Finite Group Databasebeta

← #11775064

Subgroups — #11775064

Order 1152.

613 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594910C211yesmaximal, characteristic
2C3×#4718C211yesmaximal, characteristic, complemented
3#10591242C211yesmaximal, characteristic, complemented
4#10589336C211yesmaximal, characteristic, complemented
5C3×#4470C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#70789—31nomaximal
9#68277—31nomaximal
10C2×#3804—21no—
11#64139C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14#63978—21no—
15C2×Dic3⋊Dic3—21no—
16C2×Dic32—21no—
17#63918C411yescharacteristic, complemented
18#63911C411yescharacteristic, complemented
19#63894C411yescharacteristic, complemented
20Dic3×D12C411yescharacteristic, complemented
21#63880—21no—
22#63852—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63658C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×Dic3⋊C8—21no—
28C3×C8×Dic3—21no—
29#5596—31no—
30#5477—31no—
31C3×#431—31no—
32C4×C4⋊Dic3—31no—
33#4718D311yescharacteristic, complemented
34#4649—31no—
35C3×#327—31no—
36#4537—31no—
37#4470—31no—
38#4470—31no—
39#4470—31no—
40#4470—31no—
41#4470—61no—
42#4470D311yescharacteristic, complemented
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×D12C2×C411yescharacteristic
53C2×#627—21no—
54C2×#626—21no—
55C2×#626—21no—
56C2×#624—21no—
57#3804—42no—
58#3804—42no—
59C2×D3×Dic3—21no—
60C2×C32×C8—21no—
61#3752—21no—
62C4⋊(C3⋊Dic3)C2×C411yescharacteristic
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3C2×C411yescharacteristic
65C3×C4×Dic3C2×C411yescharacteristic
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70Dic3⋊Dic3—24no—
71Dic3⋊Dic3—21no—
72#3722—21no—
73(C2×D3)⋊Dic3—21no—
74Dic32—42no—
75#1502—91noSylow
76C2×#237—61no—
77C2×#235—61no—
78C3×#121—31no—
79C2×C3×C42—31no—
80#940—31no—
81#939—61no—
82D4×Dic3—31no—
83#930—31no—
84#930—31no—
85#930—61no—
86#930—61no—
87#930C2×D311yescharacteristic
88C2×C4⋊Dic3—61no—
89C2×Dic3⋊C4—61no—
90C2×C4×Dic3—61no—
91C2×C4×Dic3—61no—
92C2×C4×Dic3C2×D311yescharacteristic
93#893—31no—
94#888—31no—
95#885—61no—
96#67⋊C4—61no—
97#875—61no—
98#874—31no—
99C4×D12—31no—
100C4×D12—31no—
101C4×D12—61no—
102#869—31no—
103C3×C4⋊C8—61no—
104C3×C22⋊C8—21no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8C2×D311yescharacteristic
107C3×C22⋊C8C2×D311yescharacteristic
108C3×C4×C8—61no—
109C3×#95—31no—
110C3⋊#95—31no—
111C3⋊#95—31no—
112C3⋊#95—61no—
113C3⋊#95C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115Dic3⋊C8—21no—
116C8×Dic3—21no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3×D3—21no—
120C2×C32×C4—41no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123#638—41no—
124#638—41no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C4⋊(C3⋊D3)—41no—
130C3×#67—41no—
131C3×#67—41no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3C22⋊C411yescharacteristic
138C2×C3×Dic3C22⋊C411yescharacteristic
139C2×C3×Dic3C22⋊C411yescharacteristic
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3D812yes—
142C2×C3×Dic3SD1612yes—
143C3×D12—41no—
144#627—42no—
145#626—42no—
146#626—42no—
147#624—42no—
148D3×Dic3—42no—
149C32×C8—41no—
150C3×C3⋊C8—41no—
151#532—91no—
152#431—31no—
153C4×C4⋊C4—91no—
154#327—31no—
155#327—91no—
156#327—91no—
157#327—91no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C2×#67—21no—
167C2×#67—61no—
168C2×#67—61no—
169C2×#67—61no—
170C2×#67—61no—
171C2×#67—121no—
