Finite Group Databasebeta

← #11773429

Subgroups — #11773429

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63658C211yesmaximal, characteristic
2C2×C3×C3⋊#95C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×#63579C211yesmaximal, characteristic
5C2×#63579C211yesmaximal, characteristic
6C2×#63579C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#69417—31nomaximal
9#69417—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17#63658—22no—
18C3×C3⋊#95—22no—
19C3×C3⋊#95—22no—
20#63579—22no—
21#63579—22no—
22#63579—22no—
23#63579C414yescomplemented
24C2×C3×#95—31no—
25C2×C3×#95—31no—
26C2×C3⋊#95—31no—
27C2×C3⋊#95—31no—
28C2×C3⋊#95—31no—
29C2×C3⋊#95—31no—
30C2×C3⋊#95—31no—
31C2×C3⋊#95—31no—
32C2×C3⋊#95—31no—
33C2×C3⋊#95—31no—
34C2×C3⋊#95—31no—
35C2×C3⋊#95—31no—
36C2×C3⋊#95—61no—
37C2×C3⋊#95D311yescharacteristic
38C2×C3⋊#95D311yescharacteristic
39C24×C32C2311yescharacteristic
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4Q812yes—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3—21no—
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⋊Dic3C2×C412yes—
60C22×C3⋊Dic3D412yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
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×Dic3C2×C412yes—
86C22×C3×Dic3C2×C412yes—
87C22×C3×Dic3D412yes—
88C22×C3×Dic3D412yes—
89#1443—91noSylow
90C23×C3×C4—21no—
91C23×C3×C4—31no—
92C23×C3×C4—31no—
93C23×C3×C4—31no—
94C23×C3×C4—31no—
95C23×C3×C4C2×D311yescharacteristic
96C23×C3×C4C2×D311yescharacteristic
97C23×Dic3—31no—
98C23×Dic3—31no—
99C23×Dic3—31no—
100C23×Dic3—31no—
101C23×Dic3—61no—
102C23×Dic3—61no—
103C23×Dic3C2×D311yescharacteristic
104C23×Dic3C2×D311yescharacteristic
105C23×Dic3C2×D311yescharacteristic
106C23×Dic3C2×D311yescharacteristic
107C3×#95—62no—
108C3×#95—62no—
109C3⋊#95—22no—
110C3⋊#95—22no—
111C3⋊#95—34no—
112C3⋊#95—34no—
113C3⋊#95—62no—
114C3⋊#95—62no—
115C3⋊#95—62no—
116C3⋊#95—62no—
117C3⋊#95—62no—
118C3⋊#95—62no—
119C3⋊#95—64no—
120C3⋊#95—62no—
121C3⋊#95—62no—
122C23×C32C22×C411yescharacteristic
123C23×C32C2×D411yescharacteristic
124C23×C32C2×D411yescharacteristic
125C23×C32C2×D411yescharacteristic
126C23×C32C2×Q811yescharacteristic
127C23×C32#4111yescharacteristic
128C23×C32#4111yescharacteristic
129C23×C32#4111yescharacteristic
130C23×C32#4111yescharacteristic
131C23×C32#4111yescharacteristic
132C23×C32#4111yescharacteristic
133C23×C32#4111yescharacteristic
134C23×C32#4111yescharacteristic
135C23×C32#4111yescharacteristic
136C23×C32#4111yescharacteristic
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4—22no—
140C2×C32×C4—41no—
141C2×C32×C4—41no—
142C2×C32×C4—41no—
143C2×C32×C4—41no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—41no—
151C2×C3⋊Dic3—41no—
152C2×C3⋊Dic3—41no—
153C2×C3⋊Dic3—41no—
154C2×C3⋊Dic3—41no—
155C2×C3⋊Dic3—41no—
156C2×C3⋊Dic3—41no—
157C2×C3⋊Dic3—41no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
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—22no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—41no—
173C2×C3×Dic3—41no—
174C2×C3×Dic3—41no—
175C2×C3×Dic3—41no—
176C2×C3×Dic3—41no—
177C2×C3×Dic3—41no—
178C2×C3×Dic3—41no—
179C2×C3×Dic3—41no—
180C2×C3×Dic3—41no—
