Finite Group Databasebeta

← #11810323

Subgroups — #11810323

Order 1152.

1717 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63922C211yesmaximal, characteristic
2C2×#63921C211yesmaximal, characteristic, complemented
3C2×#63884C211yesmaximal, characteristic, complemented
4C2×#63881C211yesmaximal, characteristic, complemented
5#10592688C211yesmaximal, characteristic, complemented
6C3×#4993C211yesmaximal, characteristic, complemented
7C3×#4991C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591390C211yesmaximal, characteristic, complemented
10#10591367C211yesmaximal, characteristic, complemented
11#10591363C211yesmaximal, characteristic, complemented
12#10591301C211yesmaximal, characteristic, complemented
13#10591284C211yesmaximal, characteristic, complemented
14#10591281C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#78101—31nomaximal
17#77111—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic, complemented
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×Dic3⋊Dic3C2211yescharacteristic, complemented
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
46C2×Dic32C2211yescharacteristic, complemented
47#63922—24no—
48#63921—24no—
49#63884—24no—
50#63881—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×#937—31no—
58C2×#935—31no—
59C2×#894—31no—
60C2×#893—31no—
61C2×#882—31no—
62C2×#67⋊C4—31no—
63C2×D3×C22⋊C4—31no—
64C2×D3×C22⋊C4—31no—
65C3×#399—31no—
66C3×#394—31no—
67#4993D311yescharacteristic, complemented
68#4992—31no—
69#4991D311yescharacteristic, complemented
70#4989—31no—
71#4989—31no—
72#4989—61no—
73#4987—31no—
74#4961—31no—
75#4959—31no—
76#4958—31no—
77#4956—31no—
78#4956—31no—
79#4955—31no—
80#4955—31no—
81#4952—31no—
82#4945—31no—
83#4944—31no—
84#4670—31no—
85#4669—31no—
86#4667—31no—
87#4665—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×D32—22no—
93C22×D32—22no—
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—22no—
97C22×D32—41no—
98C22×D32—41no—
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—22no—
107C2×C4×C3⋊D3—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×C3×D12—22no—
114C2×C3×D12—22no—
115C2×C3×D12—41no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626D414yes—
119C2×#625—22no—
120C2×#625—22no—
121C2×#625—41no—
122C2×#624—22no—
123C2×#624—22no—
124C2×#624—41no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—41no—
128C32×C4⋊C4—41no—
129#3752—22no—
130#3752—22no—
131#3750—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—41no—
137C3×(C2×D3)⋊C4—41no—
138C3×(C2×D3)⋊C4—41no—
139C3×Dic3⋊C4—22no—
140C3×Dic3⋊C4—22no—
141Dic3⋊Dic3—41no—
142#3722—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3D414yescomplemented
149Dic32—22no—
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C22×C3×D4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C23×Dic3—31no—
158C22×D12—31no—
159C22×D12C2×D311yescharacteristic
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—61no—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
170C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
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—61no—
199C2×(C2×D3)⋊C4—61no—
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
206C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
207C2×C4⋊Dic3—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—61no—
212C2×Dic3⋊C4C2×D311yescharacteristic, complemented
213C2×Dic3⋊C4C2×D311yescharacteristic, complemented
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216#894—64no—
217#893—64no—
218#882—64no—
219#67⋊C4—64no—
220D3×C22⋊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—61no—
233C3⋊#95—61no—
234C3⋊#95C2×D311yescharacteristic, complemented
235C3⋊#95C2×D311yescharacteristic, complemented
236C23×C32C2411yescharacteristic
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3C2×D412yes—
242C22×C3⋊D3#4112yes—
243C22×C3⋊D3#4112yes—
