Finite Group Databasebeta

← D3×#5111 #11859223

Subgroups — D3×#5111 #11859223

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
1C22×C3×D3×C8C211yesmaximal, characteristic, complemented
2C4×D3×#67C211yesmaximal, characteristic
3C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4#10592810C211yesmaximal, characteristic, complemented
5C3×#5111C211yesmaximal, characteristic, complemented
6#10591157C211yesmaximal, characteristic, complemented
7#10591155C211yesmaximal, characteristic, complemented
8D3×#830C211yesmaximal, characteristic, complemented
9D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
10#10590727C211yesmaximal, characteristic, complemented
11#10590726C211yesmaximal, characteristic, complemented
12#10590723C211yesmaximal, characteristic, complemented
13#10590722C211yesmaximal, characteristic, complemented
14D3×#815C211yesmaximal, characteristic, complemented
15D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
16C2×#5111—31nomaximal
17D3×#435—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C2×D3×#67C411yescharacteristic
20C2×C4×D32C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic, complemented
22C4×#638C2211yescharacteristic
23C2×#3743C2211yescharacteristic, complemented
24C3×C4×#67C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic, complemented
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
27C2×C3×D3×C8—24no—
28C2×C3×D3×C8C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic, complemented
31C2×C3×D3×C8C2211yescharacteristic, complemented
32Dic3×#67C411yescharacteristic
33D3×#217C411yescharacteristic
34#63952C411yescharacteristic
35D3×(C2×D3)⋊C4C411yescharacteristic
36#63904C411yescharacteristic
37C4×#626C2211yescharacteristic
38C4×#625C2211yescharacteristic
39#63879C411yescharacteristic
40D3×Dic3⋊C4C411yescharacteristic
41C4×D3×Dic3C2211yescharacteristic
42C2×#3712C2211yescharacteristic, complemented
43C2×#3711C2211yescharacteristic, complemented
44C2×D3×C3⋊C8C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46D3×ΓL(1,𝔽25)—24no—
47#63657C2211yescharacteristic, complemented
48#63647C2211yescharacteristic, complemented
49#63642C2211yescharacteristic, complemented
50#63641C2211yescharacteristic, complemented
51C3×#830C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55#63572C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63557C2211yescharacteristic, complemented
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63555C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C23×C3×C8—31no—
64C2×C4×#67—31no—
65C2×D3×M16—31no—
66C22×ΓL(1,𝔽25)—31no—
67C22×D3×C8D311yescharacteristic, complemented
68C4×D3×D4—31no—
69C3×#435—31no—
70C2×#830—31no—
71#5127—31no—
72#5111—31no—
73#5111—31no—
74#5111—31no—
75#5111—31no—
76#5111—31no—
77#5111—31no—
78#5111—31no—
79#5111—31no—
80#5111—61no—
81#5111D311yescharacteristic, direct product factor
82C2×(C2×D3)⋊C8—31no—
83C2×#815—31no—
84C2×Dic3⋊C8—31no—
85#5011—31no—
86#4836—31no—
87D3×C4⋊C8—31no—
88#4730—31no—
89#4728—31no—
90D3×C22⋊C8—31no—
91D3×C22⋊C8—31no—
92#4706—31no—
93D3×#97—31no—
94C23×C3×D3C2×C411yescharacteristic
95C22×D32C2×C411yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638C2×C411yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×#67C2×C411yescharacteristic
100C22×C3×Dic3C2×C411yescharacteristic
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3C2×C411yescharacteristic
104C2×C3×C4×D3C2×C411yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108D3×#67—24no—
109C2×#626C2×C411yescharacteristic
110C2×#625C2×C411yescharacteristic
111C2×#624C2×C411yescharacteristic
112C2×D3×Dic3C2×C411yescharacteristic
113C2×D3×Dic3C2×C411yescharacteristic
114C2×D3×Dic3C2×C411yescharacteristic
115C2×D3×Dic3C2×C411yescharacteristic
116C4×D32—22no—
