Finite Group Databasebeta

← #11805121

Subgroups — #11805121

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×#63836C211yesmaximal, characteristic
2C4×#3752C211yesmaximal, characteristic
3C3×#4933C211yesmaximal, characteristic, complemented
4C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10591374C211yesmaximal, characteristic
6#10591371C211yesmaximal, characteristic
7#10591370C211yesmaximal, characteristic
8#10591334C211yesmaximal, characteristic, complemented
9#10591290C211yesmaximal, characteristic
10#10591254C211yesmaximal, characteristic, complemented
11#10591252C211yesmaximal, characteristic, complemented
12#10591245C211yesmaximal, characteristic, complemented
13#10591233C211yesmaximal, characteristic
14#10591223C211yesmaximal, characteristic, complemented
15#10591201C211yesmaximal, characteristic, complemented
16#75304—31nomaximal
17#73766—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37#63836C418yescomplemented
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#892—31no—
55C2×#872—31no—
56C3×#387—31no—
57C3×C4×C4⋊C4—31no—
58#4989—31no—
59#4989—31no—
60#4989—31no—
61#4980—31no—
62#4978—31no—
63#4978—31no—
64#4977—31no—
65C4×(C2×D3)⋊C4—31no—
66C4×(C2×D3)⋊C4—31no—
67C4×(C2×D3)⋊C4—31no—
68C4×(C2×D3)⋊C4—61no—
69#4937—31no—
70#4933—31no—
71#4933D311yescharacteristic, complemented
72C4×Dic3⋊C4D311yescharacteristic, complemented
73#4668—31no—
74#4666—31no—
75#4664—31no—
76#4664—31no—
77D3×#95—31no—
78D3×#95—31no—
79#4654—31no—
80#4653—31no—
81#4651—31no—
82#4650—31no—
83#4648—31no—
84#4648—31no—
85C23×C3⋊D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C2×C4×C3⋊D3—22no—
93C2×C4×C3⋊D3—22no—
94C2×C4×C3⋊D3—41no—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×#624—22no—
104C2×#624—22no—
105C2×#624—22no—
106C2×#624—22no—
107C2×#624—41no—
108C2×#624C2×C414yes—
109C32×C42—41no—
110#3752—22no—
111#3752C2×C414yes—
112C4×C3⋊Dic3—22no—
113C3×Dic3⋊C4—22no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—41no—
116C3×Dic3⋊C4C2×C414yescomplemented
117C3×C4×Dic3—41no—
118C3×C4×Dic3C2×C414yescomplemented
119Dic3⋊Dic3—41no—
120Dic3⋊Dic3C2×C414yescomplemented
121#3722—22no—
122#3722C2×C414yes—
123Dic32—22no—
124Dic32C2×C414yescomplemented
125#2343—91noSylow
126C22×C4×D3—31no—
127C22×C4×D3—31no—
128C22×C4×D3—31no—
129C22×C4×D3—31no—
130C22×C4×D3—31no—
131C22×C4×D3—31no—
132C22×C4×D3—61no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C42—21no—
138C2×C3×C42—31no—
139C2×C3×C42—31no—
140C2×C3×C42C2×D311yescharacteristic
141C2×C3×C42C2×D311yescharacteristic
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—61no—
151C2×(C2×D3)⋊C4—61no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4C2×D311yescharacteristic
157C2×Dic3⋊C4C2×D311yescharacteristic
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—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—61no—
167C2×C4×Dic3C2×D311yescharacteristic
168C2×C4×Dic3C2×D311yescharacteristic
169#892—38no—
170#872—38no—
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—61no—
198C3⋊#95—61no—
199C3⋊#95C2×D311yescharacteristic
200C3⋊#95C2×D311yescharacteristic
201C3⋊#95C2×D311yescharacteristic
202C3⋊#95C2×D311yescharacteristic
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—21no—
207C22×C3⋊D3—21no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3C22×C412yes—
211C22×C3⋊D3#4112yes—
212C22×C3⋊D3#4112yes—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4C22×C412yes—
221C2×C32×C4#4112yes—
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⋊Dic3C22×C412yes—
231C4×C3⋊D3—44no—
232C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C22×C412yes—
255C2×C3×Dic3#4112yes—
256#624—28no—
257#624—44no—
258C2×#117—91no—
259#387—31no—
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—31no—
269C4×C22⋊C4—91no—
270C4×C22⋊C4—91no—
271#376—91no—
272C2×#95—91no—
273C23×D3—31no—
274C23×D3—31no—
275C23×D3—61no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
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×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3—61no—
302C22×Dic3C22×D311yescharacteristic
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C2×C4×D3—34no—
311C2×C4×D3—34no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C2×C4×D3—62no—
