Finite Group Databasebeta

← D3×#4727 #11857392

Subgroups — D3×#4727 #11857392

Order 1152.

1663 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3C2×D32×C8C211yesmaximal, characteristic, complemented
4#10592426C211yesmaximal, characteristic, complemented
5C3×#4727C211yesmaximal, characteristic, complemented
6C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
7#10591153C211yesmaximal, characteristic, complemented
8#10591145C211yesmaximal, characteristic, complemented
9D3×#830C211yesmaximal, characteristic, complemented
10#10590959C211yesmaximal, characteristic, complemented
11#10590958C211yesmaximal, characteristic, complemented
12#10590955C211yesmaximal, characteristic, complemented
13#10590953C211yesmaximal, characteristic, complemented
14D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
16D3×#408—31nomaximal
17C2×#4727—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×D3×#67C411yescharacteristic
22C2×D3×#67C411yescharacteristic
23C2×#3804C411yescharacteristic
24C2×#3804C411yescharacteristic
25D3×#235—24no—
26D3×#235—24no—
27C2×D3×D12C411yescharacteristic
28C2×C4×D32C2211yescharacteristic
29C2×C4×D32C2211yescharacteristic
30C2×#3799C411yescharacteristic
31C2×#3798C2211yescharacteristic
32C2×#3798C2211yescharacteristic
33C2×#3795C411yescharacteristic
34C2×D3×Dic6C411yescharacteristic
35C2×#3743C2211yescharacteristic, complemented
36C2×C8×C3⋊D3C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C2×C3×D3×C8C2211yescharacteristic
39C2×C3×D3×C8C2211yescharacteristic
40C2×C3×D3×C8C2211yescharacteristic, complemented
41C2×#3712C2211yescharacteristic, complemented
42C2×#3711C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C2×D3×C3⋊C8C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46C2×D3×C3⋊C8C2211yescharacteristic, complemented
47D3×ΓL(1,𝔽25)—24no—
48D32×C8—24no—
49C32×C22⋊C8C2211yescharacteristic, complemented
50#63657C2211yescharacteristic, complemented
51#63647C2211yescharacteristic, complemented
52#63647C2211yescharacteristic, complemented
53C3×#830C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63557C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#235—31no—
67C2×D3×M16—31no—
68C22×ΓL(1,𝔽25)—31no—
69C22×D3×C8—31no—
70C22×D3×C8—31no—
71C3×#408—31no—
72C2×C3×C22⋊C8—31no—
73#5234—31no—
74C2×#830—31no—
75#5129—31no—
76#5110—31no—
77C2×(C2×D3)⋊C8—31no—
78C2×(C2×D3)⋊C8—31no—
79#4727—31no—
80#4727—31no—
81#4727—31no—
82#4727—31no—
83#4727—31no—
84#4727—31no—
85#4727—31no—
86#4727—31no—
87#4727—31no—
88#4727—31no—
89#4727—31no—
90#4727—61no—
91#4727D311yescharacteristic, direct product factor
92D3×C22⋊C8—31no—
93D3×C22⋊C8—31no—
94D3×C22⋊C8—31no—
95D3×C22⋊C8D311yescharacteristic, complemented
96C23×C3×D3C2×C411yescharacteristic
97C22×D32C2×C411yescharacteristic
98C22×D32C2×C411yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#638C2×C411yescharacteristic
