Finite Group Databasebeta

← #11810341

Subgroups — #11810341

Order 1152.

1931 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic
2C2×#63975C211yesmaximal, characteristic, complemented
3C2×#63974C211yesmaximal, characteristic, complemented
4C2×#63894C211yesmaximal, characteristic, complemented
5C3×#4953C211yesmaximal, characteristic, complemented
6C3×#4944C211yesmaximal, characteristic, complemented
7#10591714C211yesmaximal, characteristic, complemented
8#10591712C211yesmaximal, characteristic, complemented
9#10591380C211yesmaximal, characteristic, complemented
10#10591380C211yesmaximal, characteristic, complemented
11#10591375C211yesmaximal, characteristic, complemented
12#10591367C211yesmaximal, characteristic, complemented
13#10591350C211yesmaximal, characteristic, complemented
14#10591321C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#77669—31nomaximal
17#75844—31nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28#64091—24no—
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
35C2×C3×C4×Dic3C2211yescharacteristic, complemented
36#63975—24no—
37#63974—24no—
38C2×Dic3⋊Dic3C2211yescharacteristic, complemented
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×#3722C2211yescharacteristic, complemented
48C2×#3722C2211yescharacteristic, complemented
49C2×#3722C2211yescharacteristic, complemented
50#63894—24no—
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#893—31no—
58C2×#883—31no—
59C2×#883—31no—
60C2×#882—31no—
61C2×#882—31no—
62C2×#882—61no—
63C2×D3×C22⋊C4—31no—
64C2×D3×C22⋊C4—31no—
65C2×C4×D12—31no—
66C3×#397—31no—
67C3×#388—31no—
68#4993—31no—
69#4991—31no—
70#4987—31no—
71#4961—31no—
72#4959—31no—
73#4955—31no—
74#4955—31no—
75#4953D311yescharacteristic, complemented
76#4944D311yescharacteristic, complemented
77#4940—31no—
78#4677—31no—
79#4672—31no—
80#4670—31no—
81#4668—31no—
82#4668—31no—
83#4667—31no—
84#4665—31no—
85#4665—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
101C2×#638—22no—
102C2×#638—22no—
103C2×#638—41no—
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C4⋊(C3⋊D3)—22no—
106C2×C4⋊(C3⋊D3)—22no—
107C2×C4⋊(C3⋊D3)—22no—
108C2×C4⋊(C3⋊D3)—22no—
109C2×C4⋊(C3⋊D3)—41no—
110C2×C4⋊(C3⋊D3)D414yes—
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—22no—
122C2×#624—22no—
123C2×#624—22no—
124C2×#624—22no—
125C2×#624—41no—
126C2×#624—41no—
127C2×#624—41no—
128C32×C22⋊C4—22no—
129#3752—22no—
130#3752—22no—
131C3×#217—22no—
132C3×#217—22no—
133C3×#217—41no—
134C3×#217D414yescomplemented
135C3×C4⋊Dic3—22no—
136C3×Dic3⋊C4—41no—
137C3×C4×Dic3—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—41no—
141#3722—22no—
142#3722—22no—
143#3722—22no—
144#3722—22no—
145#3722—22no—
146#3722—22no—
147#3722—22no—
148#3722—41no—
149#3722—41no—
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C24×D3—61no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—61no—
157C22×D12—31no—
158C22×D12—31no—
159C22×D12—31no—
160C22×D12—31no—
161C22×D12—61no—
162C22×D12—61no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C22⋊C4—21no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4C2×D311yescharacteristic
177C2×C3×C22⋊C4C2×D311yescharacteristic
178C2×C3×C42—31no—
179C2×#217C2×D311yescharacteristic
180C2×#217C2×D311yescharacteristic
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
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—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4—61no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3C2×D311yescharacteristic, complemented
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4C2×D311yescharacteristic, complemented
215C2×C4×Dic3C2×D311yescharacteristic, complemented
216#893—64no—
217#883—64no—