181C2×C3×Dic3—41no—
182C2×C3×Dic3—41no—
183C2×C3×Dic3—41no—
184C2×C3×Dic3—41no—
185C2×C3×Dic3—41no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—91no—
189C2×#95—91no—
190C2×#95—91no—
191C2×#95—91no—
192C2×#95—91no—
193C24×C3—21no—
194C24×C3C22×D311yescharacteristic
195C24×C3C22×D311yescharacteristic
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—32no—
215C22×C3×C4—41no—
216C22×C3×C4—41no—
217C22×C3×C4—41no—
218C22×C3×C4—41no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4—61no—
223C22×C3×C4—61no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C22×C3×C4—61no—
232C22×C3×C4—61no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4—61no—
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×C4Dic612yes—
244C22×C3×C4Dic612yes—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
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—32no—
270C22×Dic3—32no—
271C22×Dic3—32no—
272C22×Dic3—32no—
273C22×Dic3—62no—
274C22×Dic3—62no—
275C22×Dic3—62no—
276C22×Dic3—62no—
277C22×Dic3—62no—
278C22×Dic3—62no—
279C22×Dic3—61no—
280C22×Dic3—61no—
281C22×Dic3—61no—
282C22×Dic3—61no—
283C22×Dic3—61no—
284C22×Dic3—61no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288C22×Dic3—61no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294C22×Dic3—61no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—121no—
304C22×Dic3—121no—
305C22×Dic3—121no—
306C22×Dic3—121no—
307C22×Dic3—121no—
308C22×Dic3—121no—
309C22×Dic3—121no—
310C22×Dic3—121no—
311C22×Dic3C4×D312yes—
312C22×Dic3C4×D312yes—
313C22×Dic3#6712yes—
314C22×Dic3#6712yes—
315C22×C32#11711yescharacteristic
316C22×C32#11711yescharacteristic
317C22×C32#11711yescharacteristic
318C22×C32C4×D411yescharacteristic
319C22×C32C4×D411yescharacteristic
320C22×C32C4×D411yescharacteristic
321C22×C32C4×Q811yescharacteristic
322C22×C32#12111yescharacteristic
323C22×C32#12111yescharacteristic
324C22×C32#12111yescharacteristic
325C22×C32C22⋊Q811yescharacteristic
326C22×C32C22⋊Q811yescharacteristic
327C22×C32C22⋊Q811yescharacteristic
328C22×C32#12311yescharacteristic
329C22×C32#12311yescharacteristic
330C22×C32#12311yescharacteristic
331C22×C32#12311yescharacteristic
332C22×C32#12311yescharacteristic
333C22×C32#12311yescharacteristic
334C22×C32#12411yescharacteristic
335C22×C32#12411yescharacteristic
336C22×C32#12411yescharacteristic
337C22×C32#12511yescharacteristic
338C22×C32#12511yescharacteristic
339C22×C32#12511yescharacteristic
340C22×C32#12611yescharacteristic
341C22×C32#12611yescharacteristic
342C22×C32#12611yescharacteristic
343C22×C32#12611yescharacteristic
344C22×C32#12611yescharacteristic
345C22×C32#12611yescharacteristic
346C22×C32#12611yescharacteristic
347C22×C32#12611yescharacteristic
348C22×C32#12611yescharacteristic
349C22×C32#12611yescharacteristic
350C32×C4—42no—
351C3⋊Dic3—42no—
352C3⋊Dic3—42no—
353C3×Dic3—42no—
354C3×Dic3—42no—
355C3×Dic3—42no—
356C3×Dic3—42no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—91no—
362C23×C4—91no—
363C23×C4D3211yescharacteristic
364#95—62no—
365#95—62no—
366#95—94no—
367#95—182no—
368#95—182no—
369#95—182no—
370#95—182no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3C2×Dic611yescharacteristic
