Finite Group Databasebeta

← #11810339

Subgroups — #11810339

Order 1152.

1695 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63976C211yesmaximal, characteristic
2C2×#63969C211yesmaximal, characteristic, complemented
3C2×D3×#217C211yesmaximal, characteristic, complemented
4C2×#63902C211yesmaximal, characteristic, complemented
5#10592644C211yesmaximal, characteristic, complemented
6C3×#4961C211yesmaximal, characteristic, complemented
7C3×#4955C211yesmaximal, characteristic, complemented
8#10591694C211yesmaximal, characteristic, complemented
9#10591388C211yesmaximal, characteristic, complemented
10#10591377C211yesmaximal, characteristic, complemented
11#10591369C211yesmaximal, characteristic, complemented
12#10591363C211yesmaximal, characteristic, complemented
13#10591363C211yesmaximal, characteristic, complemented
14#10591324C211yesmaximal, characteristic, complemented
15#10591286C211yesmaximal, characteristic, complemented
16#77111—31nomaximal
17#73826—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×#625C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3750C2211yescharacteristic, complemented
29C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39#63976—24no—
40#63969—24no—
41D3×#217—24no—
42C2×#3724C2211yescharacteristic, complemented
43C2×#3724C2211yescharacteristic, complemented
44C2×Dic3⋊Dic3C2211yescharacteristic, complemented
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
50#63902—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#953—31no—
58C22×#217—31no—
59C2×#937—31no—
60C2×#935—31no—
61C2×#883—31no—
62C2×#67⋊C4—31no—
63C2×#67⋊C4—31no—
64C2×D3×C22⋊C4—31no—
65C3×#394—31no—
66C3×#379—31no—
67#4993—31no—
68#4989—31no—
69#4961D311yescharacteristic, complemented
70#4959—31no—
71#4959—31no—
72#4958—31no—
73#4958—31no—
74#4956—31no—
75#4956—31no—
76#4955D311yescharacteristic, complemented
77#4952—31no—
78#4952—31no—
79#4951—31no—
80#4950—31no—
81#4949—31no—
82#4945—31no—
83#4945—31no—
84#4945—61no—
85#4942—31no—
86#4669—31no—
87#4667—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—41no—
95C23×C3×D3—41no—
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×#625—22no—
114C2×#625—22no—
115C2×#625—22no—
116C2×#625—22no—
117C2×#625—41no—
118C2×#625D414yes—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3—41no—
127C2×D3×Dic3—41no—
128C32×C22⋊C4—41no—
129#3757—22no—
130#3757D414yescomplemented
131#3750—41no—
132C4×C3⋊Dic3—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—41no—
140C3×(C2×D3)⋊C4—41no—
141C3×C4⋊Dic3—41no—
142#3724—22no—
143#3724—22no—
144Dic3⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149(C2×D3)⋊Dic3—22no—
150#2418—91noSylow
151C25×C3—31no—
152C24×D3C2×D311yescharacteristic
153C22×C3×D4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67C2×D311yescharacteristic
159C23×Dic3—31no—
160C23×Dic3—31no—
161C23×Dic3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C22⋊C4—21no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4C2×D311yescharacteristic
176C2×C3×C22⋊C4C2×D311yescharacteristic
177#953—64no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—61no—
188C2×#217—61no—
189C2×#217—64no—
190C2×#217C2×D311yescharacteristic
191C2×#217C2×D311yescharacteristic
192#937—64no—
193#935—64no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4C2×D311yescharacteristic
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
204C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3C2×D311yescharacteristic, complemented
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—61no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—31no—