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—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—21no—
262C22×C3×D3C2×D412yes—
263C22×C3×D3C2×D412yes—
264C22×C3×D3#4112yes—
265C2×D32—28no—
266C2×D32—44no—
267C2×D32—44no—
268C2×D32—44no—
269C2×D32—44no—
270C2×D32—44no—
271C2×D32—44no—
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×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—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⋊Dic3—21no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3C2×D412yes—
290C4×C3⋊D3—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×Dic3C2×D412yes—
305C2×C3×Dic3C2×D412yes—
306C3×D12—44no—
307#626—28no—
308#625—44no—
309#624—44no—
310D3×Dic3—44no—
311C2×#123—91no—
312C2×#120—91no—
313C2×C4×D4—91no—
314C22×C22⋊C4—91no—
315#399—31no—
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—91no—
326C24×C3—31no—
327C24×C3—31no—
328C24×C3—31no—
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—61no—
332C23×D3—62no—
333C23×D3—62no—
334C23×D3—62no—
335C23×D3—62no—
336C23×D3—62no—
337C23×D3—62no—
338C23×D3—62no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—121no—
343C23×D3—121no—
344C23×D3—121no—
345C23×D3—121no—
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—21no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C2×#67—34no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—121no—
374C2×#67—121no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—62no—
385C22×Dic3—62no—
386C22×Dic3—121no—
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C2×D12—22no—
393C2×D12—22no—
394C2×D12—34no—
395C2×D12—41no—
396C2×D12—62no—
397C2×D12—62no—
398C2×C4×D3—62no—
399C2×C4×D3—62no—
400C2×C4×D3—62no—
401C2×C4×D3—62no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×C4×D3—62no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—122no—
409C2×C4×D3—122no—
410C2×C4×D3—121no—
411C2×C4×D3—121no—
412C2×C4×D3—121no—
413C2×C4×D3—121no—
414C2×C4×D3—121no—
415C2×C4×D3—122no—
416C3×C4⋊C4—41no—
417C3×C4⋊C4—41no—
418C3×C4⋊C4—42no—
419C3×C4⋊C4—62no—
420C3×C4⋊C4—62no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—121no—
426C3×C22⋊C4—121no—
427C3×C22⋊C4—121no—
428#217—34no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—62no—
434(C2×D3)⋊C4—22no—
435(C2×D3)⋊C4—22no—
436(C2×D3)⋊C4—22no—
437(C2×D3)⋊C4—22no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—41no—
440(C2×D3)⋊C4—41no—
441(C2×D3)⋊C4—41no—
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—64no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—122no—
455C4⋊Dic3—121no—
456Dic3⋊C4—22no—
457Dic3⋊C4—22no—
458Dic3⋊C4—62no—
459Dic3⋊C4—62no—
460Dic3⋊C4—122no—
461Dic3⋊C4—121no—
462C4×Dic3—62no—
463C4×Dic3—62no—
464C22×C32C22×D411yescharacteristic
465C22×C32C22×D411yescharacteristic
466C22×C32C2×#4111yescharacteristic
467C22×C32C2×#4111yescharacteristic
468C22×C32C2×#4111yescharacteristic
469C22×C32H(5,𝔽2)11yescharacteristic
470C22×C32H(5,𝔽2)11yescharacteristic
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3#12314yescomplemented
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—41no—
488C2×C3×D3—41no—
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—41no—
498C2×C3×D3—41no—
499D32—416no—
500C32×C4—41no—
501C32×C4—41no—
502C32×C4—41no—
503C3⋊Dic3—22no—
504C3⋊Dic3—41no—
505C3⋊Dic3—41no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C25—91no—
512C22×D4—31no—
513C22×D4—91no—
514C22×D4—91no—
515C23×C4—91no—
516C23×C4—91no—
517C23×C4—91no—
518#123—184no—
519#120—184no—
520C4×D4—184no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4D3211yescharacteristic, complemented
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—31no—
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—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—184no—
543C2×C42—91no—
544#95—31no—
545#95—31no—
546#95—91no—
547#95—91no—
548#95—91no—
549#95—91no—
550C23×C3—21no—
551C23×C3—32no—
552C23×C3—32no—
553C23×C3—32no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3C23×D311yescharacteristic