387C23×C3C2×Dic611yescharacteristic
388C23×C3C2×C4×D311yescharacteristic
389C23×C3C2×C4×D311yescharacteristic
390C23×C3#23511yescharacteristic
391C23×C3#23511yescharacteristic
392C23×C3#23511yescharacteristic
393C23×C3#23511yescharacteristic
394C23×C3#23511yescharacteristic
395C23×C3#23511yescharacteristic
396C23×C3#23511yescharacteristic
397C23×C3#23511yescharacteristic
398C23×C3D3×D411yescharacteristic
399C23×C3D3×D411yescharacteristic
400C23×C3D3×D411yescharacteristic
401C23×C3D3×D411yescharacteristic
402C23×C3#23711yescharacteristic
403C23×C3#23711yescharacteristic
404C23×C3#23711yescharacteristic
405C23×C3#23711yescharacteristic
406C23×C3#23711yescharacteristic
407C23×C3#23711yescharacteristic
408C23×C3#23711yescharacteristic
409C23×C3#23711yescharacteristic
410C23×C3#23911yescharacteristic
411C23×C3#23911yescharacteristic
412C23×C3#23911yescharacteristic
413C23×C3#23911yescharacteristic
414C23×C3C2×#6711yescharacteristic
415C23×C3C2×#6711yescharacteristic
416C2×C3×C4—24no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—62no—
438C2×C3×C4—62no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4—62no—
444C2×C3×C4—62no—
445C2×C3×C4—62no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—121no—
450C2×C3×C4—121no—
451C2×C3×C4—121no—
452C2×C3×C4—121no—
453C2×C3×C4—121no—
454C2×C3×C4—121no—
455C2×C3×C4—121no—
456C2×C3×C4—121no—
457C2×C3×C4—121no—
458C2×C3×C4—121no—
459C2×C3×C4—121no—
460C2×C3×C4—121no—
461C2×C3×C4—121no—
462C2×C3×C4—121no—
463C2×C3×C4—121no—
464C2×C3×C4—121no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—64no—
494C2×Dic3—64no—
495C2×Dic3—62no—
496C2×Dic3—62no—
497C2×Dic3—62no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—62no—
504C2×Dic3—62no—
505C2×Dic3—62no—
506C2×Dic3—62no—
507C2×Dic3—122no—
508C2×Dic3—122no—
509C2×Dic3—122no—
510C2×Dic3—122no—
511C2×Dic3—122no—
512C2×Dic3—122no—
513C2×Dic3—122no—
514C2×Dic3—122no—
515C2×Dic3—122no—
516C2×Dic3—122no—
517C2×Dic3—122no—
518C2×Dic3—122no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—121no—
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×C32#38311yescharacteristic
536C2×C32#38711yescharacteristic
537C2×C32#38711yescharacteristic
538C2×C32#38711yescharacteristic
539C2×C32#38811yescharacteristic
540C2×C32#38811yescharacteristic
541C2×C32#38811yescharacteristic
542C2×C32#39611yescharacteristic
543C2×C32#39711yescharacteristic
544C2×C32#39711yescharacteristic
545C2×C32#39711yescharacteristic
546C2×C32#40011yescharacteristic
547C2×C32#40011yescharacteristic
548C2×C32#40011yescharacteristic
549C2×C32#40111yescharacteristic
550C24C2×D3211yescharacteristic
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—92no—
586C22×C4—92no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4#62712yes—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
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×C3C4×Dic611yescharacteristic
636C22×C3C4×Dic611yescharacteristic
637C22×C3#87011yescharacteristic
638C22×C3#87011yescharacteristic
639C22×C3#87211yescharacteristic
640C22×C3#87211yescharacteristic
641C22×C3#87611yescharacteristic
642C22×C3#87611yescharacteristic
643C22×C3#87711yescharacteristic
