Finite Group Databasebeta

← #11808849

Subgroups — #11808849

Order 1152.

1099 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63844C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic
3#10592678C211yesmaximal, characteristic
4C3×#4982C211yesmaximal, characteristic
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic
6#10591356C211yesmaximal, characteristic
7#10591354C211yesmaximal, characteristic
8#10591345C211yesmaximal, characteristic
9#10591338C211yesmaximal, characteristic
10#10591338C211yesmaximal, characteristic
11#10591243C211yesmaximal, characteristic
12#10591242C211yesmaximal, characteristic
13Dic3×Dic3⋊C4C211yesmaximal, characteristic
14#10591239C211yesmaximal, characteristic
15#10591198C211yesmaximal, characteristic
16#77740—31nomaximal
17#73669—31nomaximal
18C22×#634C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×#3724C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63844—24no—
42#63837—24no—
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#887—31no—
56C2×#887—31no—
57C2×C4×Dic6—31no—
58C2×C4×Dic6—31no—
59C3×#398—31no—
60C3×C4×C4⋊C4—31no—
61#4983—31no—
62#4982—31no—
63#4982D311yescharacteristic
64#4979—31no—
65#4979—31no—
66#4979—31no—
67#4979—31no—
68#4979—31no—
69#4979—61no—
70Dic3×C4⋊C4—31no—
71Dic3×C4⋊C4D311yescharacteristic
72C4×C4⋊Dic3—31no—
73#4932—31no—
74C4×Dic3⋊C4—31no—
75C4×Dic3⋊C4—31no—
76#4657—31no—
77#4657—31no—
78#4657—31no—
79#4657—31no—
80#4656—31no—
81#4656—31no—
82#4656—31no—
83#4649—31no—
84#4649—31no—
85#4648—31no—
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×#634—22no—
94C2×#634—22no—
95C2×#634—22no—
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×#627—22no—
105C2×#627—22no—
106C2×#627—22no—
107C32×C4⋊C4—22no—
108#3750—22no—
109#3750—22no—
110C3×C4⋊Dic3—22no—
111C3×C4⋊Dic3—22no—
112C3×Dic3⋊C4—22no—
113C3×Dic3⋊C4—22no—
114C3×C4×Dic3—22no—
115C3×C4×Dic3—22no—
116C3×C4×Dic3Q814yescomplemented
117#3724—22no—
118#3724—22no—
119#3724—22no—
120Dic3⋊Dic3—22no—
121Dic3⋊Dic3—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—22no—
124Dic32—22no—
125Dic32—22no—
126Dic32D414yes—
127Dic32Q814yescomplemented
128#2399—91noSylow
129C22×Dic6—31no—
130C22×Dic6—31no—
131C22×Dic6—31no—
132C22×Dic6—31no—
133C22×Dic6—61no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4C2×D311yescharacteristic
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3C2×D311yescharacteristic
149C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—61no—
165C2×Dic3⋊C4—61no—
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×Dic3C2×D311yescharacteristic
177C2×C4×Dic3C2×D311yescharacteristic
178C2×C4×Dic3C2×D311yescharacteristic
179#887—64no—
180#887—64no—
181C4×Dic6—64no—
182C4×Dic6—64no—
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—31no—
202C3⋊#95—61no—
203C3⋊#95—61no—
204C3⋊#95—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C23×C32C2411yescharacteristic
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4C2×Q812yes—
219C2×C32×C4#4112yes—
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⋊Dic3C2×D412yes—
229C2×C3⋊Dic3C2×Q812yes—
230C2×C3⋊Dic3#4112yes—
231C2×C3⋊Dic3#4112yes—
232#634—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×Dic3C2×D412yes—
251C2×C3×Dic3C2×D412yes—
252C2×C3×Dic3C2×Q812yes—
253C2×C3×Dic3C2×Q812yes—
254C2×C3×Dic3C2×Q812yes—
255C2×C3×Dic3C2×Q812yes—
256C2×C3×Dic3#4112yes—
257#627—28no—
258C2×C4×Q8—91no—
259C2×C4×Q8—91no—
260#398—31no—
261#398—91no—
262#398—91no—
263#398—91no—
264#395—91no—
265#395—91no—
266#395—91no—
267#395—91no—
268C4×C4⋊C4—31no—
269C4×C4⋊C4—91no—
270C4×C4⋊C4—91no—
271C4×C4⋊C4—91no—
