Finite Group Databasebeta

← #11773247

Subgroups — #11773247

Order 1152.

1389 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C22×Dic32C211yesmaximal, characteristic
3C2×#63658C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×#63579C211yesmaximal, characteristic
6C2×#63579C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#71564—31nomaximal
9#69407—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3—22no—
18C2×C3×C4⋊Dic3—22no—
19C2×C3×C4⋊Dic3C414yescomplemented
20C2×Dic32—22no—
21C2×Dic32—22no—
22C2×Dic32—22no—
23#63658C414yescomplemented
24C3×C3⋊#95C414yescomplemented
25#63579—22no—
26#63579—22no—
27#63579—22no—
28C22×C3×C4⋊C4—31no—
29C22×C4⋊Dic3D311yescharacteristic
30C22×C4×Dic3—31no—
31C22×C4×Dic3—31no—
32C2×C3×#95—31no—
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⋊#95—61no—
42C2×C3⋊#95D311yescharacteristic
43C24×C32C2311yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4C2×C412yes—
49C22×C32×C4C2×C412yes—
50C22×C32×C4C2×C412yes—
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⋊Dic3C2×C412yes—
63C22×C3⋊Dic3D412yes—
64C22×C3⋊Dic3Q812yes—
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×Dic3C2×C412yes—
88C22×C3×Dic3C2×C412yes—
89C22×C3×Dic3D412yes—
90C22×C3×Dic3D412yes—
91C22×C3×Dic3D412yes—
92C22×C3×Dic3Q812yes—
93C3×C4⋊Dic3—28no—
94Dic32—28no—
95#1436—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×C3×C4⋊C4—34no—
114C2×C3×C4⋊C4—62no—
115C2×C3×C4⋊C4—62no—
116C2×C4⋊Dic3—22no—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3Dic314yescomplemented
119C2×C4×Dic3—62no—
120C2×C4×Dic3—62no—
121C2×C4×Dic3—62no—
122C2×C4×Dic3—62no—
123C2×C4×Dic3—62no—
124C2×C4×Dic3—62no—
125C3×#95—34no—
126C3⋊#95—34no—
127C3⋊#95—34no—
128C3⋊#95—64no—
129C3⋊#95—62no—
130C3⋊#95—62no—
131C3⋊#95—62no—
132C3⋊#95—62no—
133C3⋊#95—62no—
134C3⋊#95—62no—
135C3⋊#95Dic314yescomplemented
136C23×C32C22×C411yescharacteristic
137C23×C32C22×C411yescharacteristic
138C23×C32C22×C411yescharacteristic
139C23×C32C2×D411yescharacteristic
140C23×C32C2×D411yescharacteristic
141C23×C32C2×D411yescharacteristic
142C23×C32C2×D411yescharacteristic
143C23×C32C2×Q811yescharacteristic
144C23×C32C2×Q811yescharacteristic
145C23×C32#4111yescharacteristic
146C23×C32#4111yescharacteristic
147C23×C32#4111yescharacteristic
148C23×C32#4111yescharacteristic
149C23×C32#4111yescharacteristic
150C23×C32#4111yescharacteristic
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C4214yescomplemented
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—41no—
168C2×C3⋊Dic3—41no—
169C2×C3⋊Dic3—41no—
170C2×C3⋊Dic3—41no—
171C2×C3⋊Dic3C4⋊C414yescomplemented
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
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—22no—
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×Dic3C22⋊C414yes—
199C2×C3×Dic3C4⋊C414yescomplemented
200C22×C4⋊C4—31no—
201C22×C42—91no—
202C2×#95—31no—
203C2×#95—91no—
204C2×#95—91no—
205C2×#95—91no—
206C2×#95—91no—
207C24×C3—21no—
208C24×C3C22×D311yescharacteristic
209C24×C3C22×D311yescharacteristic
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4—32no—
228C22×C3×C4—32no—
229C22×C3×C4—41no—
230C22×C3×C4—41no—
231C22×C3×C4—41no—
232C22×C3×C4—41no—
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×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×C4C4×D312yes—
254C22×C3×C4C4×D312yes—
