Finite Group Databasebeta

← #11773308

Subgroups — #11773308

Order 1152.

1725 conjugacy classes of subgroups.

The subgroup lattice has 1145 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
4C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
5C2×#63658C211yesmaximal, characteristic, complemented
6C2×#63579C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#71570—31nomaximal
9#71547—31nomaximal
10C24×C3×D3C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—22no—
18C2×C3×(C2×D3)⋊C4—22no—
19C2×C3×(C2×D3)⋊C4—22no—
20C2×C3×Dic3⋊C4—22no—
21C2×C3×Dic3⋊C4—22no—
22C2×C3×Dic3⋊C4—22no—
23C2×(C2×D3)⋊Dic3—22no—
24C2×(C2×D3)⋊Dic3—22no—
25C2×(C2×D3)⋊Dic3—22no—
26C2×(C2×D3)⋊Dic3—22no—
27C2×(C2×D3)⋊Dic3—22no—
28C2×(C2×D3)⋊Dic3C414yescomplemented
29#63658—22no—
30#63579—22no—
31#63579—22no—
32C22×C3×C4⋊C4—31no—
33C22×C3×C22⋊C4—31no—
34C22×#217—31no—
35C22×#217—31no—
36C22×(C2×D3)⋊C4—31no—
37C22×(C2×D3)⋊C4—31no—
38C22×(C2×D3)⋊C4D311yescharacteristic
39C22×Dic3⋊C4D311yescharacteristic, complemented
40C2×C3⋊#95—31no—
41C2×C3⋊#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44C2×C3⋊#95—31no—
45C2×C3⋊#95—31no—
46C2×C3⋊#95—61no—
47C24×C32C2311yescharacteristic
48C23×C3×D3—21no—
49C23×C3×D3—21no—
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C23×C3×D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3—21no—
55C23×C3×D3—21no—
56C23×C3×D3—21no—
57C23×C3×D3—21no—
58C23×C3×D3—21no—
59C23×C3×D3—21no—
60C23×C3×D3C2×C412yes—
61C23×C3×D3D412yes—
62C23×C3×D3Q812yes—
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4D412yes—
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⋊Dic3C2×C412yes—
83C22×C3⋊Dic3D412yes—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3C2×C412yes—
101C22×C3×Dic3D412yes—
102C22×C3×Dic3D412yes—
103C22×C3×Dic3D412yes—
104C22×C3×Dic3D412yes—
105C3×(C2×D3)⋊C4—28no—
106C3×Dic3⋊C4—28no—
107(C2×D3)⋊Dic3—28no—
108(C2×D3)⋊Dic3—28no—
109#1439—91noSylow
110C25×C3—31no—
111C24×D3C2×D311yescharacteristic
112C23×C3×C4—21no—
113C23×C3×C4—31no—
114C23×C3×C4—31no—
115C23×C3×C4—31no—
116C23×C3×C4C2×D311yescharacteristic
117C23×C3×C4C2×D311yescharacteristic
118C23×Dic3—31no—
119C23×Dic3—31no—
120C23×Dic3—31no—
121C23×Dic3—31no—
122C23×Dic3—61no—
123C23×Dic3—61no—
124C23×Dic3C2×D311yescharacteristic
125C23×Dic3C2×D311yescharacteristic
126C23×Dic3C2×D311yescharacteristic
127C2×C3×C4⋊C4—62no—
128C2×C3×C4⋊C4—62no—
129C2×C3×C4⋊C4—62no—
130C2×C3×C22⋊C4—62no—
131C2×C3×C22⋊C4—62no—
132C2×C3×C22⋊C4—62no—
133C2×#217—34no—
134C2×#217—62no—
135C2×#217—62no—
136C2×#217—62no—
137C2×#217—62no—
138C2×#217—62no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—34no—
143C2×(C2×D3)⋊C4—62no—
144C2×(C2×D3)⋊C4—62no—
145C2×(C2×D3)⋊C4—62no—
146C2×(C2×D3)⋊C4—62no—
147C2×(C2×D3)⋊C4—62no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C3⋊#95—62no—
152C3⋊#95—62no—
153C3⋊#95—62no—
154C3⋊#95—62no—
155C3⋊#95—64no—