101C2×#638C2×C411yescharacteristic
102#3828—22no—
103#3828—22no—
104C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2×C411yescharacteristic
108C2×C3×#67C2×C411yescharacteristic
109C2×C3×#67C2×C411yescharacteristic
110C22×C3×Dic3C2×C411yescharacteristic
111C3×#235—22no—
112C3×#235—22no—
113C2×C3×D12C2×C411yescharacteristic
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3C2×C411yescharacteristic
117C2×C3×C4×D3C2×C411yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6C2×C411yescharacteristic
123D3×#67—24no—
124D3×#67—24no—
125C2×#627C2×C411yescharacteristic
126C2×#627C2×C411yescharacteristic
127C2×#626C2×C411yescharacteristic
128C2×#626C2×C411yescharacteristic
129C2×#626C2×C411yescharacteristic
130C2×#626C2×C411yescharacteristic
131C2×#625C2×C411yescharacteristic
132C2×#625C2×C411yescharacteristic
133C2×#624C2×C411yescharacteristic
134C2×#624C2×C411yescharacteristic
135#3804—24no—
136#3804—24no—
137C2×D3×Dic3C2×C411yescharacteristic
138C2×D3×Dic3C2×C411yescharacteristic
139C2×D3×Dic3C2×C411yescharacteristic
140C2×D3×Dic3C2×C411yescharacteristic
141D3×D12—24no—
142C4×D32—22no—
143C4×D32—22no—
144C4×D32D414yes—
145C4×D32D414yes—
146#3799—24no—
147#3798—22no—
148#3798—22no—
149#3798—22no—
150#3798—22no—
151#3795—24no—
152D3×Dic6—24no—
153C2×C32×C8C2311yescharacteristic
154C2×C32×C8C2311yescharacteristic
155C2×C3⋊(C3⋊C8)C2311yescharacteristic
156C2×C3⋊(C3⋊C8)C2311yescharacteristic
157#3743—22no—
158C8×C3⋊D3—22no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C2×C3×C3⋊C8C2311yescharacteristic
162C2×C3×C3⋊C8C2311yescharacteristic
163C3×ΓL(1,𝔽25)—22no—
164C3×D3×C8—22no—
165C3×D3×C8—22no—
166C3×D3×C8—22no—
167#3712—22no—
168#3711—22no—
169#3710—22no—
170D3×C3⋊C8—22no—
171D3×C3⋊C8—22no—
172D3×C3⋊C8—22no—
173C2×#408—91noSylow
174C2×C3×#41—31no—
175C23×C3×C4—31no—
176C22×#67—31no—
177C22×#67—31no—
178D3×#41—64no—
179D3×#41—64no—
180C2×#239—31no—
181C2×D3×Q8—31no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—31no—
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×#235—31no—
189C2×#235—31no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—31no—
197C2×#235—31no—
198C2×#235—61no—
199C2×#235—64no—
200C2×#235—64no—
201C2×#235C2×D311yescharacteristic
202C22×D12—31no—
203C22×C4×D3—31no—
204C22×C4×D3—31no—
205C22×C4×D3—31no—
206C22×C4×D3—31no—
207C22×C4×D3C2×D311yescharacteristic
208C22×Dic6—31no—
209C2×C3×M16—31no—
210C22×C3×C8—31no—
211C22×C3×C8—31no—
212C22×C3×C8—31no—
213C2×#208—31no—
214C22×C3⋊C8—31no—
215C22×C3⋊C8—31no—
216C22×C3⋊C8—31no—
217D3×M16—64no—
218C2×ΓL(1,𝔽25)—31no—
219C2×ΓL(1,𝔽25)—31no—
220C2×ΓL(1,𝔽25)—31no—
221C2×ΓL(1,𝔽25)—31no—
222C2×ΓL(1,𝔽25)—31no—
223C2×ΓL(1,𝔽25)—61no—
224C2×ΓL(1,𝔽25)—64no—
225C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
226C2×D3×C8—31no—
227C2×D3×C8—31no—
228C2×D3×C8—31no—
229C2×D3×C8—31no—