218#883—64no—
219#882—64no—
220#882—64no—
221#882—68no—
222D3×C22⋊C4—64no—
223D3×C22⋊C4—64no—
224C4×D12—64no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95—31no—
229C3×#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95C2×D311yescharacteristic, complemented
233C3⋊#95C2×D311yescharacteristic, complemented
234C3⋊#95C2×D311yescharacteristic, complemented
235C3⋊#95C2×D311yescharacteristic, complemented
236C3⋊#95C2×D311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32C2×D412yes—
244C23×C32C2411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—28no—
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—21no—
262C22×C3⋊D3—44no—
263C22×C3⋊D3—44no—
264C22×C3⋊D3—44no—
265C22×C3⋊D3—44no—
266C22×C3⋊D3—44no—
267C22×C3⋊D3—44no—
268C22×C3⋊D3C2×D412yes—
269C22×C3⋊D3C2×D412yes—
270C22×C3⋊D3#4112yes—
271C22×C3⋊D3#4112yes—
272C22×C3⋊D3#4112yes—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4C2×D412yes—
279#638—44no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C4⋊(C3⋊D3)—28no—
284C4⋊(C3⋊D3)—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×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3C2×D412yes—
309#624—44no—
310#624—44no—
311#624—44no—
312C2×#123—91no—
313C2×#120—91no—
314C2×C4×D4—91no—
315C22×C22⋊C4—91no—
316#399—91no—
317#397—31no—
318#394—91no—
319#394—91no—
320#388—31no—
321#388—91no—
322#386—91no—
323#386—91no—
324#385—91no—
325#380—91no—
326#379—91no—
327C24×C3—21no—
328C24×C3C22×D311yescharacteristic
329C24×C3C22×D311yescharacteristic
330C23×D3—31no—
331C23×D3—31no—
332C23×D3—31no—
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—31no—
336C23×D3—61no—
337C23×D3—61no—
338C23×D3—61no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—62no—
343C23×D3—62no—
344C23×D3—62no—
345C23×D3—62no—
346C23×D3—62no—
347C23×D3—62no—
348C23×D3—62no—
349C23×D3—64no—
350C23×D3—122no—
351C23×D3—122no—
352C23×D3—122no—
353C23×D3—122no—
354C23×D3—121no—
355C23×D3—121no—
356C23×D3—121no—
357C23×D3—121no—
358C23×D3—122no—
359C23×D3—122no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—31no—
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—62no—
375C2×#67—62no—
376C2×#67—64no—
377C2×#67—62no—
378C2×#67—62no—
379C2×#67—122no—
380C2×#67—121no—
381C2×#67—121no—
382C2×#67—122no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—61no—
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C2×D12—34no—
395C2×D12—34no—
396C2×D12—64no—
397C2×D12—62no—
398C2×D12—62no—
399C2×D12—62no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—62no—
404C2×D12—62no—
405C2×D12—64no—
406C2×D12—122no—
407C2×D12—122no—
408C2×D12—122no—
409C2×D12—121no—
410C2×D12—121no—
411C2×D12—122no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—62no—
416C2×C4×D3—62no—
417C2×C4×D3—62no—
418C2×C4×D3—62no—
419C2×C4×D3—62no—
420C2×C4×D3—62no—
421C2×C4×D3—62no—
422C2×C4×D3—62no—
423C2×C4×D3—62no—
424C2×C4×D3—121no—
425C2×C4×D3—121no—
426C2×C4×D3—121no—
427C2×C4×D3—121no—
428C2×C4×D3—121no—
429C2×C4×D3—121no—
430C3×C4⋊C4—62no—
431C3×C4⋊C4—121no—
432C3×C22⋊C4—24no—
433C3×C22⋊C4—22no—
434C3×C22⋊C4—22no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—62no—
437C3×C22⋊C4—62no—
438C3×C22⋊C4—121no—
439C3×C42—62no—
440#217—22no—
441#217—22no—
442#217—41no—
443#217D1214yescomplemented
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—62no—
456(C2×D3)⋊C4—62no—
457(C2×D3)⋊C4—64no—
458(C2×D3)⋊C4—64no—
459(C2×D3)⋊C4—62no—
460(C2×D3)⋊C4—62no—
461(C2×D3)⋊C4—62no—
462(C2×D3)⋊C4—62no—
463(C2×D3)⋊C4—62no—
464(C2×D3)⋊C4—121no—
465(C2×D3)⋊C4—121no—
466(C2×D3)⋊C4—121no—
467(C2×D3)⋊C4—121no—
468C4⋊Dic3—22no—
469C4⋊Dic3—62no—
470C4⋊Dic3—62no—
471C4⋊Dic3—121no—
472Dic3⋊C4—41no—
473Dic3⋊C4—62no—
474Dic3⋊C4—62no—
