Finite Group Databasebeta

← C2×#10594668 #11918499

Subgroups — C2×#10594668 #11918499

Order 1152.

3053 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C2×#64110C211yesmaximal, characteristic, complemented
3C2×C3×#901C211yesmaximal, characteristic, complemented
4C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
5C2×#63817C211yesmaximal, characteristic, complemented
6C2×#63814C211yesmaximal, characteristic, complemented
7C2×D3×#208C211yesmaximal, characteristic, complemented
8C2×#63805C212yesmaximal, complemented
9C2×#63804C212yesmaximal, complemented
10#10594668C2116yesmaximal, direct product factor
11C2×#63791C212yesmaximal, complemented
12C2×D3×ΓL(1,𝔽25)C212yesmaximal, complemented
13C2×#5750—31nomaximal
14C2×#5745—31nomaximal
15C2×#3828C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×D3×#67C412yes—
19C2×#3804C412yes—
20D3×#235C418yes—
21D3×#235C2218yes—
22C2×D3×D12C411yescharacteristic
23C2×C4×D32C2212yes—
24C2×#3799C411yescharacteristic
25C2×#3798C2212yes—
26C2×#3795C411yescharacteristic
27C2×D3×Dic6C411yescharacteristic
28C22×C32×C8C2211yescharacteristic, complemented
29C2×#3748C2211yescharacteristic, complemented
30#64110C2218yescomplemented
31C2×#3743C2212yescomplemented
32C2×C8×C3⋊D3C2212yescomplemented
33C2×C3×#208C2211yescharacteristic, complemented
34C22×C3×C3⋊C8C2211yescharacteristic, complemented
35C3×#901C2218yescomplemented
36C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
38C2×C3×ΓL(1,𝔽25)C2218yescomplemented
39C2×C3×ΓL(1,𝔽25)C2212yescomplemented
40C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
42C2×C3×D3×C8C2212yescomplemented
43C2×#3712C2212yescomplemented
44C2×#3711C2212yes—
45C2×#3711C2212yescomplemented
46#63817C2218yescomplemented
47C2×#3710C2212yescomplemented
48#63814C2218yescomplemented
49D3×#208C2218yescomplemented
50C2×D3×C3⋊C8C2212yescomplemented
51C2×D3×C3⋊C8C2212yescomplemented
52#63805C22116yescomplemented
53#63804C22116yescomplemented
54#63791C22116yescomplemented
55D3×ΓL(1,𝔽25)C22116yescomplemented
56C2×D3×#41—31no—
57C22×#235—31no—
58C2×C3×#131—31no—
59C22×C3×M16—31no—
60C2×#948—31no—
61C22×#208—31no—
62#5750—316no—
63#5745—316no—
64C2×#907—31no—
65C2×#907—32no—
66C2×#907—32no—
67C2×#907—32no—
68C2×D3×M16—31no—
69C2×D3×M16—32no—
70C2×D3×M16—32no—
71C2×D3×M16—32no—
72C2×#901—31no—
73C2×#901—31no—
74C2×#901—31no—
75C2×#901—31no—
76C2×#901—32no—
77C2×#901—61no—
78C2×#901D311yescharacteristic, complemented
79C22×ΓL(1,𝔽25)—32no—
80C22×ΓL(1,𝔽25)D311yescharacteristic, complemented
81C23×C3×D3C2×C411yescharacteristic
82C22×D32C2×C412yes—
83C22×C32×C4C2311yescharacteristic
84C2×#638C2×C412yes—
85#3828C2×C414yes—
86#3828C2314yes—
87C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
88C2×C4×C3⋊D3C2312yes—
89C2×#634C2×C411yescharacteristic
90C2×C3×#67C2×C412yes—
91C22×C3×Dic3C2×C411yescharacteristic
92C3×#235C2×C414yes—
93C3×#235C2314yes—