230C2×D3×C8—31no—
231C2×D3×C8—31no—
232C2×D3×C8—31no—
233C2×D3×C8—61no—
234C2×D3×C8—64no—
235C2×D3×C8—64no—
236C2×D3×C8C2×D311yescharacteristic
237C2×D3×C8C2×D311yescharacteristic
238C2×D3×C8C2×D311yescharacteristic, complemented
239C3×C22⋊C8—21no—
240C3×C22⋊C8—31no—
241C3×C22⋊C8—31no—
242C3×C22⋊C8—31no—
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×C22⋊C8—31no—
246C3×C22⋊C8C2×D311yescharacteristic, complemented
247C3×C22⋊C8C2×D311yescharacteristic, complemented
248#830—31no—
249#830—31no—
250#830—31no—
251#830—31no—
252#830—31no—
253#830—31no—
254#830—61no—
255#830C2×D311yescharacteristic, complemented
256#830C2×D311yescharacteristic, complemented
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—31no—
268(C2×D3)⋊C8—31no—
269(C2×D3)⋊C8—61no—
270(C2×D3)⋊C8—61no—
271(C2×D3)⋊C8C2×D311yescharacteristic, complemented
272(C2×D3)⋊C8C2×D311yescharacteristic, complemented
273(C2×D3)⋊C8C2×D311yescharacteristic, complemented
274(C2×D3)⋊C8C2×D311yescharacteristic, complemented
275C23×C32C22×C411yescharacteristic
276C22×C3⋊D3C22×C411yescharacteristic
277C22×C3⋊D3C22×C411yescharacteristic
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3C22×C411yescharacteristic
282C22×C3×D3C22×C411yescharacteristic
283C22×C3×D3C22×C411yescharacteristic
284C22×C3×D3C22×C411yescharacteristic
285C2×D32—22no—
286C2×D32—22no—
287C2×D32—22no—
288C2×D32—22no—
289C2×D32—22no—
290C2×D32C22⋊C414yes—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4C22×C411yescharacteristic
294C2×C32×C4C2411yescharacteristic
295#638—22no—
296#638—22no—
297C2×C3⋊Dic3C22×C411yescharacteristic
298C2×C3⋊Dic3C22×C411yescharacteristic
299C4⋊(C3⋊D3)—22no—
300C4×C3⋊D3—21no—
301C4×C3⋊D3—21no—
302C4×C3⋊D3C2×D412yes—
303C4×C3⋊D3C2×D412yes—
304#634—22no—
305C3×#67—22no—
306C3×#67—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3C22×C411yescharacteristic
309C2×C3×Dic3C22×C411yescharacteristic
310C2×C3×Dic3C22×C411yescharacteristic
311C2×C3×Dic3C22×C411yescharacteristic
312C3×D12—22no—
313C3×C4×D3—22no—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—22no—
319C3×C4×D3C2×D412yes—
320C3×C4×D3C2×D412yes—
321C3×C4×D3C2×D412yes—
322C3×C4×D3C2×D412yes—
323C3×Dic6—22no—
324#627—22no—
325#627—22no—
326#626—22no—
327#626—22no—
328#626—22no—
329#626—22no—
330#625—22no—
331#625—22no—
332#624—22no—
333#624C22⋊C414yes—
334D3×Dic3—22no—
335D3×Dic3—22no—
336D3×Dic3C22⋊C414yes—
337D3×Dic3C22⋊C414yes—
338C32×C8—21no—
339C32×C8—21no—
340C3⋊(C3⋊C8)—21no—
341C3⋊(C3⋊C8)—21no—
342C3×C3⋊C8—21no—
343C3×C3⋊C8—21no—
344C3×C3⋊C8—21no—
345C3×C3⋊C8—21no—
346C22×#41—91no—
347C22×M16—91no—
348C23×C8—91no—
349#408—31no—
350#408—91no—
351#408—91no—
352#408—91no—
353#408—91no—
354#408—91no—
355#408—91no—
356#408—91no—
357C2×C22⋊C8—31no—
358C2×C22⋊C8—91no—
359C2×C22⋊C8—91no—
360C2×C22⋊C8—91no—
361C24×C3—31no—
362C23×D3—31no—
363C23×D3—31no—
364C23×D3—31no—
