Finite Group Databasebeta

← #11861343

Subgroups — #11861343

Order 1152.

791 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593882C211yesmaximal, characteristic
2#10592536C211yesmaximal, characteristic
3C3×#4831C211yesmaximal, characteristic, complemented
4C3×#4830C211yesmaximal, characteristic, complemented
5#10590910C212yesmaximal
6#10590789C212yesmaximal, complemented
7#10590702C212yesmaximal
8#10590644C212yesmaximal, complemented
9C4×#3710C211yesmaximal, characteristic
10#10590258C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#79958—31nomaximal
13#79917—31nomaximal
14C2×#3743C2212yes—
15C42×C3⋊D3C2211yescharacteristic
16C3×C4×Dic6C2211yescharacteristic
17C3×C4×Dic6C2211yescharacteristic
18#63919C411yescharacteristic
19C4×#627C2212yes—
20#63874C2212yes—
21#63873C411yescharacteristic
22#63871C411yescharacteristic
23#63871C411yescharacteristic
24#63870C412yes—
25#63865C412yes—
26C2×#3710C2211yescharacteristic
27C2×#3710C2211yescharacteristic
28C32×C4⋊C8C2211yescharacteristic
29#63641C2212yes—
30C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
31C3×#815C2212yes—
32C3×Dic3⋊C8C2212yes—
33C3×Dic3⋊C8C2212yes—
34C3×C8×Dic3C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37Dic3⋊(C3⋊C8)C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63554C2212yes—
40#63553C2211yescharacteristic
41#63553C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43#5578—31no—
44#5578—31no—
45C3×#446—31no—
46C3×C8×Q8—31no—
47#5024—31no—
48Q8×C3⋊C8—31no—
49#4839—32no—
50#4839—32no—
51#4837—31no—
52#4837—31no—
53#4837—61no—
54#4831D311yescharacteristic, complemented
55#4830—32no—
56#4830D311yescharacteristic, complemented
57#4828—32no—
58#4708—32no—
59#4701—32no—
60#4689—32no—
61C4×D3×C8—31no—
62C4×D3×C8—31no—
63#4679—31no—
64C8×Dic6—31no—
65C8×Dic6—32no—
66C2×C4×C3⋊D3C2×C411yescharacteristic
67C2×C4×C3⋊D3C2×C411yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C3×Dic6C2×C411yescharacteristic
70C2×C3×Dic6C2×C411yescharacteristic
71C2×#627C2×C412yes—
72C2×C32×C8C2312yes—
73C32×C42C2311yescharacteristic
74C4×C3⋊Dic3C2×C411yescharacteristic
75C4×C3⋊Dic3C2×C411yescharacteristic
76C4×C3⋊Dic3C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2312yes—
78#3743—24no—
79C3×C4⋊Dic3C2×C411yescharacteristic
80C3×C4⋊Dic3C2×C411yescharacteristic
81C3×Dic3⋊C4C2×C412yes—
82C3×Dic3⋊C4C2×C412yes—
83C3×C4×Dic3C2312yes—
84C3×C4×Dic3C2312yes—
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89#3724C2×C412yes—
90#3724C2×C412yes—
91#3724C2×C412yes—
92Dic3⋊Dic3C2×C412yes—
93Dic3⋊Dic3C2×C412yes—
94#3722C2×C412yes—
95#3722C2×C412yes—
96#3710—22no—
97#3710Q814yescomplemented
98#2960—91noSylow
99C3×C4×Q8—31no—
100C3×C4×Q8—31no—
101#946—31no—
102#946—31no—
103#944—31no—
104#944—31no—
105C2×ΓL(1,𝔽25)—32no—