272#376—91no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
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×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—61no—
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×Dic6—62no—
311C2×Dic6—62no—
312C2×Dic6—62no—
313C2×Dic6—62no—
314C2×Dic6—62no—
315C2×Dic6—62no—
316C2×Dic6—62no—
317C2×Dic6—62no—
318C2×Dic6—62no—
319C2×Dic6—62no—
320C2×Dic6—62no—
321C2×Dic6—62no—
322C2×Dic6—122no—
323C2×Dic6—122no—
324C2×Dic6—122no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—22no—
327C3×C4⋊C4—42no—
328C3×C4⋊C4—62no—
329C3×C4⋊C4—62no—
330C3×C4⋊C4—62no—
331C3×C4⋊C4—62no—
332C3×C42—34no—
333C3×C42—62no—
334C3×C42—62no—
335C4⋊Dic3—22no—
336C4⋊Dic3—22no—
337C4⋊Dic3—62no—
338C4⋊Dic3—62no—
339C4⋊Dic3—62no—
340C4⋊Dic3—62no—
341Dic3⋊C4—22no—
342Dic3⋊C4—22no—
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—62no—
352Dic3⋊C4—62no—
353Dic3⋊C4—62no—
354Dic3⋊C4—62no—
355Dic3⋊C4—62no—
356Dic3⋊C4—62no—
357Dic3⋊C4—122no—
358Dic3⋊C4—122no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361C4×Dic3—34no—
362C4×Dic3—34no—
363C4×Dic3—34no—
364C4×Dic3—34no—
365C4×Dic3—62no—
366C4×Dic3—62no—
367C4×Dic3—62no—
368C4×Dic3—62no—
369C4×Dic3Dic614yescomplemented
370C22×C32C22×D411yescharacteristic
371C22×C32C22×Q811yescharacteristic
372C22×C32C22×Q811yescharacteristic
373C22×C32C2×#4111yescharacteristic
374C22×C32C2×#4111yescharacteristic
375C22×C32C2×#4111yescharacteristic
376C22×C32C2×#4111yescharacteristic
377C32×C4—22no—
378C32×C4—22no—
379C32×C4—41no—
380C3⋊Dic3—22no—
381C3⋊Dic3—22no—
382C3⋊Dic3—22no—
383C3⋊Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C3×Dic3C4⋊Q814yes—
392C22×Q8—91no—
393C22×Q8—91no—
394C4×Q8—184no—
395C4×Q8—184no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4—91no—
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⋊C4D3211yescharacteristic
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—31no—
413C2×C42—91no—
414C2×C42—91no—
415C2×C42—91no—
416C2×C42—91no—
417#95—31no—
418#95—31no—
419#95—31no—
420#95—31no—
421#95—31no—
422#95—91no—
423#95—91no—
424#95—91no—
425#95—91no—
426#95—91no—
427#95—91no—
428#95—91no—
429C23×C3—21no—
430C23×C3C23×D311yescharacteristic
431C23×C3C23×D311yescharacteristic
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
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—22no—
447C2×C3×C4—22no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
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×C4C2×Dic612yes—
480C2×C3×C4#23512yes—
481C2×C3×C4#23712yes—
482C2×C3×C4D3×Q812yes—
483C2×Dic3—21no—
484C2×Dic3—21no—
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—62no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
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—121no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3C2×Dic612yes—
537C2×Dic3C2×Dic612yes—
538C2×Dic3#23512yes—
539C2×Dic3D3×D412yes—
540C2×Dic3D3×D412yes—
541C2×Dic3D3×Q812yes—
542C2×Dic3D3×Q812yes—
543Dic6—68no—
544Dic6—68no—
545Dic6—68no—
546Dic6—68no—
547Dic6—128no—
548C2×C32#52511yescharacteristic
549C2×C32#52511yescharacteristic
550C2×C32C2×C4⋊Q811yescharacteristic
551C2×C32#53311yescharacteristic
552C2×C32#53311yescharacteristic
553C2×C32#53311yescharacteristic
554C2×C32#53311yescharacteristic
555C2×Q8—182no—
556C2×Q8—182no—
557C2×Q8—182no—
558C2×Q8—182no—
559C2×Q8—182no—
560C2×Q8—182no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—91no—
570C22×C4—91no—
571C22×C4—91no—
572C22×C4—91no—
573C22×C4C2×D3211yescharacteristic
574C22×C4C2×D3211yescharacteristic
575C22×C4C2×D3211yescharacteristic
