C2—21no—
947C2—21no—
948C2—21no—
949C2—21no—
950C2—21no—
951C2—21no—
952C2—81no—
953C2—241no—
954C2#7400311yescharacteristic
955C2C2×#474011yescharacteristic
956C2D3×#41011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1799C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#939C22
cosocleC24×C3C24
hypercenter#1799D3
hypocenterC3#21875
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #73864C2semidirect
3. #73863C2semidirect
4. C3×#1799C2semidirect
5. #71619C2semidirect
7. #70029C2semidirect
8. #69530C2semidirect
9. #69530C2semidirect
10. #68955C2semidirect
11. #68954C2semidirect
16. C2×C4×#67C4semidirect
18. C2×#926C4semidirect
28. C2×#898C4semidirect
29. C2×#889C4semidirect
31. C2×#885C4semidirect
32. C2×#879C4semidirect
35. C2×#872C4semidirect
36. C2×C4×Dic6C4semidirect
70. #1799D3semidirect
945. C3#21875semidirect

Maximal subgroups

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

subgroupindex
C2×#55382
#738642
#738632
C3×#17992
#716192
#700302
#700292
#695302
#689552
#689542
#218753