Finite Group Databasebeta

← #11786657

Subgroups — #11786657

Order 1152.

579 conjugacy classes of subgroups.

The subgroup lattice has 425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594780C211yesmaximal, characteristic
2#10592831C211yesmaximal, characteristic
3C3×#5125C211yesmaximal, characteristic, complemented
4#10591143C211yesmaximal, characteristic, complemented
5#10591073C211yesmaximal, characteristic
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70734—31nomaximal
9#68945—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×C3×#208C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63818—22no—
18#63817—22no—
19#63817—22no—
20#63651C412yes—
21#63650C412yes—
22C3×#819—22no—
23#63578—22no—
24#63557—22no—
25#5745—31no—
26#5745—31no—
27C3×#430—31no—
28#5132—31no—
29#5132—31no—
30#5132—61no—
31#5129—31no—
32#5125D311yescharacteristic, complemented
33#5124—31no—
34#5124—31no—
35#5110—31no—
36C3×#341—31no—
37#4558—31no—
38#4558D311yescharacteristic, complemented
39#4552—31no—
40C22×C32×C4C2311yescharacteristic
41C2×#638Q812yes—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
47C2×C4×C3⋊D3D412yes—
48C2×#634C2×C411yescharacteristic
49C32×M16—21no—
50C32×M16C2×C412yes—
51C2×C32×C8—21no—
52#3748—21no—
53#3748C2×C412yes—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208D412yes—
60C3×#208D412yes—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3712—24no—
68#3710—24no—
69#1858—91noSylow
70C2×#235—31no—
71C2×#235—31no—
72C2×#235—61no—
73C2×C3×M16—21no—
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C2×C3×M16—31no—
77C2×C3×M16C2×D311yescharacteristic
78C2×C3×M16C2×D311yescharacteristic
79C22×C3×C8—31no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8C2×D311yescharacteristic
87#907—62no—
88#907—62no—
89D3×M16—62no—
90D3×M16—62no—
91#901—62no—
92#901—62no—
93C3×#108—62no—
94#824—32no—
95#824—32no—
96#824—62no—
97#823—32no—
98#823—32no—
99#823—62no—
100#822—62no—
101#822—62no—
102(C2×D3)⋊C8—62no—
103(C2×D3)⋊C8—62no—
104#819—22no—
105C23×C32C2×Q811yescharacteristic
106C22×C3⋊D3C4⋊C412yes—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113#638—22no—
114#638—22no—
115C2×C3⋊Dic3C4⋊C412yes—
116C4⋊(C3⋊D3)—21no—
117C4⋊(C3⋊D3)—21no—
118C4×C3⋊D3—22no—
119C4×C3⋊D3—22no—
120#634—21no—
121#634—21no—
122C32×C8—22no—
123C3⋊(C3⋊C8)—22no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127C3×C3⋊C8—41no—
128#568—91no—
129#430—31no—
130#430—91no—
131#413—91no—
132#408—91no—
133#341—31no—
134#341—91no—
135C22×C3×C4—21no—
136C22×C3×C4C22×D311yescharacteristic
137C22×C3×C4C22×D311yescharacteristic
138C2×#67—32no—
139C2×#67—32no—
140C2×#67—62no—
141#235—61no—
142#235—61no—
143#235—61no—
144#235—61no—
145#235—61no—
146#235—61no—
147#235—61no—
148#235—61no—
149#235—121no—
150#235—121no—
151#235—121no—
152#235—121no—
153C2×D12—31no—
154C2×D12—31no—
155C2×D12—61no—
156C2×C4×D3—32no—
157C2×C4×D3—32no—
158C2×C4×D3—62no—
159C2×Dic6—31no—
