Finite Group Databasebeta

← #11773360

Subgroups — #11773360

Order 1152.

1337 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×Dic3⋊Dic3C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×#63579C211yesmaximal, characteristic
6C2×#63579C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#69411—31nomaximal
9#69409—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×#3750—22no—
18C2×#3750—22no—
19C2×#3750—22no—
20C2×Dic3⋊Dic3—22no—
21C2×Dic3⋊Dic3—22no—
22C2×Dic3⋊Dic3C414yescomplemented
23C3×C3⋊#95—22no—
24C3×C3⋊#95—22no—
25#63579—22no—
26#63579—22no—
27#63579—22no—
28C22×C4⋊Dic3—31no—
29C22×Dic3⋊C4—31no—
30C22×Dic3⋊C4—31no—
31C22×Dic3⋊C4—31no—
32C22×Dic3⋊C4—61no—
33C2×C3×#95—31no—
34C2×C3×#95—31no—
35C2×C3⋊#95—31no—
36C2×C3⋊#95—31no—
37C2×C3⋊#95—31no—
38C2×C3⋊#95—31no—
39C2×C3⋊#95—31no—
40C2×C3⋊#95—31no—
41C2×C3⋊#95D311yescharacteristic
42C2×C3⋊#95D311yescharacteristic
43C24×C32C2311yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4D412yes—
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3—21no—
58C22×C3⋊Dic3—21no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3—21no—
61C22×C3⋊Dic3C2×C412yes—
62C22×C3⋊Dic3D412yes—
63C22×C3⋊Dic3D412yes—
64C22×C3⋊Dic3D412yes—
65C22×C3×Dic3—21no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—21no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—21no—
71C22×C3×Dic3—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3C2×C412yes—
88C22×C3×Dic3C2×C412yes—
89C22×C3×Dic3D412yes—
90C22×C3×Dic3Q812yes—
91C22×C3×Dic3Q812yes—
92C22×C3×Dic3Q812yes—
93#3750—28no—
94Dic3⋊Dic3—28no—
95#1441—91noSylow
96C23×C3×C4—21no—
97C23×C3×C4—31no—
98C23×C3×C4—31no—
99C23×C3×C4—31no—
100C23×C3×C4—31no—
101C23×C3×C4C2×D311yescharacteristic
102C23×C3×C4C2×D311yescharacteristic
103C23×Dic3—31no—
104C23×Dic3—31no—
105C23×Dic3—31no—
106C23×Dic3—31no—
107C23×Dic3—61no—
108C23×Dic3—61no—
109C23×Dic3C2×D311yescharacteristic
110C23×Dic3C2×D311yescharacteristic
111C23×Dic3C2×D311yescharacteristic
112C23×Dic3C2×D311yescharacteristic
113C2×C4⋊Dic3—34no—
114C2×C4⋊Dic3—62no—
115C2×C4⋊Dic3—62no—
116C2×Dic3⋊C4—34no—
117C2×Dic3⋊C4—62no—
118C2×Dic3⋊C4—62no—
119C2×Dic3⋊C4—62no—
120C2×Dic3⋊C4—62no—
121C2×Dic3⋊C4—62no—
122C2×Dic3⋊C4—62no—
123C2×Dic3⋊C4—64no—
124C2×Dic3⋊C4—64no—
125C2×Dic3⋊C4—64no—
126C2×Dic3⋊C4—62no—
127C2×Dic3⋊C4—62no—
128C3×#95—62no—
129C3×#95—62no—
130C3⋊#95—22no—
131C3⋊#95—22no—
132C3⋊#95—62no—
133C3⋊#95—62no—
134C3⋊#95—62no—
135C3⋊#95—62no—
136C3⋊#95—62no—
137C3⋊#95—62no—
138C23×C32C22×C411yescharacteristic
139C23×C32C2×D411yescharacteristic
140C23×C32C2×D411yescharacteristic
141C23×C32C2×D411yescharacteristic
142C23×C32C2×D411yescharacteristic
143C23×C32C2×D411yescharacteristic
144C23×C32C2×Q811yescharacteristic
145C23×C32C2×Q811yescharacteristic
146C23×C32C2×Q811yescharacteristic
147C23×C32#4111yescharacteristic
148C23×C32#4111yescharacteristic
149C23×C32#4111yescharacteristic
150C23×C32#4111yescharacteristic
151C23×C32#4111yescharacteristic
152C23×C32#4111yescharacteristic
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—41no—
157C2×C32×C4—41no—
158C2×C32×C4—41no—
159C2×C32×C4—41no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—41no—
170C2×C3⋊Dic3—41no—
171C2×C3⋊Dic3—41no—
172C2×C3⋊Dic3—41no—
173C2×C3⋊Dic3C22⋊C414yes—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—41no—
190C2×C3×Dic3—41no—
191C2×C3×Dic3—41no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3—41no—
