Finite Group Databasebeta

← #11805614

Subgroups — #11805614

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63838C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic
3C2×#63837C211yesmaximal, characteristic
4#10592346C211yesmaximal, characteristic
5C3×#4650C211yesmaximal, characteristic
6C3×#4647C211yesmaximal, characteristic
7#10591268C211yesmaximal, characteristic
8Dic3×C4⋊Dic3C211yesmaximal, characteristic
9#10591264C211yesmaximal, characteristic
10#10591247C211yesmaximal, characteristic
11#10591246C211yesmaximal, characteristic
12#10591245C211yesmaximal, characteristic
13#10591243C211yesmaximal, characteristic
14#10591241C211yesmaximal, characteristic
15#10591234C211yesmaximal, characteristic
16#75982—31nomaximal
17#74157—31nomaximal
18C22×#627C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63838—24no—
44#63837—24no—
45#63837C418yescomplemented
46C32×#95C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#887—31no—
57C2×#887—31no—
58C2×#887—31no—
59C2×#887—31no—
60C2×C4×Dic6—31no—
61C2×C4×Dic6—31no—
62C3×#389—31no—
63C3×#382—31no—
64#4984—31no—
65#4977—31no—
66#4976—31no—
67#4976—31no—
68Dic3×C4⋊C4—31no—
69Dic3×C4⋊C4—31no—
70#4972—31no—
71#4972—31no—
72C4×C4⋊Dic3—31no—
73C4×Dic3⋊C4—31no—
74#4650—31no—
75#4650—31no—
76#4650—31no—
77#4650D311yescharacteristic
78#4649—31no—
79#4649—31no—
80#4647—31no—
81#4647—31no—
82#4647—31no—
83#4647—31no—
84#4647—31no—
85#4647—61no—
86#4647D311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×#627C2×C414yes—
103C2×#627D414yes—
104C2×#627Q814yes—
105C4⋊(C3⋊Dic3)—22no—
106#3750—22no—
107#3750—22no—
108#3750C2×C414yes—
109C4×C3⋊Dic3—22no—
110C3×C4⋊Dic3—22no—
111C3×Dic3⋊C4—22no—
112C3×Dic3⋊C4—22no—
113C3×Dic3⋊C4—22no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4C2×C414yes—
116C3×C4×Dic3—22no—
117C3×C4×Dic3C2×C414yes—
118#3724—22no—
119#3724—22no—
120Dic3⋊Dic3—22no—
121Dic3⋊Dic3—22no—
122Dic3⋊Dic3C2×C414yes—
123Dic32—22no—
124Dic32—22no—
125Dic32—22no—
126Dic32—22no—
127Dic32C2×C414yes—
128Dic32C2×C414yes—
129#2351—91noSylow
130C22×Dic6—31no—
131C22×Dic6—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C42—31no—
139C2×C3×C42—31no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—61no—
146C2×C4⋊Dic3C2×D311yescharacteristic
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—61no—
161C2×Dic3⋊C4—61no—
162C2×Dic3⋊C4—61no—
163C2×Dic3⋊C4C2×D311yescharacteristic
164C2×Dic3⋊C4C2×D311yescharacteristic
165C2×Dic3⋊C4C2×D311yescharacteristic
166C2×Dic3⋊C4C2×D311yescharacteristic
167C2×Dic3⋊C4C2×D311yescharacteristic
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—61no—
183C2×C4×Dic3C2×D311yescharacteristic
184C2×C4×Dic3C2×D311yescharacteristic
185#887—38no—
186#887—64no—
187#887—64no—
188#887—64no—
189C4×Dic6—38no—
190C4×Dic6—64no—
191C3×#95—21no—
192C3×#95—31no—
193C3×#95—31no—
194C3×#95—31no—
195C3×#95—31no—
196C3×#95C2×D311yescharacteristic
197C3×#95C2×D311yescharacteristic
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—61no—
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C23×C32C2411yescharacteristic
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×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4C22×C412yes—
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—
231C2×C3⋊Dic3C22×C412yes—
232C2×C3⋊Dic3C2×D412yes—
233C2×C3⋊Dic3C2×Q812yes—
234C2×C3⋊Dic3#4112yes—
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×Dic3C22×C412yes—
251C2×C3×Dic3C22×C412yes—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C2×D412yes—
255C2×C3×Dic3C2×D412yes—
256C2×C3×Dic3C2×Q812yes—
257C2×C3×Dic3C2×Q812yes—
258C2×C3×Dic3#4112yes—
259#627C4⋊C4116yescomplemented
260C2×C4×Q8—91no—
261C2×C4×Q8—91no—
262C2×C4×Q8—91no—
263#389—31no—
264#389—91no—
