Finite Group Databasebeta

← #11805101

Subgroups — #11805101

Order 1152.

1193 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#877C211yesmaximal, characteristic
2C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic
3C3×Dic3×C22⋊C4C211yesmaximal, characteristic
4#10591719C211yesmaximal, characteristic
5#10591718C211yesmaximal, characteristic
6#10591696C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
9#10591223C211yesmaximal, characteristic, complemented
10#10591222C211yesmaximal, characteristic, complemented
11#10591206C211yesmaximal, characteristic, complemented
12#10591201C211yesmaximal, characteristic, complemented
13#10591201C211yesmaximal, characteristic, complemented
14#10591192C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#82237—31nomaximal
17#73455—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×#877C418yescomplemented
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42#63579C2211yescharacteristic
43#63579C2211yescharacteristic
44#63579C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×#117—31no—
55C2×#877D311yescharacteristic
56C3×C4×C22⋊C4—31no—
57#5211—31no—
58#5210—31no—
59C2×C3⋊#95—31no—
60C2×C3⋊#95—31no—
61#4980—31no—
62#4980—31no—
63#4980—31no—
64#4980—31no—
65#4950—31no—
66#4950—31no—
67#4946—31no—
68#4943—31no—
69Dic3×C22⋊C4—31no—
70Dic3×C22⋊C4—31no—
71Dic3×C22⋊C4—61no—
72Dic3×C22⋊C4D311yescharacteristic
73#4937—31no—
74#4936—31no—
75C4×C4⋊Dic3—31no—
76#4933—31no—
77#4933—31no—
78#4932—31no—
79#4932—31no—
80C4×Dic3⋊C4—31no—
81#4652—31no—
82#4652—31no—
83#4651—31no—
84#4650—31no—
85C24×C32C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3—22no—
89C22×C3⋊Dic3—22no—
90C22×C3⋊Dic3—41no—
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3×Dic3—22no—
96C22×C3×Dic3—22no—
97C22×C3×Dic3—22no—
98C22×C3×Dic3—22no—
99C22×C3×Dic3—41no—
100C22×C3×Dic3C2×C414yes—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C32×C22⋊C4C2×C414yes—
110#3757—22no—
111C4×C3⋊Dic3—22no—
112C4×C3⋊Dic3—41no—
113C3×#217—22no—
114C3×#217C2×C414yes—
115C3×Dic3⋊C4C2×C414yescomplemented
116C3×Dic3⋊C4C2×C414yescomplemented
117C3×C4×Dic3—22no—
118C3×C4×Dic3—41no—
119C3×C4×Dic3C2×C414yescomplemented
120C3×C4×Dic3C2×C414yescomplemented
121Dic3⋊Dic3—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125#2343—91noSylow
126C23×C3×C4—31no—
127C23×C3×C4—31no—
128C23×Dic3—31no—
129C23×Dic3—31no—
130C23×Dic3—61no—
131C23×Dic3C2×D311yescharacteristic
132C23×Dic3C2×D311yescharacteristic
133C3×#117—38no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4C2×D311yescharacteristic
140C2×C3×C22⋊C4C2×D311yescharacteristic
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×#217—31no—
146C2×#217—31no—
147C2×#217—61no—
148C2×#217C2×D311yescharacteristic
149C2×#217C2×D311yescharacteristic
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4C2×D311yescharacteristic
159C2×Dic3⋊C4C2×D311yescharacteristic
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—61no—
165C2×C4×Dic3—61no—
166C2×C4×Dic3C2×D311yescharacteristic
167C2×C4×Dic3C2×D311yescharacteristic
168C2×C4×Dic3C2×D311yescharacteristic
169C2×C4×Dic3C2×D311yescharacteristic
170#877Dic318yescomplemented
171C3×#95—31no—
172C3×#95—31no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—31no—
176C3⋊#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—61no—
202C3⋊#95—61no—
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32C22×C412yes—
210C23×C32#4112yes—
211C23×C32#4112yes—
212C23×C32C2411yescharacteristic
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4C22×C412yes—
218C2×C32×C4C22×C412yes—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—44no—
231C2×C3⋊Dic3#4112yes—
232C2×C3×Dic3—28no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
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×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
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—44no—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C22×C412yes—
255C2×C3×Dic3C22×C412yes—
256C2×C3×Dic3C22×C412yes—
257C2×C3×Dic3#4112yes—
258C2×#117—31no—
259#387—91no—
260#387—91no—
261#387—91no—
262#387—91no—
263#385—91no—
264#385—91no—
265#383—91no—
266#382—91no—
267#381—91no—
