Finite Group Databasebeta

← D3×#4836 #11859248

Subgroups — D3×#4836 #11859248

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
2C2×D32×C8C211yesmaximal, characteristic, complemented
3C4×D3×D12C211yesmaximal, characteristic
4#10592535C211yesmaximal, characteristic, complemented
5C3×#4836C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
7D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
8D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
9#10590907C211yesmaximal, characteristic, complemented
10#10590738C211yesmaximal, characteristic, complemented
11#10590737C211yesmaximal, characteristic, complemented
12#10590727C211yesmaximal, characteristic, complemented
13#10590330C211yesmaximal, characteristic, complemented
14#10590328C211yesmaximal, characteristic, complemented
15D3×#803C211yesmaximal, characteristic, complemented
16D3×#435—31nomaximal
17C2×#4836—31nomaximal
18C2×D3×D12C411yescharacteristic
19C2×C4×D32C2211yescharacteristic
20C2×C4×D32C2211yescharacteristic
21C2×#3743C2211yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic, complemented
28C3×C4×D12C2211yescharacteristic
29C3×C42×D3C2211yescharacteristic
30D3×(C2×D3)⋊C4C411yescharacteristic
31D3×(C2×D3)⋊C4C411yescharacteristic
32C4×#626C2211yescharacteristic
33C4×#626C2211yescharacteristic
34#63894C411yescharacteristic
35Dic3×D12C411yescharacteristic
36D3×C4⋊Dic3C411yescharacteristic
37#63880C411yescharacteristic
38#63880C411yescharacteristic
39C2×#3712C2211yescharacteristic, complemented
40C2×#3711C2211yescharacteristic, complemented
41C2×#3710C2211yescharacteristic, complemented
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic, complemented
45D3×ΓL(1,𝔽25)—24no—
46D32×C8—24no—
47C32×C4⋊C8C2211yescharacteristic, complemented
48#63647C2211yescharacteristic, complemented
49#63647C2211yescharacteristic, complemented
50#63630C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56C3×#803C2211yescharacteristic, complemented
57#63557C2211yescharacteristic, complemented
58#63557C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63554C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×D3×M16—31no—
64C22×ΓL(1,𝔽25)—31no—
65C22×D3×C8—31no—
66C22×D3×C8—31no—
67C4×D3×D4—31no—
68C2×C4×D12—31no—
69C3×#435—31no—
70C2×C3×C4⋊C8—31no—
71#5127—31no—
72#5111—31no—
73C2×(C2×D3)⋊C8—31no—
74C2×(C2×D3)⋊C8—31no—
75#5011—31no—
76C2×#803—31no—
77#4836—31no—
78#4836—31no—
79#4836—31no—
80#4836—31no—
81#4836—31no—
82#4836—31no—
83#4836—31no—
84#4836—31no—
85#4836—61no—
86#4836D311yescharacteristic, direct product factor
87D3×C4⋊C8D311yescharacteristic, complemented
88#4730—31no—
89#4728—31no—
90D3×C22⋊C8—31no—
91D3×C22⋊C8—31no—
92#4706—31no—
93D3×#97—31no—
94C22×D32C2×C411yescharacteristic
95C22×D32C2×C411yescharacteristic
96C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×D12C2×C411yescharacteristic
100C2×C3×C4×D3C2×C411yescharacteristic
101C2×C3×C4×D3C2×C411yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626C2×C411yescharacteristic
106C2×#626C2×C411yescharacteristic
107C2×#624C2×C411yescharacteristic
108C2×#624C2×C411yescharacteristic
109C2×D3×Dic3C2×C411yescharacteristic
110C2×D3×Dic3C2×C411yescharacteristic
