Finite Group Databasebeta

← #11810338

Subgroups — #11810338

Order 1152.

1853 conjugacy classes of subgroups.

The subgroup lattice has 1117 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63981C211yesmaximal, characteristic
2C2×#63974C211yesmaximal, characteristic, complemented
3C2×#63969C211yesmaximal, characteristic, complemented
4C2×#63880C211yesmaximal, characteristic, complemented
5#10592654C211yesmaximal, characteristic, complemented
6C3×#4961C211yesmaximal, characteristic, complemented
7C3×#4945C211yesmaximal, characteristic, complemented
8#10591717C211yesmaximal, characteristic, complemented
9#10591378C211yesmaximal, characteristic, complemented
10#10591367C211yesmaximal, characteristic, complemented
11#10591364C211yesmaximal, characteristic, complemented
12#10591350C211yesmaximal, characteristic, complemented
13#10591291C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#77111—31nomaximal
17#75844—31nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C3×C4×Dic3C2211yescharacteristic, complemented
39#63981—24no—
40#63974—24no—
41#63969—24no—
42C2×#3724C2211yescharacteristic, complemented
43C2×Dic3⋊Dic3C2211yescharacteristic, complemented
44C2×Dic3⋊Dic3C2211yescharacteristic, complemented
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×#3722C2211yescharacteristic
48C2×#3722C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
50#63880—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#937—31no—
58C2×#935—31no—
59C2×#883—31no—
60C2×#882—31no—
61C2×#67⋊C4—31no—
62C2×D3×C22⋊C4—31no—
63C2×D3×C22⋊C4—31no—
64C2×C4×D12—31no—
65C3×#394—31no—
66C3×#388—31no—
67#4993—31no—
68#4991—31no—
69#4989—31no—
70#4987—31no—
71#4961D311yescharacteristic, complemented
72#4959—31no—
73#4958—31no—
74#4956—31no—
75#4955—31no—
76#4955—31no—
77#4955—61no—
78#4953—31no—
79#4952—31no—
80#4945D311yescharacteristic, complemented
81#4940—31no—
82#4677—31no—
83#4669—31no—
84#4668—31no—
85#4667—31no—
86#4665—31no—
87#4665—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
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—41no—
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×#626—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—41no—
118C2×#626D414yes—
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—22no—
122C2×#624—22no—
123C2×#624—41no—
124C2×#624—41no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—41no—
128C32×C22⋊C4—41no—
129#3757—22no—
130#3752—22no—
131#3752—22no—
132#3752—22no—
133#3752—41no—
134C3×#217—22no—
135C3×#217—22no—
136C3×#217D414yescomplemented
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—41no—
139C3×C4⋊Dic3—41no—
140C3×Dic3⋊C4—41no—
141C3×C4×Dic3—22no—
142#3724—22no—
143Dic3⋊Dic3—22no—
144Dic3⋊Dic3—22no—
145#3722—22no—
146#3722—22no—
147#3722—22no—
148#3722—22no—
149(C2×D3)⋊Dic3—22no—
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C24×D3—61no—
154C22×C3×D4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67C2×D311yescharacteristic
158C23×Dic3—31no—
159C22×D12—31no—
160C22×D12—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—21no—
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⋊C4C2×D311yescharacteristic
175C2×C3×C22⋊C4C2×D311yescharacteristic
176C2×C3×C42—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—61no—
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183C2×#217C2×D311yescharacteristic
184#937—64no—
185#935—64no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
