Finite Group Databasebeta

← #11858355

Subgroups — #11858355

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C2×#63817C212yesmaximal
3C3×#4924C211yesmaximal, characteristic, complemented
4C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5#10591119C212yesmaximal, complemented
6#10590340C212yesmaximal, complemented
7#10590332C214yesmaximal, complemented
8#10590331C212yesmaximal, complemented
9#79049—31nomaximal
10#79012—31nomaximal
11C2×#3828C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C4×#638C412yes—
14C4×#638C412yes—
15#64135C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C411yescharacteristic
17C4×C4⋊(C3⋊D3)C411yescharacteristic
18#64081C2212yes—
19C42×C3⋊D3C2212yes—
20C4×#634C411yescharacteristic
21C4×#634C411yescharacteristic
22C2×C3×#208C2212yes—
23C22×C3×C3⋊C8C2212yes—
24C2×#3712C2214yes—
25#63817—28no—
26C2×#3710C2214yes—
27C3×C4⋊(C3⋊C8)C2211yescharacteristic
28C3×C4⋊(C3⋊C8)C2212yes—
29C3×C4⋊(C3⋊C8)C2211yescharacteristic
30C3×C4⋊(C3⋊C8)C2212yes—
31C3×C4⋊(C3⋊C8)C2212yes—
32#63572C2214yes—
33#63572C2214yes—
34C2×#907—32no—
35C2×#901—32no—
36C4×#235—31no—
37C4×#235—31no—
38C4×#235—61no—
39C3×#423—31no—
40C2×C3×C4⋊C8—31no—
41#5119—32no—
42#5102—32no—
43#4924D311yescharacteristic, complemented
44C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
45#4839—34no—
46#4839—34no—
47#4837—32no—
48#4837—32no—
49D3×C4⋊C8—32no—
50D3×C4⋊C8—32no—
51C22×C32×C4C2×C411yescharacteristic
52C22×C32×C4C2×C411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C2×#638C2×C412yes—
55#3828D414yes—
56#3828Q814yes—
57C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
58C2×C4×C3⋊D3C2×C412yes—
59C2×C4×C3⋊D3C2×C412yes—
60C2×C4×C3⋊D3C2312yes—
61C2×#634C2×C411yescharacteristic
62C32×C42C2×C411yescharacteristic
63C32×C42C2×C411yescharacteristic
64C32×C42C2311yescharacteristic
65C32×C42C2311yescharacteristic
66#3757C2×C412yes—
67#3752C2×C412yes—
68#3752C2×C412yes—
69C4⋊(C3⋊Dic3)C2×C411yescharacteristic
70C4⋊(C3⋊Dic3)C2×C411yescharacteristic
71#3750C2×C412yes—
72#3750C2×C412yes—
73C4×C3⋊Dic3C2×C412yes—
74C4×C3⋊Dic3C2×C412yes—
75C4×C3⋊Dic3C2312yes—
76C3×#208—24no—
77C2×C3×C3⋊C8—24no—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2314yes—
81#3712—28no—
82#3710—28no—
83#2906—91noSylow
84C2×#235—31no—
85C2×#235—31no—
86C2×#235—61no—
87C2×C3×M16—32no—
88C22×C3×C8—32no—
89C2×C3×C42—21no—
90C2×C3×C42C2×D311yescharacteristic
91C2×C3×C42C2×D311yescharacteristic
92C4×#67—32no—
93C4×#67—32no—
94C4×#67—32no—
95C4×#67—32no—
96C4×#67—62no—
97C4×#67—62no—
98#926—31no—
99#926—31no—
100#926—61no—
101C2×#208C2×D312yes—
102C22×C3⋊C8C2×D312yes—
103#907—68no—
104#901—68no—
105C2×ΓL(1,𝔽25)—34no—
106C2×ΓL(1,𝔽25)—34no—
107C2×D3×C8—34no—
108C2×D3×C8—34no—
109C4×D12—31no—
110C4×D12—31no—
111C4×D12—31no—
112C4×D12—31no—
113C4×D12—61no—
114C4×D12—61no—
115#872—32no—
116#872—32no—
117#872—62no—