111C2×D3×Dic3C2×C411yescharacteristic
112C2×D3×Dic3C2×C411yescharacteristic
113D3×D12—24no—
114C4×D32—22no—
115C4×D32—22no—
116C4×D32—22no—
117C4×D32—22no—
118C2×C32×C8C2311yescharacteristic
119C2×C32×C8C2311yescharacteristic
120C32×C42C2311yescharacteristic
121#3752C2×C411yescharacteristic
122#3752C2×C411yescharacteristic
123C4⋊(C3⋊Dic3)C2×C411yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3743—22no—
127C8×C3⋊D3—22no—
128C3×(C2×D3)⋊C4C2×C411yescharacteristic
129C3×(C2×D3)⋊C4C2×C411yescharacteristic
130C3×C4⋊Dic3C2×C411yescharacteristic
131C3×C4×Dic3C2×C411yescharacteristic
132C3×C4×Dic3C2×C411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×ΓL(1,𝔽25)—22no—
139C3×D3×C8—22no—
140C3×D3×C8—22no—
141C3×D3×C8—22no—
142Dic3⋊Dic3C2×C411yescharacteristic
143Dic3⋊Dic3C2×C411yescharacteristic
144#3722C2×C411yescharacteristic
145#3722C2×C411yescharacteristic
146(C2×D3)⋊Dic3C2×C411yescharacteristic
147(C2×D3)⋊Dic3C2×C411yescharacteristic
148#3712—22no—
149#3711—22no—
150#3710—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8—22no—
153D3×C3⋊C8D414yescomplemented
154C2×#435—91noSylow
155C2×D3×D4—31no—
156C22×D12—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C2×C3×M16—31no—
162C22×C3×C8—31no—
163C22×C3×C8—31no—
164C22×C3×C8—31no—
165C3×C4×D4—31no—
166C2×C3×C42—31no—
167D4×Dic3—31no—
168C4×#67—31no—
169C4×#67—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×C4⋊Dic3—31no—
173C2×#208—31no—
174C22×C3⋊C8—31no—
175C22×C3⋊C8—31no—
176C22×C3⋊C8—31no—
177D3×M16—64no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—61no—
184C2×ΓL(1,𝔽25)—64no—
185C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
186C2×D3×C8—31no—
187C2×D3×C8—31no—
188C2×D3×C8—31no—
189C2×D3×C8—31no—
190C2×D3×C8—31no—
191C2×D3×C8—31no—
192C2×D3×C8—31no—
193C2×D3×C8—61no—
194C2×D3×C8—64no—
195C2×D3×C8—64no—
196C2×D3×C8C2×D311yescharacteristic
197C2×D3×C8C2×D311yescharacteristic
198C2×D3×C8C2×D311yescharacteristic, complemented
199#893—31no—
200D3×C4⋊C4—31no—
201#67⋊C4—31no—
202#67⋊C4—31no—
203D3×C22⋊C4—31no—
204D3×C22⋊C4—31no—
205C4×D12—31no—
206C4×D12—31no—
207C4×D12—31no—
208C4×D12—31no—
209C4×D12—31no—
210C4×D12—31no—
211C4×D12—31no—
212C4×D12—31no—
213C4×D12—61no—
214C4×D12C2×D311yescharacteristic
215C42×D3C2×D311yescharacteristic
216C3×C4⋊C8—21no—
217C3×C4⋊C8—31no—
218C3×C4⋊C8—31no—
219C3×C4⋊C8—31no—
220C3×C4⋊C8C2×D311yescharacteristic, complemented
221C3×C4⋊C8C2×D311yescharacteristic, complemented
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×#97—31no—
225#830—31no—
226#830—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8—31no—
234(C2×D3)⋊C8—31no—
235(C2×D3)⋊C8—31no—
236(C2×D3)⋊C8—31no—
237(C2×D3)⋊C8—61no—
238(C2×D3)⋊C8—61no—
239(C2×D3)⋊C8C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8C2×D311yescharacteristic, complemented
241#815—31no—
242#815—31no—
243Dic3⋊C8C2×D311yescharacteristic, complemented
244Dic3⋊C8C2×D311yescharacteristic, complemented
245C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
246#803—31no—
247#803—31no—
248#803—31no—
249#803—31no—
250#803—61no—
251#803C2×D311yescharacteristic, complemented
252C22×C3⋊D3C22×C411yescharacteristic
253C22×C3⋊D3C22×C411yescharacteristic
