Finite Group Databasebeta

← #11775403

Subgroups — #11775403

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595005C211yesmaximal, characteristic
2C3×#4726C211yesmaximal, characteristic, complemented
3#10591295C211yesmaximal, characteristic, complemented
4#10589336C211yesmaximal, characteristic, complemented
5C3×#4467C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#69979—31nomaximal
9#68337—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×#3799C411yescharacteristic, complemented
12#64139C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×ΓL(1,𝔽25)—21no—
15#63977—21no—
16C2×Dic3⋊Dic3—21no—
17C2×(C2×D3)⋊Dic3—21no—
18#63952—21no—
19#63909C411yescharacteristic, complemented
20#63904—21no—
21#63856C411yescharacteristic, complemented
22#63850—21no—
23#63841C411yescharacteristic, complemented
24C32×C22⋊C8C2211yescharacteristic
25#63658C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28C3×(C2×D3)⋊C8—21no—
29#5791—31no—
30#5627—31no—
31C3×#407—31no—
32#5212—31no—
33#4726D311yescharacteristic, complemented
34#4667—31no—
35C3×#328—31no—
36#4538—31no—
37#4470—31no—
38#4470—31no—
39#4470—31no—
40#4470—61no—
41#4467—31no—
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3—21no—
48C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×C4×D3—42no—
52C2×C3×C4×D3C2×C411yescharacteristic
53C2×C3×C4×D3C2×C411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×Dic6C2×C411yescharacteristic
57C2×#626—21no—
58C2×#626—21no—
59C2×#624—21no—
60#3799—42no—
61C2×C32×C8—21no—
62#3752—21no—
63C4⋊(C3⋊Dic3)C2×C411yescharacteristic
64C3×#217—21no—
65C3×C4⋊Dic3C2×C411yescharacteristic
66C3×Dic3⋊C4—21no—
67C2×C3×C3⋊C8—21no—
68C3×ΓL(1,𝔽25)—42no—
69#3724—21no—
70Dic3⋊Dic3—42no—
71#3722—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74(C2×D3)⋊Dic3—42no—
75Dic32—21no—
76#1513—91noSylow
77C23×C3×C4—31no—
78C2×#239—31no—
79C2×#235—31no—
80C22×C4×D3C2×D311yescharacteristic
81C2×C3×M16—61no—
82C3×C22⋊Q8—31no—
83#953—61no—
84C2×#217—61no—
85#946—31no—
86#930—31no—
87#930—31no—
88#930—31no—
89#930—61no—
90#929—61no—
91C4×#67—61no—
92C4×#67—61no—
93C2×(C2×D3)⋊C4—61no—
94#926—31no—
95C2×C4⋊Dic3—61no—
96#924—31no—
97#924C2×D311yescharacteristic
98C2×Dic3⋊C4—61no—
99C2×ΓL(1,𝔽25)—21no—
100#895—31no—
101#894—61no—
102#893—61no—
103#892—31no—
104#882—61no—
105#67⋊C4—61no—
106C3×C22⋊C8—21no—
107C3×C22⋊C8—31no—
108C3×C22⋊C8—61no—
109C3×C22⋊C8C2×D311yescharacteristic
110C3×C22⋊C8C2×D311yescharacteristic
111C3×#95—31no—
112C3⋊#95—31no—
113C3⋊#95—31no—
114C3⋊#95—61no—
115C3⋊#95C2×D311yescharacteristic
116#830C2×D311yescharacteristic
117(C2×D3)⋊C8—21no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3C22⋊C411yescharacteristic
125C22×C3×D3C22⋊C411yescharacteristic
126C2×C32×C4—41no—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129#638—41no—
130#638—41no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C4⋊(C3⋊D3)—41no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3C22⋊C411yescharacteristic
143C2×C3×Dic3C22⋊C411yescharacteristic
144C3×C4×D3—22no—
145C3×C4×D3—22no—
146C3×C4×D3—41no—
147C3×C4×D3—41no—
148C3×Dic6—41no—
149#626—42no—
150#626—42no—
151#624—42no—
152C32×C8—41no—
153C3×C3⋊C8—41no—
154#525—91no—
155#407—31no—
156#380—91no—
157#328—31no—
158#328—91no—
159#327—91no—
160#327—91no—
161C24×C3—31no—
162C23×D3D1211yescharacteristic
163C2×C3×Q8—31no—
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—61no—
171C22×C3×C4—122no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C2×#67—61no—