365C23×D3—31no—
366C23×D3C4×D311yescharacteristic
367C3×#41—62no—
368C3×#41—62no—
369C2×C3×Q8—31no—
370C2×C3×D4—31no—
371C2×C3×D4—31no—
372C2×C3×D4—31no—
373C22×C3×C4—21no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—62no—
382C22×C3×C4—62no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C2×#67—31no—
386C2×#67—31no—
387C2×#67—31no—
388C2×#67—31no—
389C2×#67—31no—
390C2×#67—31no—
391C2×#67—31no—
392C2×#67—31no—
393C2×#67—31no—
394C2×#67—31no—
395C2×#67—31no—
396C2×#67—31no—
397C2×#67—61no—
398C2×#67—61no—
399C2×#67—64no—
400C2×#67—64no—
401C2×#67C4×D311yescharacteristic
402C2×#67C4×D311yescharacteristic
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—31no—
406C22×Dic3—31no—
407C22×Dic3C4×D311yescharacteristic
408#239—64no—
409D3×Q8—64no—
410#237—64no—
411#237—64no—
412#237—64no—
413D3×D4—64no—
414D3×D4—64no—
415D3×D4—64no—
416#235—22no—
417#235—22no—
418#235—64no—
419#235—62no—
420#235—62no—
421#235—62no—
422#235—62no—
423#235—62no—
424#235—62no—
425#235—64no—
426#235—64no—
427#235—64no—
428#235—62no—
429#235—62no—
430#235—62no—
431#235—62no—
432#235—62no—
433#235—62no—
434#235—122no—
435#235—122no—
436C2×D12—31no—
437C2×D12—31no—
438C2×D12—31no—
439C2×D12—31no—
440C2×D12—31no—
441C2×D12—31no—
442C2×D12—61no—
443C2×D12—64no—
444C2×D12C4×D311yescharacteristic
445C2×C4×D3—22no—
446C2×C4×D3—22no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—34no—
454C2×C4×D3—34no—
455C2×C4×D3—34no—
456C2×C4×D3—34no—
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—31no—
460C2×C4×D3—31no—
461C2×C4×D3—31no—
462C2×C4×D3—31no—
463C2×C4×D3—61no—
464C2×C4×D3—61no—
465C2×C4×D3—62no—
466C2×C4×D3—62no—
467C2×C4×D3—62no—
468C2×C4×D3—62no—
469C2×C4×D3C4×D311yescharacteristic
470C2×C4×D3C4×D311yescharacteristic
471C2×C4×D3C22×D311yescharacteristic
472C2×C4×D3C22×D311yescharacteristic
473C2×C4×D3C22×D311yescharacteristic
474C2×C4×D3C22×D311yescharacteristic
475C2×Dic6—31no—
476C2×Dic6—31no—
477C2×Dic6—31no—
478C2×Dic6—31no—
479C2×Dic6—31no—
480C2×Dic6—31no—
481C2×Dic6—61no—
482C2×Dic6—64no—
483C2×Dic6C4×D311yescharacteristic
484C3×M16—62no—
485C2×C3×C8—21no—
486C2×C3×C8—21no—
487C2×C3×C8—31no—
488C2×C3×C8—31no—
489C2×C3×C8—31no—
490C2×C3×C8—31no—
491C2×C3×C8—62no—
492C2×C3×C8—62no—
493C2×C3×C8—62no—
494C2×C3×C8C22×D311yescharacteristic
495C2×C3×C8C22×D311yescharacteristic
496C2×C3×C8C22×D311yescharacteristic
497C2×C3×C8C22×D311yescharacteristic
498#208—62no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—31no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8—61no—
505C2×C3⋊C8—62no—
506C2×C3⋊C8—62no—
507C2×C3⋊C8—62no—
508C2×C3⋊C8C22×D311yescharacteristic
509C2×C3⋊C8C22×D311yescharacteristic
510C2×C3⋊C8C22×D311yescharacteristic
511C2×C3⋊C8C22×D311yescharacteristic
512ΓL(1,𝔽25)—22no—
513ΓL(1,𝔽25)—62no—
514ΓL(1,𝔽25)—62no—
515ΓL(1,𝔽25)—62no—
516ΓL(1,𝔽25)—62no—
517ΓL(1,𝔽25)—62no—