94C2×C3×D12C2×C411yescharacteristic
95C2×C3×C4×D3C2×C411yescharacteristic
96C2×C3×C4×D3C2×C411yescharacteristic
97C2×C3×C4×D3C2×C414yes—
98C2×C3×C4×D3C2312yes—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2314yes—
102C2×C3×Dic6C2×C411yescharacteristic
103D3×#67C2×C4116yes—
104C2×#627C2×C412yes—
105C2×#626C2×C412yes—
106C2×#626C2×C412yes—
107C2×#625C2×C412yes—
108C2×#624C2×C412yes—
109#3804C2×C4116yes—
110C2×D3×Dic3C2×C412yes—
111C2×D3×Dic3C2×C412yes—
112D3×D12C2×C418yes—
113C4×D32C2×C418yes—
114C4×D32C2318yes—
115#3799C2×C418yes—
116#3798C2×C418yes—
117#3798C2318yes—
118#3795C2×C418yes—
119D3×Dic6C2×C418yes—
120C2×C32×C8C2311yescharacteristic
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2314yescomplemented
123#3748C2314yescomplemented
124C2×C3⋊(C3⋊C8)C2312yes—
125#3743C2318yescomplemented
126C8×C3⋊D3C2318yescomplemented
127C3×#208C2314yescomplemented
128C2×C3×C3⋊C8C2312yes—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2314yescomplemented
132C3×ΓL(1,𝔽25)C2314yes—
133C3×ΓL(1,𝔽25)C2314yes—
134C3×ΓL(1,𝔽25)C2314yescomplemented
135C3×ΓL(1,𝔽25)C2314yescomplemented
136C3×ΓL(1,𝔽25)C2318yescomplemented
137C3×D3×C8C2318yescomplemented
138#3712C2318yescomplemented
139#3711C2318yes—
140#3711C2318yescomplemented
141#3710C2318yescomplemented
142D3×C3⋊C8C2318yescomplemented
143D3×C3⋊C8C2318yescomplemented
144C2×#568—91noSylow
145C2×C3×#41—31no—
146C23×C3×C4—31no—
147C22×#67—32no—
148D3×#41—38no—
149D3×#41—38no—
150C2×#239—31no—
151C2×D3×Q8—31no—
152C2×#237—32no—
153C2×#237—31no—
154C2×D3×D4—32no—
155C2×D3×D4—31no—
156C2×#235—31no—
157C2×#235—31no—
158C2×#235—32no—
159C2×#235—38no—
160C2×#235—38no—
161C2×#235—31no—
162C2×#235—32no—
163C2×#235—32no—
164C2×#235—31no—
165C2×#235—61no—
166C2×#235C2×D311yescharacteristic
167C22×D12—31no—
168C22×C4×D3—32no—
169C22×C4×D3—32no—
170C22×C4×D3C2×D311yescharacteristic
171C22×Dic6—31no—
172C3×#131—38no—
173C2×C3×M16—31no—
174C2×C3×M16—31no—
175C2×C3×M16—31no—
176C2×C3×M16—31no—
177C2×C3×M16—31no—
178C2×C3×M16—32no—
179C2×C3×M16—38no—
180C22×C3×C8—21no—
181C22×C3×C8—31no—
182C22×C3×C8—32no—
183C22×C3×C8C2×D311yescharacteristic, complemented
184C22×C3×C8C2×D311yescharacteristic, complemented
185#948—38no—
186C2×#208—31no—
187C2×#208—31no—
188C2×#208—38no—
189C2×#208—32no—
190C2×#208—32no—
191C2×#208—61no—
192C2×#208C2×D311yescharacteristic, complemented
193C22×C3⋊C8—32no—
194C22×C3⋊C8—32no—
195C22×C3⋊C8C2×D311yescharacteristic, complemented
196#907—38no—
197#907—316no—
198#907—316no—
199#907—316no—
200D3×M16—38no—
201D3×M16—316no—
202D3×M16—316no—
203D3×M16—316no—
204#901—38no—
205#901—38no—
206#901—38no—
207#901—38no—
208#901—316no—
209#901—68no—
210#901C2×D318yescomplemented
211C2×ΓL(1,𝔽25)—32no—
212C2×ΓL(1,𝔽25)—32no—
213C2×ΓL(1,𝔽25)—32no—
214C2×ΓL(1,𝔽25)—32no—
215C2×ΓL(1,𝔽25)—32no—
216C2×ΓL(1,𝔽25)—32no—
217C2×ΓL(1,𝔽25)—316no—
218C2×ΓL(1,𝔽25)—62no—