194C2×C3×Dic3—41no—
195C2×C3×Dic3—41no—
196C2×C3×Dic3—41no—
197C2×C3×Dic3—41no—
198C2×C3×Dic3—41no—
199C2×C3×Dic3—41no—
200C2×C3×Dic3—41no—
201C2×C3×Dic3C4⋊C414yescomplemented
202C22×C4⋊C4—91no—
203C22×C4⋊C4—91no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—91no—
207C2×#95—91no—
208C2×#95—91no—
209C24×C3—21no—
210C24×C3C22×D311yescharacteristic
211C24×C3C22×D311yescharacteristic
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—32no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4—41no—
234C22×C3×C4—41no—
235C22×C3×C4—41no—
236C22×C3×C4—41no—
237C22×C3×C4—61no—
238C22×C3×C4—61no—
239C22×C3×C4—61no—
240C22×C3×C4—61no—
241C22×C3×C4—61no—
242C22×C3×C4—61no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C22×C3×C4—61no—
246C22×C3×C4—61no—
247C22×C3×C4—61no—
248C22×C3×C4—61no—
249C22×C3×C4—61no—
250C22×C3×C4—61no—
251C22×C3×C4—61no—
252C22×C3×C4—61no—
253C22×C3×C4—61no—
254C22×C3×C4—61no—
255C22×C3×C4—61no—
256C22×C3×C4—61no—
257C22×C3×C4—61no—
258C22×C3×C4—61no—
259C22×C3×C4D1212yes—
260C22×C3×C4#6712yes—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—32no—
284C22×Dic3—32no—
285C22×Dic3—32no—
286C22×Dic3—32no—
287C22×Dic3—32no—
288C22×Dic3—32no—
289C22×Dic3—32no—
290C22×Dic3—32no—
291C22×Dic3—62no—
292C22×Dic3—62no—
293C22×Dic3—62no—
294C22×Dic3—62no—
295C22×Dic3—62no—
296C22×Dic3—62no—
297C22×Dic3—62no—
298C22×Dic3—62no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—62no—
308C22×Dic3—62no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322C22×Dic3—121no—
323C22×Dic3—121no—
324C22×Dic3—121no—
325C22×Dic3Dic612yes—
326C22×Dic3Dic612yes—
327C22×Dic3Dic612yes—
328C22×Dic3C4×D312yes—
329C22×Dic3C4×D312yes—
330C22×Dic3#6712yes—
331C4⋊Dic3—68no—
332Dic3⋊C4—68no—
333Dic3⋊C4—616no—
334Dic3⋊C4—68no—
335Dic3⋊C4—68no—
336C22×C32C2×C22⋊C411yescharacteristic
337C22×C32C2×C4⋊C411yescharacteristic
338C22×C32#11711yescharacteristic
339C22×C32C4×D411yescharacteristic
340C22×C32C4×D411yescharacteristic
341C22×C32C4×Q811yescharacteristic
342C22×C32C4×Q811yescharacteristic
343C22×C32#12011yescharacteristic
344C22×C32#12111yescharacteristic
345C22×C32#12111yescharacteristic
346C22×C32#12111yescharacteristic
347C22×C32#12111yescharacteristic
348C22×C32#12111yescharacteristic
349C22×C32#12111yescharacteristic
350C22×C32C22⋊Q811yescharacteristic
351C22×C32C22⋊Q811yescharacteristic
352C22×C32C22⋊Q811yescharacteristic
353C22×C32C22⋊Q811yescharacteristic
354C22×C32C22⋊Q811yescharacteristic
355C22×C32C22⋊Q811yescharacteristic
356C22×C32C22⋊Q811yescharacteristic
357C22×C32C22⋊Q811yescharacteristic
358C22×C32#12311yescharacteristic
359C22×C32#12311yescharacteristic
360C22×C32#12311yescharacteristic
361C22×C32#12411yescharacteristic
362C22×C32#12511yescharacteristic
363C22×C32#12511yescharacteristic
364C22×C32#12511yescharacteristic
365C22×C32#12511yescharacteristic
366C22×C32#12611yescharacteristic
367C22×C32#12611yescharacteristic
368C22×C32C4⋊Q811yescharacteristic
369C22×C32C4⋊Q811yescharacteristic
370C22×C32C4⋊Q811yescharacteristic
371C32×C4—42no—
372C3⋊Dic3—24no—
373C3⋊Dic3—42no—
374C3×Dic3—24no—
375C3×Dic3—42no—
376C3×Dic3—42no—
377C3×Dic3—42no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—91no—
383C23×C4—91no—
384C23×C4D3211yescharacteristic
385C2×C4⋊C4—94no—
386C2×C4⋊C4—182no—
387C2×C4⋊C4—182no—
388C2×C4⋊C4—182no—
389C2×C4⋊C4—182no—
390C2×C4⋊C4—182no—
391#95—62no—