118C42×D3—32no—
119C42×D3—32no—
120C42×D3—62no—
121C4×Dic6—31no—
122C4×Dic6—31no—
123C4×Dic6—31no—
124C4×Dic6—31no—
125C4×Dic6—61no—
126C4×Dic6—61no—
127C3×C4⋊C8—31no—
128C3×C4⋊C8—31no—
129C3×C4⋊C8—32no—
130C3×C4⋊C8—32no—
131C3×C4⋊C8—32no—
132Dic3⋊C8—34no—
133Dic3⋊C8—34no—
134Dic3⋊C8—34no—
135Dic3⋊C8—34no—
136C4⋊(C3⋊C8)C2×D311yescharacteristic
137C4⋊(C3⋊C8)C2×D311yescharacteristic
138C4⋊(C3⋊C8)C2×D312yes—
139C4⋊(C3⋊C8)C2×D312yes—
140C4⋊(C3⋊C8)C2×D312yes—
141C23×C32C22×C411yescharacteristic
142C22×C3⋊D3C22×C412yes—
143C2×C32×C4—22no—
144C2×C32×C4—41no—
145C2×C32×C4C22×C411yescharacteristic
146C2×C32×C4C22×C411yescharacteristic
147C2×C32×C4C22×C411yescharacteristic
148C2×C32×C4C22×C411yescharacteristic
149C2×C32×C4C22×C411yescharacteristic
150C2×C32×C4C2×D412yes—
151C2×C32×C4C2×Q812yes—
152C2×C32×C4C2411yescharacteristic
153#638C4⋊C418yes—
154C2×C3⋊Dic3C22×C412yes—
155C2×C3⋊Dic3C22×C412yes—
156C2×C3⋊Dic3C22×C412yes—
157C4⋊(C3⋊D3)C4⋊C414yes—
158C4×C3⋊D3—24no—
159C4×C3⋊D3—42no—
160C4×C3⋊D3C2×D414yes—
161C4×C3⋊D3C2×Q814yes—
162#634C4⋊C414yes—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—24no—
165C3×C3⋊C8—22no—
166C2×#131—92no—
167C4×#41—91no—
168#424—94no—
169#424—92no—
170#423—31no—
171#423—92no—
172C2×C4⋊C8—31no—
173C2×C4⋊C8—92no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4C4×D311yescharacteristic
178C22×C3×C4C4×D311yescharacteristic
179C22×C3×C4C4×D311yescharacteristic
180C22×C3×C4C4×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—32no—
184C2×#67—32no—
185C2×#67—62no—
186#235—34no—
187#235—34no—
188#235—34no—
189#235—34no—
190#235—64no—
191#235—64no—
192C2×D12—31no—
193C2×D12—31no—
194C2×D12—61no—
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—32no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×Dic6—31no—
205C2×Dic6—31no—
206C2×Dic6—61no—
207C3×M16—64no—
208C2×C3×C8—32no—
209C2×C3×C8—34no—
210C2×C3×C8—32no—
211C2×C3×C8—64no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42C4×D311yescharacteristic
217C3×C42C4×D311yescharacteristic
218C3×C42C4×D311yescharacteristic
219C3×C42C4×D311yescharacteristic
220C3×C42C22×D311yescharacteristic
221C3×C42C22×D311yescharacteristic
222C3×C42C22×D311yescharacteristic
223C3×C42C22×D311yescharacteristic
224#217—32no—
225#217—32no—
226#217—62no—
227(C2×D3)⋊C4—32no—
228(C2×D3)⋊C4—32no—
229(C2×D3)⋊C4—32no—
230(C2×D3)⋊C4—32no—
231(C2×D3)⋊C4—62no—
232(C2×D3)⋊C4—62no—
233C4⋊Dic3—31no—
234C4⋊Dic3—31no—
235C4⋊Dic3—31no—
236C4⋊Dic3—31no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239Dic3⋊C4—32no—
240Dic3⋊C4—32no—
241Dic3⋊C4—32no—
242Dic3⋊C4—32no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245C4×Dic3—32no—
246C4×Dic3—32no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—32no—
250C4×Dic3—32no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3—62no—
254#208—24no—
255C2×C3⋊C8—24no—
256C2×C3⋊C8C22×D312yes—