219C2×ΓL(1,𝔽25)C2×D311yescharacteristic
220C2×ΓL(1,𝔽25)C2×D311yescharacteristic
221C2×ΓL(1,𝔽25)C2×D318yescomplemented
222C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
223C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
224C2×ΓL(1,𝔽25)C2×D312yescomplemented
225C2×D3×C8—32no—
226C2×D3×C8—32no—
227C2×D3×C8—32no—
228C2×D3×C8—32no—
229C2×D3×C8—32no—
230C2×D3×C8—32no—
231C2×D3×C8—62no—
232C2×D3×C8C2×D312yescomplemented
233C23×C32C22×C411yescharacteristic
234C22×C3⋊D3C22×C412yes—
235C22×C3×D3—42no—
236C22×C3×D3C22×C411yescharacteristic
237C22×C3×D3C22×C412yes—
238C22×C3×D3C22×C411yescharacteristic
239C22×C3×D3C22×C414yes—
240C2×D32—44no—
241C2×D32C22×C418yes—
242C2×C32×C4C22×C411yescharacteristic
243C2×C32×C4C22×C412yes—
244C2×C32×C4C2411yescharacteristic
245C2×C32×C4C2412yes—
246#638C22×C418yes—
247C2×C3⋊Dic3C22×C412yes—
248C4⋊(C3⋊D3)C22×C414yes—
249C4×C3⋊D3C22×C414yes—
250C4×C3⋊D3C2414yes—
251#634C22×C414yes—
252C3×#67C22×C418yes—
253C2×C3×Dic3C22×C411yescharacteristic
254C2×C3×Dic3C22×C412yes—
255C2×C3×Dic3C22×C414yes—
256C2×C3×Dic3C22×C411yescharacteristic
257C3×D12C22×C414yes—
258C3×C4×D3C22×C414yes—
259C3×C4×D3C22×C414yes—
260C3×C4×D3C22×C412yes—
261C3×C4×D3C22×C414yes—
262C3×C4×D3C22×C412yes—
263C3×C4×D3C2412yes—
264C3×C4×D3C2414yes—
265C3×C4×D3C2412yes—
266C3×Dic6C22×C414yes—
267#627C22×C418yes—
268#626C22×C418yes—
269#626C22×C418yes—
270#625C22×C418yes—
271#624C22×C418yes—
272D3×Dic3C22×C418yes—
273D3×Dic3C22×C418yes—
274C32×C8C2412yes—
275C32×C8C2412yes—
276C3⋊(C3⋊C8)C2414yes—
277C3×C3⋊C8C2412yes—
278C3×C3⋊C8C2414yes—
279C3×C3⋊C8C2412yes—
280C22×#41—91no—
281#568—916no—
282C2×#131—31no—
283C2×#131—91no—
284C2×#131—92no—
285C2×#131—91no—
286C2×#131—92no—
287C2×#131—91no—
288C22×M16—31no—
289C22×M16—92no—
290C22×M16—92no—
291C22×M16—91no—
292C24×C3—31no—
293C23×D3—32no—
294C23×D3—32no—
295C23×D3C4×D311yescharacteristic
296C3×#41—34no—
297C3×#41—34no—
298C2×C3×Q8—31no—
299C2×C3×D4—32no—
300C2×C3×D4—31no—
301C22×C3×C4—21no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—34no—
306C22×C3×C4—31no—
307C22×C3×C4—32no—
308C22×C3×C4—31no—
309C22×C3×C4—34no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—32no—
313C2×#67—32no—
314C2×#67—32no—
315C2×#67—32no—
316C2×#67—316no—
317C2×#67—32no—
318C2×#67—32no—
319C2×#67—62no—
320C2×#67C4×D312yes—
321C22×Dic3—32no—
322C22×Dic3—32no—
323C22×Dic3C4×D311yescharacteristic
324#239—38no—
325D3×Q8—38no—
326#237—316no—
327#237—38no—
328D3×D4—316no—
329D3×D4—38no—
330#235—34no—
331#235—34no—
332#235—34no—
333#235—34no—
334#235—316no—
335#235—38no—
336#235—38no—
337#235—38no—
338#235—38no—
339#235—38no—
340#235—38no—
341#235—64no—
342#235—64no—
343#235C4×D314yes—
344#235C22×D314yes—
345C2×D12—32no—
346C2×D12—32no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—38no—
350C2×D12—61no—
351C2×D12C4×D311yescharacteristic
352C2×C4×D3—32no—
