Finite Group Databasebeta

← #11808911

Subgroups — #11808911

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592647C211yesmaximal, characteristic
2C3×#4953C211yesmaximal, characteristic
3C3×Dic3×C22⋊C4C211yesmaximal, characteristic
4Dic3×#217C211yesmaximal, characteristic
5Dic3×#217C211yesmaximal, characteristic
6#10591694C211yesmaximal, characteristic
7#10591694C211yesmaximal, characteristic
8Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9#10591243C211yesmaximal, characteristic, complemented
10#10591243C211yesmaximal, characteristic, complemented
11#10591239C211yesmaximal, characteristic, complemented
12#10591228C211yesmaximal, characteristic, complemented
13#10591227C211yesmaximal, characteristic, complemented
14#10591218C211yesmaximal, characteristic, complemented
15#10591217C211yesmaximal, characteristic, complemented
16#77461—31nomaximal
17#73482—31nomaximal
18C23×C3×Dic3C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×Dic32C2211yescharacteristic
34C2×Dic32C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37#63658C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43#63579C2211yescharacteristic
44#63579C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53C3×#397—31no—
54C3×C4×C22⋊C4—31no—
55C4×#217—31no—
56C4×#217—31no—
57#4985—31no—
58Dic3×C4⋊C4—31no—
59#4953D311yescharacteristic
60#4952—31no—
61#4952—31no—
62#4952—31no—
63#4952—31no—
64#4948—31no—
65#4948—31no—
66#4948—61no—
67Dic3×C22⋊C4—31no—
68Dic3×C22⋊C4—31no—
69Dic3×C22⋊C4D311yescharacteristic
70C4×C4⋊Dic3—31no—
71#4932—31no—
72C4×Dic3⋊C4—31no—
73C4×Dic3⋊C4—31no—
74C3⋊#401—31no—
75C3⋊#401—31no—
76#4660—31no—
77#4660—31no—
78#4659—31no—
79#4658—31no—
80#4658—31no—
81#4649—31no—
82#4649—31no—
83#4648—31no—
84C24×C32C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3×Dic3—22no—
92C22×C3×Dic3—22no—
93C22×C3×Dic3—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×C22⋊C4—22no—
103#3757—22no—
104#3757—22no—
105C4⋊(C3⋊Dic3)—22no—
106#3750—22no—
107#3750—22no—
108C3×#217—22no—
109C3×#217—22no—
110C3×#217—22no—
111C3×C4⋊Dic3—22no—
112C3×C4×Dic3—22no—
113C3×C4×Dic3—22no—
114#3724—22no—
115#3724—22no—
116Dic32—22no—
117Dic32—22no—
118Dic32—22no—
119Dic32—22no—
120#2401—91noSylow
121C23×C3×C4—31no—
122C23×Dic3C2×D311yescharacteristic
123C2×C3×C4⋊C4—31no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—31no—
126C2×C3×C22⋊C4—31no—
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4C2×D311yescharacteristic
129C2×C3×C22⋊C4C2×D311yescharacteristic
130C2×C3×C42—31no—
131C2×C3×C42—31no—
132C2×#217—31no—
133C2×#217—31no—
134C2×#217—31no—
135C2×#217—31no—
136C2×#217—61no—
137C2×#217—61no—
138C2×#217C2×D311yescharacteristic
139C2×#217C2×D311yescharacteristic
140C2×#217C2×D311yescharacteristic
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—61no—
144C2×C4⋊Dic3C2×D311yescharacteristic
145C2×Dic3⋊C4—31no—
146C2×Dic3⋊C4—31no—
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—61no—
154C2×Dic3⋊C4—61no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3C2×D311yescharacteristic
164C2×C4×Dic3C2×D311yescharacteristic
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—31no—
191C3⋊#95—31no—
192C3⋊#95—61no—
193C3⋊#95C2×D311yescharacteristic
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32#4112yes—
205C23×C32C2411yescharacteristic
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4#4112yes—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
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#4112yes—
223C2×C3⋊Dic3#4112yes—
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—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—44no—
246C2×C3×Dic3#4112yes—
247C2×C3×Dic3#4112yes—
248C2×C3×Dic3#4112yes—
249#401—91no—
250#400—91no—
251#400—91no—
252#400—91no—
253#397—31no—