265#389—91no—
266#389—91no—
267#389—91no—
268#389—91no—
269#382—31no—
270#382—91no—
271#382—91no—
272C4×C4⋊C4—91no—
273C4×C4⋊C4—91no—
274C4×C4⋊C4—91no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—31no—
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×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C2×Dic6—34no—
313C2×Dic6—34no—
314C2×Dic6—34no—
315C2×Dic6—34no—
316C2×Dic6—34no—
317C2×Dic6—34no—
318C3×C4⋊C4—34no—
319C3×C4⋊C4—62no—
320C3×C4⋊C4—62no—
321C3×C4⋊C4—62no—
322C3×C4⋊C4—62no—
323C3×C4⋊C4—62no—
324C3×C42—34no—
325C3×C42—62no—
326C4⋊Dic3—22no—
327C4⋊Dic3—34no—
328C4⋊Dic3—62no—
329C4⋊Dic3—62no—
330C4⋊Dic3—62no—
331C4⋊Dic3—62no—
332C4⋊Dic3—122no—
333Dic3⋊C4—22no—
334Dic3⋊C4—22no—
335Dic3⋊C4—22no—
336Dic3⋊C4—22no—
337Dic3⋊C4—34no—
338Dic3⋊C4—34no—
339Dic3⋊C4—34no—
340Dic3⋊C4—64no—
341Dic3⋊C4—62no—
342Dic3⋊C4—62no—
343Dic3⋊C4—62no—
344Dic3⋊C4—62no—
345Dic3⋊C4—62no—
346Dic3⋊C4—62no—
347Dic3⋊C4—62no—
348Dic3⋊C4—62no—
349Dic3⋊C4—62no—
350Dic3⋊C4—62no—
351Dic3⋊C4—122no—
352Dic3⋊C4—122no—
353Dic3⋊C4C4×D314yes—
354C4×Dic3—22no—
355C4×Dic3—34no—
356C4×Dic3—34no—
357C4×Dic3—34no—
358C4×Dic3—34no—
359C4×Dic3—62no—
360C4×Dic3—62no—
361C4×Dic3—62no—
362C4×Dic3—62no—
363C4×Dic3—62no—
364C4×Dic3—62no—
365C4×Dic3—62no—
366C4×Dic3—62no—
367C4×Dic3—62no—
368C4×Dic3—62no—
369C4×Dic3—122no—
370C4×Dic3C4×D314yes—
371C22×C32C23×C411yescharacteristic
372C22×C32C22×D411yescharacteristic
373C22×C32C22×Q811yescharacteristic
374C22×C32C2×#4111yescharacteristic
375C22×C32C2×#4111yescharacteristic
376C22×C322−1+411yescharacteristic
377C22×C322−1+411yescharacteristic
378C32×C4—22no—
379C32×C4—41no—
380C32×C4—41no—
381C3⋊Dic3—22no—
382C3⋊Dic3—22no—
383C3⋊Dic3—41no—
384C3⋊Dic3C2×C4⋊C414yes—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C3×Dic3C2×C4⋊C414yes—
392C3×Dic3C2×C4⋊C414yes—
393C22×Q8—91no—
394C4×Q8—98no—
395C4×Q8—184no—
396C4×Q8—184no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
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×C4⋊C4—91no—
406C2×C4⋊C4—91no—
407C2×C4⋊C4—91no—
408C2×C4⋊C4—91no—
409C2×C4⋊C4—91no—
410C2×C4⋊C4—91no—
411C2×C4⋊C4—91no—
412C2×C42—31no—
413C2×C42—31no—
414C2×C42—91no—
415C2×C42—91no—
416C2×C42—91no—
417C2×C42—91no—
418C2×C42—91no—
419C2×C42—91no—
420C2×C42—91no—
421#95—31no—
422#95—31no—
423#95—31no—
424#95—31no—
425#95—91no—
426#95—91no—
427#95—91no—
428#95—91no—
429#95—91no—
430#95D3211yescharacteristic
431C23×C3—21no—
432C23×C3C23×D311yescharacteristic
433C23×C3C23×D311yescharacteristic
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—32no—
456C2×C3×C4—32no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—32no—
460C2×C3×C4—32no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
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×C4C2×C4×D312yes—
484C2×C3×C4C2×C4×D312yes—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—32no—
501C2×Dic3—32no—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—32no—
505C2×Dic3—32no—
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—32no—
509C2×Dic3—32no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—62no—
513C2×Dic3—62no—
514C2×Dic3—62no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3C2×C4×D312yes—
537C2×Dic3C2×C4×D312yes—
538C2×Dic3C2×C4×D312yes—
539C2×Dic3C2×C4×D312yes—
540C2×Dic3D3×D412yes—
541C2×Dic3D3×D412yes—
542C2×Dic3#23712yes—
543C2×Dic3D3×Q812yes—
544C2×Dic3D3×Q812yes—
545Dic6—316no—
546Dic6—316no—
547C2×C32C22×C4⋊C411yescharacteristic
548C2×C32C4×#4111yescharacteristic
549C2×C32#51911yescharacteristic
550C2×C32#54811yescharacteristic
551C2×C32#54811yescharacteristic
552C2×C32#55711yescharacteristic
553C2×C32#55711yescharacteristic
554C2×Q8—94no—
555C2×Q8—94no—
556C2×Q8—94no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—91no—