573C23×C3C23×D311yescharacteristic
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—32no—
593C22×D3—32no—
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—32no—
597C22×D3—32no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—68no—
602C22×D3—68no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3—124no—
616C22×D3—124no—
617C22×D3—124no—
618C22×D3—124no—
619C22×D3—124no—
620C22×D3—124no—
621C22×D3—124no—
622C22×D3—124no—
623C22×D3—124no—
624C22×D3—124no—
625C22×D3—124no—
626C22×D3—124no—
627C22×D3D3×D412yes—
628C22×D3D3×D412yes—
629C22×D3#23912yes—
630C3×D4—124no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
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—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673#67—68no—
674#67—124no—
675#67—124no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—32no—
690C2×Dic3—32no—
691C2×Dic3—62no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—62no—
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—124no—
717C2×Dic3D3×D412yes—
718C2×Dic3D3×D412yes—
719D12—44no—
720D12—68no—
721C4×D3—124no—
722C4×D3—124no—
723C4×D3—124no—
724C4×D3—124no—
725C4×D3—124no—
726C4×D3—128no—
727C2×C32C2×#12311yescharacteristic
728C2×C32#52511yescharacteristic
729C2×C32#53811yescharacteristic
730C2×C32D4211yescharacteristic
731C2×C32#54611yescharacteristic
732C2×C32#54611yescharacteristic
733C2×C32#55111yescharacteristic
734C3⋊D3—24no—
735C3×D3—42no—
736C3×D3—42no—
737C3×D3—42no—
738C24—31no—
739C24—31no—
740C24—31no—
741C24—91no—
742C24—182no—
743C24—182no—
744C24—182no—
745C24—182no—
746C24—182no—
747C24—361no—
748C24—361no—
749C2×D4—62no—
750C2×D4—62no—
751C2×D4—94no—
752C2×D4—121no—
753C2×D4—182no—
754C2×D4—182no—
755C2×D4—182no—
756C2×D4—182no—
757C2×D4—361no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—91no—
764C22×C4—91no—
765C22×C4—91no—
766C22×C4—182no—
767C22×C4—182no—
768C22×C4—182no—
769C22×C4—182no—
770C22×C4—182no—
771C22×C4—182no—
772C22×C4—361no—
773C22×C4—361no—
774C22×C4—361no—
775C22×C4C2×D3211yescharacteristic
776C22×C4C2×D3211yescharacteristic
777C22×C4C2×D3211yescharacteristic
778C4⋊C4—41no—
779C4⋊C4—62no—
780C4⋊C4—62no—
781C4⋊C4—182no—
782C4⋊C4—361no—
783C22⋊C4—62no—
784C22⋊C4—62no—
785C22⋊C4—62no—
786C22⋊C4—62no—
787C22⋊C4—94no—
788C22⋊C4—121no—
789C22⋊C4—121no—
790C22⋊C4—121no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—182no—
795C22⋊C4—182no—
796C22⋊C4—182no—
797C22⋊C4—182no—
798C22⋊C4—182no—
799C42—182no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—121no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3—121no—
825C22×C3—121no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3C2×D3×D411yescharacteristic
829C22×C3C2×D3×D411yescharacteristic
830C22×C3C2×D3×D411yescharacteristic
831C22×C3C2×D3×D411yescharacteristic
832C22×C3#100411yescharacteristic
833C22×C3#100411yescharacteristic
834C22×C3#100411yescharacteristic
835C22×C3C2×#23911yescharacteristic
836C22×C3D3×#4111yescharacteristic
837C22×C3D3×#4111yescharacteristic
838C22×C3D3×#4111yescharacteristic
839C22×C3D3×#4111yescharacteristic
840C22×C3D3×#4111yescharacteristic
841C22×C3#100911yescharacteristic
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—34no—
852C2×D3—34no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—41no—
865C2×D3—64no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—122no—
879C2×D3—122no—
880C2×D3—122no—
881C2×D3—122no—
882C2×D3—122no—
883C2×D3—122no—
884C2×D3—1216no—
885C2×D3—1216no—
886C3×C4—42no—
887C3×C4—42no—
888C3×C4—41no—
889C3×C4—41no—
890C3×C4—41no—
891C3×C4—41no—
892C3×C4—41no—
893C3×C4—41no—
894C3×C4—62no—
895C3×C4—62no—
896C3×C4—81no—
897C3×C4—121no—
898C3×C4—121no—
899C3×C4—121no—
900Dic3—22no—
901Dic3—22no—
902Dic3—41no—
903Dic3—41no—
904Dic3—41no—
905Dic3—62no—
906Dic3—62no—
907Dic3—122no—
908Dic3—122no—
909Dic3—121no—
910Dic3—121no—
911Dic3—121no—
912Dic3—121no—