518ΓL(1,𝔽25)—122no—
519D3×C8—22no—
520D3×C8—22no—
521D3×C8—22no—
522D3×C8—62no—
523D3×C8—62no—
524D3×C8—62no—
525D3×C8—62no—
526D3×C8—62no—
527D3×C8—62no—
528D3×C8—62no—
529D3×C8—122no—
530C22×C32—21no—
531C22×C32—21no—
532C22×C32—21no—
533C22×C32C23×C411yescharacteristic
534C2×C3⋊D3—21no—
535C2×C3⋊D3—21no—
536C2×C3⋊D3—21no—
537C2×C3⋊D3—21no—
538C2×C3⋊D3—21no—
539C2×C3⋊D3C2×C22⋊C412yes—
540C2×C3×D3—21no—
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3—21no—
544C2×C3×D3—21no—
545C2×C3×D3—21no—
546C2×C3×D3—21no—
547C2×C3×D3—21no—
548C2×C3×D3—44no—
549C2×C3×D3C2×C22⋊C412yes—
550C2×C3×D3C2×C22⋊C412yes—
551C2×C3×D3#13112yes—
552C2×C3×D3#13112yes—
553D32—28no—
554D32—44no—
555C32×C4—21no—
556C32×C4C22×D411yescharacteristic
557C32×C4C22×D411yescharacteristic
558C3⋊Dic3—21no—
559C3⋊Dic3C2×C22⋊C412yes—
560C3×Dic3—21no—
561C3×Dic3—21no—
562C3×Dic3C2×C22⋊C412yes—
563C3×Dic3C2×C22⋊C412yes—
564C2×#41—31no—
565C2×#41—91no—
566C2×#41—91no—
567C2×#41—91no—
568C2×#41—91no—
569C2×#41—91no—
570C2×#41—91no—
571C2×#41—91no—
572C2×#41—184no—
573C2×#41—184no—
574C22×Q8—91no—
575C22×D4—91no—
576C22×D4—91no—
577C22×D4—91no—
578C23×C4—31no—
579C23×C4—91no—
580C23×C4—91no—
581C2×M16—31no—
582C2×M16—91no—
583C2×M16—91no—
584C2×M16—91no—
585C2×M16—184no—
586C22×C8—31no—
587C22×C8—31no—
588C22×C8—31no—
589C22×C8—91no—
590C22×C8—91no—
591C22×C8—91no—
592C22×C8—91no—
593C22×C8—91no—
594C22×C8—184no—
595C22⋊C8—31no—
596C22⋊C8—31no—
597C22⋊C8—31no—
598C22⋊C8—31no—
599C22⋊C8—31no—
600C22⋊C8—31no—
601C22⋊C8—91no—
602C22⋊C8—91no—
603C22⋊C8—91no—
604C22⋊C8—91no—
605C22⋊C8—91no—
606C22⋊C8—91no—
607C22⋊C8—91no—
608C22⋊C8—91no—
609C22⋊C8—91no—
610C22⋊C8D3211yescharacteristic, complemented
611C23×C3—21no—
612C23×C3—31no—
613C23×C3—31no—
614C23×C3—31no—
615C23×C3—31no—
616C23×C3—62no—
617C23×C3—62no—
618C23×C3—62no—
619C23×C3C2×C4×D311yescharacteristic
620C23×C3C2×C4×D311yescharacteristic
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—31no—
625C22×D3—31no—
626C22×D3—34no—
627C22×D3—34no—
628C22×D3—31no—
629C22×D3—31no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—62no—
633C22×D3—62no—
634C22×D3—62no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—62no—
641C22×D3—62no—
642C22×D3C2×C4×D311yescharacteristic
643C22×D3C2×C4×D311yescharacteristic
644C22×D3C2×C4×D311yescharacteristic
645C22×D3C2×C4×D311yescharacteristic
646C3×Q8—62no—
647C3×D4—62no—
648C3×D4—62no—
649C3×D4—62no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—31no—
657C2×C3×C4—31no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—31no—
663C2×C3×C4—31no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4C2×C4×D311yescharacteristic
674C2×C3×C4C2×C4×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677#67—22no—
678#67—22no—
679#67—62no—
680#67—62no—
681#67—62no—
682#67—62no—
683#67—62no—
684#67—62no—
685#67—62no—
