Finite Group Databasebeta

← #11773306

Subgroups — #11773306

Order 1152.

1769 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic, complemented
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
4C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#63579C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#71547—31nomaximal
9#69428—31nomaximal
10C24×C3×D3C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
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×C3×(C2×D3)⋊C4—22no—
21C2×C3×(C2×D3)⋊C4—22no—
22C2×C3×(C2×D3)⋊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
29C3×C3⋊#95—22no—
30#63579—22no—
31#63579—22no—
32C22×C3×C22⋊C4—31no—
33C22×#217—31no—
34C22×#217—31no—
35C22×(C2×D3)⋊C4—31no—
36C22×(C2×D3)⋊C4—31no—
37C22×(C2×D3)⋊C4D311yescharacteristic
38C22×Dic3⋊C4—31no—
39C22×Dic3⋊C4—31no—
40C22×Dic3⋊C4—61no—
41C2×C3×#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44C2×C3⋊#95—31no—
45C2×C3⋊#95—31no—
46C2×C3⋊#95D311yescharacteristic, complemented
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⋊Dic3C2×C412yes—
81C22×C3⋊Dic3D412yes—
82C22×C3⋊Dic3D412yes—
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×Dic3—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3C2×C412yes—
103C22×C3×Dic3D412yes—
104C22×C3×Dic3D412yes—
105#3750—28no—
106C3×(C2×D3)⋊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×C22⋊C4—62no—
128C2×C3×C22⋊C4—62no—
129C2×C3×C22⋊C4—62no—
130C2×#217—34no—
131C2×#217—62no—
132C2×#217—62no—
133C2×#217—62no—
134C2×#217—62no—
135C2×#217—62no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—34no—
140C2×(C2×D3)⋊C4—62no—
141C2×(C2×D3)⋊C4—62no—
142C2×(C2×D3)⋊C4—62no—
143C2×(C2×D3)⋊C4—62no—
144C2×(C2×D3)⋊C4—62no—
145C2×Dic3⋊C4—62no—
146C2×Dic3⋊C4—62no—
147C2×Dic3⋊C4—62no—
148C2×Dic3⋊C4—62no—
149C2×Dic3⋊C4—64no—
150C2×Dic3⋊C4—64no—
151C2×Dic3⋊C4—64no—
152C2×Dic3⋊C4—62no—
153C2×Dic3⋊C4—62no—
154C3×#95—62no—
155C3⋊#95—22no—
156C3⋊#95—62no—
157C3⋊#95—62no—
158C3⋊#95—62no—
159C3⋊#95—62no—
160C23×C32C22×C411yescharacteristic
161C23×C32C2×D411yescharacteristic
162C23×C32C2×D411yescharacteristic
163C23×C32C2×D411yescharacteristic
164C23×C32C2×D411yescharacteristic
165C23×C32C2×D411yescharacteristic
166C23×C32C2×D411yescharacteristic
167C23×C32C2×D411yescharacteristic
168C23×C32C2×Q811yescharacteristic
169C23×C32#4111yescharacteristic
170C23×C32#4111yescharacteristic
171C23×C32#4111yescharacteristic
172C23×C32#4111yescharacteristic
173C23×C32#4111yescharacteristic
174C23×C32#4111yescharacteristic
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—22no—
192C22×C3×D3—22no—
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×D3—41no—
208C22×C3×D3—41no—
209C22×C3×D3C4⋊C414yescomplemented
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—41no—
214C2×C32×C4—41no—
215C2×C32×C4—41no—
216C2×C32×C4—41no—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3—22no—
222C2×C3⋊Dic3—22no—
223C2×C3⋊Dic3—22no—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3—22no—
226C2×C3⋊Dic3—41no—
227C2×C3⋊Dic3—41no—
228C2×C3⋊Dic3—41no—
229C2×C3⋊Dic3—41no—
230C2×C3⋊Dic3C22⋊C414yescomplemented
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—41no—
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×Dic3—41no—
250C2×C3×Dic3—41no—
251C2×C3×Dic3—41no—
252C22×C4⋊C4—91no—
253C22×C22⋊C4—31no—
254C22×C22⋊C4—91no—
255C22×C22⋊C4—91no—
256C2×#95—31no—
257C2×#95—91no—
258C2×#95—91no—
259C24×C3—21no—
260C24×C3—32no—
261C24×C3—32no—
262C24×C3—32no—
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×C3—61no—
274C24×C3—61no—
275C24×C3C22×D311yescharacteristic
276C24×C3C22×D311yescharacteristic
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×D3—21no—
288C23×D3—21no—
289C23×D3Dic612yes—
290C23×D3C4×D312yes—