315C2×C4×D3—62no—
316C2×C4×D3—62no—
317C2×C4×D3—62no—
318C2×C4×D3—62no—
319C2×C4×D3—62no—
320C2×C4×D3—62no—
321C2×C4×D3—64no—
322C2×C4×D3—62no—
323C2×C4×D3—62no—
324C2×C4×D3—62no—
325C2×C4×D3—122no—
326C2×C4×D3—121no—
327C2×C4×D3—121no—
328C2×C4×D3—121no—
329C2×C4×D3—121no—
330C2×C4×D3—122no—
331C3×C4⋊C4—34no—
332C3×C4⋊C4—62no—
333C3×C4⋊C4—62no—
334C3×C4⋊C4—121no—
335C3×C42—34no—
336C3×C42—41no—
337C3×C42—41no—
338C3×C42—42no—
339C3×C42—121no—
340(C2×D3)⋊C4—34no—
341(C2×D3)⋊C4—34no—
342(C2×D3)⋊C4—34no—
343(C2×D3)⋊C4—34no—
344(C2×D3)⋊C4—64no—
345(C2×D3)⋊C4—62no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—62no—
348(C2×D3)⋊C4—62no—
349(C2×D3)⋊C4—64no—
350C4⋊Dic3—34no—
351C4⋊Dic3—121no—
352Dic3⋊C4—22no—
353Dic3⋊C4—22no—
354Dic3⋊C4—34no—
355Dic3⋊C4—41no—
356Dic3⋊C4—121no—
357Dic3⋊C4C4×D314yescomplemented
358C4×Dic3—34no—
359C4×Dic3—34no—
360C4×Dic3—41no—
361C4×Dic3—62no—
362C4×Dic3—62no—
363C4×Dic3—62no—
364C4×Dic3—62no—
365C4×Dic3—122no—
366C4×Dic3C4×D314yescomplemented
367C22×C32C23×C411yescharacteristic
368C22×C32C2×#4111yescharacteristic
369C22×C32C2×#4111yescharacteristic
370C22×C32C2×#4111yescharacteristic
371C22×C32C2×#4111yescharacteristic
372C22×C32H(5,𝔽2)11yescharacteristic
373C22×C322−1+411yescharacteristic
374C2×C3⋊D3—22no—
375C2×C3⋊D3—22no—
376C2×C3⋊D3—22no—
377C2×C3⋊D3—22no—
378C2×C3⋊D3—22no—
379C2×C3⋊D3—22no—
380C2×C3⋊D3#11714yes—
381C32×C4—22no—
382C32×C4—22no—
383C32×C4—41no—
384C3⋊Dic3—22no—
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—91no—
396C23×C4—91no—
397C23×C4—91no—
398#117—98no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—91no—
404C2×C4⋊C4—91no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—91no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—91no—
412C2×C42—91no—
413C2×C42—91no—
414C2×C42D3211yescharacteristic
415#95—31no—
416#95—31no—
417#95—31no—
418#95—31no—
419#95—31no—
420#95—31no—
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×C3C23×D311yescharacteristic
433C23×C3C23×D311yescharacteristic
434C22×D3—32no—
435C22×D3—32no—
436C22×D3—32no—
437C22×D3—32no—
438C22×D3—32no—
439C22×D3—32no—
440C22×D3—62no—
441C22×D3—62no—
442C22×D3—62no—
443C22×D3—61no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—61no—
447C22×D3—61no—
448C22×D3—61no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—121no—
452C22×D3—121no—
453C22×D3—121no—
454C22×D3—121no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
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—21no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—32no—
475C2×C3×C4—32no—
476C2×C3×C4—32no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
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—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4C2×C4×D312yes—
503C2×C3×C4C2×C4×D312yes—
504C2×C3×C4#23512yes—
505C2×C3×C4#23912yes—
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—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—32no—
526C2×Dic3—32no—
527C2×Dic3—62no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—62no—
533C2×Dic3—62no—
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—121no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—121no—
552C2×Dic3C2×C4×D312yes—
553C2×Dic3C2×C4×D312yes—
554C2×Dic3C2×C4×D312yes—
555C2×Dic3C2×C4×D312yes—
556C2×Dic3#23512yes—
557C4×D3—68no—
558C4×D3—68no—
559C4×D3—124no—
560C4×D3—124no—
561C4×D3—124no—
562C4×D3—124no—
563C4×D3—128no—
564C2×C32C2×#11711yescharacteristic
565C2×C32C4×#4111yescharacteristic
566C2×C32#52011yescharacteristic
567C2×C32#55111yescharacteristic
568C2×C32#55111yescharacteristic
569C2×C32#55211yescharacteristic
570C2×C32#55211yescharacteristic
571C3⋊D3—24no—
572C24—91no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—94no—
582C22×C4—91no—
583C22×C4—91no—
584C22×C4—91no—
585C22×C4—182no—
586C22×C4—182no—
587C22×C4—182no—
588C22×C4—182no—
589C22×C4—182no—
590C22×C4—182no—
591C22×C4—361no—
592C22×C4—361no—
593C22×C4C2×D3211yescharacteristic
594C22×C4C2×D3211yescharacteristic
595C22×C4C2×D3211yescharacteristic
596C4⋊C4—34no—
597C4⋊C4—62no—
598C4⋊C4—62no—
599C4⋊C4—94no—
600C4⋊C4—121no—
601C4⋊C4—361no—
602C22⋊C4—94no—
603C22⋊C4—94no—