353C2×C4×D3—32no—
354C2×C4×D3—32no—
355C2×C4×D3—32no—
356C2×C4×D3—32no—
357C2×C4×D3—32no—
358C2×C4×D3—38no—
359C2×C4×D3—38no—
360C2×C4×D3—38no—
361C2×C4×D3—38no—
362C2×C4×D3—62no—
363C2×C4×D3C4×D311yescharacteristic
364C2×C4×D3C4×D311yescharacteristic
365C2×C4×D3C4×D314yes—
366C2×C4×D3C22×D311yescharacteristic
367C2×C4×D3C22×D312yes—
368C2×C4×D3C22×D311yescharacteristic
369C2×C4×D3C22×D314yes—
370C2×Dic6—31no—
371C2×Dic6—31no—
372C2×Dic6—32no—
373C2×Dic6—32no—
374C2×Dic6—38no—
375C2×Dic6—61no—
376C2×Dic6C4×D311yescharacteristic
377C3×M16—34no—
378C3×M16—34no—
379C3×M16—34no—
380C3×M16—38no—
381C3×M16—34no—
382C3×M16—34no—
383C2×C3×C8—21no—
384C2×C3×C8—21no—
385C2×C3×C8—24no—
386C2×C3×C8—31no—
387C2×C3×C8—32no—
388C2×C3×C8—31no—
389C2×C3×C8—34no—
390C2×C3×C8—38no—
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C22×D314yescomplemented
396C2×C3×C8C22×D314yescomplemented
397#208—34no—
398#208—34no—
399#208—38no—
400#208—38no—
401#208—64no—
402#208C22×D314yescomplemented
403C2×C3⋊C8—32no—
404C2×C3⋊C8—32no—
405C2×C3⋊C8—38no—
406C2×C3⋊C8—38no—
407C2×C3⋊C8—62no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D312yes—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D314yescomplemented
412ΓL(1,𝔽25)—38no—
413ΓL(1,𝔽25)—38no—
414ΓL(1,𝔽25)—38no—
415ΓL(1,𝔽25)—38no—
416ΓL(1,𝔽25)—38no—
417ΓL(1,𝔽25)—38no—
418ΓL(1,𝔽25)—68no—
419ΓL(1,𝔽25)C22×D314yes—
420ΓL(1,𝔽25)C22×D314yes—
421ΓL(1,𝔽25)C22×D314yescomplemented
422ΓL(1,𝔽25)C22×D314yescomplemented
423ΓL(1,𝔽25)C22×D318yescomplemented
424D3×C8—38no—
425D3×C8—38no—
426D3×C8—38no—
427D3×C8—38no—
428D3×C8—38no—
429D3×C8—38no—
430D3×C8—68no—
431D3×C8C22×D318yescomplemented
432C22×C32—22no—
433C22×C32C23×C412yes—
434C22×C32C23×C411yescharacteristic
435C2×C3⋊D3—24no—
436C2×C3⋊D3C23×C414yes—
437C2×C3×D3—22no—
438C2×C3×D3—24no—
439C2×C3×D3—22no—
440C2×C3×D3—44no—
441C2×C3×D3C23×C412yes—
442C2×C3×D3C23×C414yes—
443C2×C3×D3C23×C412yes—
444D32—48no—
445C32×C4C23×C412yes—
446C32×C4C23×C411yescharacteristic
447C32×C4C2511yescharacteristic
448C3⋊Dic3C23×C414yes—
449C3×Dic3C23×C412yes—
450C3×Dic3C23×C414yes—
451C3×Dic3C23×C412yes—
452C2×#41—31no—
453C2×#41—92no—
454C2×#41—92no—
455C2×#41—91no—
456C2×#41—91no—
457C2×#41—98no—
458C2×#41—98no—
459C2×#41—91no—
460C22×Q8—91no—
461C22×D4—91no—
462C22×D4—92no—
463C23×C4—31no—
464C23×C4—92no—
465#131—38no—
466#131—98no—
467#131—916no—
468#131—98no—
469#131—916no—
470#131—98no—
471C2×M16—31no—
472C2×M16—31no—
473C2×M16—31no—
474C2×M16—31no—
475C2×M16—31no—
476C2×M16—32no—
477C2×M16—38no—
478C2×M16—92no—
479C2×M16—916no—
480C2×M16—92no—
481C2×M16—92no—
482C2×M16—916no—
483C2×M16—98no—
484C2×M16—91no—
485C2×M16—92no—
486C22×C8—31no—
487C22×C8—32no—
488C22×C8—92no—
489C22×C8—92no—
490C22×C8—92no—
491C22×C8—92no—
492C22×C8D3211yescharacteristic, complemented
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—32no—
496C23×C3—31no—