217C2×C4×Dic3—61no—
218#883—64no—
219#67⋊C4—64no—
220#67⋊C4—64no—
221D3×C22⋊C4—64no—
222C3×#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—61no—
234C3⋊#95—61no—
235C3⋊#95C2×D311yescharacteristic, complemented
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32C2×D412yes—
243C23×C32C2411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—28no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3C2×D412yes—
268C22×C3×D3C2×D412yes—
269C22×C3×D3#4112yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3C2×D412yes—
288C2×C3⋊Dic3C2×D412yes—
289C2×C3⋊Dic3C2×D412yes—
290C3×#67—44no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306#625—28no—
307#625—44no—
308D3×Dic3—44no—
309D3×Dic3—44no—
310D3×Dic3—44no—
311C2×#123—91no—
312C2×#120—91no—
313C2×C4×D4—91no—
314C22×C22⋊C4—91no—
315#399—91no—
316#397—91no—
317#394—31no—
318#394—91no—
319#388—91no—
320#388—91no—
321#386—91no—
322#386—91no—
323#385—91no—
324#380—91no—
325#379—31no—
326C24×C3—21no—
327C24×C3—31no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—121no—
336C24×C3—121no—
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C23×D3—22no—
340C23×D3—22no—
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—41no—
345C23×D3—41no—
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D311yescharacteristic
348C23×D3C22×D311yescharacteristic
349C2×C3×D4—62no—
350C2×C3×D4—62no—
351C2×C3×D4—121no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C2×#67—22no—
364C2×#67—22no—
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—41no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—121no—
377C2×#67—121no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—61no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—62no—
391C22×Dic3—62no—
392C22×Dic3—62no—
393C22×Dic3—62no—
394C22×Dic3—62no—
395C22×Dic3—62no—
396C22×Dic3—121no—
397C22×Dic3—121no—
398C22×Dic3—121no—
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C2×C4×D3—62no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—121no—
411C2×C4×D3—121no—
412C2×C4×D3—121no—
413C3×C4⋊C4—121no—
414C3×C22⋊C4—41no—
415C3×C22⋊C4—41no—
416C3×C22⋊C4—42no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—121no—
424C3×C22⋊C4—121no—
425#217—22no—
426#217—22no—
427#217—34no—
428#217—34no—
429#217—64no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—62no—
434#217—62no—
435#217—62no—
436#217—62no—
437#217—122no—
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—22no—
440(C2×D3)⋊C4—22no—
441(C2×D3)⋊C4—22no—
442(C2×D3)⋊C4—41no—
443(C2×D3)⋊C4—41no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449C4⋊Dic3—41no—
450C4⋊Dic3—62no—
451Dic3⋊C4—62no—
452Dic3⋊C4—62no—
453Dic3⋊C4—62no—
454Dic3⋊C4—62no—
455Dic3⋊C4—62no—
456Dic3⋊C4—121no—
457Dic3⋊C4—121no—
458Dic3⋊C4—122no—
459C4×Dic3—62no—
460C4×Dic3—62no—
461C4×Dic3—122no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C22×C32C22×D411yescharacteristic
471C22×C32C2×#4111yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32C2×#4111yescharacteristic
474C22×C32H(5,𝔽2)11yescharacteristic
475C22×C32H(5,𝔽2)11yescharacteristic
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—416no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3#12314yescomplemented
498C32×C4—41no—
499C32×C4—41no—
500C3⋊Dic3—22no—
501C3⋊Dic3—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C25—31no—
510C22×D4—31no—
511C22×D4—91no—
512C22×D4—91no—
513C23×C4—91no—
514C23×C4—91no—
515C23×C4—91no—
516#123—184no—
517#120—184no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—184no—
540C2×C22⋊C4D3211yescharacteristic
541C2×C42—91no—
542#95—31no—
543#95—91no—
544#95—91no—