156C3⋊#95—62no—
157C3⋊#95—62no—
158C23×C32C22×C411yescharacteristic
159C23×C32C2×D411yescharacteristic
160C23×C32C2×D411yescharacteristic
161C23×C32C2×D411yescharacteristic
162C23×C32C2×D411yescharacteristic
163C23×C32C2×D411yescharacteristic
164C23×C32C2×D411yescharacteristic
165C23×C32C2×D411yescharacteristic
166C23×C32C2×Q811yescharacteristic
167C23×C32#4111yescharacteristic
168C23×C32#4111yescharacteristic
169C23×C32#4111yescharacteristic
170C23×C32#4111yescharacteristic
171C23×C32#4111yescharacteristic
172C23×C32#4111yescharacteristic
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3—22no—
190C22×C3×D3—22no—
191C22×C3×D3—41no—
192C22×C3×D3—41no—
193C22×C3×D3—41no—
194C22×C3×D3—41no—
195C22×C3×D3—41no—
196C22×C3×D3—41no—
197C22×C3×D3—41no—
198C22×C3×D3—41no—
199C22×C3×D3—41no—
200C22×C3×D3—41no—
201C22×C3×D3—41no—
202C22×C3×D3—41no—
203C22×C3×D3—41no—
204C22×C3×D3—41no—
205C22×C3×D3—41no—
206C22×C3×D3—41no—
207C22×C3×D3C4⋊C414yescomplemented
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—22no—
211C2×C32×C4—41no—
212C2×C32×C4—41no—
213C2×C32×C4—41no—
214C2×C32×C4—41no—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3—22no—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3—41no—
222C2×C3⋊Dic3—41no—
223C2×C3⋊Dic3—41no—
224C2×C3⋊Dic3—41no—
225C2×C3⋊Dic3—41no—
226C2×C3⋊Dic3—41no—
227C2×C3⋊Dic3—41no—
228C2×C3⋊Dic3—41no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—41no—
243C2×C3×Dic3—41no—
244C2×C3×Dic3—41no—
245C2×C3×Dic3—41no—
246C2×C3×Dic3—41no—
247C2×C3×Dic3—41no—
248C2×C3×Dic3—41no—
249C2×C3×Dic3C22⋊C414yescomplemented
250C22×C4⋊C4—31no—
251C22×C22⋊C4—31no—
252C22×C22⋊C4—91no—
253C22×C22⋊C4—91no—
254C2×#95—91no—
255C2×#95—91no—
256C2×#95—91no—
257C24×C3—21no—
258C24×C3—32no—
259C24×C3—32no—
260C24×C3—32no—
261C24×C3—61no—
262C24×C3—61no—
263C24×C3—61no—
264C24×C3—61no—
265C24×C3—61no—
266C24×C3—61no—
267C24×C3—61no—
268C24×C3—61no—
269C24×C3—61no—
270C24×C3—61no—
271C24×C3—61no—
272C24×C3—61no—
273C24×C3C22×D311yescharacteristic
274C24×C3C22×D311yescharacteristic
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—21no—
285C23×D3—21no—
286C23×D3—21no—
287C23×D3Dic612yes—
288C23×D3C4×D312yes—
289C23×D3#6712yes—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—22no—
305C22×C3×C4—32no—
306C22×C3×C4—32no—
307C22×C3×C4—32no—
308C22×C3×C4—32no—
309C22×C3×C4—32no—
310C22×C3×C4—41no—
311C22×C3×C4—41no—
312C22×C3×C4—41no—
313C22×C3×C4—41no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4#6712yes—
331C22×C3×C4#6712yes—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—32no—
349C22×Dic3—32no—
350C22×Dic3—32no—
351C22×Dic3—32no—
352C22×Dic3—62no—
353C22×Dic3—62no—
354C22×Dic3—62no—
355C22×Dic3—62no—
356C22×Dic3—62no—
357C22×Dic3—62no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374C22×Dic3—61no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—121no—
383C22×Dic3—121no—