254C22×C3×D3C22×C411yescharacteristic
255C22×C3×D3C22×C411yescharacteristic
256C22×C3×D3C22×C411yescharacteristic
257C2×D32—22no—
258C2×D32—22no—
259C2×D32—22no—
260C2×D32—22no—
261C2×D32—22no—
262C2×D32M1614yescomplemented
263C2×C32×C4C22×C411yescharacteristic
264C2×C32×C4C22×C411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3C22×C411yescharacteristic
267C2×C3⋊Dic3C22×C411yescharacteristic
268C4⋊(C3⋊D3)—22no—
269C4×C3⋊D3—21no—
270C4×C3⋊D3—21no—
271C4×C3⋊D3—21no—
272C4×C3⋊D3—21no—
273C2×C3×Dic3C22×C411yescharacteristic
274C2×C3×Dic3C22×C411yescharacteristic
275C2×C3×Dic3C22×C411yescharacteristic
276C2×C3×Dic3C22×C411yescharacteristic
277C2×C3×Dic3C22×C411yescharacteristic
278C3×D12—22no—
279C3×C4×D3—22no—
280C3×C4×D3—22no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3C2×D412yes—
286C3×C4×D3#4112yes—
287#626—22no—
288#626—22no—
289#624—22no—
290#624—22no—
291D3×Dic3—22no—
292D3×Dic3—22no—
293D3×Dic3—22no—
294D3×Dic3—22no—
295C32×C8—21no—
296C32×C8—21no—
297C3⋊(C3⋊C8)—21no—
298C3⋊(C3⋊C8)C2×D412yescomplemented
299C3×C3⋊C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yescomplemented
303C22×M16—91no—
304C23×C8—91no—
305C2×C4×D4—91no—
306#435—31no—
307#435—91no—
308#435—91no—
309#435—91no—
310#435—91no—
311#435—91no—
312#435—91no—
313#435—91no—
314C2×C4⋊C8—31no—
315C2×C22⋊C8—91no—
316C2×C22⋊C8—91no—
317C2×#97—91no—
318C23×D3—31no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—31no—
322C2×C3×D4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C2×#67—31no—
329C2×#67—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334D3×D4—64no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—64no—
341C2×D12C4×D311yescharacteristic
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3C4×D311yescharacteristic
365C2×C4×D3C4×D311yescharacteristic
366C2×C4×D3C22×D311yescharacteristic
367C2×C4×D3C22×D311yescharacteristic
368C2×C4×D3C22×D311yescharacteristic
369C3×M16—62no—
370C2×C3×C8—21no—
371C2×C3×C8—21no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C2×C3×C8—31no—
375C2×C3×C8—31no—
376C2×C3×C8—62no—
377C2×C3×C8—62no—
378C2×C3×C8—62no—
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C22×D311yescharacteristic
383C3×C4⋊C4—31no—
384C3×C22⋊C4—31no—
385C3×C22⋊C4—31no—
386C3×C42—21no—
387C3×C42—31no—
388C3×C42—31no—
389C3×C42—31no—
390C3×C42C22×D311yescharacteristic
391C3×C42C22×D311yescharacteristic
392#217—31no—
393#217—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4C4×D311yescharacteristic
407(C2×D3)⋊C4C4×D311yescharacteristic
408C4⋊Dic3—31no—
409C4⋊Dic3—31no—
410C4⋊Dic3—31no—
411C4⋊Dic3—31no—
412C4⋊Dic3—61no—
413C4⋊Dic3C4×D311yescharacteristic
414Dic3⋊C4—31no—
415Dic3⋊C4—31no—
416C4×Dic3C4×D311yescharacteristic
417C4×Dic3C4×D311yescharacteristic
418C4×Dic3C22×D311yescharacteristic
419#208—62no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—31no—
422C2×C3⋊C8—34no—
423C2×C3⋊C8—31no—
424C2×C3⋊C8—31no—
425C2×C3⋊C8—61no—
426C2×C3⋊C8—61no—
427C2×C3⋊C8—62no—
428C2×C3⋊C8—62no—
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431C2×C3⋊C8C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433ΓL(1,𝔽25)—22no—
434ΓL(1,𝔽25)—62no—
435ΓL(1,𝔽25)—62no—
436ΓL(1,𝔽25)—62no—
437ΓL(1,𝔽25)—62no—