475Dic3⋊C4—121no—
476C4×Dic3—22no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32C22×D411yescharacteristic
485C22×C32C22×D411yescharacteristic
486C22×C32C2×#4111yescharacteristic
487C22×C32C2×#4111yescharacteristic
488C22×C32C2×#4111yescharacteristic
489C22×C32H(5,𝔽2)11yescharacteristic
490C22×C32H(5,𝔽2)11yescharacteristic
491C2×C3⋊D3—22no—
492C2×C3⋊D3—22no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—416no—
504C2×C3⋊D3—41no—
505C2×C3⋊D3—41no—
506C2×C3⋊D3—41no—
507C2×C3⋊D3—41no—
508C2×C3⋊D3—41no—
509C2×C3⋊D3—41no—
510C2×C3⋊D3—41no—
511C2×C3⋊D3—41no—
512C2×C3⋊D3#12314yescomplemented
513C32×C4—22no—
514C32×C4—41no—
515C3⋊Dic3—41no—
516C3×Dic3—22no—
517C3×Dic3—22no—
518C3×Dic3—41no—
519C3×Dic3—41no—
520C3×Dic3—41no—
521C3×Dic3—41no—
522C3×Dic3—41no—
523C3×Dic3—41no—
524C25—91no—
525C22×D4—91no—
526C22×D4—91no—
527C22×D4—91no—
528C23×C4—91no—
529C23×C4—91no—
530C23×C4—91no—
531#123—184no—
532#120—184no—
533C4×D4—184no—
534C2×C4⋊C4—31no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—91no—
537C2×C4⋊C4—91no—
538C2×C4⋊C4—91no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—31no—
541C2×C22⋊C4—31no—
542C2×C22⋊C4—31no—
543C2×C22⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C22⋊C4—91no—
547C2×C22⋊C4—91no—
548C2×C22⋊C4—91no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—184no—
555C2×C22⋊C4D3211yescharacteristic
556C2×C42—31no—
557#95—31no—
558#95—31no—
559#95—31no—
560#95—31no—
561#95—31no—
562#95—91no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—22no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3C2×D1212yes—
584C23×C3D3×D412yes—
585C23×C3C23×D311yescharacteristic
586C23×C3C23×D311yescharacteristic
587C22×D3—32no—
588C22×D3—32no—
589C22×D3—32no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—32no—
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—32no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—62no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—68no—
613C22×D3—68no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—61no—
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—61no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—61no—
635C22×D3—61no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—121no—
639C22×D3—121no—
640C22×D3—121no—
641C22×D3—121no—
642C22×D3—121no—
643C22×D3—121no—
644C22×D3—121no—
645C22×D3—121no—
646C22×D3—128no—
647C22×D3—121no—
648C22×D3—121no—
649C22×D3—121no—
650C22×D3—121no—
651C22×D3—121no—
652C22×D3—121no—
653C22×D3—124no—
654C22×D3—124no—
655C22×D3—124no—
656C22×D3—124no—
657C22×D3—124no—
658C22×D3—124no—
659C22×D3—124no—
660C22×D3—124no—
661C22×D3—124no—
662C22×D3—124no—
663C22×D3—128no—
664C22×D3—128no—
665C22×D3—124no—
666C22×D3—124no—
667C22×D3—128no—
668C22×D3—128no—
669C22×D3—128no—
670C22×D3—128no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—22no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—22no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
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—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4D3×D412yes—
712C2×C3×C4D3×D412yes—
713#67—124no—
714#67—124no—
715#67—128no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—21no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—21no—
733C2×Dic3—21no—
734C2×Dic3—21no—
735C2×Dic3—21no—
736C2×Dic3—21no—
737C2×Dic3—21no—
738C2×Dic3—62no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—61no—
745C2×Dic3—121no—
746C2×Dic3—121no—
747C2×Dic3C2×D1212yes—
748C2×Dic3C2×D1212yes—
749D12—68no—
750D12—68no—
751D12—128no—
752D12—124no—
753D12—124no—
754D12—128no—
755C4×D3—124no—
756C4×D3—124no—
757C4×D3—124no—
758C4×D3—124no—
759C4×D3—124no—
760C4×D3—124no—
761C2×C32—42no—
