Finite Group Databasebeta

← #11808913

Subgroups — #11808913

Order 1152.

993 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3752C211yesmaximal, characteristic
2C3×#4932C211yesmaximal, characteristic, complemented
3C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#10591347C211yesmaximal, characteristic
5#10591341C211yesmaximal, characteristic, complemented
6C4×#3724C211yesmaximal, characteristic, complemented
7C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8C4×#3722C211yesmaximal, characteristic
9C4×#3722C211yesmaximal, characteristic
10#10591228C211yesmaximal, characteristic, complemented
11#10591216C211yesmaximal, characteristic
12#10591211C211yesmaximal, characteristic, complemented
13#10591208C211yesmaximal, characteristic
14#10591204C211yesmaximal, characteristic
15#10591199C211yesmaximal, characteristic, complemented
16#73779—31nomaximal
17#73420—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×C32×C42C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×#3724C2211yescharacteristic
30C2×#3724C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37#63658C2211yescharacteristic
38#63658C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53C3×C4×C4⋊C4—31no—
54C3×#376—31no—
55#4994—31no—
56#4992—31no—
57#4986—31no—
58#4985—31no—
59C4×(C2×D3)⋊C4—31no—
60C4×(C2×D3)⋊C4—31no—
61C4×(C2×D3)⋊C4—31no—
62C4×(C2×D3)⋊C4—31no—
63C4×(C2×D3)⋊C4—31no—
64C4×(C2×D3)⋊C4—31no—
65C4×(C2×D3)⋊C4—61no—
66C4×C4⋊Dic3—31no—
67#4932D311yescharacteristic, complemented
68C4×Dic3⋊C4—31no—
69C4×Dic3⋊C4—31no—
70C4×Dic3⋊C4—31no—
71C4×Dic3⋊C4D311yescharacteristic, complemented
72#4676—31no—
73#4675—31no—
74#4675—31no—
75#4675—31no—
76#4675—31no—
77#4674—31no—
78C3⋊#401—31no—
79C3⋊#401—31no—
80#4660—31no—
81#4658—31no—
82#4658—31no—
83#4658—31no—
84C23×C3⋊D3C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C2×C4×C3⋊D3—22no—
92C2×C4×C3⋊D3—22no—
93C2×C4×C3⋊D3—22no—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C32×C42—22no—
103#3752—22no—
104#3752—22no—
105C4×C3⋊Dic3—22no—
106C3×Dic3⋊C4—22no—
107C3×Dic3⋊C4—22no—
108C3×C4×Dic3—22no—
109C3×C4×Dic3—22no—
110C3×C4×Dic3—22no—
111C3×C4×Dic3—22no—
112#3724—22no—
113#3724—22no—
114Dic3⋊Dic3—22no—
115Dic3⋊Dic3—22no—
116#3722—22no—
117#3722—22no—
118#3722—22no—
119#3722—22no—
120#2401—91noSylow
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—61no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C42—21no—
127C2×C3×C42—31no—
128C2×C3×C42—31no—
129C2×C3×C42—31no—
130C2×C3×C42—31no—
131C2×C3×C42C2×D311yescharacteristic
132C2×C3×C42C2×D311yescharacteristic
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—61no—
146C2×(C2×D3)⋊C4—61no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—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⋊C4C2×D311yescharacteristic
156C2×Dic3⋊C4C2×D311yescharacteristic
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—61no—
160C2×C4×Dic3C2×D311yescharacteristic
161C2×C4×Dic3C2×D311yescharacteristic
162C2×C4×Dic3C2×D311yescharacteristic
163C2×C4×Dic3C2×D311yescharacteristic
164C3×#95—31no—
165C3×#95—31no—
166C3×#95—31no—
167C3×#95—31no—
168C3×#95—31no—
169C3×#95—31no—
170C3⋊#95—31no—
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—61no—
191C3⋊#95—61no—
192C3⋊#95C2×D311yescharacteristic
193C3⋊#95C2×D311yescharacteristic
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C23×C32C2411yescharacteristic
199C22×C3⋊D3—21no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—21no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3—21no—
205C22×C3⋊D3#4112yes—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4#4112yes—
213C2×C32×C4#4112yes—
214C2×C32×C4#4112yes—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3#4112yes—
224C4×C3⋊D3—44no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
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#4112yes—
248C2×C3×Dic3#4112yes—
249#401—91no—
250#400—91no—
251#400—91no—
252#400—91no—
253#397—91no—
254#397—91no—
255#397—91no—
256#396—91no—
257C4×C4⋊C4—31no—
258C4×C4⋊C4—91no—
259C4×C4⋊C4—91no—
260C4×C22⋊C4—91no—
261C4×C22⋊C4—91no—
262C4×C22⋊C4—91no—
263#376—31no—