117C4×D32—22no—
118C2×C32×C8—22no—
119C2×C32×C8C2311yescharacteristic
120C2×C32×C8C2311yescharacteristic
121#3757C2×C411yescharacteristic
122#3752C2×C411yescharacteristic
123#3750C2×C411yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3743—22no—
128C3×#217C2×C411yescharacteristic
129C3×(C2×D3)⋊C4C2×C411yescharacteristic
130C3×Dic3⋊C4C2×C411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8—22no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×ΓL(1,𝔽25)—22no—
138C3×D3×C8—22no—
139C3×D3×C8—22no—
140C3×D3×C8—22no—
141C3×D3×C8D414yescomplemented
142#3724C2×C411yescharacteristic
143Dic3⋊Dic3C2×C411yescharacteristic
144#3722C2×C411yescharacteristic
145(C2×D3)⋊Dic3C2×C411yescharacteristic
146(C2×D3)⋊Dic3C2×C411yescharacteristic
147(C2×D3)⋊Dic3C2×C411yescharacteristic
148Dic32C2×C411yescharacteristic
149Dic32C2×C411yescharacteristic
150#3712—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153D3×C3⋊C8—22no—
154C2×#435—91noSylow
155C23×C3×C4—31no—
156C22×#67—31no—
157C2×D3×D4—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3C2×D311yescharacteristic
161C2×C3×M16—31no—
162C22×C3×C8—21no—
163C22×C3×C8—31no—
164C22×C3×C8—31no—
165C22×C3×C8—31no—
166C22×C3×C8—31no—
167C22×C3×C8—31no—
168C22×C3×C8—64no—
169C22×C3×C8C2×D311yescharacteristic, complemented
170C22×C3×C8C2×D311yescharacteristic, complemented
171C3×C4×D4—31no—
172C2×#217—31no—
173D4×Dic3—31no—
174C4×#67—31no—
175C4×#67—31no—
176C4×#67—31no—
177C4×#67—31no—
178C4×#67—31no—
179C4×#67—31no—
180C4×#67—31no—
181C4×#67—31no—
182C4×#67—31no—
183C4×#67—61no—
184C4×#67C2×D311yescharacteristic
185C2×(C2×D3)⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×C4×Dic3—31no—
188C2×#208—31no—
189C22×C3⋊C8—31no—
190C22×C3⋊C8—31no—
191C22×C3⋊C8C2×D311yescharacteristic, complemented
192D3×M16—64no—
193C2×ΓL(1,𝔽25)—31no—
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—31no—
198C2×ΓL(1,𝔽25)—61no—
199C2×ΓL(1,𝔽25)—64no—
200C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
201C2×D3×C8—24no—
202C2×D3×C8—31no—
203C2×D3×C8—31no—
204C2×D3×C8C2×D311yescharacteristic
205C2×D3×C8C2×D311yescharacteristic
206C2×D3×C8C2×D311yescharacteristic, complemented
207C2×D3×C8C2×D311yescharacteristic, complemented
208#893—31no—
209D3×C4⋊C4—31no—
210#67⋊C4—31no—
211#67⋊C4—31no—
212D3×C22⋊C4—31no—
213D3×C22⋊C4—31no—
214C4×D12—31no—
215C42×D3—31no—
216C3×C4⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8—31no—
219C3×#97—31no—
220#830—31no—
221#830—31no—
222#830—31no—
223#830—31no—
224#830—31no—
225#830—61no—
226#830C2×D311yescharacteristic, complemented
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—61no—
235(C2×D3)⋊C8C2×D311yescharacteristic, complemented
236#815—31no—
237#815—31no—
238#815—31no—
239#815—31no—
240#815—31no—
241#815—61no—
242#815C2×D311yescharacteristic, complemented
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—31no—
247Dic3⋊C8—31no—
248Dic3⋊C8—61no—
249Dic3⋊C8C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251#803—31no—
252C23×C32C22×C411yescharacteristic
253C22×C3⋊D3C22×C411yescharacteristic
254C22×C3×D3—22no—
255C22×C3×D3—22no—
256C22×C3×D3M1614yescomplemented
257C22×C3×D3C22×C411yescharacteristic
258C22×C3×D3C22×C411yescharacteristic
259C22×C3×D3C22×C411yescharacteristic
260C2×D32—22no—
261C2×D32—22no—
262C2×D32—22no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C22×C411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—22no—
268C2×C3⋊Dic3C22×C411yescharacteristic
269C2×C3⋊Dic3C22×C411yescharacteristic
270C2×C3⋊Dic3C22×C411yescharacteristic
271C4×C3⋊D3—21no—
272C4×C3⋊D3—21no—
273C3×#67—22no—
274C2×C3×Dic3—22no—
275C2×C3×Dic3C22×C411yescharacteristic
276C2×C3×Dic3C22×C411yescharacteristic
277C2×C3×Dic3C22×C411yescharacteristic
278C2×C3×Dic3C22×C411yescharacteristic