576C4⋊C4—22no—
577C4⋊C4—62no—
578C4⋊C4—62no—
579C4⋊C4—62no—
580C4⋊C4—62no—
581C4⋊C4—182no—
582C4⋊C4—182no—
583C4⋊C4—182no—
584C4⋊C4—182no—
585C4⋊C4—182no—
586C4⋊C4—182no—
587C4⋊C4—182no—
588C4⋊C4—182no—
589C4⋊C4—182no—
590C42—34no—
591C42—62no—
592C42—62no—
593C42—94no—
594C42—94no—
595C42—182no—
596C42—182no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3C22×Dic611yescharacteristic
605C22×C3C2×#23511yescharacteristic
606C22×C3C2×#23511yescharacteristic
607C22×C3C2×D3×D411yescharacteristic
608C22×C3C2×D3×D411yescharacteristic
609C22×C3C2×#23711yescharacteristic
610C22×C3C2×D3×Q811yescharacteristic
611C22×C3C2×D3×Q811yescharacteristic
612C22×C3C2×D3×Q811yescharacteristic
613C22×C3D3×#4111yescharacteristic
614C22×C3D3×#4111yescharacteristic
615C22×C3D3×#4111yescharacteristic
616C22×C3D3×#4111yescharacteristic
617C22×C3D3×#4111yescharacteristic
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—34no—
623C3×C4—42no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—62no—
628C3×C4—62no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—81no—
632C3×C4—121no—
633C3×C4—121no—
634C3×C4—121no—
635Dic3—22no—
636Dic3—22no—
637Dic3—22no—
638Dic3—22no—
639Dic3—41no—
640Dic3—41no—
641Dic3—41no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—62no—
646Dic3—62no—
647Dic3—62no—
648Dic3—62no—
649Dic3—62no—
650Dic3—122no—
651Dic3—122no—
652Dic3—122no—
653Dic3—122no—
654Dic3#88814yes—
655C32#239911yescharacteristic, complemented, Sylow
656C23C22×D3211yescharacteristic
657Q8—188no—
658Q8—188no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—32no—
672C2×C4—32no—
673C2×C4—61no—
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—61no—
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×C4—181no—
702C2×C4D3×Dic612yes—
703C2×C4#380412yes—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3#547011yescharacteristic
712C2×C3C2×#88811yescharacteristic
713C2×C3#551711yescharacteristic
714C2×C3#554711yescharacteristic
715C2×C3#554711yescharacteristic
716C2×C3#557811yescharacteristic
717C2×C3#557811yescharacteristic
718C2×C3#560611yescharacteristic
719C2×C3#562211yescharacteristic
720C2×C3#562211yescharacteristic
721C2×C3#565611yescharacteristic
722C2×C3#568811yescharacteristic
723C2×C3#568811yescharacteristic
724C2×C3D3×C4⋊Q811yescharacteristic
725C22C2×D3×Dic611yescharacteristic
726C22D3×#23511yescharacteristic
727C22D32×D411yescharacteristic
728C22#6431211yescharacteristic
729C22D32×Q811yescharacteristic
730C22#6431911yescharacteristic
731C22C2×#380411yescharacteristic
732C4—22no—
733C4—22no—
734C4—34no—
735C4—41no—
736C4—62no—
737C4—62no—
738C4—62no—
739C4—62no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—182no—
744C4—182no—
745C4—182no—
746C4—182no—
747C3—21no—
748C3#7366911yescharacteristic, complemented
749C3#7774011yescharacteristic, complemented
750C2D3×#88811yescharacteristic
751C2#1059439811yescharacteristic
752C2#1059447711yescharacteristic
753C2#1059461411yescharacteristic
754C2#1059480811yescharacteristic
755C2#1059513811yescharacteristic
756C2#1059536711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, prime radical, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
116. C3×C4×Dic3Q8semidirect
127. Dic32Q8semidirect
369. C4×Dic3Dic6semidirect
655. C32#2399semidirect
748. C3#73669semidirect
749. C3#77740semidirect

Maximal subgroups

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

subgroupindex
C2×#638442
C2×#638372
#105926782
C3×#49822
C3×Dic3×C4⋊C42
#105913562
#105913542
#105913452
#105913382
#105912432
#105912422
Dic3×Dic3⋊C42
#105912392
#105911982
#777403
#736693