264C23×D3—31no—
265C23×D3—31no—
266C23×D3—61no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D311yescharacteristic
301C2×C4×D3—64no—
302C2×C4×D3—62no—
303C2×C4×D3—62no—
304C2×C4×D3—62no—
305C2×C4×D3—62no—
306C2×C4×D3—62no—
307C2×C4×D3—62no—
308C2×C4×D3—122no—
309C2×C4×D3—122no—
310C3×C4⋊C4—62no—
311C3×C4⋊C4—62no—
312C3×C42—22no—
313C3×C42—22no—
314C3×C42—42no—
315C3×C42—62no—
316C3×C42—62no—
317C3×C42—62no—
318C3×C42—62no—
319(C2×D3)⋊C4—62no—
320(C2×D3)⋊C4—62no—
321(C2×D3)⋊C4—62no—
322(C2×D3)⋊C4—62no—
323(C2×D3)⋊C4—62no—
324(C2×D3)⋊C4—62no—
325(C2×D3)⋊C4—62no—
326(C2×D3)⋊C4—62no—
327(C2×D3)⋊C4—62no—
328(C2×D3)⋊C4—62no—
329(C2×D3)⋊C4—64no—
330(C2×D3)⋊C4—64no—
331(C2×D3)⋊C4—62no—
332(C2×D3)⋊C4—62no—
333C4⋊Dic3—62no—
334C4⋊Dic3—62no—
335Dic3⋊C4—22no—
336Dic3⋊C4—22no—
337Dic3⋊C4—62no—
338Dic3⋊C4—62no—
339Dic3⋊C4—62no—
340Dic3⋊C4—62no—
341Dic3⋊C4—62no—
342Dic3⋊C4—62no—
343C4×Dic3—22no—
344C4×Dic3—22no—
345C4×Dic3—22no—
346C4×Dic3—22no—
347C4×Dic3—62no—
348C4×Dic3—62no—
349C4×Dic3—122no—
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32C2×#4111yescharacteristic
353C22×C32C2×#4111yescharacteristic
354C22×C32C2×#4111yescharacteristic
355C22×C32C2×#4111yescharacteristic
356C22×C32C2×#4111yescharacteristic
357C2×C3⋊D3—22no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—22no—
360C2×C3⋊D3—41no—
361C2×C3⋊D3—41no—
362C2×C3⋊D3—41no—
363C2×C3⋊D3—41no—
364C32×C4—41no—
365C32×C4—41no—
366C32×C4#12614yes—
367C3⋊Dic3—22no—
368C3⋊Dic3—41no—
369C3⋊Dic3—41no—
370C3×Dic3—22no—
371C3×Dic3—22no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C3×Dic3—41no—
376C3×Dic3—41no—
377C3×Dic3—41no—
378C23×C4—91no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—91no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4—91no—
387C2×C22⋊C4—91no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4—91no—
391C2×C42—31no—
392C2×C42—31no—
393C2×C42—31no—
394C2×C42—31no—
395C2×C42—91no—
396C2×C42D3211yescharacteristic
397#95—31no—
398#95—31no—
399#95—31no—
400#95—31no—
401#95—31no—
402#95—31no—
403#95—91no—
404#95—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95—91no—
411#95—91no—
412#95—91no—
413C23×C3—21no—
414C23×C3C23×D311yescharacteristic
415C23×C3C23×D311yescharacteristic
416C22×D3—32no—
417C22×D3—32no—
418C22×D3—62no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—61no—
422C22×D3—61no—
423C22×D3—61no—
424C22×D3—61no—
425C22×D3—61no—
426C22×D3—61no—
427C22×D3—61no—
428C22×D3—61no—
429C22×D3—61no—
430C22×D3—61no—
431C22×D3—61no—
432C22×D3—61no—
433C22×D3—121no—
434C22×D3—121no—
435C22×D3—121no—
436C22×D3—121no—
437C2×C3×C4—22no—
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—22no—
453C2×C3×C4—22no—
454C2×C3×C4—32no—
455C2×C3×C4—32no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
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×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4#23512yes—
483C2×C3×C4#23512yes—
484C2×C3×C4#23512yes—
485C2×C3×C4#23512yes—
486C2×C3×C4#23712yes—
487C2×C3×C4#23912yes—
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—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—32no—
511C2×Dic3—32no—
512C2×Dic3—62no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—62no—
518C2×Dic3—62no—
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—61no—
530C2×Dic3—61no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3#23512yes—
538C2×Dic3#23512yes—
539C4×D3—128no—
540C4×D3—124no—
541C4×D3—124no—
542C2×C32C2×#12611yescharacteristic
543C2×C32#52911yescharacteristic
544C2×C32#52911yescharacteristic
545C2×C32#52911yescharacteristic
546C2×C32#52911yescharacteristic
547C2×C32#52911yescharacteristic
548C2×C32#52911yescharacteristic
549C3⋊D3—42no—
550C24—91no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—91no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4—182no—
563C22×C4—182no—
564C22×C4—182no—
565C22×C4C2×D3211yescharacteristic
566C22×C4C2×D3211yescharacteristic
567C22×C4C2×D3211yescharacteristic
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—182no—
571C4⋊C4—182no—
572C4⋊C4—182no—
573C4⋊C4—182no—
574C22⋊C4—182no—
575C22⋊C4—182no—