106C2×ΓL(1,𝔽25)—32no—
107C2×ΓL(1,𝔽25)—62no—
108C2×D3×C8—31no—
109C2×D3×C8—31no—
110C2×D3×C8—31no—
111C2×D3×C8—31no—
112#897—31no—
113#897—31no—
114#896—32no—
115#896—32no—
116#889—32no—
117#889—32no—
118#888—31no—
119#888—31no—
120#872—32no—
121#872—32no—
122C42×D3—31no—
123C42×D3—31no—
124C42×D3—61no—
125C4×Dic6—32no—
126C4×Dic6—32no—
127C4×Dic6C2×D311yescharacteristic
128C4×Dic6C2×D311yescharacteristic
129C3×C4⋊C8—21no—
130C3×C4⋊C8—32no—
131C3×C4⋊C8—32no—
132C3×C4⋊C8C2×D311yescharacteristic
133C3×C4⋊C8C2×D311yescharacteristic
134C3×#97—32no—
135C3×C4×C8—32no—
136C3×C4×C8—31no—
137C3×C4×C8—31no—
138#815—32no—
139#815C2×D312yes—
140Dic3⋊C8—32no—
141Dic3⋊C8—32no—
142Dic3⋊C8—32no—
143Dic3⋊C8—32no—
144Dic3⋊C8—62no—
145Dic3⋊C8C2×D312yes—
146Dic3⋊C8C2×D312yes—
147C8×Dic3—32no—
148C8×Dic3—31no—
149C8×Dic3—31no—
150C8×Dic3—31no—
151C8×Dic3—31no—
152C8×Dic3C2×D312yes—
153C4⋊(C3⋊C8)—31no—
154C4⋊(C3⋊C8)—31no—
155C4⋊(C3⋊C8)—32no—
156C4⋊(C3⋊C8)—32no—
157C4⋊(C3⋊C8)—61no—
158#803—32no—
159C4×C3⋊C8—32no—
160C4×C3⋊C8C2×D311yescharacteristic
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3⋊D3C22×C411yescharacteristic
163C2×C32×C4C22×C411yescharacteristic
164C2×C32×C4C22×C411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3C22×C411yescharacteristic
167C2×C3⋊Dic3C22×C411yescharacteristic
168C2×C3⋊Dic3C22×C411yescharacteristic
169C4×C3⋊D3—22no—
170C4×C3⋊D3—22no—
171C4×C3⋊D3C2×Q812yes—
172C4×C3⋊D3#4112yes—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C2×C3×Dic3C22×C412yes—
177C3×Dic6—22no—
178C3×Dic6—22no—
179#627—24no—
180C32×C8—22no—
181C3⋊(C3⋊C8)—22no—
182C3×C3⋊C8—21no—
183C3×C3⋊C8—21no—
184C3×C3⋊C8C2×Q812yes—
185C3×C3⋊C8C2×Q812yes—
186#533—91no—
187#446—31no—
188#446—91no—
189#446—92no—
190C8×Q8—31no—
191C8×Q8—92no—
192C8×Q8—91no—
193#424—92no—
194#423—91no—
195#405—92no—
196C2×C4×C8—91no—
197C2×C3×Q8—31no—
198C2×C3×Q8—31no—
199C2×C4×D3—31no—
200C2×C4×D3—31no—
201C2×C4×D3—31no—
202C2×C4×D3—31no—
203C2×C4×D3—31no—
204C2×C4×D3—31no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×Dic6—32no—
209C2×Dic6—32no—
210C2×Dic6C4×D311yescharacteristic
211C2×Dic6C4×D311yescharacteristic
212C2×C3×C8—22no—
213C2×C3×C8—31no—
214C2×C3×C8—31no—
215C2×C3×C8—31no—
216C2×C3×C8—31no—
217C2×C3×C8C22×D312yes—
218C2×C3×C8C22×D312yes—
219C3×C4⋊C4—31no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—32no—
223C3×C42—21no—
224C3×C42—32no—
225C3×C42—32no—
226C3×C42C22×D311yescharacteristic
227C3×C42C22×D311yescharacteristic
228(C2×D3)⋊C4—32no—
229(C2×D3)⋊C4—32no—
230(C2×D3)⋊C4—32no—
231(C2×D3)⋊C4—32no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3C4×D311yescharacteristic
235C4⋊Dic3C4×D311yescharacteristic
236Dic3⋊C4—32no—
237Dic3⋊C4—32no—
238Dic3⋊C4—32no—
239Dic3⋊C4—32no—
240Dic3⋊C4—32no—
241Dic3⋊C4—32no—