762C2×C32C2×#12311yescharacteristic
763C2×C32#52511yescharacteristic
764C2×C32#53811yescharacteristic
765C2×C32D4211yescharacteristic
766C2×C32#54611yescharacteristic
767C2×C32#54611yescharacteristic
768C2×C32#55111yescharacteristic
769C3⋊D3—24no—
770C3⋊D3—42no—
771C3⋊D3—42no—
772C24—91no—
773C24—91no—
774C24—91no—
775C24—182no—
776C24—182no—
777C24—182no—
778C24—182no—
779C24—182no—
780C24—361no—
781C24—361no—
782C24C2×D3211yescharacteristic
783C2×D4—94no—
784C2×D4—182no—
785C2×D4—182no—
786C2×D4—182no—
787C2×D4—182no—
788C2×D4—182no—
789C2×D4—182no—
790C2×D4—361no—
791C2×D4—361no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—91no—
801C22×C4—182no—
802C22×C4—182no—
803C22×C4—182no—
804C22×C4—182no—
805C22×C4—182no—
806C22×C4—182no—
807C22×C4—361no—
808C22×C4—361no—
809C22×C4—361no—
810C22×C4C2×D3211yescharacteristic
811C22×C4C2×D3211yescharacteristic
812C4⋊C4—62no—
813C4⋊C4—121no—
814C4⋊C4—182no—
815C4⋊C4—182no—
816C4⋊C4—361no—
817C22⋊C4—22no—
818C22⋊C4—34no—
819C22⋊C4—62no—
820C22⋊C4—62no—
821C22⋊C4—121no—
822C22⋊C4—182no—
823C22⋊C4—182no—
824C22⋊C4—182no—
825C22⋊C4—182no—
826C22⋊C4—182no—
827C22⋊C4—182no—
828C22⋊C4—182no—
829C22⋊C4—182no—
830C22⋊C4—182no—
831C22⋊C4—361no—
832C22⋊C4—361no—
833C42—62no—
834C22×C3—24no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—41no—
857C22×C3—41no—
858C22×C3—41no—
859C22×C3—41no—
860C22×C3—41no—
861C22×C3—41no—
862C22×C3C22×D1211yescharacteristic
863C22×C3C2×D3×D411yescharacteristic
864C22×C3C2×D3×D411yescharacteristic
865C22×C3C2×D3×D411yescharacteristic
866C22×C3#100411yescharacteristic
867C22×C3D3×#4111yescharacteristic
868C22×C3D3×#4111yescharacteristic
869C22×C3D3×#4111yescharacteristic
870C22×C3D3×#4111yescharacteristic
871C22×C3D3×#4111yescharacteristic
872C22×C3D3×#4111yescharacteristic
873C22×C3#100911yescharacteristic
874C22×C3#100911yescharacteristic
875C22×C3#100911yescharacteristic
876C2×D3—34no—
877C2×D3—34no—
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—62no—
899C2×D3—62no—
900C2×D3—62no—
901C2×D3—62no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—122no—
905C2×D3—122no—
906C2×D3—122no—
907C2×D3—122no—
908C2×D3—122no—
909C2×D3—122no—
910C2×D3—122no—
911C2×D3—122no—
912C2×D3—122no—
913C2×D3—122no—
914C2×D3—122no—
915C2×D3—1216no—
916C2×D3—1216no—
917C2×D3—122no—
918C2×D3—122no—
919C2×D3—122no—
920C2×D3—122no—
921C2×D3—1232no—
922C2×D3—121no—
923C2×D3—121no—
924C2×D3—121no—
925C2×D3—121no—
926C2×D3—121no—
927C2×D3—121no—
928C2×D3—121no—
929C2×D3—121no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—121no—
934C2×D3—121no—
935C2×D3—121no—
936C2×D3—121no—
937C2×D3—121no—
938C2×D3—241no—
939C2×D3—241no—
940C2×D3—241no—
941C2×D3—241no—
942C3×C4—22no—
943C3×C4—22no—
944C3×C4—42no—
945C3×C4—42no—
946C3×C4—41no—
947C3×C4—41no—
948C3×C4—62no—
949C3×C4—62no—
950C3×C4—121no—
951C3×C4—121no—
952C3×C4—121no—
953C3×C4—121no—
954C3×C4—121no—
955C3×C4—121no—
956Dic3—22no—
957Dic3—22no—
958Dic3—41no—
959Dic3—41no—
960Dic3—41no—
961Dic3—41no—
962Dic3—41no—
963Dic3—41no—
964Dic3—122no—
965Dic3—121no—
966Dic3—121no—
967C32#241811yescharacteristic, complemented, Sylow
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—92no—
975C23—92no—
976C23—92no—
977C23—92no—
978C23—92no—
979C23—188no—
980C23—181no—
981C23—181no—
982C23—181no—
983C23—181no—
984C23—181no—
985C23—181no—
986C23—181no—
987C23—181no—
988C23—181no—
989C23—181no—
990C23—181no—
991C23—181no—
992C23—181no—
993C23—181no—
994C23—181no—
995C23—181no—
996C23—364no—
997C23—364no—
998C23—364no—
999C23—364no—
1000C23—364no—
1001C23—364no—
1002C23D3×D1212yes—
1003C23C22×D3211yescharacteristic
1004D4—188no—
1005D4—364no—
1006D4—364no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—32no—