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)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4—61no—
207C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
208C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3C2×D311yescharacteristic, complemented
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4C2×D311yescharacteristic, complemented
217C2×C4×Dic3C2×D311yescharacteristic, complemented
218#883—64no—
219#882—64no—
220#67⋊C4—64no—
221D3×C22⋊C4—64no—
222D3×C22⋊C4—64no—
223C4×D12—64no—
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⋊#95C2×D311yescharacteristic, complemented
234C3⋊#95C2×D311yescharacteristic, complemented
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—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—28no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—44no—
256C22×C3⋊D3—44no—
257C22×C3⋊D3—44no—
258C22×C3⋊D3—44no—
259C22×C3⋊D3—44no—
260C22×C3⋊D3—44no—
261C22×C3⋊D3C2×D412yes—
262C22×C3⋊D3#4112yes—
263C22×C3⋊D3#4112yes—
264C22×C3⋊D3#4112yes—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3C2×D412yes—
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—
284C3×#67—44no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
304C2×C3×Dic3C2×D412yes—
305C2×C3×Dic3C2×D412yes—
306#626—28no—
307#626—44no—
308#624—44no—
309#624—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—31no—
320#388—91no—
321#386—91no—
322#386—91no—
323#385—91no—
324#380—91no—
325#379—91no—
326C24×C3—21no—
327C24×C3—31no—
328C24×C3C22×D311yescharacteristic
329C24×C3C22×D311yescharacteristic
330C23×D3—31no—
331C23×D3—31no—
332C23×D3—31no—
333C23×D3—31no—
334C23×D3—61no—
335C23×D3—61no—
336C23×D3—62no—
337C23×D3—62no—
338C23×D3—62no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—62no—
343C23×D3—62no—
344C23×D3—62no—
345C23×D3—62no—
346C23×D3—64no—
347C23×D3—122no—
348C23×D3—122no—
349C23×D3—122no—
350C23×D3—122no—
351C23×D3—121no—
352C23×D3—121no—
353C23×D3—121no—
354C23×D3—121no—
355C23×D3—122no—
356C23×D3—122no—
357C23×D3C22×D311yescharacteristic
358C2×C3×D4—62no—
359C2×C3×D4—62no—
360C2×C3×D4—121no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C2×#67—22no—
375C2×#67—22no—
376C2×#67—34no—
377C2×#67—41no—
378C2×#67—62no—
379C2×#67—62no—
380C2×#67—62no—
381C2×#67—62no—
382C2×#67—121no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—62no—
390C22×Dic3—62no—
391C22×Dic3—121no—
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C2×D12—34no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—62no—
404C2×D12—121no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—121no—
416C2×C4×D3—121no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—121no—
420C3×C4⋊C4—121no—
421C3×C4⋊C4—121no—
422C3×C22⋊C4—34no—
423C3×C22⋊C4—41no—
424C3×C22⋊C4—41no—
425C3×C22⋊C4—42no—
426C3×C22⋊C4—62no—
427C3×C22⋊C4—62no—
428C3×C22⋊C4—62no—
429C3×C22⋊C4—121no—
430C3×C42—62no—
431#217—22no—
432#217—22no—
433#217—62no—
434#217—62no—
435#217—62no—
436#217—122no—
437#217D1214yescomplemented
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—41no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
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—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—122no—
456(C2×D3)⋊C4—122no—
457(C2×D3)⋊C4—122no—
458(C2×D3)⋊C4—121no—
459(C2×D3)⋊C4—121no—
460(C2×D3)⋊C4—122no—
461C4⋊Dic3—41no—
462C4⋊Dic3—62no—
463C4⋊Dic3—62no—
464Dic3⋊C4—41no—
465Dic3⋊C4—62no—
466Dic3⋊C4—62no—
467Dic3⋊C4—62no—
468Dic3⋊C4—62no—