242Dic3⋊C4—32no—
243Dic3⋊C4—32no—
244Dic3⋊C4C4×D312yes—
245Dic3⋊C4C4×D312yes—
246C4×Dic3—31no—
247C4×Dic3—31no—
248C4×Dic3—31no—
249C4×Dic3—31no—
250C4×Dic3—31no—
251C4×Dic3—31no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3C22×D312yes—
256C4×Dic3C22×D312yes—
257C2×C3⋊C8—32no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—62no—
260C2×C3⋊C8C22×D311yescharacteristic
261C2×C3⋊C8C22×D311yescharacteristic
262C2×C3⋊C8C22×D311yescharacteristic
263C2×C3⋊C8C22×D311yescharacteristic
264ΓL(1,𝔽25)—64no—
265ΓL(1,𝔽25)—64no—
266ΓL(1,𝔽25)—124no—
267D3×C8—34no—
268D3×C8—34no—
269D3×C8—62no—
270D3×C8—62no—
271C22×C32C23×C411yescharacteristic
272C2×C3⋊D3—21no—
273C2×C3⋊D3—21no—
274C2×C3⋊D3C4×Q812yes—
275C32×C4—21no—
276C32×C4#13112yes—
277C32×C4C22×Q811yescharacteristic
278C32×C4C2×#4111yescharacteristic
279C3⋊Dic3—21no—
280C3⋊Dic3C4×Q812yes—
281C3⋊Dic3#13112yes—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C2×M16—92no—
287C22×C8—91no—
288C22×C8—91no—
289C4⋊Q8—91no—
290C4⋊Q8—91no—
291#125—92no—
292C22⋊Q8—92no—
293C22⋊Q8—91no—
294C22⋊Q8—91no—
295C4×Q8—31no—
296C4×Q8—31no—
297C4×Q8—92no—
298#117—92no—
299C2×C42—91no—
300C4⋊C8—32no—
301C4⋊C8—32no—
302C4⋊C8—92no—
303C4⋊C8—92no—
304C4⋊C8—92no—
305C4⋊C8—91no—
306C4⋊C8D3211yescharacteristic
307#97—32no—
308#97—92no—
309C4×C8—32no—
310C4×C8—31no—
311C4×C8—31no—
312C4×C8—92no—
313C4×C8—91no—
314C4×C8—91no—
315C22×D3—31no—
316C22×D3—31no—
317C22×D3—61no—
318C3×Q8—62no—
319C3×Q8—62no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—32no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×Dic3—31no—
334C2×Dic3—31no—
335C2×Dic3—31no—
336C2×Dic3—31no—
337C2×Dic3—31no—
338C2×Dic3—31no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3C2×C4×D312yes—
343C2×Dic3C2×C4×D312yes—
344C2×Dic3C2×C4×D312yes—
345C2×Dic3C2×C4×D312yes—
346C4×D3—32no—
347C4×D3—32no—
348C4×D3—32no—
349C4×D3—32no—
350C4×D3—62no—
351C4×D3—62no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—62no—
355C4×D3—62no—
356C4×D3—122no—
357C4×D3—122no—
358Dic6—22no—
359Dic6—22no—
360Dic6—64no—
361Dic6—64no—
362C3×C8—22no—
363C3×C8—22no—
364C3×C8—32no—
365C3×C8—32no—
366C3×C8—42no—
367C3×C8—61no—
368C3×C8—61no—
369C3⋊C8—21no—
370C3⋊C8—21no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C3⋊C8—122no—
374C3⋊C8D3×Q812yes—
375C3⋊C8D3×Q812yes—
376C2×C32C2×C4×Q811yescharacteristic
377C2×C32C2×#13111yescharacteristic
378C2×C32C2×#13111yescharacteristic
379C3⋊D3—22no—
380C2×Q8—31no—
381C2×Q8—31no—
382C2×Q8—92no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—91no—
386M16—184no—
387C2×C8—31no—
388C2×C8—31no—
389C2×C8—31no—
390C2×C8—31no—
391C2×C8—94no—
392C2×C8—92no—
393C2×C8—182no—
394C2×C8C2×D3212yes—
395C4⋊C4—32no—
396C4⋊C4—32no—
397C4⋊C4—31no—
398C4⋊C4—31no—
399C4⋊C4—92no—
400C4⋊C4—92no—