257C2×C3⋊C8C22×D314yes—
258C2×C3⋊C8C22×D312yes—
259ΓL(1,𝔽25)—68no—
260ΓL(1,𝔽25)—68no—
261D3×C8—68no—
262D3×C8—68no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32C2×C4⋊C412yes—
266C22×C32C23×C411yescharacteristic
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3C2×C4⋊C414yes—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4—21no—
273C32×C4C2×C4⋊C412yes—
274C32×C4#13112yescomplemented
275C32×C4C22×D411yescharacteristic
276C32×C4C22×Q811yescharacteristic
277C3⋊Dic3—22no—
278C3⋊Dic3—22no—
279C3⋊Dic3C2×C4⋊C414yes—
280C2×#41—91no—
281#131—188no—
282C2×M16—32no—
283C2×M16—94no—
284C22×C8—32no—
285C22×C8—94no—
286C4×Q8—91no—
287C4×Q8—91no—
288C4×D4—92no—
289C4×D4—92no—
290C4×D4—91no—
291C4×D4—91no—
292#117—91no—
293#117—92no—
294C2×C42—92no—
295C2×C42D3211yescharacteristic
296C4⋊C8—31no—
297C4⋊C8—31no—
298C4⋊C8—32no—
299C4⋊C8—32no—
300C4⋊C8—32no—
301C4⋊C8—94no—
302C4⋊C8—94no—
303C23×C3—21no—
304C23×C3C2×C4×D311yescharacteristic
305C23×C3C2×C4×D311yescharacteristic
306C22×D3—32no—
307C22×D3—32no—
308C22×D3—62no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—42no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—42no—
323C2×C3×C4C2×C4×D311yescharacteristic
324C2×C3×C4C2×C4×D311yescharacteristic
325C2×C3×C4C2×C4×D311yescharacteristic
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C2×C4×D311yescharacteristic
333C2×C3×C4D3×D412yes—
334C2×C3×C4D3×D412yes—
335C2×C3×C4D3×Q812yes—
336C2×C3×C4D3×Q812yes—
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339#67—38no—
340#67—38no—
341#67—68no—
342C2×Dic3—32no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—32no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351D12—34no—
352D12—34no—
353D12—64no—
354C4×D3—34no—
355C4×D3—34no—
356C4×D3—34no—
357C4×D3—34no—
358C4×D3—64no—
359C4×D3—64no—
360C4×D3—64no—
361C4×D3—64no—
362C4×D3—124no—
363C4×D3—122no—
364C4×D3—122no—
365C4×D3—124no—
366Dic6—34no—
367Dic6—34no—
368Dic6—64no—
369C3×C8—62no—
370C3×C8—64no—
371C3×C8—62no—
372C3⋊C8—22no—
373C3⋊C8—24no—
374C3⋊C8—22no—
375C2×C32—22no—
376C2×C32C22×C4⋊C411yescharacteristic
377C2×C32C2×#13111yescharacteristic
378C2×C32#56811yescharacteristic
379C3⋊D3—24no—
380#41—94no—
381#41—94no—
382C2×Q8—91no—
383C2×D4—92no—
384C2×D4—91no—
385C22×C4—92no—
386C22×C4—92no—
387C22×C4—92no—
388C22×C4#62411yescharacteristic
389C22×C4#62411yescharacteristic
390C22×C4C2×D3211yescharacteristic
391M16—64no—
392M16—188no—
393C2×C8—32no—
394C2×C8—32no—
395C2×C8—34no—
396C2×C8—64no—
397C2×C8—188no—
398C4⋊C4—92no—
399C4⋊C4—92no—
400C4⋊C4—91no—
401C4⋊C4—91no—
402C22⋊C4—92no—
403C22⋊C4—92no—
404C22⋊C4—92no—
405C42—92no—
406C42—92no—
407C42—92no—
408C42#62411yescharacteristic
409C42#62411yescharacteristic
410C42C2×D3211yescharacteristic
411C42C2×D3211yescharacteristic
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—22no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3D3×C4⋊C412yes—