1013C2×C4—32no—
1014C2×C4—61no—
1015C2×C4—61no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—61no—
1029C2×C4—61no—
1030C2×C4—61no—
1031C2×C4—61no—
1032C2×C4—61no—
1033C2×C4—61no—
1034C2×C4—61no—
1035C2×C4—61no—
1036C2×C4—181no—
1037C2×C4—181no—
1038C2×C4—181no—
1039C2×C4—364no—
1040C2×C4—364no—
1041C2×C4—364no—
1042C2×C4#381112yes—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—44no—
1051C2×C3—42no—
1052C2×C3—42no—
1053C2×C3#552411yescharacteristic
1054C2×C3D4×D1211yescharacteristic
1055C2×C3#555411yescharacteristic
1056C2×C3#560911yescharacteristic
1057C2×C3#561211yescharacteristic
1058C2×C3D3×#12311yescharacteristic
1059C2×C3D3×#12311yescharacteristic
1060C2×C3#565411yescharacteristic
1061C2×C3#565611yescharacteristic
1062C2×C3#567611yescharacteristic
1063C2×C3#567811yescharacteristic
1064C2×C3#570411yescharacteristic
1065C2×C3#570511yescharacteristic
1066C2×C3#570511yescharacteristic
1067D3—64no—
1068D3—64no—
1069D3—124no—
1070D3—124no—
1071D3—122no—
1072D3—122no—
1073D3—122no—
1074D3—122no—
1075D3—242no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—94no—
1084C22—182no—
1085C22—182no—
1086C22—182no—
1087C22—182no—
1088C22—182no—
1089C22—182no—
1090C22—182no—
1091C22—182no—
1092C22—182no—
1093C22—182no—
1094C22—182no—
1095C22—182no—
1096C22—3616no—
1097C22—361no—
1098C22—361no—
1099C22—361no—
1100C22—361no—
1101C22—361no—
1102C22—361no—
1103C22—361no—
1104C22—361no—
1105C22C2×D3×D1211yescharacteristic
1106C22#6430811yescharacteristic
1107C22#6431211yescharacteristic
1108C22#6431211yescharacteristic
1109C22#6431211yescharacteristic
1110C22#6431411yescharacteristic
1111C22C2×#381111yescharacteristic
1112C4—22no—
1113C4—41no—
1114C4—62no—
1115C4—62no—
1116C4—121no—
1117C4—121no—
1118C4—121no—
1119C4—121no—
1120C4—121no—
1121C4—121no—
1122C4—361no—
1123C3—21no—
1124C3#7584411yescharacteristic, complemented
1125C3#7766911yescharacteristic, complemented
1126C2—42no—
1127C2—184no—
1128C2—362no—
1129C2—362no—
1130C2#1059407911yescharacteristic
1131C2#1059416211yescharacteristic
1132C2#1059416511yescharacteristic
1133C2#1059429311yescharacteristic
1134C2#1059507411yescharacteristic
1135C2#1059516911yescharacteristic
1136C2#1059524311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#64091C2
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×#63975C2semidirect
3. C2×#63974C2semidirect
4. C2×#63894C2semidirect
5. C3×#4953C2semidirect
6. C3×#4944C2semidirect
7. #10591714C2semidirect
8. #10591712C2semidirect
9. #10591380C2semidirect
10. #10591380C2semidirect
11. #10591375C2semidirect
12. #10591367C2semidirect
13. #10591350C2semidirect
14. #10591321C2semidirect
15. #10591194C2semidirect
24. C22×#624C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×Dic3⋊C4C22semidirect
35. C2×C3×C4×Dic3C22semidirect
38. C2×Dic3⋊Dic3C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
47. C2×#3722C22semidirect
48. C2×#3722C22semidirect
49. C2×#3722C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. #63579C22semidirect
75. #4953D3semidirect
76. #4944D3semidirect
134. C3×#217D4semidirect
210. C2×C4⋊Dic3C2×D3semidirect
214. C2×Dic3⋊C4C2×D3semidirect
215. C2×C4×Dic3C2×D3semidirect
232. C3⋊#95C2×D3semidirect
233. C3⋊#95C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
236. C3⋊#95C2×D3semidirect
443. #217D12semidirect
512. C2×C3⋊D3#123semidirect
967. C32#2418semidirect
1124. C3#75844semidirect
1125. C3#77669semidirect

Maximal subgroups

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

subgroupindex
C2×#640912
C2×#639752
C2×#639742
C2×#638942
C3×#49532
C3×#49442
#105917142
#105917122
#105913802
#105913752
#105913672
#105913502
#105913212
#105911942
#776693
#758443