392#95—62no—
393#95—182no—
394#95—182no—
395#95—182no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3C2×Dic611yescharacteristic
412C23×C3C2×Dic611yescharacteristic
413C23×C3C2×Dic611yescharacteristic
414C23×C3C2×C4×D311yescharacteristic
415C23×C3C2×C4×D311yescharacteristic
416C23×C3C2×D1211yescharacteristic
417C23×C3#23511yescharacteristic
418C23×C3#23511yescharacteristic
419C23×C3#23511yescharacteristic
420C23×C3#23511yescharacteristic
421C23×C3#23511yescharacteristic
422C23×C3#23511yescharacteristic
423C23×C3D3×D411yescharacteristic
424C23×C3D3×D411yescharacteristic
425C23×C3D3×D411yescharacteristic
426C23×C3D3×D411yescharacteristic
427C23×C3D3×D411yescharacteristic
428C23×C3D3×D411yescharacteristic
429C23×C3D3×D411yescharacteristic
430C23×C3#23711yescharacteristic
431C23×C3#23711yescharacteristic
432C23×C3#23711yescharacteristic
433C23×C3#23711yescharacteristic
434C23×C3#23711yescharacteristic
435C23×C3D3×Q811yescharacteristic
436C23×C3D3×Q811yescharacteristic
437C23×C3D3×Q811yescharacteristic
438C23×C3#23911yescharacteristic
439C23×C3C2×#6711yescharacteristic
440C23×C3C2×#6711yescharacteristic
441C2×C3×C4—24no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—34no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
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—41no—
463C2×C3×C4—62no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470C2×C3×C4—62no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—62no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—121no—
479C2×C3×C4—121no—
480C2×C3×C4—121no—
481C2×C3×C4—121no—
482C2×C3×C4—121no—
483C2×C3×C4—121no—
484C2×C3×C4—121no—
485C2×C3×C4—121no—
486C2×C3×C4—121no—
487C2×C3×C4—121no—
488C2×C3×C4—121no—
489C2×C3×C4—121no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—34no—
506C2×Dic3—34no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—64no—
520C2×Dic3—64no—
521C2×Dic3—64no—
522C2×Dic3—64no—
523C2×Dic3—64no—
524C2×Dic3—64no—
525C2×Dic3—64no—
526C2×Dic3—62no—
527C2×Dic3—62no—
528C2×Dic3—62no—
529C2×Dic3—62no—
530C2×Dic3—62no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—62no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—64no—
539C2×Dic3—62no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—122no—
546C2×Dic3—122no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3—122no—
550C2×Dic3—122no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—121no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3Dic3⋊C414yescomplemented
560C2×C32#38011yescharacteristic
561C2×C32#38611yescharacteristic
562C2×C32#38711yescharacteristic
563C2×C32#38711yescharacteristic
564C2×C32#38911yescharacteristic
565C2×C32#38911yescharacteristic
566C2×C32#39111yescharacteristic
567C2×C32#39411yescharacteristic
568C2×C32#39511yescharacteristic
569C2×C32#39611yescharacteristic
570C2×C32#39611yescharacteristic
571C2×C32#39811yescharacteristic
572C2×C32#39811yescharacteristic
573C2×C32#39811yescharacteristic
574C2×C32#40011yescharacteristic
575C24C2×D3211yescharacteristic
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—32no—
585C22×C4—32no—
586C22×C4—32no—
587C22×C4—32no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—92no—
611C22×C4—92no—
612C22×C4—92no—
613C22×C4—92no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4#62612yes—
625C4⋊C4—188no—
626C4⋊C4—188no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3C4×Dic611yescharacteristic