401C4⋊C4—92no—
402C4⋊C4—92no—
403C4⋊C4—92no—
404C22⋊C4—92no—
405C22⋊C4—92no—
406C42—32no—
407C42—32no—
408C42—91no—
409C42—91no—
410C42—91no—
411C42C2×D3211yescharacteristic
412C22×C3—21no—
413C22×C3C22×C4×D311yescharacteristic
414C22×C3C22×C4×D311yescharacteristic
415C2×D3—32no—
416C2×D3—32no—
417C2×D3—62no—
418C2×D3—61no—
419C2×D3—61no—
420C2×D3—61no—
421C2×D3—61no—
422C2×D3—121no—
423C2×D3—121no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—22no—
428C3×C4—21no—
429C3×C4—41no—
430C3×C4—62no—
431C3×C4—62no—
432C3×C4—62no—
433C3×C4—62no—
434C3×C4#90112yes—
435C3×C4#90712yes—
436C3×C4C2×D3×Q811yescharacteristic
437C3×C4C2×D3×Q811yescharacteristic
438C3×C4D3×#4111yescharacteristic
439C3×C4D3×#4111yescharacteristic
440Dic3—22no—
441Dic3—22no—
442Dic3—22no—
443Dic3—22no—
444Dic3—32no—
445Dic3—32no—
446Dic3—32no—
447Dic3—32no—
448Dic3—62no—
449Dic3—62no—
450Dic3—61no—
451Dic3—61no—
452Dic3—121no—
453C32#296011yescharacteristic, complemented, Sylow
454C23—91no—
455Q8—62no—
456Q8—62no—
457Q8—184no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—32no—
461C2×C4—32no—
462C2×C4—91no—
463C2×C4—91no—
464C2×C4—92no—
465C2×C4—92no—
466C2×C4—91no—
467C2×C4—182no—
468C2×C4—182no—
469C2×C4C4×D3211yescharacteristic
470C2×C4C4×D3211yescharacteristic
471C2×C4C22×D3211yescharacteristic
472C8—22no—
473C8—32no—
474C8—32no—
475C8—61no—
476C8—61no—
477C8—182no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3C4×D3×Q811yescharacteristic
482C2×C3C4×D3×Q811yescharacteristic
483C2×C3C2×#90111yescharacteristic
484C2×C3C2×#90711yescharacteristic
485C2×C3D3×#13111yescharacteristic
486C2×C3D3×#13111yescharacteristic
487D3—62no—
488D3—62no—
489D3—122no—
490C22—92no—
491C22—181no—
492C22—181no—
493C22C2×C4×D3211yescharacteristic
494C4—21no—
495C4—62no—
496C4—62no—
497C4—62no—
498C4—62no—
499C4—92no—
500C4—92no—
501C4—181no—
502C4#6380412yes—
503C4#6431211yescharacteristic
504C4D32×Q811yescharacteristic
505C3—21no—
506C3#7991711yescharacteristic, complemented
507C3#7995811yescharacteristic, complemented
508C2—182no—
509C2#1059436311yescharacteristic
510C2C2×#6380411yescharacteristic
511C2#1059470711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32#2960
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. C3×#4831C2semidirect
4. C3×#4830C2semidirect
6. #10590789C2semidirect
8. #10590644C2semidirect
10. #10590258C2semidirect
11. C3⋊C8×Dic6C2semidirect
54. #4831D3semidirect
56. #4830D3semidirect
97. #3710Q8semidirect
453. C32#2960semidirect
506. C3#79917semidirect
507. C3#79958semidirect

Maximal subgroups

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

subgroupindex
#105938822
#105925362
C3×#48312
C3×#48302
#105909102
#105907892
#105907022
#105906442
C4×#37102
#105902582
C3⋊C8×Dic62
#799583
#799173