566C22×C4—91no—
567C22×C4—91no—
568C22×C4—91no—
569C22×C4C2×D3211yescharacteristic
570C22×C4C2×D3211yescharacteristic
571C22×C4C2×D3211yescharacteristic
572C4⋊C4—34no—
573C4⋊C4—62no—
574C4⋊C4—62no—
575C4⋊C4—62no—
576C4⋊C4—62no—
577C4⋊C4—62no—
578C4⋊C4—94no—
579C4⋊C4—94no—
580C4⋊C4—182no—
581C4⋊C4—182no—
582C4⋊C4—182no—
583C4⋊C4—182no—
584C4⋊C4—182no—
585C4⋊C4—182no—
586C4⋊C4—182no—
587C42—34no—
588C42—62no—
589C42—94no—
590C42—94no—
591C42—182no—
592C42—182no—
593C42—182no—
594C42—182no—
595C42—182no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3C22×C4×D311yescharacteristic
604C22×C3C22×C4×D311yescharacteristic
605C22×C3C2×D3×D411yescharacteristic
606C22×C3C2×D3×D411yescharacteristic
607C22×C3C2×#23711yescharacteristic
608C22×C3C2×D3×Q811yescharacteristic
609C22×C3C2×D3×Q811yescharacteristic
610C22×C3#100711yescharacteristic
611C22×C3D3×#4111yescharacteristic
612C22×C3D3×#4111yescharacteristic
613C22×C3D3×#4111yescharacteristic
614C22×C3#101011yescharacteristic
615C22×C3#101011yescharacteristic
616C22×C3#101011yescharacteristic
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—34no—
620C3×C4—34no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—62no—
628C3×C4—62no—
629C3×C4—62no—
630C3×C4—81no—
631C3×C4—121no—
632C3×C4—121no—
633C3×C4—121no—
634Dic3—22no—
635Dic3—22no—
636Dic3—22no—
637Dic3—34no—
638Dic3—34no—
639Dic3—41no—
640Dic3—41no—
641Dic3—41no—
642Dic3—64no—
643Dic3—62no—
644Dic3—62no—
645Dic3—62no—
646Dic3—62no—
647Dic3—122no—
648Dic3—122no—
649Dic3—121no—
650Dic3—121no—
651Dic3—241no—
652Dic3D3×C4⋊C414yes—
653Dic3D3×C4⋊C414yes—
654C32#235111yescharacteristic, complemented, Sylow
655C23C22×D3211yescharacteristic
656Q8—916no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—32no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—92no—
690C2×C4—92no—
691C2×C4—92no—
692C2×C4—92no—
693C2×C4—92no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4—181no—
698C2×C4—181no—
699C2×C4—181no—
700C2×C4—181no—
701C2×C4C4×D3212yes—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3C2×D3×C4⋊C411yescharacteristic
710C2×C3C2×D3×C4⋊C411yescharacteristic
711C2×C3#551611yescharacteristic
712C2×C3#552211yescharacteristic
713C2×C3C4×#23711yescharacteristic
714C2×C3#557211yescharacteristic
715C2×C3#559811yescharacteristic
716C2×C3#563311yescharacteristic
717C2×C3#567711yescharacteristic
718C2×C3#567711yescharacteristic
719C2×C3#568511yescharacteristic
720C2×C3#568511yescharacteristic
721C2×C3#568511yescharacteristic
722C2×C3#572111yescharacteristic
723C22#6429711yescharacteristic
724C22#6429811yescharacteristic
725C22C2×C4×D3211yescharacteristic
726C22D32×D411yescharacteristic
727C22D3×#23711yescharacteristic
728C22#6431211yescharacteristic
729C22D32×Q811yescharacteristic
730C4—22no—
731C4—34no—
732C4—34no—
733C4—41no—
734C4—41no—
735C4—62no—
736C4—62no—
737C4—62no—
738C4—94no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—182no—
743C4—182no—
744C4—361no—
745C3—21no—
746C3#7415711yescharacteristic, complemented
747C3#7598211yescharacteristic, complemented
748C2#1059388511yescharacteristic
749C2#1059404811yescharacteristic
750C2#1059407511yescharacteristic
751C2#1059407611yescharacteristic
752C2#1059431411yescharacteristic
753C2#1059431511yescharacteristic
754C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2351
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
45. #63837C4semidirect
259. #627C4⋊C4semidirect
654. C32#2351semidirect
746. C3#74157semidirect
747. C3#75982semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
C2×#638372
#105923462
C3×#46502
C3×#46472
#105912682
Dic3×C4⋊Dic32
#105912642
#105912472
#105912462
#105912452
#105912432
#105912412
#105912342
#759823
#741573