663C22×C3C4×Dic611yescharacteristic
664C22×C3#86911yescharacteristic
665C22×C3#87011yescharacteristic
666C22×C3#87011yescharacteristic
667C22×C3#87211yescharacteristic
668C22×C3C4×D1211yescharacteristic
669C22×C3#87611yescharacteristic
670C22×C3#87711yescharacteristic
671C22×C3#87811yescharacteristic
672C22×C3#87811yescharacteristic
673C22×C3#87811yescharacteristic
674C22×C3#87811yescharacteristic
675C22×C3#87811yescharacteristic
676C22×C3#87811yescharacteristic
677C22×C3#87911yescharacteristic
678C22×C3#87911yescharacteristic
679C22×C3D3×C22⋊C411yescharacteristic
680C22×C3D3×C22⋊C411yescharacteristic
681C22×C3#67⋊C411yescharacteristic
682C22×C3#88211yescharacteristic
683C22×C3#88311yescharacteristic
684C22×C3#88311yescharacteristic
685C22×C3#88311yescharacteristic
686C22×C3#88411yescharacteristic
687C22×C3#88411yescharacteristic
688C22×C3#88411yescharacteristic
689C22×C3#88411yescharacteristic
690C22×C3#88411yescharacteristic
691C22×C3#88511yescharacteristic
692C22×C3#88511yescharacteristic
693C22×C3#88611yescharacteristic
694C22×C3#88711yescharacteristic
695C22×C3#88711yescharacteristic
696C22×C3#88811yescharacteristic
697C22×C3#88811yescharacteristic
698C22×C3#88811yescharacteristic
699C22×C3#88811yescharacteristic
700C22×C3#88911yescharacteristic
701C22×C3#88911yescharacteristic
702C22×C3#88911yescharacteristic
703C22×C3#88911yescharacteristic
704C22×C3#89011yescharacteristic
705C22×C3#89011yescharacteristic
706C22×C3D3×C4⋊C411yescharacteristic
707C22×C3#89311yescharacteristic
708C22×C3#89411yescharacteristic
709C22×C3#89511yescharacteristic
710C22×C3#89611yescharacteristic
711C22×C3#89611yescharacteristic
712C22×C3#89611yescharacteristic
713C22×C3#89611yescharacteristic
714C22×C3#89611yescharacteristic
715C22×C3#89611yescharacteristic
716C22×C3#89711yescharacteristic
717C22×C3#89811yescharacteristic
718C22×C3C2×Dic3⋊C411yescharacteristic
719C22×C3#92411yescharacteristic
720C22×C3#92411yescharacteristic
721C22×C3C4×#6711yescharacteristic
722C22×C3#92911yescharacteristic
723C22×C3#93011yescharacteristic
724C22×C3#93711yescharacteristic
725C22×C3#93811yescharacteristic
726C22×C3#93811yescharacteristic
727C22×C3#93911yescharacteristic
728C22×C3#93911yescharacteristic
729C22×C3#93911yescharacteristic
730C22×C3#94411yescharacteristic
731C22×C3#94611yescharacteristic
732C3×C4—44no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—64no—
736C3×C4—122no—
737C3×C4—122no—
738C3×C4—122no—
739Dic3—24no—
740Dic3—42no—
741Dic3—42no—
742Dic3—42no—
743Dic3—68no—
744Dic3—64no—
745Dic3—64no—
746Dic3—124no—
747Dic3—122no—
748Dic3—122no—
749C32#144111yescharacteristic, complemented, Sylow
750C23D3×Dic611yescharacteristic
751C23D3×Dic611yescharacteristic
752C23D3×Dic611yescharacteristic
753C23#379511yescharacteristic
754C23#379611yescharacteristic
755C23#379811yescharacteristic
756C23C4×D3211yescharacteristic
757C23#380211yescharacteristic
758C23#380411yescharacteristic
759C23#380411yescharacteristic
760C23#380411yescharacteristic
761C23C2×#62611yescharacteristic
762C23D3×#6711yescharacteristic
763C23#381111yescharacteristic
764C23#381111yescharacteristic
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—34no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—94no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—182no—
802C2×C4—182no—
803C2×C4—182no—
804C2×C4—182no—
805C2×C4—182no—