421C22×C3D3×C4⋊C412yes—
422C22×C3C22×C4×D311yescharacteristic
423C22×C3C22×C4×D311yescharacteristic
424C2×D3—34no—
425C2×D3—34no—
426C2×D3—64no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—62no—
431C2×D3—122no—
432C2×D3—122no—
433C3×C4—22no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4D3×C4⋊C412yes—
447C3×C4D3×C4⋊C412yes—
448C3×C4#90112yescomplemented
449C3×C4#90712yescomplemented
450C3×C4C2×D3×D411yescharacteristic
451C3×C4C2×D3×D411yescharacteristic
452C3×C4C2×D3×Q811yescharacteristic
453C3×C4C2×D3×Q811yescharacteristic
454Dic3—34no—
455Dic3—34no—
456Dic3—64no—
457Dic3—62no—
458Dic3—62no—
459Dic3—62no—
460Dic3—62no—
461Dic3—122no—
462Dic3—122no—
463C32#290611yescharacteristic, complemented, Sylow
464C23—92no—
465C23C2×#62411yescharacteristic
466Q8—94no—
467D4—98no—
468D4—94no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—92no—
472C2×C4—94no—
473C2×C4—94no—
474C2×C4—92no—
475C2×C4—92no—
476C2×C4—184no—
477C2×C4—362no—
478C2×C4#379712yes—
479C2×C4#380212yes—
480C2×C4C2×#62411yescharacteristic
481C2×C4C2×#62411yescharacteristic
482C2×C4C2×#62411yescharacteristic
483C2×C4C2×#62411yescharacteristic
484C2×C4C2×#62411yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—62no—
487C8—62no—
488C8—64no—
489C2×C3—22no—
490C2×C3—22no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—42no—
495C2×C3C2×D3×C4⋊C411yescharacteristic
496C2×C3C2×D3×C4⋊C411yescharacteristic
497C2×C3C2×#90111yescharacteristic
498C2×C3C2×#90711yescharacteristic
499C2×C3#574511yescharacteristic
500C2×C3#574511yescharacteristic
501D3—64no—
502D3—64no—
503D3—124no—
504C22—21no—
505C22—21no—
506C22—94no—
507C22—182no—
508C22—182no—
509C22#6390012yes—
510C22C22×#62411yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—94no—
515C4—182no—
516C4—182no—
517C4#6381712yescomplemented
518C4#6390012yes—
519C4C2×#379711yescharacteristic
520C4C2×#380211yescharacteristic
521C3—21no—
522C3#7901211yescharacteristic, complemented
523C3#7904911yescharacteristic, complemented
524C2—22no—
525C2—184no—
526C2C2×#6381711yescharacteristic
527C2#1059478011yescharacteristic
528C2C2×#6390011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×C42C22
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32#2906
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×#4924C2semidirect
4. C2×C3×C4⋊(C3⋊C8)C2semidirect
5. #10591119C2semidirect
6. #10590340C2semidirect
7. #10590332C2semidirect
8. #10590331C2semidirect
43. #4924D3semidirect
44. C2×C4⋊(C3⋊C8)D3semidirect
274. C32×C4#131semidirect
448. C3×C4#901semidirect
449. C3×C4#907semidirect
463. C32#2906semidirect
517. C4#63817semidirect
522. C3#79012semidirect
523. C3#79049semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C2×#638172
C3×#49242
C2×C3×C4⋊(C3⋊C8)2
#105911192
#105903402
#105903322
#105903312
#790493
#790123