279C2×C3×Dic3C22×C411yescharacteristic
280C3×C4×D3—22no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—22no—
286C3×C4×D3C2×D412yes—
287C3×C4×D3#4112yes—
288#626—22no—
289#625—22no—
290#624—22no—
291D3×Dic3—22no—
292D3×Dic3—22no—
293D3×Dic3—22no—
294D3×Dic3—22no—
295C32×C8—21no—
296C32×C8C2×D412yescomplemented
297C3⋊(C3⋊C8)—21no—
298C3⋊(C3⋊C8)—21no—
299C3×C3⋊C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yescomplemented
303C22×M16—91no—
304C23×C8—31no—
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—91no—
315C2×C22⋊C8—91no—
316C2×C22⋊C8—91no—
317C2×#97—91no—
318C24×C3—31no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3C4×D311yescharacteristic
322C2×C3×D4—31no—
323C22×C3×C4—21no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C2×#67—31no—
335C2×#67—31no—
336C2×#67—31no—
337C2×#67—31no—
338C2×#67—31no—
339C2×#67—61no—
340C2×#67—64no—
341C2×#67C4×D311yescharacteristic
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3C4×D311yescharacteristic
347D3×D4—64no—
348C2×D12—31no—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—31no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—61no—
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—22no—
371C2×C3×C8—22no—
372C2×C3×C8—21no—
373C2×C3×C8—21no—
374C2×C3×C8—31no—
375C2×C3×C8—34no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C2×C3×C8—42no—
380C2×C3×C8—62no—
381C2×C3×C8—62no—
382C2×C3×C8—62no—
383C2×C3×C8—62no—
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C3×C4⋊C4—31no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C42—31no—
392#217—31no—
393#217—31no—
394#217—31no—
395#217—31no—
396#217—31no—
397#217—61no—
398#217C4×D311yescharacteristic
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—31no—
405(C2×D3)⋊C4—31no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4C4×D311yescharacteristic
408C4⋊Dic3—31no—
409Dic3⋊C4—31no—
410Dic3⋊C4—31no—
411Dic3⋊C4—31no—
412Dic3⋊C4—31no—
413Dic3⋊C4—31no—
414Dic3⋊C4—61no—
415Dic3⋊C4C4×D311yescharacteristic
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—61no—
423C4×Dic3C22×D311yescharacteristic
424#208—62no—
425C2×C3⋊C8—22no—
426C2×C3⋊C8—31no—
427C2×C3⋊C8—31no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—61no—
431C2×C3⋊C8—61no—
432C2×C3⋊C8—62no—
433C2×C3⋊C8—62no—
434C2×C3⋊C8C22×D311yescharacteristic
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438ΓL(1,𝔽25)—22no—
439ΓL(1,𝔽25)—62no—
440ΓL(1,𝔽25)—62no—
441ΓL(1,𝔽25)—62no—
442ΓL(1,𝔽25)—62no—
443ΓL(1,𝔽25)—62no—
444ΓL(1,𝔽25)—122no—
445D3×C8—22no—
446D3×C8—22no—
447D3×C8—22no—
448D3×C8—62no—
449D3×C8—62no—
450D3×C8#6714yescomplemented
451C22×C32—21no—
452C22×C32—21no—
453C22×C32C2×M1612yescomplemented
454C22×C32C23×C411yescharacteristic
455C2×C3⋊D3—21no—
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—28no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3C4×D412yes—
465C2×C3×D3C2×M1612yes—
466C2×C3×D3C2×M1612yescomplemented
467C2×C3×D3#13112yes—
468D32—44no—
469C32×C4—21no—
470C32×C4C22×D411yescharacteristic
471C32×C4C2×#4111yescharacteristic
472C3⋊Dic3—21no—
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—31no—
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—31no—
492C22×C8—31no—
493C22×C8—64no—
494C22×C8—91no—
495C22×C8—91no—
496C22×C8D3211yescharacteristic, complemented
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—91no—
509C4⋊C8—31no—
510C4⋊C8—91no—
511C4⋊C8—91no—
512C4⋊C8—91no—
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—21no—
526C23×C3—31no—
527C23×C3—34no—
528C23×C3—31no—
529C23×C3—31no—
530C23×C3—62no—
531C23×C3—62no—
532C23×C3C2×C4×D311yescharacteristic
533C23×C3C2×C4×D311yescharacteristic
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—61no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3ΓL(1,𝔽25)14yescomplemented