268C4×C4⋊C4—91no—
269C4×C22⋊C4—31no—
270C4×C22⋊C4—91no—
271#376—91no—
272C2×#95—91no—
273C24×C3—21no—
274C24×C3C22×D311yescharacteristic
275C24×C3C22×D311yescharacteristic
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—34no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—62no—
288C22×C3×C4—62no—
289C22×C3×C4—62no—
290C22×C3×C4—62no—
291C22×C3×C4—121no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—41no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—62no—
314C22×Dic3—62no—
315C22×Dic3—64no—
316C22×Dic3—62no—
317C22×Dic3—62no—
318C22×Dic3—122no—
319C22×Dic3—121no—
320C22×Dic3—121no—
321C22×Dic3—122no—
322C22×Dic3C2×Dic314yes—
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C3×C4⋊C4—34no—
332C3×C4⋊C4—34no—
333C3×C22⋊C4—24no—
334C3×C22⋊C4—34no—
335C3×C22⋊C4—62no—
336C3×C22⋊C4C4×D314yes—
337C3×C22⋊C4C2×Dic314yes—
338C3×C42—34no—
339C3×C42—34no—
340C3×C42—62no—
341C3×C42—121no—
342#217—22no—
343#217—64no—
344#217—62no—
345#217—62no—
346#217C2×Dic314yes—
347C4⋊Dic3—62no—
348C4⋊Dic3—62no—
349C4⋊Dic3—121no—
350C4⋊Dic3—121no—
351Dic3⋊C4—62no—
352Dic3⋊C4—62no—
353Dic3⋊C4—121no—
354Dic3⋊C4—121no—
355Dic3⋊C4C2×Dic314yescomplemented
356Dic3⋊C4C2×Dic314yescomplemented
357C4×Dic3—22no—
358C4×Dic3—41no—
359C4×Dic3—62no—
360C4×Dic3—62no—
361C4×Dic3—122no—
362C4×Dic3—121no—
363C4×Dic3—121no—
364C4×Dic3—122no—
365C4×Dic3C2×Dic314yescomplemented
366C4×Dic3C2×Dic314yescomplemented
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—22no—
372C22×C32—22no—
373C22×C32#11714yes—
374C22×C32C23×C411yescharacteristic
375C22×C32C2×#4111yescharacteristic
376C22×C32C2×#4111yescharacteristic
377C22×C32C2×#4111yescharacteristic
378C22×C32C2×#4111yescharacteristic
379C22×C32H(5,𝔽2)11yescharacteristic
380C22×C322−1+411yescharacteristic
381C32×C4—22no—
382C32×C4—22no—
383C3⋊Dic3—22no—
384C3⋊Dic3—41no—
385C3⋊Dic3—41no—
386C3⋊Dic3—41no—
387C3×Dic3—22no—
388C3×Dic3—22no—
389C3×Dic3—22no—
390C3×Dic3—22no—
391C3×Dic3—22no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C3×Dic3—41no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—91no—
398#117—38no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4—91no—
403C2×C4⋊C4—91no—
404C2×C4⋊C4—91no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4D3211yescharacteristic
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—31no—
413C2×C42—91no—
414C2×C42—91no—
415#95—31no—
416#95—31no—
417#95—91no—
418#95—91no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95—91no—
424#95—91no—
425#95—91no—
426#95—91no—
427#95—91no—
428#95—91no—
429#95—91no—
430#95—91no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3C2×C4×D312yes—
448C23×C3#23512yes—
449C23×C3#23512yes—
450C23×C3#23512yes—
451C23×C3#23512yes—
452C23×C3C22×Dic312yes—
453C23×C3C23×D311yescharacteristic
454C23×C3C23×D311yescharacteristic
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—32no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—68no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—124no—
495C2×C3×C4C2×C4×D312yes—
496C2×C3×C4C2×C4×D312yes—
497C2×C3×C4C22×Dic312yes—
498C2×C3×C4C22×Dic312yes—
499C2×Dic3—28no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—44no—
522C2×Dic3—62no—
523C2×Dic3—62no—
524C2×Dic3—62no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—62no—
530C2×Dic3—62no—
531C2×Dic3—62no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—121no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—121no—
555C2×Dic3—121no—
556C2×Dic3—124no—
557C2×Dic3—124no—
558C2×Dic3—128no—
559C2×Dic3#23712yes—
560C2×Dic3C22×Dic312yes—
561C2×Dic3C22×Dic312yes—
562C2×Dic3C22×Dic312yes—
563C2×Dic3C22×Dic312yes—
564C2×C32—24no—
565C2×C32C2×#11711yescharacteristic
566C2×C32C4×#4111yescharacteristic
567C2×C32#52011yescharacteristic
568C2×C32#55111yescharacteristic
569C2×C32#55111yescharacteristic
570C2×C32#55211yescharacteristic
571C2×C32#55211yescharacteristic
572C24C2×D3211yescharacteristic
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—34no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—62no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—91no—
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—91no—
590C22×C4—121no—