497C23×C3—34no—
498C23×C3—122no—
499C23×C3C2×C4×D311yescharacteristic
500C23×C3C2×C4×D311yescharacteristic
501C22×D3—32no—
502C22×D3—32no—
503C22×D3—38no—
504C22×D3—38no—
505C22×D3—42no—
506C22×D3—62no—
507C22×D3—124no—
508C22×D3—124no—
509C22×D3C2×C4×D311yescharacteristic
510C22×D3C2×C4×D312yes—
511C22×D3C2×C4×D311yescharacteristic
512C22×D3C2×C4×D314yes—
513C3×Q8—34no—
514C3×D4—38no—
515C3×D4—34no—
516C2×C3×C4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—31no—
521C2×C3×C4—32no—
522C2×C3×C4—31no—
523C2×C3×C4—34no—
524C2×C3×C4—34no—
525C2×C3×C4—32no—
526C2×C3×C4—34no—
527C2×C3×C4—32no—
528C2×C3×C4—34no—
529C2×C3×C4—32no—
530C2×C3×C4—34no—
531C2×C3×C4—32no—
532C2×C3×C4C2×C4×D311yescharacteristic
533C2×C3×C4C2×C4×D311yescharacteristic
534C2×C3×C4C2×C4×D312yes—
535C2×C3×C4C2×C4×D312yes—
536C2×C3×C4C23×D312yes—
537C2×C3×C4C23×D312yes—
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—38no—
541#67—38no—
542#67—38no—
543#67—38no—
544#67—38no—
545#67—38no—
546#67—68no—
547#67C2×C4×D318yes—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—38no—
551C2×Dic3—38no—
552C2×Dic3—62no—
553C2×Dic3C2×C4×D311yescharacteristic
554C2×Dic3C2×C4×D312yes—
555C2×Dic3C2×C4×D311yescharacteristic
556C2×Dic3C2×C4×D314yes—
557D12—38no—
558D12—38no—
559D12—34no—
560D12—34no—
561D12—64no—
562D12C2×C4×D314yes—
563C4×D3—38no—
564C4×D3—38no—
565C4×D3—34no—
566C4×D3—34no—
567C4×D3—34no—
568C4×D3—34no—
569C4×D3—38no—
570C4×D3—38no—
571C4×D3—64no—
572C4×D3—64no—
573C4×D3C2×C4×D312yes—
574C4×D3C2×C4×D314yes—
575C4×D3C2×C4×D312yes—
576C4×D3C2×C4×D314yes—
577C4×D3C2×C4×D314yes—
578C4×D3C23×D312yes—
579C4×D3C23×D314yes—
580C4×D3C23×D312yes—
581Dic6—34no—
582Dic6—34no—
583Dic6—38no—
584Dic6—38no—
585Dic6—64no—
586Dic6C2×C4×D314yes—
587C3×C8—22no—
588C3×C8—22no—
589C3×C8—32no—
590C3×C8—34no—
591C3×C8—32no—
592C3×C8C23×D312yes—
593C3×C8C23×D312yes—
594C3×C8C23×D312yes—
595C3×C8C23×D312yes—
596C3⋊C8—34no—
597C3⋊C8—34no—
598C3⋊C8—64no—
599C3⋊C8C23×D312yes—
600C3⋊C8C23×D314yes—
601C3⋊C8C23×D312yes—
602C2×C32—22no—
603C2×C32#56812yescomplemented
604C2×C32C24×C411yescharacteristic
605C3⋊D3—24no—
606C3×D3—22no—
607C3×D3—24no—
608C3×D3—22no—
609C24—31no—
610C24—92no—
611#41—34no—
612#41—34no—
613#41—98no—
614#41—98no—
615#41—916no—
616#41—98no—
617#41—98no—
618#41—94no—
619#41—94no—
620C2×Q8—31no—
621C2×Q8—92no—
622C2×Q8—98no—
623C2×Q8—91no—
624C2×D4—32no—
625C2×D4—31no—
626C2×D4—98no—
627C2×D4—92no—
628C2×D4—92no—
629C2×D4—916no—
630C2×D4—92no—
631C2×D4—92no—
632C2×D4—91no—
633C22×C4—31no—
634C22×C4—34no—
635C22×C4—32no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—34no—
641C22×C4—98no—
642C22×C4—92no—
643C22×C4—98no—
644C22×C4—92no—
645C22×C4—92no—
646C22×C4—92no—
647C22×C4C2×D3211yescharacteristic
648M16—34no—
649M16—34no—
650M16—34no—
651M16—34no—
652M16—34no—
653M16—38no—
654M16—98no—
655M16—98no—
656M16—98no—