576C22⋊C4—182no—
577C22⋊C4—182no—
578C22⋊C4—182no—
579C22⋊C4—182no—
580C42—22no—
581C42—62no—
582C42—62no—
583C42—62no—
584C42—62no—
585C42—182no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3C2×#23511yescharacteristic
594C22×C3C2×#23511yescharacteristic
595C22×C3C2×#23511yescharacteristic
596C22×C3C2×#23511yescharacteristic
597C22×C3C2×#23511yescharacteristic
598C22×C3C2×#23511yescharacteristic
599C22×C3C2×#23711yescharacteristic
600C22×C3C2×#23911yescharacteristic
601C22×C3D3×#4111yescharacteristic
602C22×C3D3×#4111yescharacteristic
603C22×C3D3×#4111yescharacteristic
604C22×C3D3×#4111yescharacteristic
605C22×C3D3×#4111yescharacteristic
606C22×C3D3×#4111yescharacteristic
607C2×D3—64no—
608C2×D3—62no—
609C2×D3—62no—
610C2×D3—62no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—122no—
615C2×D3—122no—
616C2×D3—122no—
617C2×D3—122no—
618C2×D3—122no—
619C2×D3—122no—
620C2×D3—121no—
621C2×D3—121no—
622C2×D3—121no—
623C2×D3—121no—
624C2×D3—121no—
625C2×D3—121no—
626C2×D3—121no—
627C2×D3—121no—
628C3×C4—24no—
629C3×C4—42no—
630C3×C4—42no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—62no—
636C3×C4—62no—
637C3×C4—121no—
638C3×C4—121no—
639C3×C4—121no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4#87614yes—
644C3×C4#89814yes—
645Dic3—22no—
646Dic3—22no—
647Dic3—41no—
648Dic3—41no—
649Dic3—41no—
650Dic3—41no—
651Dic3—41no—
652Dic3—41no—
653Dic3—62no—
654Dic3—62no—
655Dic3—122no—
656Dic3—122no—
657Dic3—122no—
658Dic3—121no—
659Dic3—121no—
660Dic3—121no—
661Dic3—121no—
662C32#240111yescharacteristic, complemented, Sylow
663C23—92no—
664C23—181no—
665C23—181no—
666C23—181no—
667C23—181no—
668C23—181no—
669C23—181no—
670C23C22×D3211yescharacteristic
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—32no—
678C2×C4—32no—
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—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—92no—
702C2×C4—181no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—364no—
711C2×C4#379812yes—
712C2×C4#379912yes—
713C2×C4#380412yes—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3C2×#87611yescharacteristic
722C2×C3#547911yescharacteristic
723C2×C3C2×#89811yescharacteristic
724C2×C3#552811yescharacteristic
725C2×C3#552811yescharacteristic
726C2×C3#552811yescharacteristic
727C2×C3#552811yescharacteristic
728C2×C3#552811yescharacteristic
729C2×C3#552811yescharacteristic
730C2×C3#552811yescharacteristic
731C2×C3#553811yescharacteristic
732C2×C3#555711yescharacteristic
733C2×C3#558011yescharacteristic
734C2×C3#558011yescharacteristic
735D3—124no—
736D3—122no—
737D3—122no—
738C22—182no—
739C22—182no—
740C22—182no—
741C22—361no—
742C22—361no—
743C22—361no—
744C22—361no—
745C22C2×#379811yescharacteristic
746C22C2×#379911yescharacteristic
747C22D3×#23511yescharacteristic
748C22D3×#23511yescharacteristic
749C22#6430611yescharacteristic
750C22#6430611yescharacteristic
751C22C2×#380411yescharacteristic
752C4—41no—
753C4—41no—
754C4—62no—
755C4—62no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—182no—
763C4—361no—
764C4—361no—
765C4#6386814yes—
766C3—21no—
767C3#7342011yescharacteristic, complemented
768C3#7377911yescharacteristic, complemented
769C2—362no—
770C2#1059393411yescharacteristic
771C2#1059393411yescharacteristic
772C2#1059397311yescharacteristic
773C2#1059398011yescharacteristic
774C2#1059483611yescharacteristic
775C2C2×#6386811yescharacteristic
776C2#1059493311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2401
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4932C2semidirect
3. C3×C4×Dic3⋊C4C2semidirect
5. #10591341C2semidirect
6. C4×#3724C2semidirect
7. C4×Dic3⋊Dic3C2semidirect
10. #10591228C2semidirect
12. #10591211C2semidirect
15. #10591199C2semidirect
67. #4932D3semidirect
71. C4×Dic3⋊C4D3semidirect
662. C32#2401semidirect
767. C3#73420semidirect
768. C3#73779semidirect

Maximal subgroups

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

subgroupindex
C4×#37522
C3×#49322
C3×C4×Dic3⋊C42
#105913472
#105913412
C4×#37242
C4×Dic3⋊Dic32
C4×#37222
#105912282
#105912162
#105912112
#105912082
#105912042
#105911992
#737793
#734203