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—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—31no—
557C2×C3×C4—32no—
558C2×C3×C4—32no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4C2×C4×D311yescharacteristic
573C2×C3×C4C2×C4×D311yescharacteristic
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576#67—22no—
577#67—62no—
578#67—62no—
579#67—62no—
580#67—62no—
581#67—62no—
582#67—122no—
583C2×Dic3—22no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—62no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3C2×C4×D311yescharacteristic
598C2×Dic3C2×C4×D311yescharacteristic
599C2×Dic3C2×C4×D311yescharacteristic
600C2×Dic3C2×C4×D311yescharacteristic
601C2×Dic3C2×C4×D311yescharacteristic
602D12—62no—
603C4×D3—22no—
604C4×D3—21no—
605C4×D3—21no—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—22no—
609C4×D3—62no—
610C4×D3—62no—
611C4×D3—62no—
612C4×D3—62no—
613C4×D3—62no—
614C4×D3—61no—
615C4×D3—61no—
616C4×D3—61no—
617C4×D3—61no—
618C4×D3—62no—
619C4×D3—121no—
620C4×D3—121no—
621C4×D3#23512yes—
622C4×D3C2×#6712yes—
623C3×C8—21no—
624C3×C8—21no—
625C3×C8—22no—
626C3×C8—32no—
627C3×C8—41no—
628C3×C8—61no—
629C3×C8—61no—
630C3×C8—61no—
631C3×C8D3×D412yescomplemented
632C3×C8C2×#6712yescomplemented
633C3⋊C8—21no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8—121no—
642C3⋊C8C2×#6712yescomplemented
643C2×C32—22no—
644C2×C32C2×C4×D411yescharacteristic
645C2×C32C22×M1611yescharacteristic
646C2×C32C2×#13111yescharacteristic
647C3⋊D3—41no—
648C3×D3—22no—
649C3×D3—41no—
650C3×D3#43514yescomplemented
651C24—31no—
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—31no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—91no—
667C22×C4—91no—
668C22×C4—91no—
669C22×C4—91no—
670C22×C4—91no—
671C22×C4—91no—
672C22×C4—182no—
673C22×C4—182no—
674C22×C4C2×D3211yescharacteristic
675M16—62no—
676M16—182no—
677M16—182no—
678M16—182no—
679C2×C8—22no—
680C2×C8—31no—
681C2×C8—34no—
682C2×C8—31no—
683C2×C8—31no—
684C2×C8—31no—
685C2×C8—62no—
686C2×C8—62no—
687C2×C8—62no—
688C2×C8—62no—
689C2×C8—91no—
690C2×C8—91no—
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—91no—
709C42—91no—
710C42—91no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—22no—
716C22×C3—21no—
717C22×C3—32no—
718C22×C3—32no—
719C22×C3—32no—
720C22×C3—32no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—68no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3C2×ΓL(1,𝔽25)12yescomplemented
730C22×C3D3×M1612yescomplemented
731C22×C3C22×C4×D311yescharacteristic
732C22×C3C22×C4×D311yescharacteristic
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—28no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—124no—
749C2×D3—124no—
750C2×D3C2×ΓL(1,𝔽25)12yes—
751C2×D3C2×ΓL(1,𝔽25)12yescomplemented
752C2×D3#90112yes—
753C2×D3C4×#6712yes—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—32no—
759C3×C4—41no—
760C3×C4—61no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4C2×#23511yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4D3×#4111yescharacteristic
767C3×C4C22×#6711yescharacteristic
768Dic3—21no—
769Dic3—21no—
770Dic3—21no—
771Dic3—21no—
772Dic3—61no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—121no—
779Dic3—121no—
780Dic3—121no—
781Dic3C4×#6712yes—
782C32C2×#43511yescharacteristic, complemented, Sylow
783C23—31no—
784C23—34no—
785C23—31no—
786C23—31no—
787C23—62no—
788C23—62no—
789C23—91no—
790C23—182no—
791C23—182no—
792C23—182no—
793C23C4×D3211yescharacteristic
794D4—62no—
795D4—182no—
796D4—182no—
797D4—182no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—31no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—182no—
818C2×C4—182no—
819C2×C4—182no—
820C2×C4—182no—
821C2×C4—182no—
822C2×C4—181no—
823C2×C4—181no—