644C22×C3#87711yescharacteristic
645C22×C3#87811yescharacteristic
646C22×C3#87811yescharacteristic
647C22×C3#87811yescharacteristic
648C22×C3#87811yescharacteristic
649C22×C3#87911yescharacteristic
650C22×C3#87911yescharacteristic
651C22×C3#87911yescharacteristic
652C22×C3#87911yescharacteristic
653C22×C3#87911yescharacteristic
654C22×C3#87911yescharacteristic
655C22×C3#87911yescharacteristic
656C22×C3#87911yescharacteristic
657C22×C3#67⋊C411yescharacteristic
658C22×C3#67⋊C411yescharacteristic
659C22×C3#88311yescharacteristic
660C22×C3#88311yescharacteristic
661C22×C3#88411yescharacteristic
662C22×C3#88411yescharacteristic
663C22×C3#88511yescharacteristic
664C22×C3#88511yescharacteristic
665C22×C3#88511yescharacteristic
666C22×C3#88511yescharacteristic
667C22×C3#89011yescharacteristic
668C22×C3#89011yescharacteristic
669C22×C3#89011yescharacteristic
670C22×C3#89011yescharacteristic
671C22×C3#89211yescharacteristic
672C22×C3#89211yescharacteristic
673C22×C3#89311yescharacteristic
674C22×C3#89311yescharacteristic
675C22×C3#89411yescharacteristic
676C22×C3#89411yescharacteristic
677C22×C3#89411yescharacteristic
678C22×C3#89411yescharacteristic
679C22×C3#89411yescharacteristic
680C22×C3#89411yescharacteristic
681C22×C3#89811yescharacteristic
682C22×C3#89811yescharacteristic
683C22×C3#89811yescharacteristic
684C22×C3#89811yescharacteristic
685C22×C3#89811yescharacteristic
686C22×C3#89811yescharacteristic
687C22×C3#89811yescharacteristic
688C22×C3#89811yescharacteristic
689C22×C3#89811yescharacteristic
690C22×C3#89811yescharacteristic
691C22×C3#92411yescharacteristic
692C22×C3#92411yescharacteristic
693C22×C3C4×#6711yescharacteristic
694C22×C3C4×#6711yescharacteristic
695C22×C3#92911yescharacteristic
696C22×C3#92911yescharacteristic
697C22×C3#93511yescharacteristic
698C22×C3#93511yescharacteristic
699C22×C3#93811yescharacteristic
700C22×C3#93811yescharacteristic
701C22×C3#93911yescharacteristic
702C22×C3#93911yescharacteristic
703C22×C3#94711yescharacteristic
704C22×C3#94711yescharacteristic
705C3×C4—44no—
706C3×C4—42no—
707C3×C4—42no—
708C3×C4—122no—
709C3×C4—122no—
710C3×C4—122no—
711C3×C4—122no—
712Dic3—42no—
713Dic3—42no—
714Dic3—42no—
715Dic3—42no—
716Dic3—124no—
717Dic3—124no—
718Dic3—122no—
719Dic3—122no—
720Dic3—122no—
721Dic3—122no—
722C32#144311yescharacteristic, complemented, Sylow
723C23#379511yescharacteristic
724C23#379511yescharacteristic
725C23#379611yescharacteristic
726C23#379611yescharacteristic
727C23#379811yescharacteristic
728C23#379911yescharacteristic
729C23#379911yescharacteristic
730C23C4×D3211yescharacteristic
731C23#380411yescharacteristic
732C23#380411yescharacteristic
733C23#380511yescharacteristic
734C23C2×#62711yescharacteristic
735C23D3×#6711yescharacteristic
736C23D3×#6711yescharacteristic
737C23#381111yescharacteristic
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—121no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—182no—
774C2×C4—182no—
775C2×C4—182no—
776C2×C4—182no—
777C2×C4—182no—
778C2×C4—182no—
779C2×C4—361no—
780C2×C4—361no—
781C2×C4—361no—
782C2×C4—361no—
783C2×C4—361no—
784C2×C4—361no—
785C2×C4—361no—