384C22×Dic3—121no—
385C22×Dic3—121no—
386C22×Dic3—121no—
387C22×Dic3—121no—
388C22×Dic3—121no—
389C22×Dic3—121no—
390C22×Dic3C4×D312yes—
391C22×Dic3D1212yes—
392C22×Dic3#6712yes—
393C22×Dic3#6712yes—
394C22×Dic3#6712yes—
395C3×C4⋊C4—68no—
396C3×C22⋊C4—68no—
397#217—68no—
398#217—68no—
399(C2×D3)⋊C4—28no—
400(C2×D3)⋊C4—68no—
401(C2×D3)⋊C4—68no—
402Dic3⋊C4—28no—
403C22×C32C2×C22⋊C411yescharacteristic
404C22×C32C2×C4⋊C411yescharacteristic
405C22×C32#11711yescharacteristic
406C22×C32C4×D411yescharacteristic
407C22×C32C4×D411yescharacteristic
408C22×C32C4×D411yescharacteristic
409C22×C32C4×D411yescharacteristic
410C22×C32#12011yescharacteristic
411C22×C32#12011yescharacteristic
412C22×C32#12011yescharacteristic
413C22×C32#12111yescharacteristic
414C22×C32#12111yescharacteristic
415C22×C32#12111yescharacteristic
416C22×C32#12111yescharacteristic
417C22×C32#12111yescharacteristic
418C22×C32#12111yescharacteristic
419C22×C32#12111yescharacteristic
420C22×C32#12111yescharacteristic
421C22×C32C22⋊Q811yescharacteristic
422C22×C32C22⋊Q811yescharacteristic
423C22×C32C22⋊Q811yescharacteristic
424C22×C32C22⋊Q811yescharacteristic
425C22×C32C22⋊Q811yescharacteristic
426C22×C32C22⋊Q811yescharacteristic
427C22×C32#12311yescharacteristic
428C22×C32#12311yescharacteristic
429C22×C32#12311yescharacteristic
430C22×C32#12311yescharacteristic
431C22×C32#12311yescharacteristic
432C22×C32#12411yescharacteristic
433C22×C32#12411yescharacteristic
434C22×C32#12411yescharacteristic
435C22×C32#12611yescharacteristic
436C22×C32#12611yescharacteristic
437C22×C32#12711yescharacteristic
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—24no—
441C2×C3×D3—42no—
442C2×C3×D3—42no—
443C2×C3×D3—42no—
444C2×C3×D3—42no—
445C2×C3×D3—42no—
446C2×C3×D3—42no—
447C2×C3×D3—42no—
448C2×C3×D3—42no—
449C2×C3×D3—42no—
450C2×C3×D3—42no—
451C2×C3×D3—42no—
452C2×C3×D3—42no—
453C32×C4—42no—
454C3⋊Dic3—42no—
455C3⋊Dic3—42no—
456C3×Dic3—24no—
457C3×Dic3—42no—
458C3×Dic3—42no—
459C25—31no—
460C23×C4—31no—
461C23×C4—31no—
462C23×C4—31no—
463C23×C4—91no—
464C23×C4—91no—
465C23×C4D3211yescharacteristic
466C2×C4⋊C4—62no—
467C2×C4⋊C4—62no—
468C2×C4⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—94no—
473C2×C22⋊C4—182no—
474C2×C22⋊C4—182no—
475C2×C22⋊C4—182no—
476C2×C22⋊C4—182no—
477C2×C22⋊C4—182no—
478#95—182no—
479#95—182no—
480#95—182no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—34no—
497C23×C3—62no—
498C23×C3—62no—
499C23×C3—62no—
500C23×C3—62no—
501C23×C3—62no—
502C23×C3—62no—
503C23×C3—62no—
504C23×C3—62no—
505C23×C3—62no—
506C23×C3—62no—
507C23×C3—62no—
508C23×C3—62no—
509C23×C3—62no—
510C23×C3—62no—
511C23×C3—62no—
512C23×C3—62no—
513C23×C3—62no—
514C23×C3—62no—
515C23×C3—121no—
516C23×C3—121no—
517C23×C3—121no—
518C23×C3—121no—
519C23×C3—121no—
520C23×C3—121no—
521C23×C3—121no—
522C23×C3—121no—
523C23×C3—121no—
524C23×C3—121no—
525C23×C3—121no—