291C23×D3#6712yes—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
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—21no—
305C22×C3×C4—21no—
306C22×C3×C4—22no—
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—61no—
331C22×C3×C4—61no—
332C22×C3×C4D1212yes—
333C22×C3×C4#6712yes—
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—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—32no—
353C22×Dic3—32no—
354C22×Dic3—32no—
355C22×Dic3—32no—
356C22×Dic3—32no—
357C22×Dic3—32no—
358C22×Dic3—32no—
359C22×Dic3—32no—
360C22×Dic3—62no—
361C22×Dic3—62no—
362C22×Dic3—62no—
363C22×Dic3—62no—
364C22×Dic3—62no—
365C22×Dic3—62no—
366C22×Dic3—62no—
367C22×Dic3—62no—
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—62no—
377C22×Dic3—62no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—121no—
391C22×Dic3—121no—
392C22×Dic3—121no—
393C22×Dic3—121no—
394C22×Dic3C4×D312yes—
395C22×Dic3#6712yes—
396C22×Dic3#6712yes—
397C3×C22⋊C4—68no—
398#217—68no—
399#217—68no—
400(C2×D3)⋊C4—28no—
401(C2×D3)⋊C4—68no—
402(C2×D3)⋊C4—68no—
403Dic3⋊C4—616no—
404Dic3⋊C4—68no—
405Dic3⋊C4—68no—
406C22×C32C2×C22⋊C411yescharacteristic
407C22×C32C2×C4⋊C411yescharacteristic
408C22×C32#11711yescharacteristic
409C22×C32C4×D411yescharacteristic
410C22×C32C4×D411yescharacteristic
411C22×C32C4×D411yescharacteristic
412C22×C32C4×D411yescharacteristic
413C22×C32#12011yescharacteristic
414C22×C32#12011yescharacteristic
415C22×C32#12011yescharacteristic
416C22×C32#12111yescharacteristic
417C22×C32#12111yescharacteristic
418C22×C32#12111yescharacteristic
419C22×C32#12111yescharacteristic
420C22×C32#12111yescharacteristic
421C22×C32#12111yescharacteristic
422C22×C32#12111yescharacteristic
423C22×C32#12111yescharacteristic
424C22×C32C22⋊Q811yescharacteristic
425C22×C32C22⋊Q811yescharacteristic
426C22×C32C22⋊Q811yescharacteristic
427C22×C32C22⋊Q811yescharacteristic
428C22×C32C22⋊Q811yescharacteristic
429C22×C32C22⋊Q811yescharacteristic
430C22×C32#12311yescharacteristic
431C22×C32#12311yescharacteristic
432C22×C32#12311yescharacteristic
433C22×C32#12311yescharacteristic
434C22×C32#12311yescharacteristic
435C22×C32#12411yescharacteristic
436C22×C32#12411yescharacteristic
437C22×C32#12411yescharacteristic
438C22×C32#12611yescharacteristic
439C22×C32#12611yescharacteristic
440C22×C32#12711yescharacteristic
441C2×C3×D3—24no—
442C2×C3×D3—24no—
443C2×C3×D3—24no—
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—
453C2×C3×D3—42no—
454C2×C3×D3—42no—
455C2×C3×D3—42no—
456C32×C4—42no—
457C3⋊Dic3—24no—
458C3⋊Dic3—42no—
459C3×Dic3—42no—
460C3×Dic3—42no—
461C3×Dic3—42no—
462C25—31no—
463C23×C4—31no—
464C23×C4—31no—
465C23×C4—31no—
466C23×C4—91no—
467C23×C4—91no—
468C23×C4D3211yescharacteristic
469C2×C4⋊C4—182no—
470C2×C4⋊C4—182no—
471C2×C4⋊C4—182no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—94no—
476C2×C22⋊C4—182no—
477C2×C22⋊C4—182no—
478C2×C22⋊C4—182no—
479C2×C22⋊C4—182no—
480C2×C22⋊C4—182no—
481#95—62no—
482#95—182no—
483#95—182no—
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—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—34no—
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—62no—
516C23×C3—62no—
517C23×C3—62no—
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×C3—121no—
532C23×C3—121no—
533C23×C3—121no—
534C23×C3C2×Dic611yescharacteristic
535C23×C3C2×C4×D311yescharacteristic
536C23×C3C2×C4×D311yescharacteristic
537C23×C3C2×D1211yescharacteristic
538C23×C3#23511yescharacteristic
539C23×C3#23511yescharacteristic
540C23×C3#23511yescharacteristic
541C23×C3#23511yescharacteristic
542C23×C3#23511yescharacteristic
543C23×C3#23511yescharacteristic
544C23×C3D3×D411yescharacteristic
545C23×C3D3×D411yescharacteristic
546C23×C3D3×D411yescharacteristic