657M16—94no—
658M16—98no—
659C2×C8—34no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—32no—
663C2×C8—38no—
664C2×C8—98no—
665C2×C8—98no—
666C2×C8—98no—
667C2×C8—92no—
668C2×C8—98no—
669C2×C8C2×D3211yescharacteristic
670C2×C8C2×D3211yescharacteristic
671C2×C8C2×D3214yescomplemented
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—21no—
675C22×C3—22no—
676C22×C3—32no—
677C22×C3—34no—
678C22×C3—32no—
679C22×C3—42no—
680C22×C3—64no—
681C22×C3—62no—
682C22×C3—62no—
683C22×C3—124no—
684C22×C3C22×C4×D312yes—
685C22×C3C22×C4×D312yes—
686C22×C3C22×C4×D311yescharacteristic
687C22×C3C22×C4×D311yescharacteristic
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—24no—
691C2×D3—34no—
692C2×D3—34no—
693C2×D3—44no—
694C2×D3—64no—
695C2×D3—64no—
696C2×D3—64no—
697C2×D3—124no—
698C2×D3—128no—
699C2×D3—128no—
700C2×D3C22×C4×D312yes—
701C2×D3C22×C4×D314yes—
702C2×D3C22×C4×D312yes—
703C3×C4—22no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—32no—
707C3×C4—34no—
708C3×C4—32no—
709C3×C4C22×C4×D312yes—
710C3×C4C22×C4×D312yes—
711C3×C4C22×C4×D311yescharacteristic
712C3×C4C22×C4×D311yescharacteristic
713C3×C4C24×D311yescharacteristic
714C3×C4C24×D311yescharacteristic
715Dic3—34no—
716Dic3—34no—
717Dic3—64no—
718Dic3C22×C4×D312yes—
719Dic3C22×C4×D314yes—
720Dic3C22×C4×D312yes—
721C32C2×#56811yescharacteristic, complemented, Sylow
722C23—31no—
723C23—31no—
724C23—32no—
725C23—34no—
726C23—98no—
727C23—92no—
728C23—122no—
729C23—364no—
730C23C4×D3211yescharacteristic
731Q8—34no—
732Q8—98no—
733Q8—94no—
734D4—38no—
735D4—34no—
736D4—98no—
737D4—98no—
738D4—98no—
739D4—98no—
740D4—94no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—34no—
744C2×C4—32no—
745C2×C4—32no—
746C2×C4—34no—
747C2×C4—34no—
748C2×C4—32no—
749C2×C4—34no—
750C2×C4—34no—
751C2×C4—32no—
752C2×C4—32no—
753C2×C4—98no—
754C2×C4—98no—
755C2×C4—98no—
756C2×C4—92no—
757C2×C4—94no—
758C2×C4—94no—
759C2×C4C4×D3211yescharacteristic
760C2×C4C4×D3212yes—
761C2×C4C22×D3212yes—
762C2×C4C22×D3211yescharacteristic
763C8—32no—
764C8—32no—
765C8—34no—
766C8—94no—
767C8C22×D3212yes—
768C8C22×D3212yes—
769C2×C3—22no—
770C2×C3—22no—
771C2×C3—21no—
772C2×C3—22no—
773C2×C3—42no—
774C2×C3—64no—
775C2×C3—62no—
776C2×C3—62no—
777C2×C3#574512yescomplemented
778C2×C3#575012yescomplemented
779C2×C3C23×C4×D311yescharacteristic
780C2×C3C23×C4×D311yescharacteristic
781D3—22no—
782D3—22no—
783D3—24no—
784D3—64no—
785D3—64no—
786D3—124no—
787C22—22no—
788C22—32no—
789C22—32no—
790C22—34no—
791C22—62no—
792C22—62no—
793C22—64no—
794C22—94no—
795C22—124no—
796C22—184no—
797C22—368no—
798C22C2×C4×D3212yes—
799C22C2×C4×D3211yescharacteristic
800C4—32no—
801C4—32no—
802C4—34no—
803C4—94no—
804C4C2×C4×D3211yescharacteristic
805C4C2×C4×D3212yes—
806C4C23×D3211yescharacteristic
807C3—21no—
808C3C2×#574511yescharacteristic, complemented
809C3C2×#575011yescharacteristic, complemented