254#397—91no—
255#397—91no—
256#396—91no—
257C4×C4⋊C4—91no—
258C4×C4⋊C4—91no—
259C4×C4⋊C4—91no—
260C4×C22⋊C4—31no—
261C4×C22⋊C4—91no—
262C4×C22⋊C4—91no—
263#376—91no—
264C24×C3—21no—
265C24×C3C22×D311yescharacteristic
266C24×C3C22×D311yescharacteristic
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—31no—
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—62no—
278C22×C3×C4—62no—
279C22×C3×C4—62no—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D311yescharacteristic
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D311yescharacteristic
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C3×C4⋊C4—62no—
308C3×C22⋊C4—22no—
309C3×C22⋊C4—22no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—62no—
312C3×C22⋊C4—62no—
313C3×C22⋊C4—62no—
314C3×C42—62no—
315C3×C42—62no—
316#217—22no—
317#217—22no—
318#217—22no—
319#217—62no—
320#217—62no—
321#217—62no—
322#217—62no—
323#217—122no—
324#217—122no—
325C4⋊Dic3—22no—
326C4⋊Dic3—62no—
327C4⋊Dic3—62no—
328C4⋊Dic3—122no—
329Dic3⋊C4—62no—
330Dic3⋊C4—62no—
331Dic3⋊C4—62no—
332Dic3⋊C4—62no—
333Dic3⋊C4—62no—
334Dic3⋊C4—62no—
335Dic3⋊C4—62no—
336Dic3⋊C4—62no—
337Dic3⋊C4—122no—
338Dic3⋊C4—122no—
339C4×Dic3—22no—
340C4×Dic3—22no—
341C4×Dic3—62no—
342C4×Dic3—62no—
343C4×Dic3—62no—
344C4×Dic3—62no—
345C4×Dic3—62no—
346C4×Dic3—62no—
347C4×Dic3—62no—
348C4×Dic3—62no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—41no—
353C22×C32—41no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32C2×#4111yescharacteristic
357C22×C32C2×#4111yescharacteristic
358C22×C32C2×#4111yescharacteristic
359C22×C32C2×#4111yescharacteristic
360C22×C32C2×#4111yescharacteristic
361C22×C32C2×#4111yescharacteristic
362C22×C32C2×#4111yescharacteristic
363C32×C4—22no—
364C32×C4—41no—
365C3⋊Dic3—22no—
366C3⋊Dic3—22no—
367C3⋊Dic3—41no—
368C3⋊Dic3—41no—
369C3×Dic3—41no—
370C3×Dic3—41no—
371C3×Dic3—41no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C3×Dic3—41no—
376C3×Dic3#12614yes—
377C23×C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—91no—
380C2×C4⋊C4—91no—
381C2×C4⋊C4—91no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—91no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4D3211yescharacteristic
390C2×C42—31no—
391C2×C42—31no—
392C2×C42—91no—
393C2×C42—91no—
394C2×C42—91no—
395C2×C42—91no—
396#95—31no—
397#95—31no—
398#95—31no—
399#95—31no—
400#95—31no—
401#95—91no—
402#95—91no—
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—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—22no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3#23512yes—
433C23×C3#23712yes—
434C23×C3C23×D311yescharacteristic
435C23×C3C23×D311yescharacteristic
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—32no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
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—124no—
477C2×C3×C4#23512yes—
478C2×C3×C4#23712yes—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
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—44no—
505C2×Dic3—62no—
506C2×Dic3—62no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
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—121no—
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×Dic3—121no—
537C2×Dic3#23512yes—
538C2×Dic3#23712yes—
539C2×Dic3#23712yes—
540C2×C32—42no—
541C2×C32C2×#12611yescharacteristic
542C2×C32#52911yescharacteristic
543C2×C32#52911yescharacteristic
544C2×C32#52911yescharacteristic
545C2×C32#52911yescharacteristic
546C2×C32#52911yescharacteristic
547C2×C32#52911yescharacteristic
548C24C2×D3211yescharacteristic
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4—91no—
563C22×C4—91no—
564C22×C4C2×D3211yescharacteristic
565C22×C4C2×D3211yescharacteristic
566C4⋊C4—62no—
567C4⋊C4—182no—
568C4⋊C4—182no—
569C4⋊C4—182no—