526C23×C3—121no—
527C23×C3—121no—
528C23×C3—121no—
529C23×C3—121no—
530C23×C3—121no—
531C23×C3C2×Dic611yescharacteristic
532C23×C3C2×C4×D311yescharacteristic
533C23×C3C2×C4×D311yescharacteristic
534C23×C3C2×D1211yescharacteristic
535C23×C3#23511yescharacteristic
536C23×C3#23511yescharacteristic
537C23×C3#23511yescharacteristic
538C23×C3#23511yescharacteristic
539C23×C3D3×D411yescharacteristic
540C23×C3D3×D411yescharacteristic
541C23×C3D3×D411yescharacteristic
542C23×C3D3×D411yescharacteristic
543C23×C3D3×D411yescharacteristic
544C23×C3D3×D411yescharacteristic
545C23×C3D3×D411yescharacteristic
546C23×C3#23711yescharacteristic
547C23×C3#23711yescharacteristic
548C23×C3#23711yescharacteristic
549C23×C3#23711yescharacteristic
550C23×C3#23711yescharacteristic
551C23×C3D3×Q811yescharacteristic
552C23×C3#23911yescharacteristic
553C23×C3#23911yescharacteristic
554C23×C3#23911yescharacteristic
555C23×C3C2×#6711yescharacteristic
556C23×C3C2×#6711yescharacteristic
557C23×C3C2×#6711yescharacteristic
558C23×C3C2×#6711yescharacteristic
559C23×C3C2×#6711yescharacteristic
560C23×C3C2×#6711yescharacteristic
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3Dic3⋊C414yescomplemented
596C2×C3×C4—24no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—34no—
604C2×C3×C4—42no—
605C2×C3×C4—42no—
606C2×C3×C4—42no—
607C2×C3×C4—42no—
608C2×C3×C4—42no—
609C2×C3×C4—42no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—62no—
619C2×C3×C4—62no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—62no—
628C2×C3×C4—62no—
629C2×C3×C4—62no—
630C2×C3×C4—121no—
631C2×C3×C4—121no—
632C2×C3×C4—121no—
633C2×C3×C4—121no—
634C2×C3×C4—121no—
635C2×C3×C4—121no—
636C2×C3×C4—121no—
637C2×C3×C4—121no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—64no—
659C2×Dic3—64no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—62no—
672C2×Dic3—122no—
673C2×Dic3—122no—
674C2×Dic3—122no—
675C2×Dic3—122no—
676C2×Dic3—122no—
677C2×Dic3—122no—
678C2×Dic3—122no—
679C2×Dic3—122no—
680C2×Dic3—122no—
681C2×Dic3—122no—
682C2×Dic3—122no—
683C2×Dic3—122no—
684C2×Dic3—121no—
685C2×Dic3—121no—
686C2×Dic3—121no—
687C2×Dic3—121no—
688C2×Dic3—121no—
689C2×Dic3—121no—
690C2×Dic3—121no—
691C2×Dic3—121no—
692C2×Dic3—121no—
693C2×Dic3—121no—
694C2×Dic3—121no—
695C2×Dic3—121no—
696C2×Dic3—121no—
697C2×Dic3—121no—
698C2×Dic3—121no—
699C2×Dic3—121no—
700C2×Dic3(C2×D3)⋊C414yescomplemented
701C2×C32#38011yescharacteristic
702C2×C32#38511yescharacteristic
703C2×C32#38511yescharacteristic
704C2×C32#38611yescharacteristic
705C2×C32#38811yescharacteristic
706C2×C32#38811yescharacteristic
707C2×C32#39011yescharacteristic
708C2×C32#39211yescharacteristic
709C2×C32#39311yescharacteristic
710C2×C32#39411yescharacteristic
711C2×C32#39411yescharacteristic
712C2×C32#39611yescharacteristic
713C2×C32#39611yescharacteristic
714C2×C32#39711yescharacteristic
715C2×C32#39911yescharacteristic