545#95—91no—
546#95—91no—
547#95—91no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—22no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—68no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—124no—
591C23×C3—124no—
592C23×C3—124no—
593C23×C3—124no—
594C23×C3—124no—
595C23×C3—124no—
596C23×C3D3×D412yes—
597C23×C3D3×D412yes—
598C23×C3C23×D311yescharacteristic
599C23×C3C23×D311yescharacteristic
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—28no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—44no—
618C22×D3—44no—
619C22×D3—44no—
620C22×D3—44no—
621C22×D3—44no—
622C22×D3—44no—
623C22×D3#23512yes—
624C22×D3D3×D412yes—
625C22×D3D3×D412yes—
626C22×D3#23712yes—
627C22×D3#23712yes—
628C3×D4—124no—
629C2×C3×C4—22no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662#67—44no—
663#67—68no—
664#67—68no—
665#67—124no—
666#67—124no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—121no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—124no—
719C2×Dic3—124no—
720C2×Dic3—124no—
721C4×D3—124no—
722C4×D3—124no—
723C4×D3—124no—
724C2×C32—42no—
725C2×C32C2×#12311yescharacteristic
726C2×C32#52511yescharacteristic
727C2×C32#53811yescharacteristic
728C2×C32D4211yescharacteristic
729C2×C32#54611yescharacteristic
730C2×C32#54611yescharacteristic
731C2×C32#55111yescharacteristic
732C3×D3—24no—
733C3×D3—42no—
734C3×D3—42no—
735C24—31no—
736C24—31no—
737C24—31no—
738C24—62no—
739C24—62no—
740C24—62no—
741C24—62no—
742C24—62no—
743C24—121no—
744C24—121no—
745C24C2×D3211yescharacteristic
746C2×D4—62no—
747C2×D4—62no—
748C2×D4—94no—
749C2×D4—121no—
750C2×D4—182no—
751C2×D4—182no—
752C2×D4—182no—
753C2×D4—182no—
754C2×D4—361no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—91no—
761C22×C4—91no—
762C22×C4—91no—
763C22×C4—91no—
764C22×C4—182no—
765C22×C4—182no—
766C22×C4—182no—
767C22×C4—182no—
768C22×C4—182no—
769C22×C4—182no—
770C22×C4—361no—
771C22×C4—361no—
772C22×C4—361no—
773C22×C4C2×D3211yescharacteristic
774C22×C4C2×D3211yescharacteristic
775C4⋊C4—121no—
776C4⋊C4—182no—
777C4⋊C4—182no—
778C4⋊C4—182no—
779C4⋊C4—361no—
780C22⋊C4—41no—
781C22⋊C4—62no—
782C22⋊C4—62no—
783C22⋊C4—62no—
784C22⋊C4—62no—
785C22⋊C4—62no—
786C22⋊C4—62no—
787C22⋊C4—94no—
788C22⋊C4—121no—
789C22⋊C4—121no—
790C22⋊C4—182no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—182no—
795C22⋊C4—182no—
796C42—182no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—34no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—1216no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3C2×#23511yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C22×C3C2×D3×D411yescharacteristic
850C22×C3C2×D3×D411yescharacteristic
851C22×C3C2×D3×D411yescharacteristic
852C22×C3C2×#23711yescharacteristic
853C22×C3C2×#23711yescharacteristic
854C22×C3#100411yescharacteristic
855C22×C3#100411yescharacteristic
856C22×C3#100411yescharacteristic
857C22×C3#100411yescharacteristic
858C22×C3D3×#4111yescharacteristic
859C22×C3D3×#4111yescharacteristic
860C22×C3D3×#4111yescharacteristic
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—416no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3#88314yescomplemented
883C3×C4—42no—
884C3×C4—41no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—41no—
888C3×C4—81no—
889C3×C4—121no—
890C3×C4—121no—
891C3×C4—121no—
892C3×C4—121no—
893C3×C4—121no—
894Dic3—41no—
895Dic3—41no—
896Dic3—41no—
897Dic3—41no—
898Dic3—41no—
899Dic3—62no—
900Dic3—62no—
901Dic3—62no—
902Dic3—62no—
903Dic3—62no—
904Dic3—62no—
905Dic3—122no—
906Dic3—122no—
907Dic3—122no—
908Dic3—121no—
909Dic3—121no—
910Dic3—241no—