438ΓL(1,𝔽25)—62no—
439ΓL(1,𝔽25)—122no—
440D3×C8—22no—
441D3×C8—22no—
442D3×C8—22no—
443D3×C8—34no—
444D3×C8—62no—
445D3×C8—62no—
446D3×C8—62no—
447D3×C8—62no—
448D3×C8—62no—
449D3×C8—62no—
450D3×C8—122no—
451C22×C32C23×C411yescharacteristic
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3—21no—
455C2×C3⋊D3—21no—
456C2×C3⋊D3—21no—
457C2×C3⋊D3C2×M1612yescomplemented
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3C4×D412yes—
464C2×C3×D3C2×M1612yes—
465C2×C3×D3C2×M1612yescomplemented
466C2×C3×D3#13112yes—
467D32—28no—
468D32—44no—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4C22×D411yescharacteristic
472C32×C4C2×#4111yescharacteristic
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3C4×D412yes—
480C22×D4—91no—
481C23×C4—91no—
482C23×C4—91no—
483C2×M16—31no—
484C2×M16—91no—
485C2×M16—91no—
486C2×M16—91no—
487C2×M16—184no—
488C22×C8—31no—
489C22×C8—31no—
490C22×C8—31no—
491C22×C8—91no—
492C22×C8—91no—
493C22×C8—91no—
494C22×C8—91no—
495C22×C8—91no—
496C22×C8—184no—
497C4×D4—31no—
498C4×D4—91no—
499C4×D4—91no—
500C4×D4—91no—
501C4×D4—91no—
502C4×D4—91no—
503C4×D4—91no—
504C4×D4—91no—
505C2×C4⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C42—31no—
509C4⋊C8—31no—
510C4⋊C8—31no—
511C4⋊C8—31no—
512C4⋊C8D3211yescharacteristic, complemented
513C22⋊C8—31no—
514C22⋊C8—31no—
515C22⋊C8—91no—
516C22⋊C8—91no—
517C22⋊C8—91no—
518C22⋊C8—91no—
519C22⋊C8—91no—
520C22⋊C8—91no—
521#97—31no—
522#97—91no—
523#97—91no—
524#97—91no—
525C23×C3—31no—
526C23×C3—31no—
527C23×C3—31no—
528C22×D3—31no—
529C22×D3—31no—
530C22×D3—34no—
531C22×D3—34no—
532C22×D3—31no—
533C22×D3—31no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3C2×C4×D311yescharacteristic
547C22×D3C2×C4×D311yescharacteristic
548C22×D3C2×C4×D311yescharacteristic
549C3×D4—62no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—31no—
554C2×C3×C4—32no—
555C2×C3×C4—32no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—62no—
561C2×C3×C4—62no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4C2×C4×D311yescharacteristic
567C2×C3×C4C2×C4×D311yescharacteristic
568C2×C3×C4C2×C4×D311yescharacteristic
569C2×C3×C4C2×C4×D311yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—62no—
573#67—62no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—62no—
581C2×Dic3—62no—
582C2×Dic3—62no—
583C2×Dic3—62no—
584C2×Dic3C2×C4×D311yescharacteristic
585C2×Dic3C2×C4×D311yescharacteristic
586C2×Dic3C2×C4×D311yescharacteristic
587C2×Dic3C2×C4×D311yescharacteristic
588C2×Dic3C2×C4×D311yescharacteristic
589D12—22no—
590D12—62no—
591D12—62no—
592D12—62no—
593D12—62no—
594D12—122no—
595C4×D3—22no—
596C4×D3—22no—
597C4×D3—21no—
598C4×D3—21no—
599C4×D3—21no—
600C4×D3—21no—
601C4×D3—62no—
602C4×D3—62no—
603C4×D3—62no—
604C4×D3—62no—
605C4×D3—62no—
606C4×D3—62no—
607C4×D3—61no—
608C4×D3—61no—
609C4×D3—61no—
610C4×D3—61no—
611C4×D3—61no—
612C4×D3—61no—
613C4×D3—61no—
614C4×D3—61no—
615C4×D3—62no—
616C4×D3—62no—
617C4×D3—121no—
618C4×D3—121no—
619C4×D3—121no—
620C4×D3—121no—
621C4×D3D3×D412yes—
622C4×D3#23912yes—
623C3×C8—21no—
624C3×C8—21no—
625C3×C8—21no—
626C3×C8—21no—
627C3×C8—32no—
628C3×C8—41no—
629C3×C8—41no—
630C3×C8—61no—
631C3×C8—61no—
632C3×C8—61no—