716C3×D3—44no—
717C24—32no—
718C24—32no—
719C24—32no—
720C24—61no—
721C24—61no—
722C24—61no—
723C24—61no—
724C24—61no—
725C24—61no—
726C24—61no—
727C24—61no—
728C24—61no—
729C24—61no—
730C24—61no—
731C24—61no—
732C24C2×D3211yescharacteristic
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—32no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—92no—
761C22×C4—92no—
762C22×C4—181no—
763C22×C4—181no—
764C22×C4—181no—
765C22×C4—181no—
766C22×C4—181no—
767C22×C4—181no—
768C22×C4—181no—
769C22×C4—181no—
770C22×C4—181no—
771C22×C4—181no—
772C22×C4—181no—
773C22×C4—181no—
774C22×C4#62512yes—
775C4⋊C4—68no—
776C22⋊C4—68no—
777C22⋊C4—188no—
778C22⋊C4—188no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—64no—
815C22×C3—64no—
816C22×C3—64no—
817C22×C3—122no—
818C22×C3—122no—
819C22×C3—122no—
820C22×C3—122no—
821C22×C3—122no—
822C22×C3—122no—
823C22×C3—122no—
824C22×C3—122no—
825C22×C3—122no—
826C22×C3—122no—
827C22×C3—122no—
828C22×C3—122no—
829C22×C3#87711yescharacteristic
830C22×C3#87811yescharacteristic
831C22×C3#87811yescharacteristic
832C22×C3#87811yescharacteristic
833C22×C3#87811yescharacteristic
834C22×C3#87911yescharacteristic
835C22×C3#87911yescharacteristic
836C22×C3D3×C22⋊C411yescharacteristic
837C22×C3#67⋊C411yescharacteristic
838C22×C3#67⋊C411yescharacteristic
839C22×C3#88311yescharacteristic
840C22×C3#88311yescharacteristic
841C22×C3#88411yescharacteristic
842C22×C3#88411yescharacteristic
843C22×C3#88511yescharacteristic
844C22×C3#88511yescharacteristic
845C22×C3D3×C4⋊C411yescharacteristic
846C22×C3#89211yescharacteristic
847C22×C3#89311yescharacteristic
848C22×C3#89311yescharacteristic
849C22×C3#89411yescharacteristic
850C22×C3#89411yescharacteristic
851C22×C3#89411yescharacteristic
852C22×C3#89411yescharacteristic
853C22×C3#89511yescharacteristic
854C22×C3#89511yescharacteristic
855C22×C3#89511yescharacteristic
856C22×C3#89611yescharacteristic
857C22×C3#89611yescharacteristic
858C22×C3#89711yescharacteristic
859C22×C3#89811yescharacteristic
860C22×C3#89811yescharacteristic
861C22×C3C2×Dic3⋊C411yescharacteristic
862C22×C3#92411yescharacteristic
863C22×C3#92411yescharacteristic
864C22×C3C2×(C2×D3)⋊C411yescharacteristic
865C22×C3C4×#6711yescharacteristic
866C22×C3C4×#6711yescharacteristic
867C22×C3C4×#6711yescharacteristic
868C22×C3C4×#6711yescharacteristic
869C22×C3#92911yescharacteristic
870C22×C3#92911yescharacteristic
871C22×C3#93011yescharacteristic
872C22×C3#93011yescharacteristic
873C22×C3#93511yescharacteristic
874C22×C3#93511yescharacteristic
875C22×C3#93611yescharacteristic
876C22×C3#93711yescharacteristic
877C22×C3#93711yescharacteristic
878C22×C3#93711yescharacteristic
879C22×C3#93711yescharacteristic
880C22×C3#93811yescharacteristic
881C22×C3#93811yescharacteristic
882C22×C3#93811yescharacteristic
883C22×C3#93911yescharacteristic
884C22×C3#93911yescharacteristic