686#67—62no—
687#67—62no—
688#67—62no—
689#67—62no—
690#67—62no—
691#67—122no—
692#67—122no—
693C2×Dic3—22no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—34no—
697C2×Dic3—34no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—62no—
703C2×Dic3—62no—
704C2×Dic3C2×C4×D311yescharacteristic
705C2×Dic3C2×C4×D311yescharacteristic
706C2×Dic3C2×C4×D311yescharacteristic
707C2×Dic3C2×C4×D311yescharacteristic
708D12—22no—
709D12—62no—
710D12—62no—
711D12—62no—
712D12—62no—
713D12—62no—
714D12—62no—
715D12—122no—
716C4×D3—22no—
717C4×D3—21no—
718C4×D3—21no—
719C4×D3—21no—
720C4×D3—21no—
721C4×D3—22no—
722C4×D3—34no—
723C4×D3—34no—
724C4×D3—32no—
725C4×D3—32no—
726C4×D3—32no—
727C4×D3—32no—
728C4×D3—34no—
729C4×D3—34no—
730C4×D3—62no—
731C4×D3—62no—
732C4×D3—62no—
733C4×D3—62no—
734C4×D3—62no—
735C4×D3—61no—
736C4×D3—61no—
737C4×D3—61no—
738C4×D3—61no—
739C4×D3—62no—
740C4×D3—121no—
741C4×D3—121no—
742C4×D3D3×D412yes—
743C4×D3D3×D412yes—
744C4×D3D3×D412yes—
745C4×D3D3×D412yes—
746Dic6—22no—
747Dic6—62no—
748Dic6—62no—
749Dic6—62no—
750Dic6—62no—
751Dic6—62no—
752Dic6—62no—
753Dic6—122no—
754C3×C8—21no—
755C3×C8—21no—
756C3×C8—21no—
757C3×C8—21no—
758C3×C8—41no—
759C3×C8—41no—
760C3×C8—61no—
761C3×C8—61no—
762C3×C8—61no—
763C3×C8—61no—
764C3⋊C8—21no—
765C3⋊C8—21no—
766C3⋊C8—21no—
767C3⋊C8—21no—
768C3⋊C8—61no—
769C3⋊C8—61no—
770C3⋊C8—61no—
771C3⋊C8—61no—
772C3⋊C8—121no—
773C3⋊C8—121no—
774C2×C32—41no—
775C2×C32C22×C22⋊C411yescharacteristic
776C2×C32C2×#13111yescharacteristic
777C2×C32C2×#13111yescharacteristic
778C3⋊D3—22no—
779C3⋊D3—41no—
780C3×D3—22no—
781C3×D3—41no—
782C3×D3—41no—
783C3×D3#40814yescomplemented
784C24—31no—
785C24—91no—
786C24—91no—
787#41—62no—
788#41—62no—
789#41—182no—
790#41—182no—
791#41—182no—
792#41—182no—
793#41—182no—
794#41—182no—
795#41—184no—
796#41—184no—
797#41—184no—
798#41—184no—
799C2×Q8—31no—
800C2×Q8—91no—
801C2×Q8—91no—
802C2×Q8—91no—
803C2×Q8—184no—
804C2×D4—31no—
805C2×D4—31no—
806C2×D4—31no—
807C2×D4—91no—
808C2×D4—91no—
809C2×D4—91no—
810C2×D4—91no—
811C2×D4—91no—
812C2×D4—91no—
813C2×D4—91no—
814C2×D4—91no—
815C2×D4—91no—
816C2×D4—184no—
817C2×D4—184no—
818C2×D4—184no—
819C22×C4—31no—
820C22×C4—31no—
821C22×C4—31no—
822C22×C4—31no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—62no—
827C22×C4—62no—
828C22×C4—94no—
829C22×C4—94no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—91no—
833C22×C4—91no—
834C22×C4—91no—
835C22×C4—91no—
836C22×C4—91no—
837C22×C4—91no—
838C22×C4—182no—
839C22×C4—182no—
840C22×C4C2×D3211yescharacteristic
841M16—62no—
842M16—182no—
843M16—182no—
844M16—182no—
845C2×C8—31no—
846C2×C8—31no—
847C2×C8—31no—
848C2×C8—31no—
849C2×C8—62no—
850C2×C8—62no—
851C2×C8—62no—
852C2×C8—91no—
853C2×C8—91no—
854C2×C8—182no—
855C2×C8—182no—
856C2×C8—182no—
857C2×C8—182no—
858C2×C8—182no—
859C2×C8C2×D3211yescharacteristic