547C23×C3D3×D411yescharacteristic
548C23×C3D3×D411yescharacteristic
549C23×C3D3×D411yescharacteristic
550C23×C3D3×D411yescharacteristic
551C23×C3D3×D411yescharacteristic
552C23×C3D3×D411yescharacteristic
553C23×C3#23711yescharacteristic
554C23×C3#23711yescharacteristic
555C23×C3#23711yescharacteristic
556C23×C3#23711yescharacteristic
557C23×C3#23711yescharacteristic
558C23×C3D3×Q811yescharacteristic
559C23×C3#23911yescharacteristic
560C23×C3C2×#6711yescharacteristic
561C23×C3C2×#6711yescharacteristic
562C23×C3C2×#6711yescharacteristic
563C23×C3C2×#6711yescharacteristic
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—22no—
580C22×D3—22no—
581C22×D3—22no—
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×D3—41no—
596C22×D3—41no—
597C22×D3—41no—
598C22×D3Dic3⋊C414yescomplemented
599C2×C3×C4—24no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—42no—
607C2×C3×C4—42no—
608C2×C3×C4—42no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—42no—
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—41no—
619C2×C3×C4—41no—
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—121no—
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×C3×C4—121no—
639C2×C3×C4—121no—
640C2×C3×C4—121no—
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—34no—
651C2×Dic3—34no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—64no—
665C2×Dic3—64no—
666C2×Dic3—64no—
667C2×Dic3—64no—
668C2×Dic3—64no—
669C2×Dic3—64no—
670C2×Dic3—64no—
671C2×Dic3—62no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—62no—
678C2×Dic3—62no—
679C2×Dic3—62no—
680C2×Dic3—62no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—64no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—122no—
691C2×Dic3—122no—
692C2×Dic3—122no—
693C2×Dic3—122no—
694C2×Dic3—122no—
695C2×Dic3—122no—
696C2×Dic3—121no—
697C2×Dic3—121no—
698C2×Dic3—121no—
699C2×Dic3—121no—
700C2×Dic3—121no—
701C2×Dic3—121no—
702C2×Dic3—121no—
703C2×Dic3—121no—
704C2×C32#38011yescharacteristic
705C2×C32#38511yescharacteristic
706C2×C32#38511yescharacteristic
707C2×C32#38611yescharacteristic
708C2×C32#38811yescharacteristic
709C2×C32#38811yescharacteristic
710C2×C32#39011yescharacteristic
711C2×C32#39211yescharacteristic
712C2×C32#39311yescharacteristic
713C2×C32#39411yescharacteristic
714C2×C32#39411yescharacteristic
715C2×C32#39611yescharacteristic
716C2×C32#39611yescharacteristic
717C2×C32#39711yescharacteristic
718C2×C32#39911yescharacteristic
719C3×D3—44no—
720C24—32no—
721C24—32no—
722C24—32no—
723C24—61no—
724C24—61no—
725C24—61no—
726C24—61no—
727C24—61no—
728C24—61no—
729C24—61no—
730C24—61no—
731C24—61no—
732C24—61no—
733C24—61no—
734C24—61no—
735C24C2×D3211yescharacteristic
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—32no—
743C22×C4—32no—
744C22×C4—32no—
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—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—92no—
764C22×C4—92no—
765C22×C4—92no—
766C22×C4—92no—
767C22×C4—181no—
768C22×C4—181no—
769C22×C4—181no—
770C22×C4—181no—
771C22×C4—181no—
772C22×C4—181no—
773C22×C4—181no—
774C22×C4—181no—
775C22×C4—181no—
776C22×C4—181no—
777C22×C4#62612yes—
778C4⋊C4—188no—
779C22⋊C4—68no—
780C22⋊C4—188no—
781C22⋊C4—188no—
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—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—64no—
818C22×C3—64no—
819C22×C3—64no—
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—122no—
830C22×C3—122no—
831C22×C3—122no—
832C22×C3#87211yescharacteristic
833C22×C3C4×D1211yescharacteristic
834C22×C3#87511yescharacteristic
835C22×C3#87611yescharacteristic
836C22×C3#87711yescharacteristic
837C22×C3#87811yescharacteristic
838C22×C3#87811yescharacteristic
839C22×C3#87811yescharacteristic