570C4⋊C4—182no—
571C4⋊C4—182no—
572C22⋊C4—22no—
573C22⋊C4—62no—
574C22⋊C4—62no—
575C22⋊C4—62no—
576C22⋊C4—182no—
577C22⋊C4—182no—
578C42—62no—
579C42—62no—
580C42—182no—
581C42—182no—
582C42—182no—
583C42—182no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3C2×#23511yescharacteristic
613C22×C3C2×#23511yescharacteristic
614C22×C3C2×#23511yescharacteristic
615C22×C3C2×#23711yescharacteristic
616C22×C3C2×#23711yescharacteristic
617C22×C3C2×#23711yescharacteristic
618C22×C3C2×#23711yescharacteristic
619C22×C3D3×#4111yescharacteristic
620C22×C3D3×#4111yescharacteristic
621C22×C3D3×#4111yescharacteristic
622C22×C3D3×#4111yescharacteristic
623C22×C3D3×#4111yescharacteristic
624C22×C3D3×#4111yescharacteristic
625C22×C3D3×#4111yescharacteristic
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—34no—
629C3×C4—42no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—81no—
633C3×C4—121no—
634C3×C4—121no—
635C3×C4—121no—
636C3×C4—121no—
637C3×C4—121no—
638C3×C4—121no—
639C3×C4—121no—
640Dic3—41no—
641Dic3—41no—
642Dic3—41no—
643Dic3—41no—
644Dic3—41no—
645Dic3—41no—
646Dic3—41no—
647Dic3—62no—
648Dic3—62no—
649Dic3—62no—
650Dic3—62no—
651Dic3—122no—
652Dic3—122no—
653Dic3—121no—
654Dic3—121no—
655Dic3—121no—
656Dic3—121no—
657Dic3—241no—
658Dic3—241no—
659Dic3#87914yes—
660C32#240111yescharacteristic, complemented, Sylow
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23#379512yes—
668C23C22×D3211yescharacteristic
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—32no—
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—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—92no—
699C2×C4—92no—
700C2×C4—124no—
701C2×C4—181no—
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—181no—
711C2×C4#380412yes—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—42no—
720C2×C3—42no—
721C2×C3—82no—
722C2×C3#547911yescharacteristic
723C2×C3C2×#87911yescharacteristic
724C2×C3#552811yescharacteristic
725C2×C3#553811yescharacteristic
726C2×C3#553811yescharacteristic
727C2×C3#553811yescharacteristic
728C2×C3#555711yescharacteristic
729C2×C3#560011yescharacteristic
730C2×C3#564911yescharacteristic
731C2×C3#564911yescharacteristic
732C2×C3#564911yescharacteristic
733C2×C3#568011yescharacteristic
734C2×C3D3×#12611yescharacteristic
735C2×C3#570611yescharacteristic
736C22—22no—
737C22—22no—
738C22—22no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22C2×#379511yescharacteristic
744C22D3×#23511yescharacteristic
745C22D3×#23711yescharacteristic
746C22D3×#23711yescharacteristic
747C22#6431211yescharacteristic
748C22#6431211yescharacteristic
749C22C2×#380411yescharacteristic
750C4—22no—
751C4—34no—
752C4—41no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—121no—
760C4—182no—
761C4—182no—
762C4—361no—
763C4—361no—
764C3—21no—
765C3#7348211yescharacteristic, complemented
766C3#7746111yescharacteristic, complemented
767C2—42no—
768C2D3×#87911yescharacteristic
769C2#1059410611yescharacteristic
770C2#1059413111yescharacteristic
771C2#1059413111yescharacteristic
772C2#1059494911yescharacteristic
773C2#1059511611yescharacteristic
774C2#1059519111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2401
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. Dic3×C4⋊Dic3C2semidirect
9. #10591243C2semidirect
10. #10591243C2semidirect
11. #10591239C2semidirect
12. #10591228C2semidirect
13. #10591227C2semidirect
14. #10591218C2semidirect
15. #10591217C2semidirect
660. C32#2401semidirect
765. C3#73482semidirect
766. C3#77461semidirect

Maximal subgroups

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

subgroupindex
#105926472
C3×#49532
C3×Dic3×C22⋊C42
Dic3×#2172
#105916942
Dic3×C4⋊Dic32
#105912432
#105912392
#105912282
#105912272
#105912182
#105912172
#774613
#734823