172C22×Dic3—21no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—121no—
177C22×Dic3D1211yescharacteristic
178C22×Dic3D1211yescharacteristic
179#237—122no—
180#237—122no—
181#235—122no—
182#235—122no—
183C2×D12—31no—
184C2×D12—31no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12C4×D311yescharacteristic
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×Dic6—61no—
193C2×Dic6—61no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—41no—
197C2×C3×C8—61no—
198C3×C4⋊C4—31no—
199C3×C22⋊C4—61no—
200C3×C42—31no—
201C3×C42—31no—
202C3×C42—31no—
203C3×C42—31no—
204#217—61no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—121no—
212C4⋊Dic3—31no—
213C4⋊Dic3—31no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4⋊Dic3—64no—
217C4⋊Dic3C4×D311yescharacteristic
218Dic3⋊C4—64no—
219Dic3⋊C4—61no—
220C4×Dic3—122no—
221C4×Dic3—122no—
222C4×Dic3C4×D311yescharacteristic
223C4×Dic3C4×D311yescharacteristic
224C4×Dic3#6711yescharacteristic
225C4×Dic3#6711yescharacteristic
226C2×C3⋊C8—21no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32C2×C22⋊C411yescharacteristic
230C22×C32C2×D811yescharacteristic
231C22×C32C2×SD1611yescharacteristic
232C2×C3⋊D3—41no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—41no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C32×C4—21no—
239C32×C4—21no—
240C3⋊Dic3—42no—
241C3⋊Dic3—41no—
242C3×Dic3—21no—
243C3×Dic3—42no—
244C3×Dic3—41no—
245C3×Dic3#10212yes—
246C3×Dic3#10212yes—
247C3×Dic3#10412yes—
248C2×#41—181no—
249C4⋊Q8—91no—
250#127—91no—
251#124—181no—
252#121—31no—
253#121—91no—
254#121—181no—
255C4×D4—91no—
256C4×D4—91no—
257C4×D4—181no—
258C2×C4⋊C4—181no—
259C2×C42—31no—
260C2×C42—181no—
261C4⋊C8—61no—
262C22⋊C8—31no—
263C22⋊C8D3211yescharacteristic
264C4×C8—61no—
265#95—31no—
266#95—91no—
267C23×C3—21no—
268C23×C3—61no—
269C23×C3C2×D1211yescharacteristic
270C23×C3D3×D411yescharacteristic
271C22×D3—21no—
272C22×D3—61no—
273C22×D3—61no—
274C22×D3—121no—
275C3×D4—121no—
276C3×D4—121no—
277C3×D4—121no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—31no—
281C2×C3×C4—31no—
282C2×C3×C4—31no—
283C2×C3×C4—32no—
284C2×C3×C4—32no—
285C2×C3×C4—31no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—61no—
291C2×C3×C4—81no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298#67—41no—
299#67—41no—
300#67—121no—
301#67—121no—
302#67—121no—
303#67—121no—
304#67—122no—
305#67—122no—
306#67—241no—
307#67—241no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—21no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—121no—
318C2×Dic3—122no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—122no—
324C2×Dic3—241no—
325C2×Dic3—241no—
326C2×Dic3#20412yes—
327C2×Dic3D2412yes—
328C2×Dic3(C2×D3)⋊C411yescharacteristic
329C2×Dic3(C2×D3)⋊C411yescharacteristic
330C2×Dic3(C2×D3)⋊C411yescharacteristic
331C2×Dic3(C2×D3)⋊C411yescharacteristic
332D12—41no—
333D12—121no—
334D12—121no—
335D12—122no—
336D12—122no—
337D12—241no—
338C4×D3—122no—
339C4×D3—122no—
340C4×D3—122no—
341Dic6—122no—
342Dic6—122no—
343C3×C8—41no—
344C3×C8—41no—
345C3×C8—81no—
346C3×C8—121no—
347C3⋊C8—41no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32#41011yescharacteristic
351C2×C32C2×#10211yescharacteristic
352C2×C32C2×#10411yescharacteristic
353C3⋊D3—81no—
354C3×D3—81no—
355#41—362no—
356#41—362no—
357C2×Q8—181no—
358C2×D4—31no—
359C2×D4—61no—
360C2×D4—91no—
361C2×D4—181no—
362C2×D4—181no—
363C2×D4—181no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—61no—