604C22⋊C4—182no—
605C22⋊C4—182no—
606C42—34no—
607C42—41no—
608C42—94no—
609C42—121no—
610C42—182no—
611C42—182no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3C22×C4×D311yescharacteristic
620C22×C3C22×C4×D311yescharacteristic
621C22×C3C2×#23511yescharacteristic
622C22×C3C2×#23511yescharacteristic
623C22×C3#100411yescharacteristic
624C22×C3#100411yescharacteristic
625C22×C3C2×#23911yescharacteristic
626C22×C3#100711yescharacteristic
627C22×C3D3×#4111yescharacteristic
628C22×C3D3×#4111yescharacteristic
629C22×C3D3×#4111yescharacteristic
630C22×C3D3×#4111yescharacteristic
631C22×C3D3×#4111yescharacteristic
632C22×C3#101011yescharacteristic
633C2×D3—34no—
634C2×D3—34no—
635C2×D3—64no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—62no—
641C2×D3—62no—
642C2×D3—62no—
643C2×D3—62no—
644C2×D3—62no—
645C2×D3—62no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—122no—
649C2×D3—122no—
650C2×D3—122no—
651C2×D3—122no—
652C2×D3—122no—
653C2×D3—122no—
654C3×C4—24no—
655C3×C4—22no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—62no—
664C3×C4—62no—
665C3×C4—62no—
666C3×C4—62no—
667C3×C4—62no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671Dic3—22no—
672Dic3—22no—
673Dic3—22no—
674Dic3—22no—
675Dic3—22no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—62no—
681Dic3—122no—
682Dic3—122no—
683Dic3—122no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688C32#234311yescharacteristic, complemented, Sylow
689C23—92no—
690C23—92no—
691C23—92no—
692C23—181no—
693C23—181no—
694C23—181no—
695C23—181no—
696C23C22×D3211yescharacteristic
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—32no—
708C2×C4—32no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
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—61no—
727C2×C4—61no—
728C2×C4—92no—
729C2×C4—188no—
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—364no—
739C2×C4—364no—
740C2×C4#379912yes—
741C2×C4C4×D3212yes—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3C4×#23511yescharacteristic
750C2×C3#550411yescharacteristic
751C2×C3D3×#11711yescharacteristic
752C2×C3D3×#11711yescharacteristic
753C2×C3#554611yescharacteristic
754C2×C3#555611yescharacteristic
755C2×C3#555611yescharacteristic
756C2×C3C4×#23911yescharacteristic
757C2×C3#558111yescharacteristic
758C2×C3#558111yescharacteristic
759C2×C3#563711yescharacteristic
760C2×C3#565911yescharacteristic
761C2×C3#569411yescharacteristic
762C2×C3#570811yescharacteristic
763D3—64no—
764D3—64no—
765D3—124no—
766C22—94no—
767C22—182no—
768C22—182no—
769C22—182no—
770C22—182no—
771C22—182no—
772C22—182no—
773C22#6429711yescharacteristic
774C22C2×#379911yescharacteristic
775C22C2×C4×D3211yescharacteristic
776C22D3×#23511yescharacteristic
777C22#6430611yescharacteristic
778C22#6430611yescharacteristic
779C22#6433011yescharacteristic
780C4—22no—
781C4—22no—
782C4—41no—
783C4—62no—
784C4—62no—
785C4—62no—
786C4—62no—
787C4—62no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—182no—
792C4—361no—
793C4—361no—
794C3—21no—
795C3#7376611yescharacteristic, complemented
796C3#7530411yescharacteristic, complemented
797C2—184no—
798C2#1059393311yescharacteristic
799C2#1059394711yescharacteristic
800C2C4×#379911yescharacteristic
801C2#1059399211yescharacteristic
802C2#1059487411yescharacteristic
803C2#1059503511yescharacteristic
804C2#1059508811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×#4933C2semidirect
4. C3×C4×Dic3⋊C4C2semidirect
8. #10591334C2semidirect
10. #10591254C2semidirect
11. #10591252C2semidirect
12. #10591245C2semidirect
14. #10591223C2semidirect
15. #10591201C2semidirect
37. #63836C4semidirect
71. #4933D3semidirect
72. C4×Dic3⋊C4D3semidirect
116. C3×Dic3⋊C4C2×C4semidirect
118. C3×C4×Dic3C2×C4semidirect
120. Dic3⋊Dic3C2×C4semidirect
124. Dic32C2×C4semidirect
357. Dic3⋊C4C4×D3semidirect
366. C4×Dic3C4×D3semidirect
688. C32#2343semidirect
795. C3#73766semidirect
796. C3#75304semidirect

Maximal subgroups

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

subgroupindex
C2×#638362
C4×#37522
C3×#49332
C3×C4×Dic3⋊C42
#105913742
#105913712
#105913702
#105913342
#105912902
#105912542
#105912522
#105912452
#105912332
#105912232
#105912012
#753043
#737663