469C4×Dic3—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32C22×D411yescharacteristic
478C22×C32C22×D411yescharacteristic
479C22×C32C2×#4111yescharacteristic
480C22×C32C2×#4111yescharacteristic
481C22×C32C2×#4111yescharacteristic
482C22×C32H(5,𝔽2)11yescharacteristic
483C22×C32H(5,𝔽2)11yescharacteristic
484C2×C3⋊D3—22no—
485C2×C3⋊D3—22no—
486C2×C3⋊D3—22no—
487C2×C3⋊D3—22no—
488C2×C3⋊D3—22no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—22no—
492C2×C3⋊D3—22no—
493C2×C3⋊D3—416no—
494C2×C3⋊D3—41no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—41no—
498C2×C3⋊D3#12314yescomplemented
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C2×C3×D3—41no—
506C32×C4—41no—
507C32×C4—41no—
508C3⋊Dic3—41no—
509C3⋊Dic3—41no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C3×Dic3—41no—
517C25—91no—
518C22×D4—31no—
519C22×D4—91no—
520C22×D4—91no—
521C23×C4—91no—
522C23×C4—91no—
523C23×C4—91no—
524#123—184no—
525#120—184no—
526C4×D4—184no—
527C2×C4⋊C4—31no—
528C2×C4⋊C4—31no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C4⋊C4—91no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C22⋊C4—91no—
547C2×C22⋊C4—184no—
548C2×C22⋊C4D3211yescharacteristic
549C2×C42—31no—
550#95—31no—
551#95—31no—
552#95—31no—
553#95—91no—
554#95—91no—
555#95—91no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—22no—
572C23×C3—32no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3C2×D1212yes—
584C23×C3D3×D412yes—
585C23×C3C23×D311yescharacteristic
586C23×C3C23×D311yescharacteristic
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—32no—
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—32no—
597C22×D3—32no—
598C22×D3—32no—
599C22×D3—32no—
600C22×D3—32no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—62no—
614C22×D3—68no—
615C22×D3—68no—
616C22×D3—62no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3—121no—
632C22×D3—121no—
633C22×D3—121no—
634C22×D3—121no—
635C22×D3—121no—
636C22×D3—121no—
637C22×D3—128no—
638C22×D3—124no—
639C22×D3—124no—
640C22×D3—124no—
641C22×D3—124no—
642C22×D3—124no—
643C22×D3—124no—
644C22×D3—124no—
645C22×D3—124no—
646C22×D3—124no—
647C22×D3—124no—
648C22×D3—128no—
649C22×D3—128no—
650C22×D3—124no—
651C22×D3—124no—
652C22×D3—128no—
653C22×D3—128no—
654C22×D3—128no—
655C22×D3—128no—
656C22×D3D3×D412yes—
657C3×D4—124no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—32no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697#67—44no—
698#67—68no—
699#67—124no—
700C2×Dic3—21no—
701C2×Dic3—21no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—21no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
708C2×Dic3—21no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—61no—
728C2×Dic3—61no—
729C2×Dic3—61no—
730C2×Dic3—121no—
731C2×Dic3—121no—
732C2×Dic3—121no—
733C2×Dic3—121no—
734C2×Dic3—121no—
735C2×Dic3—121no—
736C2×Dic3—124no—
737C2×Dic3C2×D1212yes—
738C2×Dic3C2×D1212yes—
739C2×Dic3D3×D412yes—
740D12—68no—
741D12—124no—
742C4×D3—124no—
743C4×D3—124no—
744C4×D3—124no—
745C4×D3—124no—
746C4×D3—124no—
747C2×C32—42no—
748C2×C32C2×#12311yescharacteristic
749C2×C32#52511yescharacteristic
750C2×C32#53811yescharacteristic
751C2×C32D4211yescharacteristic
752C2×C32#54611yescharacteristic
753C2×C32#54611yescharacteristic
754C2×C32#55111yescharacteristic
755C3⋊D3—24no—
756C3⋊D3—42no—
757C3×D3—42no—
758C24—31no—
759C24—91no—
760C24—91no—
761C24—182no—
762C24—182no—
763C24—182no—
764C24—182no—
765C24—182no—
766C24—361no—