367C22×C4—181no—
368C22×C4—181no—
369C22×C4—181no—
370C22×C4C2×D3211yescharacteristic
371C2×C8—21no—
372C2×C8—61no—
373C4⋊C4—31no—
374C4⋊C4—91no—
375C4⋊C4—181no—
376C4⋊C4—184no—
377C22⋊C4—61no—
378C22⋊C4—181no—
379C22⋊C4—181no—
380C22⋊C4—181no—
381C42—31no—
382C42—31no—
383C42—31no—
384C42—31no—
385C42—362no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—121no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3D3×C22⋊C411yescharacteristic
399C22×C3C2×#20411yescharacteristic
400C22×C3C2×D2411yescharacteristic
401C22×C3D3×D811yescharacteristic
402C22×C3D3×SD1611yescharacteristic
403C22×C3C2×(C2×D3)⋊C411yescharacteristic
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—121no—
410C2×D3—121no—
411C2×D3—121no—
412C2×D3—121no—
413C2×D3—241no—
414C2×D3—241no—
415C2×D3—241no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—32no—
421C3×C4—32no—
422C3×C4—32no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—61no—
426C3×C4—122no—
427C3×C4—121no—
428Dic3—21no—
429Dic3—42no—
430Dic3—41no—
431Dic3—122no—
432Dic3—122no—
433Dic3—121no—
434Dic3—121no—
435Dic3—241no—
436Dic3—242no—
437Dic3#82112yes—
438Dic3#82112yes—
439Dic3#82512yes—
440C32#150211yescharacteristic, complemented, Sylow
441C23—61no—
442C23—181no—
443C23D3×D1211yescharacteristic
444Q8—362no—
445D4—121no—
446D4—121no—
447D4—121no—
448D4—361no—
449D4—362no—
450D4—362no—
451D4—361no—
452D4—361no—
453C2×C4—32no—
454C2×C4—32no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—41no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—61no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—182no—
466C2×C4—181no—
467C2×C4—362no—
468C2×C4—362no—
469C2×C4—361no—
470C2×C4—361no—
471C2×C4C4×D3211yescharacteristic
472C2×C4D3×#6711yescharacteristic
473C8—41no—
474C8—121no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—41no—
483C2×C3—41no—
484C2×C3—241no—
485C2×C3#474011yescharacteristic
486C2×C3D3×#10211yescharacteristic
487C2×C3D3×#10411yescharacteristic
488C2×C3#500611yescharacteristic
489C2×C3C2×#82111yescharacteristic
490C2×C3C2×#82511yescharacteristic
491D3—81no—
492D3—241no—
493D3—241no—
494D3—481no—
495C22—21no—
496C22—21no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22—361no—
501C22—361no—
502C22—361no—
503C22D3×#20411yescharacteristic
504C22D3×D2411yescharacteristic
505C22D3×(C2×D3)⋊C411yescharacteristic
506C4—21no—
507C4—21no—
508C4—32no—
509C4—32no—
510C4—32no—
511C4—61no—
512C4—122no—
513C4—121no—
514C4—362no—
515C4—361no—
516C3—21no—
517C3#6827711yescharacteristic, complemented
518C3#7078911yescharacteristic, complemented
519C2—21no—
520C2—21no—
521C2—241no—
522C2—721no—
523C2#1059040511yescharacteristic
524C2D3×#82111yescharacteristic
525C2D3×#82511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10594910C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1502
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×#4718C2semidirect
3. #10591242C2semidirect
4. #10589336C2semidirect
5. C3×#4470C2semidirect
6. #10589151C2semidirect
7. #10589150C2semidirect
17. #63918C4semidirect
18. #63911C4semidirect
19. #63894C4semidirect
20. Dic3×D12C4semidirect
33. #4718D3semidirect
42. #4470D3semidirect
440. C32#1502semidirect
517. C3#68277semidirect
518. C3#70789semidirect

Maximal subgroups

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

subgroupindex
#105949102
C3×#47182
#105912422
#105893362
C3×#44702
#105891512
#105891502
#707893
#682773