633C3⋊C8—21no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—32no—
637C3⋊C8—32no—
638C3⋊C8—62no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C3⋊C8D3×D412yescomplemented
643C2×C32C2×C4×D411yescharacteristic
644C2×C32C22×M1611yescharacteristic
645C2×C32C2×#13111yescharacteristic
646C3⋊D3—22no—
647C3⋊D3—41no—
648C3×D3—22no—
649C3×D3—41no—
650C3×D3#43514yescomplemented
651C24—91no—
652C24—91no—
653C2×D4—31no—
654C2×D4—91no—
655C2×D4—91no—
656C2×D4—91no—
657C2×D4—184no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—91no—
664C22×C4—91no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—91no—
668C22×C4—91no—
669C22×C4—91no—
670C22×C4—91no—
671C22×C4—182no—
672C22×C4—182no—
673C22×C4—182no—
674C22×C4—182no—
675M16—62no—
676M16—182no—
677M16—182no—
678M16—182no—
679C2×C8—31no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—31no—
683C2×C8—62no—
684C2×C8—62no—
685C2×C8—62no—
686C2×C8—94no—
687C2×C8—91no—
688C2×C8—91no—
689C2×C8—182no—
690C2×C8—182no—
691C2×C8—182no—
692C2×C8—182no—
693C2×C8C2×D3211yescharacteristic
694C2×C8C2×D3211yescharacteristic
695C4⋊C4—31no—
696C4⋊C4—91no—
697C4⋊C4—91no—
698C4⋊C4—91no—
699C22⋊C4—31no—
700C22⋊C4—31no—
701C22⋊C4—91no—
702C22⋊C4—91no—
703C22⋊C4—91no—
704C22⋊C4—91no—
705C22⋊C4—91no—
706C22⋊C4—91no—
707C42—31no—
708C42—31no—
709C42—31no—
710C42C2×D3211yescharacteristic
711C22×C3—21no—
712C22×C3—32no—
713C22×C3—32no—
714C22×C3—32no—
715C22×C3—32no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3C22×C4×D311yescharacteristic
722C22×C3C22×C4×D311yescharacteristic
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—32no—
729C2×D3—32no—
730C2×D3—62no—
731C2×D3—68no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—68no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—124no—
749C2×D3—124no—
750C2×D3#89312yes—
751C2×D3#90112yes—
752C2×D3D3×M1612yes—
753C2×D3D3×M1612yescomplemented
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—32no—
761C3×C4—41no—
762C3×C4—41no—
763C3×C4—61no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—61no—
767C3×C4C2×D3×D411yescharacteristic
768C3×C4C2×D3×D411yescharacteristic
769C3×C4C2×#23911yescharacteristic
770C3×C4D3×#4111yescharacteristic
771Dic3—21no—
772Dic3—21no—
773Dic3—21no—
774Dic3—21no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—61no—
779Dic3—121no—
780Dic3—121no—
781Dic3#89312yes—
782C32C2×#43511yescharacteristic, complemented, Sylow
783C23—31no—
784C23—31no—
785C23—31no—
786C23—94no—
787C23—91no—
788C23—91no—
789C23—182no—
790C23—182no—
791C23—182no—
792C23—182no—
793C23—182no—
794D4—62no—
795D4—182no—
796D4—182no—
797D4—182no—
798C2×C4—31no—
799C2×C4—32no—
800C2×C4—32no—
801C2×C4—31no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—91no—
812C2×C4—91no—
813C2×C4—182no—
814C2×C4—182no—
815C2×C4—182no—
816C2×C4—182no—
817C2×C4—182no—
818C2×C4—182no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—181no—
823C2×C4C4×D3211yescharacteristic
824C2×C4C4×D3211yescharacteristic
825C2×C4C22×D3211yescharacteristic
826C8—21no—
827C8—21no—
828C8—32no—
829C8—61no—
830C8—61no—
831C8—61no—
832C8—92no—
833C8—181no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—34no—
838C2×C3—62no—