255C22×C3×C4C4×D312yes—
256C22×C3×C4C4×D312yes—
257C22×C3×C4C2×Dic312yes—
258C22×C3×C4C2×Dic312yes—
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—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—32no—
280C22×Dic3—32no—
281C22×Dic3—32no—
282C22×Dic3—32no—
283C22×Dic3—32no—
284C22×Dic3—32no—
285C22×Dic3—32no—
286C22×Dic3—32no—
287C22×Dic3—62no—
288C22×Dic3—62no—
289C22×Dic3—62no—
290C22×Dic3—62no—
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—62no—
300C22×Dic3—62no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—121no—
314C22×Dic3—121no—
315C22×Dic3—121no—
316C22×Dic3—121no—
317C22×Dic3—121no—
318C22×Dic3—121no—
319C22×Dic3—121no—
320C22×Dic3—121no—
321C22×Dic3Dic612yes—
322C22×Dic3D1212yes—
323C22×Dic3C2×Dic312yes—
324C22×Dic3C2×Dic312yes—
325C22×Dic3C2×Dic312yes—
326C22×Dic3C2×Dic312yes—
327C22×Dic3#6712yes—
328C22×Dic3#6712yes—
329C3×C4⋊C4—68no—
330C4⋊Dic3—28no—
331C4×Dic3—68no—
332C4×Dic3—68no—
333C22×C32C2×C4211yescharacteristic
334C22×C32C2×C22⋊C411yescharacteristic
335C22×C32C2×C4⋊C411yescharacteristic
336C22×C32C2×C4⋊C411yescharacteristic
337C22×C32#11711yescharacteristic
338C22×C32#11711yescharacteristic
339C22×C32#11711yescharacteristic
340C22×C32C4×D411yescharacteristic
341C22×C32C4×D411yescharacteristic
342C22×C32C4×D411yescharacteristic
343C22×C32C4×D411yescharacteristic
344C22×C32C4×D411yescharacteristic
345C22×C32C4×D411yescharacteristic
346C22×C32C4×D411yescharacteristic
347C22×C32C4×D411yescharacteristic
348C22×C32C4×Q811yescharacteristic
349C22×C32C4×Q811yescharacteristic
350C22×C32C4×Q811yescharacteristic
351C22×C32C4×Q811yescharacteristic
352C22×C32#12011yescharacteristic
353C22×C32#12111yescharacteristic
354C22×C32#12111yescharacteristic
355C22×C32C22⋊Q811yescharacteristic
356C22×C32C22⋊Q811yescharacteristic
357C22×C32C22⋊Q811yescharacteristic
358C22×C32C22⋊Q811yescharacteristic
359C22×C32#12311yescharacteristic
360C22×C32#12311yescharacteristic
361C22×C32#12311yescharacteristic
362C22×C32#12411yescharacteristic
363C22×C32#12511yescharacteristic
364C22×C32#12511yescharacteristic
365C22×C32#12611yescharacteristic
366C22×C32#12611yescharacteristic
367C22×C32C4⋊Q811yescharacteristic
368C32×C4—24no—
369C3⋊Dic3—24no—
370C3⋊Dic3—42no—
371C3×Dic3—24no—
372C3×Dic3—24no—
373C3×Dic3—42no—
374C3×Dic3—42no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—91no—
380C23×C4—91no—
381C23×C4D3211yescharacteristic
382C2×C4⋊C4—34no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—62no—
385C2×C42—182no—
386C2×C42—182no—
387C2×C42—182no—
388#95—34no—
389#95—94no—
390#95—182no—
391#95—182no—
392#95—182no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
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×C3C2×Dic611yescharacteristic
409C23×C3C2×C4×D311yescharacteristic
410C23×C3C2×C4×D311yescharacteristic
411C23×C3C2×C4×D311yescharacteristic
412C23×C3C2×C4×D311yescharacteristic
413C23×C3C2×D1211yescharacteristic
414C23×C3#23511yescharacteristic
415C23×C3#23511yescharacteristic
416C23×C3#23511yescharacteristic
417C23×C3#23511yescharacteristic
418C23×C3D3×D411yescharacteristic
419C23×C3D3×D411yescharacteristic
420C23×C3D3×D411yescharacteristic
421C23×C3D3×D411yescharacteristic
422C23×C3D3×D411yescharacteristic
423C23×C3#23711yescharacteristic
424C23×C3#23711yescharacteristic
425C23×C3#23711yescharacteristic
426C23×C3#23711yescharacteristic