786C2×C4—361no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3#465111yescharacteristic
803C2×C3#465111yescharacteristic
804C2×C3#465411yescharacteristic
805C2×C3#465411yescharacteristic
806C2×C3#465511yescharacteristic
807C2×C3#465511yescharacteristic
808C2×C3#466011yescharacteristic
809C2×C3#466011yescharacteristic
810C2×C3#466011yescharacteristic
811C2×C3#466011yescharacteristic
812C2×C3C3⋊#40111yescharacteristic
813C2×C3C3⋊#40111yescharacteristic
814C2×C3#466911yescharacteristic
815C2×C3#466911yescharacteristic
816C2×C3#467511yescharacteristic
817C2×C3#467511yescharacteristic
818C2×C3#493311yescharacteristic
819C2×C3#493311yescharacteristic
820C2×C3#494411yescharacteristic
821C2×C3#494411yescharacteristic
822C2×C3#494811yescharacteristic
823C2×C3#494811yescharacteristic
824C2×C3#495211yescharacteristic
825C2×C3#495211yescharacteristic
826C2×C3#498611yescharacteristic
827C2×C3#498611yescharacteristic
828C2×C3#499011yescharacteristic
829C2×C3#499011yescharacteristic
830C2×C3#499211yescharacteristic
831C2×C3#499211yescharacteristic
832C22#6383611yescharacteristic
833C22#6384811yescharacteristic
834C22#6384811yescharacteristic
835C22#6385011yescharacteristic
836C22#6385311yescharacteristic
837C22#6385811yescharacteristic
838C22#6385811yescharacteristic
839C22#6385911yescharacteristic
840C22#6386111yescharacteristic
841C22#6386111yescharacteristic
842C22#6386211yescharacteristic
843C22#6386811yescharacteristic
844C22#6386911yescharacteristic
845C22#6386911yescharacteristic
846C22#6387211yescharacteristic
847C22#6387711yescharacteristic
848C22#6387811yescharacteristic
849C22#6387911yescharacteristic
850C22#6388111yescharacteristic
851C22#6388411yescharacteristic
852C22#6388411yescharacteristic
853C22#6389711yescharacteristic
854C22#6390411yescharacteristic
855C22#6390511yescharacteristic
856C22#6390711yescharacteristic
857C22#6390711yescharacteristic
858C22#6391311yescharacteristic
859C22C4×#62711yescharacteristic
860C22#6395611yescharacteristic
861C22#6395811yescharacteristic
862C22#6396411yescharacteristic
863C22#6396411yescharacteristic
864C22#6397011yescharacteristic
865C22#6397111yescharacteristic
866C22#6398211yescharacteristic
867C4—42no—
868C4—122no—
869C4—122no—
870C4—122no—
871C4—122no—
872C4—362no—
873C4—362no—
874C3—21no—
875C3#6941711yescharacteristic, complemented
876C3#6941711yescharacteristic, complemented
877C2#1059120411yescharacteristic
878C2#1059121811yescharacteristic
879C2#1059122811yescharacteristic
880C2#1059124811yescharacteristic
881C2#1059125811yescharacteristic
882C2#1059128111yescharacteristic
883C2#1059128511yescharacteristic
884C2#1059129811yescharacteristic
885C2#1059130111yescharacteristic
886C2#1059133111yescharacteristic
887C2#1059133311yescharacteristic
888C2#1059133511yescharacteristic
889C2#1059134311yescharacteristic
890C2#1059134311yescharacteristic
891C2#1059169111yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
23. #63579C4semidirect
722. C32#1443semidirect
875. C3#69417semidirect
876. C3#69417semidirect

Maximal subgroups

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

subgroupindex
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#694173