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—61no—
178C2×#67—121no—
179C22×Dic3—21no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—121no—
183C22×Dic3D1211yescharacteristic
184#239—122no—
185#235—122no—
186C2×D12—31no—
187C2×D12—31no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×C4×D3—42no—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×C4×D3C4×D311yescharacteristic
195C2×C4×D3C4×D311yescharacteristic
196C2×C4×D3#6711yescharacteristic
197C2×C4×D3#6711yescharacteristic
198C2×Dic6C4×D311yescharacteristic
199C3×M16—122no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C2×C3×C8—41no—
203C2×C3×C8—61no—
204C3×C4⋊C4—31no—
205C3×C4⋊C4—61no—
206C3×C22⋊C4—61no—
207#217—21no—
208#217—61no—
209#217—61no—
210#217—122no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—121no—
218(C2×D3)⋊C4—122no—
219C4⋊Dic3—31no—
220C4⋊Dic3—31no—
221C4⋊Dic3—61no—
222C4⋊Dic3—122no—
223C4⋊Dic3C4×D311yescharacteristic
224Dic3⋊C4—21no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227Dic3⋊C4—122no—
228C4×Dic3—61no—
229C4×Dic3—61no—
230C2×C3⋊C8—21no—
231ΓL(1,𝔽25)—42no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32C2×C22⋊C411yescharacteristic
235C22×C32AGL(1,ℤ/8)11yescharacteristic
236C22×C32#13711yescharacteristic
237C2×C3⋊D3—41no—
238C2×C3⋊D3—41no—
239C2×C3⋊D3—41no—
240C2×C3×D3—21no—
241C2×C3×D3—21no—
242C2×C3×D3—21no—
243C2×C3×D3—21no—
244C2×C3×D3—21no—
245C2×C3×D3—21no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C32×C4—21no—
249C32×C4—21no—
250C3⋊Dic3—41no—
251C3⋊Dic3—81no—
252C3×Dic3—21no—
253C3×Dic3—41no—
254C3×Dic3—41no—
255C3×Dic3—81no—
256C3×Dic3#9912yes—
257C2×#41—91no—
258C23×C4—31no—
259C2×M16—61no—
260#123—181no—
261C22⋊Q8—31no—
262C22⋊Q8—91no—
263#121—91no—
264#121—91no—
265#120—181no—
266C4×D4—181no—
267C4×D4—181no—
268#117—91no—
269C2×C4⋊C4—181no—
270C2×C22⋊C4—181no—
271C22⋊C8—31no—
272C22⋊C8—61no—
273C22⋊C8D3211yescharacteristic
274#95—31no—
275#95—91no—
276C23×C3—21no—
277C23×C3—31no—
278C23×C3—31no—
279C23×C3—61no—
280C23×C3—61no—
281C23×C3—121no—
282C23×C3—121no—
283C23×C3C2×D1211yescharacteristic
284C23×C3D3×D411yescharacteristic
285C22×D3—21no—
286C22×D3—21no—
287C22×D3—41no—
288C22×D3—41no—
289C22×D3—61no—
290C22×D3—61no—
291C22×D3—121no—
292C22×D3(C2×D3)⋊C411yescharacteristic
293C22×D3(C2×D3)⋊C411yescharacteristic
294C3×Q8—121no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—31no—
298C2×C3×C4—31no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—81no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316#67—122no—
317#67—122no—
318#67—121no—
319#67—121no—
320#67—121no—
321#67—121no—
322#67—241no—
323#67—241no—
324C2×Dic3—22no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—122no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340C2×Dic3—241no—
341C2×Dic3—241no—
342C2×Dic3(C2×D3)⋊C411yescharacteristic
343C2×Dic3(C2×D3)⋊C411yescharacteristic
344D12—121no—
345D12—121no—
346D12—122no—
347D12—122no—
348D12—241no—
349C4×D3—22no—
350C4×D3—22no—
351C4×D3—41no—
352C4×D3—41no—
353C4×D3—122no—
354C4×D3—122no—
355Dic6—41no—
356C3×C8—41no—
357C3×C8—41no—
358C3×C8—81no—
359C3×C8—121no—
360C3⋊C8—41no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32C2×#9911yescharacteristic
364C2×C32#41711yescharacteristic
365C2×C32#42111yescharacteristic
366C3⋊D3—81no—
367C3×D3—41no—
368C3×D3—41no—
369C24—31no—
370#41—362no—
371C2×Q8—31no—
372C2×D4—91no—
373C2×D4—181no—
374C2×D4—181no—
375C2×D4—181no—
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—61no—
382C22×C4—122no—