824C2×C4C4×D3211yescharacteristic
825C2×C4C22×D3211yescharacteristic
826C8—21no—
827C8—32no—
828C8—61no—
829C8—61no—
830C8—61no—
831C8—181no—
832C8—181no—
833C8D3×#6712yescomplemented
834C2×C3—22no—
835C2×C3—22no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—34no—
840C2×C3—42no—
841C2×C3—62no—
842C2×C3—121no—
843C2×C3C4×D3×D411yescharacteristic
844C2×C3C22×ΓL(1,𝔽25)11yescharacteristic
845C2×C3C2×#90111yescharacteristic
846C2×C3C2×D3×M1611yescharacteristic
847C2×C3D3×#13111yescharacteristic
848C2×C3C2×C4×#6711yescharacteristic
849D3—22no—
850D3—41no—
851D3—121no—
852D3—121no—
853D3—241no—
854D3#511114yesdirect product factor
855C22—21no—
856C22—21no—
857C22—32no—
858C22—32no—
859C22—32no—
860C22—32no—
861C22—68no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—61no—
867C22—181no—
868C22—181no—
869C22—181no—
870C22—364no—
871C22D3×ΓL(1,𝔽25)12yescomplemented
872C22C2×C4×D3211yescharacteristic
873C4—21no—
874C4—32no—
875C4—61no—
876C4—61no—
877C4—61no—
878C4—61no—
879C4—181no—
880C4—181no—
881C4—181no—
882C4D3×#23511yescharacteristic
883C4C2×D3×#6711yescharacteristic
884C3—21no—
885C3D3×#43511yescharacteristic, complemented
886C3C2×#511111yescharacteristic, complemented
887C2—22no—
888C2—34no—
889C2—62no—
890C2—121no—
891C2—361no—
892C2C2×D3×ΓL(1,𝔽25)11yescharacteristic
893C2D3×#90111yescharacteristic
894C2C4×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC22×C32×C8C22
prime radicalC2×D3×#67C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#435
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×C8C2semidirect
3. C2×D3×ΓL(1,𝔽25)C2semidirect
4. #10592810C2semidirect
5. C3×#5111C2semidirect
6. #10591157C2semidirect
7. #10591155C2semidirect
8. D3×#830C2semidirect
9. D3×(C2×D3)⋊C8C2semidirect
10. #10590727C2semidirect
11. #10590726C2semidirect
12. #10590723C2semidirect
13. #10590722C2semidirect
14. D3×#815C2semidirect
15. D3×Dic3⋊C8C2semidirect
21. C22×C32×C8C22semidirect
23. C2×#3743C22semidirect
25. C22×C3×C3⋊C8C22semidirect
26. C2×C3×ΓL(1,𝔽25)C22semidirect
30. C2×C3×D3×C8C22semidirect
31. C2×C3×D3×C8C22semidirect
42. C2×#3712C22semidirect
43. C2×#3711C22semidirect
47. #63657C22semidirect
48. #63647C22semidirect
49. #63642C22semidirect
50. #63641C22semidirect
51. C3×#830C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×#815C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. #63572C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63557C22semidirect
58. (C2×D3)⋊(C3⋊C8)C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
61. #63555C22semidirect
62. #63554C22semidirect
67. C22×D3×C8D3semidirect
81. #5111D3direct (N × H)
141. C3×D3×C8D4semidirect
169. C22×C3×C8C2×D3semidirect
170. C22×C3×C8C2×D3semidirect
191. C22×C3⋊C8C2×D3semidirect
200. C2×ΓL(1,𝔽25)C2×D3semidirect
206. C2×D3×C8C2×D3semidirect
207. C2×D3×C8C2×D3semidirect
226. #830C2×D3semidirect
235. (C2×D3)⋊C8C2×D3semidirect
242. #815C2×D3semidirect
249. Dic3⋊C8C2×D3semidirect
256. C22×C3×D3M16semidirect
296. C32×C8C2×D4semidirect
302. C3×C3⋊C8C2×D4semidirect
450. D3×C8#67semidirect
453. C22×C32C2×M16semidirect
466. C2×C3×D3C2×M16semidirect
496. C22×C8D32semidirect
545. C22×D3ΓL(1,𝔽25)semidirect
631. C3×C8D3×D4semidirect
632. C3×C8C2×#67semidirect
642. C3⋊C8C2×#67semidirect
650. C3×D3#435semidirect
729. C22×C3C2×ΓL(1,𝔽25)semidirect
730. C22×C3D3×M16semidirect
751. C2×D3C2×ΓL(1,𝔽25)semidirect
782. C32C2×#435semidirect
833. C8D3×#67semidirect
854. D3#5111direct (N × H)
871. C22D3×ΓL(1,𝔽25)semidirect
885. C3D3×#435semidirect
886. C3C2×#5111semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C4×D3×#672
C2×D3×ΓL(1,𝔽25)2
#105928102
C3×#51112
#105911572
#105911552
D3×#8302
D3×(C2×D3)⋊C82
#105907272
#105907262
#105907232
#105907222
D3×#8152
D3×Dic3⋊C82
C2×#51113
D3×#4353