806C2×C4—182no—
807C2×C4—182no—
808C2×C4—182no—
809C2×C4—182no—
810C2×C4—361no—
811C2×C4—361no—
812C2×C4—361no—
813C2×C4—361no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3#464611yescharacteristic
830C2×C3#464611yescharacteristic
831C2×C3#464711yescharacteristic
832C2×C3#465211yescharacteristic
833C2×C3#465311yescharacteristic
834C2×C3#465411yescharacteristic
835C2×C3#465611yescharacteristic
836C2×C3#465711yescharacteristic
837C2×C3#465711yescharacteristic
838C2×C3#465711yescharacteristic
839C2×C3#465811yescharacteristic
840C2×C3#466011yescharacteristic
841C2×C3#466111yescharacteristic
842C2×C3#466511yescharacteristic
843C2×C3#466711yescharacteristic
844C2×C3#467611yescharacteristic
845C2×C3#492811yescharacteristic
846C2×C3#493311yescharacteristic
847C2×C3#494211yescharacteristic
848C2×C3#494811yescharacteristic
849C2×C3#494811yescharacteristic
850C2×C3#495611yescharacteristic
851C2×C3#495911yescharacteristic
852C2×C3#496111yescharacteristic
853C2×C3#497211yescharacteristic
854C2×C3#497611yescharacteristic
855C2×C3#497911yescharacteristic
856C2×C3#498211yescharacteristic
857C2×C3#498311yescharacteristic
858C2×C3#499411yescharacteristic
859C22#6383711yescharacteristic
860C22#6383711yescharacteristic
861C22#6384011yescharacteristic
862C22#6384011yescharacteristic
863C22#6384611yescharacteristic
864C22#6384611yescharacteristic
865C22#6385111yescharacteristic
866C22#6385311yescharacteristic
867C22#6385711yescharacteristic
868C22#6385811yescharacteristic
869C22#6385911yescharacteristic
870C22#6386611yescharacteristic
871C22#6386711yescharacteristic
872C22#6386711yescharacteristic
873C22D3×Dic3⋊C411yescharacteristic
874C22#6387711yescharacteristic
875C22#6388111yescharacteristic
876C22#6388511yescharacteristic
877C22#6388711yescharacteristic
878C22#6389611yescharacteristic
879C22#6389611yescharacteristic
880C22#6389911yescharacteristic
881C22#6389911yescharacteristic
882C22#6389911yescharacteristic
883C22C4×#62611yescharacteristic
884C22#6391211yescharacteristic
885C22#6391611yescharacteristic
886C22#6392111yescharacteristic
887C22#6395311yescharacteristic
888C22#6395811yescharacteristic
889C22#6396611yescharacteristic
890C22#6397111yescharacteristic
891C22#6397511yescharacteristic
892C22#6397811yescharacteristic
893C22#6398111yescharacteristic
894C4—42no—
895C4—64no—
896C4—122no—
897C4—122no—
898C4—122no—
899C4—184no—
900C4—362no—
901C3—21no—
902C3#6940911yescharacteristic, complemented
903C3#6941111yescharacteristic, complemented
904C2#1059121011yescharacteristic
905C2#1059123411yescharacteristic
906C2#1059123611yescharacteristic
907C2#1059125111yescharacteristic
908C2#1059130811yescharacteristic
909C2#1059130911yescharacteristic
910C2#1059133011yescharacteristic
911C2#1059133211yescharacteristic
912C2#1059134011yescharacteristic
913C2#1059135411yescharacteristic
914C2#1059135611yescharacteristic
915C2#1059135811yescharacteristic
916C2#1059136911yescharacteristic
917C2#1059138711yescharacteristic
918C2#1059171211yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1441
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
22. C2×Dic3⋊Dic3C4semidirect
201. C2×C3×Dic3C4⋊C4semidirect
559. C2×Dic3Dic3⋊C4semidirect
749. C32#1441semidirect
902. C3#69409semidirect
903. C3#69411semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C22×Dic3⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#694113
#694093