767C24—361no—
768C24C2×D3211yescharacteristic
769C2×D4—62no—
770C2×D4—62no—
771C2×D4—94no—
772C2×D4—121no—
773C2×D4—182no—
774C2×D4—182no—
775C2×D4—182no—
776C2×D4—182no—
777C2×D4—361no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—31no—
784C22×C4—31no—
785C22×C4—91no—
786C22×C4—91no—
787C22×C4—182no—
788C22×C4—182no—
789C22×C4—182no—
790C22×C4—182no—
791C22×C4—182no—
792C22×C4—182no—
793C22×C4—361no—
794C22×C4—361no—
795C22×C4—361no—
796C22×C4C2×D3211yescharacteristic
797C22×C4C2×D3211yescharacteristic
798C4⋊C4—121no—
799C4⋊C4—121no—
800C4⋊C4—182no—
801C4⋊C4—182no—
802C4⋊C4—182no—
803C22⋊C4—34no—
804C22⋊C4—41no—
805C22⋊C4—62no—
806C22⋊C4—62no—
807C22⋊C4—62no—
808C22⋊C4—121no—
809C22⋊C4—182no—
810C22⋊C4—182no—
811C22⋊C4—182no—
812C22⋊C4—182no—
813C22⋊C4—182no—
814C22⋊C4—182no—
815C22⋊C4—182no—
816C22⋊C4—182no—
817C22⋊C4—182no—
818C22⋊C4—361no—
819C42—62no—
820C22×C3—24no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3C22×D1211yescharacteristic
856C22×C3C2×D3×D411yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C22×C3C2×D3×D411yescharacteristic
859C22×C3#100411yescharacteristic
860C22×C3#100411yescharacteristic
861C22×C3#100411yescharacteristic
862C22×C3D3×#4111yescharacteristic
863C22×C3D3×#4111yescharacteristic
864C22×C3D3×#4111yescharacteristic
865C22×C3D3×#4111yescharacteristic
866C22×C3D3×#4111yescharacteristic
867C22×C3D3×#4111yescharacteristic
868C22×C3#100911yescharacteristic
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—34no—
873C2×D3—34no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—64no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—64no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—62no—
895C2×D3—62no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—122no—
899C2×D3—122no—
900C2×D3—122no—
901C2×D3—122no—
902C2×D3—122no—
903C2×D3—122no—
904C2×D3—122no—
905C2×D3—122no—
906C2×D3—1216no—
907C2×D3—1216no—
908C2×D3—122no—
909C2×D3—122no—
910C2×D3—122no—
911C2×D3—122no—
912C2×D3—1232no—
913C2×D3—121no—
914C2×D3—121no—
915C2×D3—121no—
916C2×D3—121no—
917C2×D3—121no—
918C2×D3—121no—
919C2×D3—121no—
920C2×D3—121no—
921C3×C4—41no—
922C3×C4—41no—
923C3×C4—41no—
924C3×C4—41no—
925C3×C4—62no—
926C3×C4—62no—
927C3×C4—62no—
928C3×C4—81no—
929C3×C4—81no—
930C3×C4—121no—
931C3×C4—121no—
932C3×C4—121no—
933C3×C4—121no—
934Dic3—22no—
935Dic3—22no—
936Dic3—22no—
937Dic3—41no—
938Dic3—41no—
939Dic3—41no—
940Dic3—41no—
941Dic3—121no—
942Dic3—121no—
943Dic3—121no—
944Dic3—121no—
945Dic3—241no—
946Dic3—241no—
947C32#241811yescharacteristic, complemented, Sylow
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—21no—
953C23—21no—
954C23—32no—
955C23—61no—
956C23—61no—
957C23—61no—
958C23—61no—
959C23—61no—
960C23—61no—
961C23—92no—
962C23—92no—
963C23—92no—
964C23—92no—
965C23—188no—
966C23—181no—
967C23—181no—
968C23—181no—
969C23—181no—
970C23—181no—
971C23—181no—
972C23—181no—
973C23—181no—
974C23—181no—
975C23—181no—
976C23—364no—
977C23—364no—
978C23—364no—
979C23—364no—
980C23—364no—
981C23—364no—
982C23D3×D1212yes—
983C23C22×D3211yescharacteristic
984D4—124no—
985D4—188no—
986D4—364no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—32no—
994C2×C4—32no—
995C2×C4—32no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—61no—
999C2×C4—61no—
1000C2×C4—61no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—61no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—61no—
1012C2×C4—61no—
1013C2×C4—61no—