839C2×C3—121no—
840C2×C3C2×#89311yescharacteristic
841C2×C3C4×D3×D411yescharacteristic
842C2×C3C2×#90111yescharacteristic
843C2×C3C2×D3×M1611yescharacteristic
844C2×C3C2×D3×M1611yescharacteristic
845C2×C3D3×#13111yescharacteristic
846D3—22no—
847D3—41no—
848D3—62no—
849D3—62no—
850D3—122no—
851D3—121no—
852D3—121no—
853D3—241no—
854D3#483614yesdirect product factor
855C22—32no—
856C22—32no—
857C22—32no—
858C22—32no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—61no—
863C22—61no—
864C22—92no—
865C22—188no—
866C22—181no—
867C22—181no—
868C22—181no—
869C22—181no—
870C22—181no—
871C22—364no—
872C22C2×C4×D3211yescharacteristic
873C4—21no—
874C4—21no—
875C4—32no—
876C4—61no—
877C4—61no—
878C4—61no—
879C4—61no—
880C4—181no—
881C4—181no—
882C4D32×D411yescharacteristic
883C4D3×#23911yescharacteristic
884C3—21no—
885C3C2×#483611yescharacteristic, complemented
886C3D3×#43511yescharacteristic, complemented
887C2—34no—
888C2—62no—
889C2—121no—
890C2—182no—
891C2—361no—
892C2D3×#89311yescharacteristic
893C2D3×#90111yescharacteristic
894C2D32×M1611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC2×D3×D12C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32C2×#435
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×D3×ΓL(1,𝔽25)C2semidirect
2. C2×D32×C8C2semidirect
4. #10592535C2semidirect
5. C3×#4836C2semidirect
6. C3×D3×C4⋊C8C2semidirect
7. D3×(C2×D3)⋊C8C2semidirect
8. D3×(C2×D3)⋊C8C2semidirect
9. #10590907C2semidirect
10. #10590738C2semidirect
11. #10590737C2semidirect
12. #10590727C2semidirect
13. #10590330C2semidirect
14. #10590328C2semidirect
15. D3×#803C2semidirect
21. C2×#3743C22semidirect
22. C2×C8×C3⋊D3C22semidirect
24. C2×C3×ΓL(1,𝔽25)C22semidirect
27. C2×C3×D3×C8C22semidirect
39. C2×#3712C22semidirect
40. C2×#3711C22semidirect
41. C2×#3710C22semidirect
44. C2×D3×C3⋊C8C22semidirect
47. C32×C4⋊C8C22semidirect
48. #63647C22semidirect
49. #63647C22semidirect
50. #63630C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. C3×C4⋊(C3⋊C8)C22semidirect
56. C3×#803C22semidirect
57. #63557C22semidirect
58. #63557C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
61. #63554C22semidirect
62. #63554C22semidirect
86. #4836D3direct (N × H)
87. D3×C4⋊C8D3semidirect
153. D3×C3⋊C8D4semidirect
185. C2×ΓL(1,𝔽25)C2×D3semidirect
198. C2×D3×C8C2×D3semidirect
220. C3×C4⋊C8C2×D3semidirect
221. C3×C4⋊C8C2×D3semidirect
239. (C2×D3)⋊C8C2×D3semidirect
240. (C2×D3)⋊C8C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
244. Dic3⋊C8C2×D3semidirect
245. C4⋊(C3⋊C8)C2×D3semidirect
251. #803C2×D3semidirect
262. C2×D32M16semidirect
298. C3⋊(C3⋊C8)C2×D4semidirect
302. C3×C3⋊C8C2×D4semidirect
457. C2×C3⋊D3C2×M16semidirect
465. C2×C3×D3C2×M16semidirect
512. C4⋊C8D32semidirect
642. C3⋊C8D3×D4semidirect
650. C3×D3#435semidirect
753. C2×D3D3×M16semidirect
782. C32C2×#435semidirect
854. D3#4836direct (N × H)
885. C3C2×#4836semidirect
886. C3D3×#435semidirect

Maximal subgroups

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

subgroupindex
C2×D3×ΓL(1,𝔽25)2
C2×D32×C82
C4×D3×D122
#105925352
C3×#48362
C3×D3×C4⋊C82
D3×(C2×D3)⋊C82
#105909072
#105907382
#105907372
#105907272
#105903302
#105903282
D3×#8032
D3×#4353
C2×#48363