427C23×C3#23711yescharacteristic
428C23×C3D3×Q811yescharacteristic
429C23×C3D3×Q811yescharacteristic
430C23×C3D3×Q811yescharacteristic
431C23×C3#23911yescharacteristic
432C23×C3#23911yescharacteristic
433C23×C3#23911yescharacteristic
434C23×C3C22×Dic311yescharacteristic
435C23×C3C22×Dic311yescharacteristic
436C23×C3C2×#6711yescharacteristic
437C23×C3C2×#6711yescharacteristic
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
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—22no—
449C2×C3×C4—22no—
450C2×C3×C4—24no—
451C2×C3×C4—34no—
452C2×C3×C4—34no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4—62no—
460C2×C3×C4—62no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
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—121no—
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×C4C4×Dic314yescomplemented
486C2×C3×C4C4×Dic314yescomplemented
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
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—64no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—62no—
523C2×Dic3—62no—
524C2×Dic3—62no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3—62no—
528C2×Dic3—64no—
529C2×Dic3—62no—
530C2×Dic3—62no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—122no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—122no—
539C2×Dic3—122no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542C2×Dic3—122no—
543C2×Dic3—122no—
544C2×Dic3—122no—
545C2×Dic3—122no—
546C2×Dic3—122no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—121no—
555C2×Dic3C4⋊Dic314yescomplemented
556C2×Dic3#21714yes—
557C2×C32C4×C22⋊C411yescharacteristic
558C2×C32C4×C4⋊C411yescharacteristic
559C2×C32C4×C4⋊C411yescharacteristic
560C2×C32#38511yescharacteristic
561C2×C32#38511yescharacteristic
562C2×C32#38611yescharacteristic
563C2×C32#38711yescharacteristic
564C2×C32#38711yescharacteristic
565C2×C32#38711yescharacteristic
566C2×C32#38711yescharacteristic
567C2×C32#38811yescharacteristic
568C2×C32#38811yescharacteristic
569C2×C32#38911yescharacteristic
570C2×C32#38911yescharacteristic
571C2×C32#39111yescharacteristic
572C24C2×D3211yescharacteristic
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—32no—
578C22×C4—32no—
579C22×C4—32no—
580C22×C4—32no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—32no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
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—92no—
606C22×C4—92no—
607C22×C4—92no—
608C22×C4—92no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4D3×Dic312yes—
620C22×C4D3×Dic312yes—
621C22×C4#62412yes—
622C4⋊C4—68no—
623C42—188no—
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×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×C3C4×Dic611yescharacteristic
660C22×C3C4×Dic611yescharacteristic
661C22×C3C4×D1211yescharacteristic
662C22×C3C4×D1211yescharacteristic
663C22×C3#87711yescharacteristic
664C22×C3#87811yescharacteristic
665C22×C3#87811yescharacteristic
666C22×C3#87911yescharacteristic
667C22×C3D3×C22⋊C411yescharacteristic
668C22×C3#67⋊C411yescharacteristic
669C22×C3#67⋊C411yescharacteristic
670C22×C3#88211yescharacteristic
671C22×C3#88311yescharacteristic
672C22×C3#88411yescharacteristic
673C22×C3#88511yescharacteristic
674C22×C3#88611yescharacteristic
675C22×C3#88711yescharacteristic
676C22×C3#88711yescharacteristic