860C2×C8C2×D3211yescharacteristic
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—21no—
868C22×C3—32no—
869C22×C3—32no—
870C22×C3—32no—
871C22×C3—32no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—41no—
875C22×C3—61no—
876C22×C3—61no—
877C22×C3—61no—
878C22×C3—61no—
879C22×C3—61no—
880C22×C3—61no—
881C22×C3—61no—
882C22×C3—61no—
883C22×C3—124no—
884C22×C3C22×C4×D311yescharacteristic
885C22×C3C22×C4×D311yescharacteristic
886C2×D3—21no—
887C2×D3—21no—
888C2×D3—21no—
889C2×D3—21no—
890C2×D3—21no—
891C2×D3—21no—
892C2×D3—21no—
893C2×D3—21no—
894C2×D3—32no—
895C2×D3—32no—
896C2×D3—44no—
897C2×D3—62no—
898C2×D3—68no—
899C2×D3—61no—
900C2×D3—61no—
901C2×D3—61no—
902C2×D3—61no—
903C2×D3—68no—
904C2×D3—61no—
905C2×D3—61no—
906C2×D3—61no—
907C2×D3—61no—
908C2×D3—61no—
909C2×D3—61no—
910C2×D3—121no—
911C2×D3—121no—
912C2×D3—121no—
913C2×D3—121no—
914C2×D3—121no—
915C2×D3—124no—
916C2×D3—124no—
917C2×D3D3×C22⋊C412yes—
918C2×D3D3×C22⋊C412yes—
919C2×D3#90112yes—
920C2×D3#90712yes—
921C3×C4—21no—
922C3×C4—21no—
923C3×C4—21no—
924C3×C4—21no—
925C3×C4—32no—
926C3×C4—32no—
927C3×C4—41no—
928C3×C4—61no—
929C3×C4—61no—
930C3×C4C2×D3×D411yescharacteristic
931C3×C4C2×D3×D411yescharacteristic
932C3×C4C2×D3×D411yescharacteristic
933C3×C4C2×D3×D411yescharacteristic
934Dic3—21no—
935Dic3—21no—
936Dic3—32no—
937Dic3—32no—
938Dic3—62no—
939Dic3—61no—
940Dic3—61no—
941Dic3—121no—
942Dic3D3×C22⋊C412yes—
943Dic3D3×C22⋊C412yes—
944C32C2×#40811yescharacteristic, complemented, Sylow
945C23—31no—
946C23—31no—
947C23—31no—
948C23—31no—
949C23—62no—
950C23—62no—
951C23—62no—
952C23—94no—
953C23—91no—
954C23—91no—
955C23—182no—
956C23—182no—
957C23—182no—
958C23—182no—
959C23—182no—
960C23C4×D3211yescharacteristic
961Q8—62no—
962Q8—182no—
963Q8—182no—
964Q8—182no—
965D4—62no—
966D4—62no—
967D4—62no—
968D4—182no—
969D4—182no—
970D4—182no—
971D4—182no—
972D4—182no—
973D4—182no—
974D4—182no—
975D4—182no—
976D4—182no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—31no—
980C2×C4—31no—
981C2×C4—32no—
982C2×C4—32no—
983C2×C4—32no—
984C2×C4—32no—
985C2×C4—31no—
986C2×C4—31no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—94no—
995C2×C4—94no—
996C2×C4—94no—
997C2×C4—91no—
998C2×C4—92no—
999C2×C4—92no—
1000C2×C4—91no—
1001C2×C4—182no—
1002C2×C4—182no—
1003C2×C4—182no—
1004C2×C4—181no—
1005C2×C4—181no—
1006C2×C4C4×D3211yescharacteristic
1007C2×C4C22×D3211yescharacteristic
1008C8—21no—
1009C8—21no—
1010C8—61no—
1011C8—61no—
1012C8—61no—
1013C8—61no—
1014C8—181no—
1015C8—181no—
1016C2×C3—21no—
1017C2×C3—21no—
1018C2×C3—21no—
1019C2×C3—34no—
1020C2×C3—41no—
1021C2×C3—41no—
1022C2×C3—62no—
1023C2×C3—81no—
1024C2×C3—121no—
1025C2×C3—121no—
1026C2×C3C2×D3×C22⋊C411yescharacteristic
1027C2×C3C2×D3×C22⋊C411yescharacteristic
1028C2×C3C2×#90111yescharacteristic
1029C2×C3C2×#90711yescharacteristic