840C22×C3#87811yescharacteristic
841C22×C3#87911yescharacteristic
842C22×C3#87911yescharacteristic
843C22×C3D3×C22⋊C411yescharacteristic
844C22×C3D3×C22⋊C411yescharacteristic
845C22×C3#67⋊C411yescharacteristic
846C22×C3#67⋊C411yescharacteristic
847C22×C3#67⋊C411yescharacteristic
848C22×C3#88211yescharacteristic
849C22×C3#88211yescharacteristic
850C22×C3#88311yescharacteristic
851C22×C3#88311yescharacteristic
852C22×C3#88311yescharacteristic
853C22×C3#88411yescharacteristic
854C22×C3#88411yescharacteristic
855C22×C3#88411yescharacteristic
856C22×C3#88411yescharacteristic
857C22×C3#88411yescharacteristic
858C22×C3#88411yescharacteristic
859C22×C3#88411yescharacteristic
860C22×C3#88511yescharacteristic
861C22×C3#88511yescharacteristic
862C22×C3#88511yescharacteristic
863C22×C3#88511yescharacteristic
864C22×C3D3×C4⋊C411yescharacteristic
865C22×C3#89311yescharacteristic
866C22×C3#89411yescharacteristic
867C22×C3#89411yescharacteristic
868C22×C3#89411yescharacteristic
869C22×C3#89511yescharacteristic
870C22×C3#89611yescharacteristic
871C22×C3#89611yescharacteristic
872C22×C3#89611yescharacteristic
873C22×C3#89611yescharacteristic
874C22×C3#89711yescharacteristic
875C22×C3#89811yescharacteristic
876C22×C3C2×Dic3⋊C411yescharacteristic
877C22×C3#92411yescharacteristic
878C22×C3#92411yescharacteristic
879C22×C3C4×#6711yescharacteristic
880C22×C3C4×#6711yescharacteristic
881C22×C3C4×#6711yescharacteristic
882C22×C3#92911yescharacteristic
883C22×C3#92911yescharacteristic
884C22×C3#93011yescharacteristic
885C22×C3#93511yescharacteristic
886C22×C3#93511yescharacteristic
887C22×C3#93611yescharacteristic
888C22×C3#93711yescharacteristic
889C22×C3#93711yescharacteristic
890C22×C3#93711yescharacteristic
891C22×C3#93811yescharacteristic
892C22×C3#93811yescharacteristic
893C22×C3#93911yescharacteristic
894C22×C3#93911yescharacteristic
895C22×C3#93911yescharacteristic
896C22×C3#93911yescharacteristic
897C22×C3#93911yescharacteristic
898C22×C3#94011yescharacteristic
899C22×C3#94011yescharacteristic
900C22×C3#94611yescharacteristic
901C22×C3#95311yescharacteristic
902C2×D3—24no—
903C2×D3—24no—
904C2×D3—24no—
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—
914C2×D3—42no—
915C2×D3—42no—
916C2×D3—42no—
917C3×C4—44no—
918C3×C4—42no—
919C3×C4—42no—
920C3×C4—122no—
921C3×C4—122no—
922C3×C4—122no—
923Dic3—42no—
924Dic3—42no—
925Dic3—42no—
926Dic3—68no—
927Dic3—64no—
928Dic3—64no—
929Dic3—124no—
930Dic3—122no—
931Dic3—122no—
932C32#143911yescharacteristic, complemented, Sylow
933C23—34no—
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—62no—
950C23—62no—
951C23—62no—
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—
965C23—121no—
966C23—121no—
967C23—121no—
968C23D3×Dic611yescharacteristic
969C23#379511yescharacteristic
970C23#379511yescharacteristic
971C23#379511yescharacteristic
972C23#379611yescharacteristic
973C23#379811yescharacteristic
974C23C4×D3211yescharacteristic
975C23#380211yescharacteristic
976C23#380411yescharacteristic
977C23C2×#62611yescharacteristic
978C23D3×#6711yescharacteristic
979C23D3×#6711yescharacteristic
980C23D3×#6711yescharacteristic
981C23#381111yescharacteristic
982C23#381111yescharacteristic
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
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—94no—
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—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—182no—
1013C2×C4—182no—
1014C2×C4—182no—
1015C2×C4—182no—
1016C2×C4—182no—
1017C2×C4—182no—
1018C2×C4—182no—
1019C2×C4—182no—
1020C2×C4—182no—
1021C2×C4—361no—
1022C2×C4—361no—
1023C2×C4—361no—
1024C2×C4—361no—
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—21no—
1038C2×C3—21no—
1039C2×C3—21no—