677C22×C3#88711yescharacteristic
678C22×C3#88811yescharacteristic
679C22×C3#88911yescharacteristic
680C22×C3#88911yescharacteristic
681C22×C3#88911yescharacteristic
682C22×C3#89011yescharacteristic
683C22×C3D3×C4⋊C411yescharacteristic
684C22×C3D3×C4⋊C411yescharacteristic
685C22×C3D3×C4⋊C411yescharacteristic
686C22×C3#89211yescharacteristic
687C22×C3#89211yescharacteristic
688C22×C3#89211yescharacteristic
689C22×C3#89311yescharacteristic
690C22×C3#89311yescharacteristic
691C22×C3#89311yescharacteristic
692C22×C3#89411yescharacteristic
693C22×C3#89411yescharacteristic
694C22×C3#89411yescharacteristic
695C22×C3#89511yescharacteristic
696C22×C3#89611yescharacteristic
697C22×C3#89611yescharacteristic
698C22×C3#89611yescharacteristic
699C22×C3#89711yescharacteristic
700C22×C3#89811yescharacteristic
701C22×C3#89811yescharacteristic
702C22×C3#89811yescharacteristic
703C22×C3C2×C4×Dic311yescharacteristic
704C22×C3C2×C4×Dic311yescharacteristic
705C22×C3C2×C4⋊Dic311yescharacteristic
706C22×C3#92611yescharacteristic
707C22×C3#92611yescharacteristic
708C22×C3C4×#6711yescharacteristic
709C22×C3C4×#6711yescharacteristic
710C22×C3C4×#6711yescharacteristic
711C22×C3C4×#6711yescharacteristic
712C22×C3D4×Dic311yescharacteristic
713C22×C3D4×Dic311yescharacteristic
714C22×C3D4×Dic311yescharacteristic
715C22×C3D4×Dic311yescharacteristic
716C22×C3D4×Dic311yescharacteristic
717C22×C3#93511yescharacteristic
718C22×C3#93711yescharacteristic
719C22×C3#93911yescharacteristic
720C22×C3#93911yescharacteristic
721C22×C3#94411yescharacteristic
722C22×C3Q8×Dic311yescharacteristic
723C22×C3Q8×Dic311yescharacteristic
724C22×C3Q8×Dic311yescharacteristic
725C22×C3#94611yescharacteristic
726C22×C3#94611yescharacteristic
727C22×C3#94711yescharacteristic
728C22×C3C2×#21711yescharacteristic
729C3×C4—24no—
730C3×C4—24no—
731C3×C4—44no—
732C3×C4—64no—
733C3×C4—64no—
734C3×C4—122no—
735C3×C4—122no—
736Dic3—24no—
737Dic3—24no—
738Dic3—42no—
739Dic3—42no—
740Dic3—64no—
741Dic3—64no—
742Dic3—124no—
743Dic3—124no—
744Dic3—122no—
745Dic3—122no—
746C32#143611yescharacteristic, complemented, Sylow
747C23D3×Dic611yescharacteristic
748C23#379511yescharacteristic
749C23#379611yescharacteristic
750C23#379611yescharacteristic
751C23#379711yescharacteristic
752C23#379911yescharacteristic
753C23D3×D1211yescharacteristic
754C23#380211yescharacteristic
755C23C2×D3×Dic311yescharacteristic
756C23C2×D3×Dic311yescharacteristic
757C23#380411yescharacteristic
758C23#380411yescharacteristic
759C23C2×#62411yescharacteristic
760C23D3×#6711yescharacteristic
761C23D3×#6711yescharacteristic
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—34no—
769C2×C4—34no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
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—182no—
798C2×C4—182no—
799C2×C4—182no—
800C2×C4—182no—
801C2×C4—182no—
802C2×C4—182no—
803C2×C4—182no—
804C2×C4—182no—
805C2×C4—182no—
806C2×C4—361no—
807C2×C4—361no—
808C2×C4—361no—
809C2×C4—361no—
810C2×C4Dic3214yescomplemented
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
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#464611yescharacteristic
827C2×C3#464711yescharacteristic
828C2×C3#465311yescharacteristic
829C2×C3#465411yescharacteristic
830C2×C3#465511yescharacteristic
831C2×C3#466511yescharacteristic
832C2×C3#466811yescharacteristic