383C22×C4—181no—
384C22×C4—181no—
385C22×C4C2×D3211yescharacteristic
386M16—122no—
387C2×C8—21no—
388C2×C8—61no—
389C4⋊C4—31no—
390C4⋊C4—61no—
391C4⋊C4—91no—
392C4⋊C4—181no—
393C4⋊C4—362no—
394C22⋊C4—61no—
395C22⋊C4—181no—
396C22⋊C4—181no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—362no—
400C42—181no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—61no—
411C22×C3—61no—
412C22×C3—61no—
413C22×C3—61no—
414C22×C3—61no—
415C22×C3—61no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3D3×C22⋊C411yescharacteristic
419C22×C3#90811yescharacteristic
420C22×C3#90911yescharacteristic
421C22×C3#91411yescharacteristic
422C22×C3#91811yescharacteristic
423C22×C3C2×(C2×D3)⋊C411yescharacteristic
424C2×D3—21no—
425C2×D3—21no—
426C2×D3—21no—
427C2×D3—21no—
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—121no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—241no—
439C2×D3—241no—
440C2×D3—241no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—32no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—61no—
449C3×C4—121no—
450C3×C4—121no—
451C3×C4—241no—
452Dic3—21no—
453Dic3—41no—
454Dic3—41no—
455Dic3—81no—
456Dic3—121no—
457Dic3—121no—
458Dic3—241no—
459Dic3—241no—
460Dic3—241no—
461Dic3—242no—
462Dic3#80612yes—
463C32#151311yescharacteristic, complemented, Sylow
464C23—31no—
465C23—31no—
466C23—61no—
467C23—61no—
468C23—121no—
469C23—121no—
470C23—181no—
471C23D3×D1211yescharacteristic
472Q8—121no—
473D4—361no—
474D4—362no—
475D4—362no—
476D4—361no—
477D4—361no—
478C2×C4—31no—
479C2×C4—31no—
480C2×C4—41no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—181no—
492C2×C4—362no—
493C2×C4—361no—
494C2×C4—361no—
495C2×C4—361no—
496C2×C4C4×D3211yescharacteristic
497C2×C4D3×#6711yescharacteristic
498C8—41no—
499C8—121no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—41no—
508C2×C3—41no—
509C2×C3—121no—
510C2×C3—121no—
511C2×C3D3×#9911yescharacteristic
512C2×C3#480311yescharacteristic
513C2×C3#482111yescharacteristic
514C2×C3C2×#80611yescharacteristic
515C2×C3#513311yescharacteristic
516C2×C3#513911yescharacteristic
517D3—41no—
518D3—41no—
519D3—241no—
520D3—241no—
521D3—481no—
522C22—21no—
523C22—21no—
524C22—61no—
525C22—61no—
526C22—61no—
527C22—61no—
528C22—61no—
529C22—61no—
530C22—122no—
531C22—122no—
532C22—361no—
533C22—361no—
534C22—361no—
535C22#6379411yescharacteristic
536C22#6380111yescharacteristic
537C22D3×(C2×D3)⋊C411yescharacteristic
538C4—21no—
539C4—21no—
540C4—32no—
541C4—61no—
542C4—121no—
543C4—121no—
544C4—241no—
545C4—361no—
546C4—721no—
547C3—21no—
548C3#6833711yescharacteristic, complemented
549C3#6997911yescharacteristic, complemented
550C2—21no—
551C2—21no—
552C2—121no—
553C2—121no—
554C2—721no—
555C2D3×#80611yescharacteristic
556C2#1059067111yescharacteristic
557C2#1059100511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10595005C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1513
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4726C2semidirect
3. #10591295C2semidirect
4. #10589336C2semidirect
5. C3×#4467C2semidirect
6. #10589152C2semidirect
7. #10589151C2semidirect
11. C2×#3799C4semidirect
19. #63909C4semidirect
21. #63856C4semidirect
23. #63841C4semidirect
33. #4726D3semidirect
42. #4467D3semidirect
463. C32#1513semidirect
548. C3#68337semidirect
549. C3#69979semidirect

Maximal subgroups

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

subgroupindex
#105950052
C3×#47262
#105912952
#105893362
C3×#44672
#105891522
#105891512
#699793
#683373