1030C2×C3D3×#13111yescharacteristic
1031C2×C3D3×#13111yescharacteristic
1032D3—22no—
1033D3—41no—
1034D3—41no—
1035D3—62no—
1036D3—62no—
1037D3—122no—
1038D3—121no—
1039D3—121no—
1040D3—241no—
1041D3#472714yesdirect product factor
1042C22—21no—
1043C22—21no—
1044C22—21no—
1045C22—32no—
1046C22—32no—
1047C22—32no—
1048C22—32no—
1049C22—61no—
1050C22—61no—
1051C22—61no—
1052C22—61no—
1053C22—61no—
1054C22—61no—
1055C22—61no—
1056C22—61no—
1057C22—92no—
1058C22—124no—
1059C22—188no—
1060C22—181no—
1061C22—181no—
1062C22—181no—
1063C22—181no—
1064C22—181no—
1065C22—364no—
1066C22C2×C4×D3211yescharacteristic
1067C4—21no—
1068C4—32no—
1069C4—32no—
1070C4—61no—
1071C4—61no—
1072C4—92no—
1073C4—181no—
1074C4D32×D411yescharacteristic
1075C4D32×D411yescharacteristic
1076C3—21no—
1077C3C2×#472711yescharacteristic, complemented
1078C3D3×#40811yescharacteristic, complemented
1079C2—34no—
1080C2—41no—
1081C2—62no—
1082C2—121no—
1083C2—121no—
1084C2—182no—
1085C2—361no—
1086C2D32×C22⋊C411yescharacteristic
1087C2D3×#90111yescharacteristic
1088C2D3×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C22⋊C8C22
prime radicalC2×D3×#235C2
cosocleC2×C32×C4C24
hypercenterC22⋊C8D32
hypocenterC32C2×#408
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×D3×ΓL(1,𝔽25)C2semidirect
3. C2×D32×C8C2semidirect
4. #10592426C2semidirect
5. C3×#4727C2semidirect
6. C3×D3×C22⋊C8C2semidirect
7. #10591153C2semidirect
8. #10591145C2semidirect
9. D3×#830C2semidirect
10. #10590959C2semidirect
11. #10590958C2semidirect
12. #10590955C2semidirect
13. #10590953C2semidirect
14. D3×(C2×D3)⋊C8C2semidirect
15. D3×(C2×D3)⋊C8C2semidirect
35. C2×#3743C22semidirect
36. C2×C8×C3⋊D3C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
40. C2×C3×D3×C8C22semidirect
41. C2×#3712C22semidirect
42. C2×#3711C22semidirect
43. C2×#3710C22semidirect
46. C2×D3×C3⋊C8C22semidirect
49. C32×C22⋊C8C22semidirect
50. #63657C22semidirect
51. #63647C22semidirect
52. #63647C22semidirect
53. C3×#830C22semidirect
54. C3×#830C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63557C22semidirect
60. #63557C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
91. #4727D3direct (N × H)
95. D3×C22⋊C8D3semidirect
225. C2×ΓL(1,𝔽25)C2×D3semidirect
238. C2×D3×C8C2×D3semidirect
246. C3×C22⋊C8C2×D3semidirect
247. C3×C22⋊C8C2×D3semidirect
255. #830C2×D3semidirect
256. #830C2×D3semidirect
271. (C2×D3)⋊C8C2×D3semidirect
272. (C2×D3)⋊C8C2×D3semidirect
273. (C2×D3)⋊C8C2×D3semidirect
274. (C2×D3)⋊C8C2×D3semidirect
610. C22⋊C8D32semidirect
783. C3×D3#408semidirect
944. C32C2×#408semidirect
1041. D3#4727direct (N × H)
1077. C3C2×#4727semidirect
1078. C3D3×#408semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×D3×ΓL(1,𝔽25)2
C2×D32×C82
#105924262
C3×#47272
C3×D3×C22⋊C82
#105911532
#105911452
D3×#8302
#105909592
#105909582
#105909552
#105909532
D3×(C2×D3)⋊C82
D3×#4083
C2×#47273