885C22×C3#93911yescharacteristic
886C22×C3#93911yescharacteristic
887C22×C3#93911yescharacteristic
888C22×C3#93911yescharacteristic
889C22×C3#94011yescharacteristic
890C22×C3#94011yescharacteristic
891C22×C3#94611yescharacteristic
892C22×C3#94611yescharacteristic
893C22×C3#94611yescharacteristic
894C22×C3#94711yescharacteristic
895C22×C3#94711yescharacteristic
896C22×C3#94711yescharacteristic
897C22×C3#95311yescharacteristic
898C22×C3#95311yescharacteristic
899C2×D3—24no—
900C2×D3—24no—
901C2×D3—24no—
902C2×D3—42no—
903C2×D3—42no—
904C2×D3—42no—
905C2×D3—42no—
906C2×D3—42no—
907C2×D3—42no—
908C2×D3—42no—
909C2×D3—42no—
910C2×D3—42no—
911C2×D3—42no—
912C2×D3—42no—
913C2×D3—42no—
914C3×C4—44no—
915C3×C4—42no—
916C3×C4—42no—
917C3×C4—64no—
918C3×C4—122no—
919C3×C4—122no—
920Dic3—24no—
921Dic3—42no—
922Dic3—42no—
923Dic3—124no—
924Dic3—124no—
925Dic3—122no—
926Dic3—122no—
927Dic3—122no—
928Dic3—122no—
929C32#143911yescharacteristic, complemented, Sylow
930C23—34no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23D3×Dic611yescharacteristic
966C23#379511yescharacteristic
967C23#379611yescharacteristic
968C23#379611yescharacteristic
969C23#379811yescharacteristic
970C23#379911yescharacteristic
971C23C4×D3211yescharacteristic
972C23D3×D1211yescharacteristic
973C23#380511yescharacteristic
974C23C2×#62511yescharacteristic
975C23D3×#6711yescharacteristic
976C23D3×#6711yescharacteristic
977C23D3×#6711yescharacteristic
978C23D3×#6711yescharacteristic
979C23#381111yescharacteristic
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—34no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—182no—
1009C2×C4—182no—
1010C2×C4—182no—
1011C2×C4—182no—
1012C2×C4—182no—
1013C2×C4—182no—
1014C2×C4—361no—
1015C2×C4—361no—
1016C2×C4—361no—
1017C2×C4—361no—
1018C2×C4—361no—
1019C2×C4—361no—
1020C2×C4—361no—
1021C2×C4—361no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—124no—
1038C2×C3#494211yescharacteristic
1039C2×C3#494411yescharacteristic
1040C2×C3#494511yescharacteristic
1041C2×C3#494611yescharacteristic
1042C2×C3#494711yescharacteristic
1043C2×C3#494811yescharacteristic
1044C2×C3#494811yescharacteristic
1045C2×C3#494911yescharacteristic
1046C2×C3#495211yescharacteristic
1047C2×C3#495611yescharacteristic
1048C2×C3#495711yescharacteristic
1049C2×C3#495911yescharacteristic
1050C2×C3#498711yescharacteristic
1051C2×C3#498811yescharacteristic
1052C2×C3#498911yescharacteristic
1053C2×C3#498911yescharacteristic
1054C2×C3#499011yescharacteristic
1055C2×C3#499011yescharacteristic
1056C2×C3#499111yescharacteristic
1057C2×C3#499111yescharacteristic
1058C2×C3#499211yescharacteristic
1059C2×C3#499311yescharacteristic
1060C2×C3#499411yescharacteristic
1061C2×C3#499411yescharacteristic
1062C2×C3#521011yescharacteristic
1063C2×C3#521311yescharacteristic
1064C2×C3#522211yescharacteristic
1065C2×C3#522311yescharacteristic
1066C2×C3#522311yescharacteristic