810C2—22no—
811C2—62no—
812C2—62no—
813C2—64no—
814C2—184no—
815C2#1059466812yesdirect product factor
816C2C22×C4×D3211yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutatorC2×C32C24×C4
FrattiniC4C23×D32
FittingC22×C32×C8C22
socleC22×C32C23×C4
prime radicalC2×D3×#235C2
cosocleC32×C4C25
hypercenterC22×C8D32
hypocenterC32C2×#568
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#64110C2semidirect
3. C2×C3×#901C2semidirect
4. C22×C3×ΓL(1,𝔽25)C2semidirect
5. C2×#63817C2semidirect
6. C2×#63814C2semidirect
7. C2×D3×#208C2semidirect
8. C2×#63805C2semidirect
9. C2×#63804C2semidirect
10. #10594668C2direct (N × H)
11. C2×#63791C2semidirect
12. C2×D3×ΓL(1,𝔽25)C2semidirect
28. C22×C32×C8C22semidirect
29. C2×#3748C22semidirect
30. #64110C22semidirect
31. C2×#3743C22semidirect
32. C2×C8×C3⋊D3C22semidirect
33. C2×C3×#208C22semidirect
34. C22×C3×C3⋊C8C22semidirect
35. C3×#901C22semidirect
38. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C2×C3×ΓL(1,𝔽25)C22semidirect
40. C2×C3×ΓL(1,𝔽25)C22semidirect
41. C2×C3×ΓL(1,𝔽25)C22semidirect
42. C2×C3×D3×C8C22semidirect
43. C2×#3712C22semidirect
45. C2×#3711C22semidirect
46. #63817C22semidirect
47. C2×#3710C22semidirect
48. #63814C22semidirect
49. D3×#208C22semidirect
50. C2×D3×C3⋊C8C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63805C22semidirect
53. #63804C22semidirect
54. #63791C22semidirect
55. D3×ΓL(1,𝔽25)C22semidirect
78. C2×#901D3semidirect
80. C22×ΓL(1,𝔽25)D3semidirect
122. C2×C32×C8C23semidirect
123. #3748C23semidirect
125. #3743C23semidirect
126. C8×C3⋊D3C23semidirect
127. C3×#208C23semidirect
131. C2×C3×C3⋊C8C23semidirect
134. C3×ΓL(1,𝔽25)C23semidirect
135. C3×ΓL(1,𝔽25)C23semidirect
136. C3×ΓL(1,𝔽25)C23semidirect
137. C3×D3×C8C23semidirect
138. #3712C23semidirect
140. #3711C23semidirect
141. #3710C23semidirect
142. D3×C3⋊C8C23semidirect
143. D3×C3⋊C8C23semidirect
183. C22×C3×C8C2×D3semidirect
184. C22×C3×C8C2×D3semidirect
192. C2×#208C2×D3semidirect
195. C22×C3⋊C8C2×D3semidirect
210. #901C2×D3semidirect
221. C2×ΓL(1,𝔽25)C2×D3semidirect
222. C2×ΓL(1,𝔽25)C2×D3semidirect
223. C2×ΓL(1,𝔽25)C2×D3semidirect
224. C2×ΓL(1,𝔽25)C2×D3semidirect
232. C2×D3×C8C2×D3semidirect
395. C2×C3×C8C22×D3semidirect
396. C2×C3×C8C22×D3semidirect
402. #208C22×D3semidirect
411. C2×C3⋊C8C22×D3semidirect
421. ΓL(1,𝔽25)C22×D3semidirect
422. ΓL(1,𝔽25)C22×D3semidirect
423. ΓL(1,𝔽25)C22×D3semidirect
431. D3×C8C22×D3semidirect
492. C22×C8D32semidirect
603. C2×C32#568semidirect
671. C2×C8C2×D32semidirect
721. C32C2×#568semidirect
777. C2×C3#5745semidirect
778. C2×C3#5750semidirect
808. C3C2×#5745semidirect
809. C3C2×#5750semidirect
815. C2#10594668direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×#641102
C2×C3×#9012
C22×C3×ΓL(1,𝔽25)2
C2×#638172
C2×#638142
C2×D3×#2082
C2×#638052
C2×#638042
#105946682
C2×#637912
C2×D3×ΓL(1,𝔽25)2
C2×#57503
C2×#57453