911C32#241811yescharacteristic, complemented, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—32no—
919C23—32no—
920C23—32no—
921C23—32no—
922C23—32no—
923C23—68no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—124no—
941C23—124no—
942C23—124no—
943C23—124no—
944C23—124no—
945C23—124no—
946C23#380212yes—
947C23C22×D3211yescharacteristic
948D4—124no—
949D4—188no—
950D4—364no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—92no—
973C2×C4—92no—
974C2×C4—92no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—181no—
982C2×C4—181no—
983C2×C4—181no—
984C2×C4—364no—
985C2×C4—364no—
986C2×C4—364no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—42no—
995C2×C3—42no—
996C2×C3—64no—
997C2×C3—82no—
998C2×C3—122no—
999C2×C3—122no—
1000C2×C3C2×#88311yescharacteristic
1001C2×C3#549011yescharacteristic
1002C2×C3#549511yescharacteristic
1003C2×C3#558611yescharacteristic
1004C2×C3#559011yescharacteristic
1005C2×C3#559011yescharacteristic
1006C2×C3#559111yescharacteristic
1007C2×C3#559311yescharacteristic
1008C2×C3#561011yescharacteristic
1009C2×C3#561011yescharacteristic
1010C2×C3#561311yescharacteristic
1011C2×C3D3×#12311yescharacteristic
1012C2×C3#565611yescharacteristic
1013C2×C3#567911yescharacteristic
1014D3—24no—
1015D3—42no—
1016D3—42no—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—34no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—62no—
1036C22—62no—
1037C22—1216no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22—121no—
1045C22—121no—
1046C22C2×#380211yescharacteristic
1047C22D3×#23511yescharacteristic
1048C22D32×D411yescharacteristic
1049C22D3×#23711yescharacteristic
1050C22D3×#23711yescharacteristic
1051C22#6431311yescharacteristic
1052C22#6433011yescharacteristic
1053C4—41no—
1054C4—41no—
1055C4—121no—
1056C4—121no—
1057C4—121no—
1058C4—121no—
1059C4—121no—
1060C4—182no—
1061C4—182no—
1062C4—182no—
1063C4—361no—
1064C3—21no—
1065C3#7382611yescharacteristic, complemented
1066C3#7711111yescharacteristic, complemented
1067C2—42no—
1068C2—64no—
1069C2—122no—
1070C2—122no—
1071C2#1059408211yescharacteristic
1072C2#1059409211yescharacteristic
1073C2D3×#88311yescharacteristic
1074C2#1059427111yescharacteristic
1075C2#1059508311yescharacteristic
1076C2#1059518111yescharacteristic
1077C2#1059529011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63976C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63969C2semidirect
3. C2×D3×#217C2semidirect
4. C2×#63902C2semidirect
5. #10592644C2semidirect
6. C3×#4961C2semidirect
7. C3×#4955C2semidirect
8. #10591694C2semidirect
9. #10591388C2semidirect
10. #10591377C2semidirect
11. #10591369C2semidirect
12. #10591363C2semidirect
13. #10591363C2semidirect
14. #10591324C2semidirect
15. #10591286C2semidirect
24. C22×D3×Dic3C22semidirect
28. C2×#3750C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
42. C2×#3724C22semidirect
43. C2×#3724C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
49. C2×(C2×D3)⋊Dic3C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
69. #4961D3semidirect
76. #4955D3semidirect
130. #3757D4semidirect
203. C2×(C2×D3)⋊C4C2×D3semidirect
204. C2×(C2×D3)⋊C4C2×D3semidirect
206. C2×C4⋊Dic3C2×D3semidirect
235. C3⋊#95C2×D3semidirect
497. C2×C3×D3#123semidirect
882. C2×D3#883semidirect
911. C32#2418semidirect
1065. C3#73826semidirect
1066. C3#77111semidirect

Maximal subgroups

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

subgroupindex
C2×#639762
C2×#639692
C2×D3×#2172
C2×#639022
#105926442
C3×#49612
C3×#49552
#105916942
#105913882
#105913772
#105913692
#105913632
#105913242
#105912862
#771113
#738263