1040C2×C3—124no—
1041C2×C3#466511yescharacteristic
1042C2×C3#466711yescharacteristic
1043C2×C3#466811yescharacteristic
1044C2×C3#466911yescharacteristic
1045C2×C3#467211yescharacteristic
1046C2×C3#467311yescharacteristic
1047C2×C3#467511yescharacteristic
1048C2×C3#467611yescharacteristic
1049C2×C3#494011yescharacteristic
1050C2×C3#494211yescharacteristic
1051C2×C3#494411yescharacteristic
1052C2×C3#494511yescharacteristic
1053C2×C3#494611yescharacteristic
1054C2×C3#494711yescharacteristic
1055C2×C3#494811yescharacteristic
1056C2×C3#494811yescharacteristic
1057C2×C3#494911yescharacteristic
1058C2×C3#495211yescharacteristic
1059C2×C3#495611yescharacteristic
1060C2×C3#495711yescharacteristic
1061C2×C3#495711yescharacteristic
1062C2×C3#495911yescharacteristic
1063C2×C3#495911yescharacteristic
1064C2×C3#496011yescharacteristic
1065C2×C3#498911yescharacteristic
1066C2×C3#499311yescharacteristic
1067C2×C3#499411yescharacteristic
1068C2×C3#521011yescharacteristic
1069C2×C3#522211yescharacteristic
1070C2×C3#522311yescharacteristic
1071D3—44no—
1072C22—64no—
1073C22—64no—
1074C22—64no—
1075C22—122no—
1076C22—122no—
1077C22—122no—
1078C22—122no—
1079C22—122no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—122no—
1084C22—122no—
1085C22—122no—
1086C22—122no—
1087C22#6385111yescharacteristic
1088C22#6385311yescharacteristic
1089C22#6385711yescharacteristic
1090C22#6385811yescharacteristic
1091C22#6385911yescharacteristic
1092C22#6386011yescharacteristic
1093C22D3×Dic3⋊C411yescharacteristic
1094C22#6387711yescharacteristic
1095C22#6387911yescharacteristic
1096C22#6387911yescharacteristic
1097C22#6388111yescharacteristic
1098C22#6388411yescharacteristic
1099C22#6388411yescharacteristic
1100C22#6388511yescharacteristic
1101C22#6388511yescharacteristic
1102C22#6388511yescharacteristic
1103C22#6388711yescharacteristic
1104C22#6389611yescharacteristic
1105C22#6389611yescharacteristic
1106C22#6389911yescharacteristic
1107C22C4×#62611yescharacteristic
1108C22#6390511yescharacteristic
1109C22#6390511yescharacteristic
1110C22#6391211yescharacteristic
1111C22#6391311yescharacteristic
1112C22#6391311yescharacteristic
1113C22#6391611yescharacteristic
1114C22#6392111yescharacteristic
1115C22#6395811yescharacteristic
1116C22#6397111yescharacteristic
1117C22#6397711yescharacteristic
1118C22#6397811yescharacteristic
1119C22#6397911yescharacteristic
1120C22#6398111yescharacteristic
1121C22#6398311yescharacteristic
1122C4—42no—
1123C4—122no—
1124C4—122no—
1125C4—122no—
1126C4—184no—
1127C4—362no—
1128C3—21no—
1129C3#6942811yescharacteristic, complemented
1130C3#7154711yescharacteristic, complemented
1131C2—124no—
1132C2#1059127811yescharacteristic
1133C2#1059128011yescharacteristic
1134C2#1059128111yescharacteristic
1135C2#1059129811yescharacteristic
1136C2#1059130211yescharacteristic
1137C2#1059130311yescharacteristic
1138C2#1059130811yescharacteristic
1139C2#1059130911yescharacteristic
1140C2#1059132211yescharacteristic
1141C2#1059136911yescharacteristic
1142C2#1059137211yescharacteristic
1143C2#1059138611yescharacteristic
1144C2#1059138711yescharacteristic
1145C2#1059138811yescharacteristic
1146C2#1059172411yescharacteristic
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
1. C22×#3750C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C2×#63579C2semidirect
7. C2×#63579C2semidirect
28. C2×(C2×D3)⋊Dic3C4semidirect
46. C2×C3⋊#95D3semidirect
209. C22×C3×D3C4⋊C4semidirect
230. C2×C3⋊Dic3C22⋊C4semidirect
598. C22×D3Dic3⋊C4semidirect
932. C32#1439semidirect
1129. C3#69428semidirect
1130. C3#71547semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C22×C3×(C2×D3)⋊C42
C22×(C2×D3)⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#715473
#694283