833C2×C3#467011yescharacteristic
834C2×C3C4×C4⋊Dic311yescharacteristic
835C2×C3Dic3×C22⋊C411yescharacteristic
836C2×C3#495011yescharacteristic
837C2×C3#495111yescharacteristic
838C2×C3Dic3×C4⋊C411yescharacteristic
839C2×C3Dic3×C4⋊C411yescharacteristic
840C2×C3Dic3×C4⋊C411yescharacteristic
841C2×C3#497611yescharacteristic
842C2×C3#497611yescharacteristic
843C2×C3#497811yescharacteristic
844C2×C3#497811yescharacteristic
845C2×C3#498011yescharacteristic
846C2×C3#498011yescharacteristic
847C2×C3#498011yescharacteristic
848C2×C3#498411yescharacteristic
849C2×C3#498911yescharacteristic
850C2×C3#498911yescharacteristic
851C2×C3#499011yescharacteristic
852C2×C3#499011yescharacteristic
853C2×C3C4×#21711yescharacteristic
854C2×C3#522011yescharacteristic
855C2×C3#522911yescharacteristic
856C22#6383911yescharacteristic
857C22#6384111yescharacteristic
858C22Dic3×Dic611yescharacteristic
859C22#6384311yescharacteristic
860C22#6384311yescharacteristic
861C22#6384411yescharacteristic
862C22#6384611yescharacteristic
863C22#6384711yescharacteristic
864C22#6384811yescharacteristic
865C22#6384911yescharacteristic
866C22#6385411yescharacteristic
867C22#6385811yescharacteristic
868C22#6388411yescharacteristic
869C22#6388511yescharacteristic
870C22#6388611yescharacteristic
871C22#6388711yescharacteristic
872C22#6388811yescharacteristic
873C22D3×C4⋊Dic311yescharacteristic
874C22#6389011yescharacteristic
875C22Dic3×D1211yescharacteristic
876C22#6389411yescharacteristic
877C22#6389511yescharacteristic
878C22#6389811yescharacteristic
879C22#6389811yescharacteristic
880C22#6389911yescharacteristic
881C22#6390011yescharacteristic
882C22#6390711yescharacteristic
883C22#6392211yescharacteristic
884C22#6395211yescharacteristic
885C22#6395211yescharacteristic
886C22C2×Dic3211yescharacteristic
887C22#6395511yescharacteristic
888C22D3×#21711yescharacteristic
889C22Dic3×#6711yescharacteristic
890C22Dic3×#6711yescharacteristic
891C4—24no—
892C4—64no—
893C4—64no—
894C4—122no—
895C4—122no—
896C4—184no—
897C4—362no—
898C3—21no—
899C3#6940711yescharacteristic, complemented
900C3#7156411yescharacteristic, complemented
901C2#1059126111yescharacteristic
902C2#1059126211yescharacteristic
903C2#1059126311yescharacteristic
904C2#1059126411yescharacteristic
905C2#1059126511yescharacteristic
906C2#1059126611yescharacteristic
907C2Dic3×C4⋊Dic311yescharacteristic
908C2#1059126911yescharacteristic
909C2#1059127011yescharacteristic
910C2#1059127411yescharacteristic
911C2#1059130711yescharacteristic
912C2#1059137611yescharacteristic
913C2#1059137711yescharacteristic
914C2#1059137811yescharacteristic
915C2Dic3×#21711yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC22×C32C2×C42
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1436
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
19. C2×C3×C4⋊Dic3C4semidirect
23. #63658C4semidirect
24. C3×C3⋊#95C4semidirect
118. C2×C4⋊Dic3Dic3semidirect
135. C3⋊#95Dic3semidirect
157. C2×C32×C4C42semidirect
171. C2×C3⋊Dic3C4⋊C4semidirect
199. C2×C3×Dic3C4⋊C4semidirect
485. C2×C3×C4C4×Dic3semidirect
486. C2×C3×C4C4×Dic3semidirect
555. C2×Dic3C4⋊Dic3semidirect
746. C32#1436semidirect
810. C2×C4Dic32semidirect
899. C3#69407semidirect
900. C3#71564semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C22×Dic322
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#715643
#694073