913Dic3—241no—
914C32#241811yescharacteristic, complemented, Sylow
915C23—32no—
916C23—32no—
917C23—32no—
918C23—61no—
919C23—61no—
920C23—61no—
921C23—61no—
922C23—61no—
923C23—61no—
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—92no—
937C23—92no—
938C23—92no—
939C23—188no—
940C23—181no—
941C23—181no—
942C23—181no—
943C23—181no—
944C23—364no—
945C23—364no—
946C23—364no—
947C23—364no—
948C23—364no—
949C23—364no—
950C23C22×D3211yescharacteristic
951D4—124no—
952D4—188no—
953D4—364no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—92no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—181no—
982C2×C4—181no—
983C2×C4—181no—
984C2×C4—181no—
985C2×C4—181no—
986C2×C4—181no—
987C2×C4—364no—
988C2×C4—364no—
989C2×C4—364no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—122no—
998C2×C3—122no—
999C2×C3—122no—
1000C2×C3#559011yescharacteristic
1001C2×C3#561011yescharacteristic
1002C2×C3#561011yescharacteristic
1003C2×C3#561311yescharacteristic
1004C2×C3#562711yescharacteristic
1005C2×C3#563011yescharacteristic
1006C2×C3#563711yescharacteristic
1007C2×C3D3×#12311yescharacteristic
1008C2×C3D3×#12311yescharacteristic
1009C2×C3#565411yescharacteristic
1010C2×C3#565611yescharacteristic
1011C2×C3#565711yescharacteristic
1012C2×C3#567911yescharacteristic
1013C2×C3#571711yescharacteristic
1014D3—42no—
1015D3—42no—
1016D3—42no—
1017D3—64no—
1018D3—64no—
1019D3—124no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—94no—
1030C22—121no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—121no—
1036C22—121no—
1037C22—121no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—182no—
1043C22—182no—
1044C22—182no—
1045C22—182no—
1046C22—182no—
1047C22—182no—
1048C22—3616no—
1049C22#6430611yescharacteristic
1050C22#6430711yescharacteristic
1051C22D32×D411yescharacteristic
1052C22D32×D411yescharacteristic
1053C22D3×#23911yescharacteristic
1054C22#6431911yescharacteristic
1055C22#6433011yescharacteristic
1056C4—41no—
1057C4—41no—
1058C4—41no—
1059C4—62no—
1060C4—62no—
1061C4—121no—
1062C4—121no—
1063C4—121no—
1064C4—182no—
1065C4—361no—
1066C4—361no—
1067C3—21no—
1068C3#7711111yescharacteristic, complemented
1069C3#7810111yescharacteristic, complemented
1070C2—122no—
1071C2—122no—
1072C2—122no—
1073C2—184no—
1074C2#1059460811yescharacteristic
1075C2#1059461511yescharacteristic
1076C2#1059461711yescharacteristic
1077C2#1059462211yescharacteristic
1078C2#1059508911yescharacteristic
1079C2#1059529511yescharacteristic
1080C2#1059543711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63922C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63921C2semidirect
3. C2×#63884C2semidirect
4. C2×#63881C2semidirect
5. #10592688C2semidirect
6. C3×#4993C2semidirect
7. C3×#4991C2semidirect
8. #10591399C2semidirect
9. #10591390C2semidirect
10. #10591367C2semidirect
11. #10591363C2semidirect
12. #10591301C2semidirect
13. #10591284C2semidirect
14. #10591281C2semidirect
15. #10591275C2semidirect
24. C22×D3×Dic3C22semidirect
25. C2×C32×C4⋊C4C22semidirect
28. C2×#3750C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×Dic3⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×Dic32C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
67. #4993D3semidirect
69. #4991D3semidirect
148. (C2×D3)⋊Dic3D4semidirect
169. C2×C3×C4⋊C4C2×D3semidirect
170. C2×C3×C4⋊C4C2×D3semidirect
205. C2×(C2×D3)⋊C4C2×D3semidirect
206. C2×(C2×D3)⋊C4C2×D3semidirect
212. C2×Dic3⋊C4C2×D3semidirect
213. C2×Dic3⋊C4C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
477. C2×C3⋊D3#123semidirect
525. C2×C4⋊C4D32semidirect
914. C32#2418semidirect
1068. C3#77111semidirect
1069. C3#78101semidirect

Maximal subgroups

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

subgroupindex
C2×#639222
C2×#639212
C2×#638842
C2×#638812
#105926882
C3×#49932
C3×#49912
#105913992
#105913902
#105913672
#105913632
#105913012
#105912842
#105912812
#105912752
#781013
#771113