1067C2×C3#523111yescharacteristic
1068D3—44no—
1069C22—64no—
1070C22—64no—
1071C22—64no—
1072C22—122no—
1073C22—122no—
1074C22—122no—
1075C22—122no—
1076C22—122no—
1077C22—122no—
1078C22—122no—
1079C22—122no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—122no—
1084C22#6385011yescharacteristic
1085C22#6385111yescharacteristic
1086C22#6385311yescharacteristic
1087C22#6385611yescharacteristic
1088C22#6386111yescharacteristic
1089C22#6386211yescharacteristic
1090C22#6386311yescharacteristic
1091C22D3×Dic3⋊C411yescharacteristic
1092C22#6387811yescharacteristic
1093C22#6387911yescharacteristic
1094C22#6388111yescharacteristic
1095C22#6388411yescharacteristic
1096C22#6388411yescharacteristic
1097C22#6388611yescharacteristic
1098C22#6388611yescharacteristic
1099C22#6388711yescharacteristic
1100C22#6388711yescharacteristic
1101C22#6389311yescharacteristic
1102C22#6389611yescharacteristic
1103C22C4×#62511yescharacteristic
1104C22#6390411yescharacteristic
1105C22#6390511yescharacteristic
1106C22#6390611yescharacteristic
1107C22#6390711yescharacteristic
1108C22#6390711yescharacteristic
1109C22#6390811yescharacteristic
1110C22#6391011yescharacteristic
1111C22D3×(C2×D3)⋊C411yescharacteristic
1112C22#6397011yescharacteristic
1113C22#6397011yescharacteristic
1114C22#6397611yescharacteristic
1115C22#6397611yescharacteristic
1116C22#6397911yescharacteristic
1117C22#6398011yescharacteristic
1118C22#6398311yescharacteristic
1119C4—42no—
1120C4—64no—
1121C4—122no—
1122C4—122no—
1123C4—362no—
1124C4—362no—
1125C3—21no—
1126C3#7154711yescharacteristic, complemented
1127C3#7157011yescharacteristic, complemented
1128C2—124no—
1129C2#1059127711yescharacteristic
1130C2#1059128311yescharacteristic
1131C2#1059128511yescharacteristic
1132C2#1059129111yescharacteristic
1133C2#1059130011yescharacteristic
1134C2#1059130111yescharacteristic
1135C2#1059130311yescharacteristic
1136C2#1059130411yescharacteristic
1137C2#1059130611yescharacteristic
1138C2#1059131911yescharacteristic
1139C2#1059136611yescharacteristic
1140C2#1059137211yescharacteristic
1141C2#1059138111yescharacteristic
1142C2#1059138411yescharacteristic
1143C2#1059172311yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, cosocleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32#1439
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic3⋊C4C2semidirect
5. C2×#63658C2semidirect
6. C2×#63579C2semidirect
7. C2×#63579C2semidirect
28. C2×(C2×D3)⋊Dic3C4semidirect
39. C22×Dic3⋊C4D3semidirect
207. C22×C3×D3C4⋊C4semidirect
249. C2×C3×Dic3C22⋊C4semidirect
595. C22×D3Dic3⋊C4semidirect
700. C2×Dic3(C2×D3)⋊C4semidirect
929. C32#1439semidirect
1126. C3#71547semidirect
1127. C3#71570semidirect

Maximal subgroups

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

subgroupindex
C22×C3×(C2×D3)⋊C42
C22×C3×Dic3⋊C42
C22×(C2×D3)⋊Dic32
C2×#636582
C2×#635792
#715703
#715473