1014C2×C4—181no—
1015C2×C4—181no—
1016C2×C4—181no—
1017C2×C4—181no—
1018C2×C4—181no—
1019C2×C4—181no—
1020C2×C4—364no—
1021C2×C4—364no—
1022C2×C4—364no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—44no—
1031C2×C3—42no—
1032C2×C3—42no—
1033C2×C3—122no—
1034C2×C3#552411yescharacteristic
1035C2×C3D4×D1211yescharacteristic
1036C2×C3#555411yescharacteristic
1037C2×C3#559011yescharacteristic
1038C2×C3#561011yescharacteristic
1039C2×C3#561011yescharacteristic
1040C2×C3#561211yescharacteristic
1041C2×C3#561311yescharacteristic
1042C2×C3D3×#12311yescharacteristic
1043C2×C3D3×#12311yescharacteristic
1044C2×C3#565611yescharacteristic
1045C2×C3#567811yescharacteristic
1046C2×C3#567911yescharacteristic
1047C2×C3#570511yescharacteristic
1048D3—42no—
1049D3—64no—
1050D3—64no—
1051D3—124no—
1052D3—124no—
1053D3—122no—
1054D3—122no—
1055C22—22no—
1056C22—22no—
1057C22—22no—
1058C22—41no—
1059C22—41no—
1060C22—41no—
1061C22—41no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—94no—
1066C22—121no—
1067C22—121no—
1068C22—121no—
1069C22—121no—
1070C22—182no—
1071C22—182no—
1072C22—182no—
1073C22—182no—
1074C22—182no—
1075C22—182no—
1076C22—182no—
1077C22—182no—
1078C22—182no—
1079C22—3616no—
1080C22—361no—
1081C22—361no—
1082C22—361no—
1083C22—361no—
1084C22C2×D3×D1211yescharacteristic
1085C22#6430611yescharacteristic
1086C22D32×D411yescharacteristic
1087C22#6431211yescharacteristic
1088C22#6431211yescharacteristic
1089C22#6431411yescharacteristic
1090C22#6433011yescharacteristic
1091C4—41no—
1092C4—41no—
1093C4—62no—
1094C4—62no—
1095C4—62no—
1096C4—121no—
1097C4—121no—
1098C4—121no—
1099C4—121no—
1100C4—361no—
1101C4—361no—
1102C3—21no—
1103C3#7584411yescharacteristic, complemented
1104C3#7711111yescharacteristic, complemented
1105C2—42no—
1106C2—122no—
1107C2—184no—
1108C2—362no—
1109C2#1059407911yescharacteristic
1110C2#1059415311yescharacteristic
1111C2#1059426011yescharacteristic
1112C2#1059427711yescharacteristic
1113C2#1059507511yescharacteristic
1114C2#1059520711yescharacteristic
1115C2#1059529611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63981C2
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×#63974C2semidirect
3. C2×#63969C2semidirect
4. C2×#63880C2semidirect
5. #10592654C2semidirect
6. C3×#4961C2semidirect
7. C3×#4945C2semidirect
8. #10591717C2semidirect
9. #10591378C2semidirect
10. #10591367C2semidirect
11. #10591364C2semidirect
12. #10591350C2semidirect
13. #10591291C2semidirect
14. #10591275C2semidirect
15. #10591202C2semidirect
24. C22×D3×Dic3C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×C4×Dic3C22semidirect
42. C2×#3724C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
49. C2×(C2×D3)⋊Dic3C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
71. #4961D3semidirect
80. #4945D3semidirect
136. C3×#217D4semidirect
207. C2×(C2×D3)⋊C4C2×D3semidirect
208. C2×(C2×D3)⋊C4C2×D3semidirect
211. C2×C4⋊Dic3C2×D3semidirect
216. C2×Dic3⋊C4C2×D3semidirect
217. C2×C4×Dic3C2×D3semidirect
233. C3⋊#95C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
437. #217D12semidirect
498. C2×C3⋊D3#123semidirect
947. C32#2418semidirect
1103. C3#75844semidirect
1104. C3#77111semidirect

Maximal subgroups

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

subgroupindex
C2×#639812
C2×#639742
C2×#639692
C2×#638802
#105926542
C3×#49612
C3×#49452
#105917172
#105913782
#105913672
#105913642
#105913502
#105912912
#105912752
#105912022
#771113
#758443