591C22×C4—182no—
592C22×C4—182no—
593C22×C4—361no—
594C22×C4C2×D3211yescharacteristic
595C22×C4C2×D3211yescharacteristic
596C4⋊C4—34no—
597C4⋊C4—34no—
598C4⋊C4—182no—
599C4⋊C4—182no—
600C4⋊C4—361no—
601C4⋊C4—361no—
602C22⋊C4—34no—
603C22⋊C4—62no—
604C22⋊C4—182no—
605C22⋊C4D3×Dic314yes—
606C42—34no—
607C42—34no—
608C42—62no—
609C42—121no—
610C42—182no—
611C42—361no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—24no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3#87214yes—
639C22×C3#92614yes—
640C22×C3C22×C4×D311yescharacteristic
641C22×C3C2×#23511yescharacteristic
642C22×C3C2×#23511yescharacteristic
643C22×C3C2×#23511yescharacteristic
644C22×C3C2×#23511yescharacteristic
645C22×C3C2×#23711yescharacteristic
646C22×C3#100411yescharacteristic
647C22×C3D3×#4111yescharacteristic
648C22×C3D3×#4111yescharacteristic
649C22×C3D3×#4111yescharacteristic
650C22×C3#100911yescharacteristic
651C22×C3#101011yescharacteristic
652C22×C3#101011yescharacteristic
653C22×C3C23×Dic311yescharacteristic
654C3×C4—22no—
655C3×C4—22no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—42no—
659C3×C4—42no—
660C3×C4—62no—
661C3×C4—62no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4—62no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668Dic3—22no—
669Dic3—22no—
670Dic3—22no—
671Dic3—22no—
672Dic3—22no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—64no—
677Dic3—62no—
678Dic3—62no—
679Dic3—122no—
680Dic3—122no—
681Dic3—122no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688C32#234311yescharacteristic, complemented, Sylow
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23#379812yes—
694C23#379812yes—
695C23C2×D3×Dic312yes—
696C23C22×D3211yescharacteristic
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—68no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—92no—
727C2×C4—124no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—364no—
740C2×C4C2×D3×Dic312yes—
741C2×C4C2×D3×Dic312yes—
742C2×C3—24no—
743C2×C3—24no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—44no—
752C2×C3C2×#87211yescharacteristic
753C2×C3#549511yescharacteristic
754C2×C3#552711yescharacteristic
755C2×C3#552711yescharacteristic
756C2×C3#553111yescharacteristic
757C2×C3#553111yescharacteristic
758C2×C3#553111yescharacteristic
759C2×C3C4×#23711yescharacteristic
760C2×C3#554111yescharacteristic
761C2×C3#554611yescharacteristic
762C2×C3#555611yescharacteristic
763C2×C3C2×#92611yescharacteristic
764C2×C3Dic3×#4111yescharacteristic
765C2×C3#582711yescharacteristic
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22#6385514yes—
773C22C2×#379811yescharacteristic
774C22C2×#379811yescharacteristic
775C22#6430911yescharacteristic
776C22D3×#23711yescharacteristic
777C22#6431211yescharacteristic
778C22#6431411yescharacteristic
779C22C22×D3×Dic311yescharacteristic
780C4—22no—
781C4—22no—
782C4—62no—
783C4—62no—
784C4—62no—
785C4—62no—
786C4—62no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—182no—
791C4—361no—
792C4—361no—
793C4—361no—
794C3—21no—
795C3#7345511yescharacteristic, complemented
796C3#8223711yescharacteristic, complemented
797C2—24no—
798C2#1059403711yescharacteristic
799C2#1059403911yescharacteristic
800C2#1059404011yescharacteristic
801C2#1059404611yescharacteristic
802C2C2×#6385511yescharacteristic
803C2Dic3×#23711yescharacteristic
804C2#1059522211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C4×Dic3⋊Dic3C2semidirect
9. #10591223C2semidirect
10. #10591222C2semidirect
11. #10591206C2semidirect
12. #10591201C2semidirect
13. #10591201C2semidirect
14. #10591192C2semidirect
15. #10591192C2semidirect
33. C3×#877C4semidirect
115. C3×Dic3⋊C4C2×C4semidirect
116. C3×Dic3⋊C4C2×C4semidirect
119. C3×C4×Dic3C2×C4semidirect
120. C3×C4×Dic3C2×C4semidirect
170. #877Dic3semidirect
355. Dic3⋊C4C2×Dic3semidirect
356. Dic3⋊C4C2×Dic3semidirect
365. C4×Dic3C2×Dic3semidirect
366. C4×Dic3C2×Dic3semidirect
688. C32#2343semidirect
795. C3#73455semidirect
796. C3#82237semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8772
C22⋊C4×C3⋊Dic32
C3×Dic3×C22⋊C42
#105917192
#105917182
#105916962
C2×#635792
C4×Dic3⋊Dic32
#105912232
#105912222
#105912062
#105912012
#105911922
#822373
#734553