160C2×Dic6—31no—
161C2×Dic6—61no—
162C3×M16—21no—
163C3×M16—21no—
164C3×M16—22no—
165C3×M16—32no—
166C3×M16—32no—
167C3×M16—41no—
168C3×M16—61no—
169C3×M16—61no—
170C3×M16—61no—
171C3×M16—61no—
172C3×M16C4×D312yes—
173C3×M16C4×D312yes—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—41no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183#208—21no—
184#208—21no—
185#208—21no—
186#208—21no—
187#208—32no—
188#208—32no—
189#208—62no—
190#208—61no—
191#208—61no—
192#208—121no—
193#208D1212yes—
194#208#6712yes—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—121no—
204ΓL(1,𝔽25)—64no—
205ΓL(1,𝔽25)—64no—
206D3×C8—64no—
207D3×C8—64no—
208C22×C32—41no—
209C22×C32C2×C4⋊C411yescharacteristic
210C22×C32C22⋊Q811yescharacteristic
211C22×C32C22⋊Q811yescharacteristic
212C2×C3⋊D3—22no—
213C2×C3⋊D3—42no—
214C32×C4C4×D411yescharacteristic
215C32×C4C4×D411yescharacteristic
216C32×C4#12011yescharacteristic
217C32×C4#12311yescharacteristic
218C3⋊Dic3—22no—
219C2×#41—91no—
220#131—182no—
221#131—182no—
222C2×M16—31no—
223C2×M16—31no—
224C2×M16—31no—
225C2×M16—91no—
226C2×M16—182no—
227C2×M16D3211yescharacteristic
228C22×C8—31no—
229#108—62no—
230#108—182no—
231#101—92no—
232#100—92no—
233C22⋊C8—182no—
234C23×C3—21no—
235C23×C3D3×Q811yescharacteristic
236C23×C3D3×Q811yescharacteristic
237C22×D3—32no—
238C22×D3—32no—
239C22×D3—62no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4C2×C4×D311yescharacteristic
247C2×C3×C4C2×C4×D311yescharacteristic
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4#23511yescharacteristic
250C2×C3×C4#23511yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4#23711yescharacteristic
256C2×C3×C4#23911yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258#67—62no—
259#67—62no—
260#67—62no—
261#67—62no—
262#67—122no—
263#67—122no—
264C2×Dic3—32no—
265C2×Dic3—32no—
266C2×Dic3—62no—
267D12—61no—
268D12—61no—
269D12—61no—
270D12—61no—
271D12—121no—
272D12—121no—
273C4×D3—62no—
274C4×D3—62no—
275C4×D3—62no—
276C4×D3—62no—
277C4×D3—122no—
278C4×D3—122no—
279Dic6—61no—
280Dic6—61no—
281Dic6—61no—
282Dic6—61no—
283Dic6—121no—
284Dic6—121no—
285C3×C8—22no—
286C3×C8—22no—
287C3×C8—42no—
288C3×C8—62no—
289C3×C8—62no—
290C3×C8—121no—
291C3×C8—121no—
292C3⋊C8—22no—
293C3⋊C8—22no—
294C3⋊C8—41no—
295C3⋊C8—41no—
296C3⋊C8—62no—
297C3⋊C8—62no—
298C3⋊C8—122no—
299C2×C32—21no—
300C2×C32—21no—
301C2×C32—21no—
302C2×C32#38511yescharacteristic
303C3⋊D3—42no—
304#41—181no—
305#41—181no—
306#41—181no—
307#41—181no—
308C2×Q8—91no—
309C2×D4—92no—
310C2×D4—91no—
311C22×C4—92no—
312C22×C4C2×D3211yescharacteristic
313M16—21no—
314M16—32no—
315M16—32no—
316M16—61no—
317M16—61no—
318M16—61no—
319M16—61no—
320M16—92no—
321M16—184no—
322M16—181no—
323M16#62412yes—
324C2×C8—21no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—61no—
329C2×C8—61no—
330C2×C8—61no—
331C2×C8—184no—
332C2×C8—181no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—81no—
339C22×C3D3×C4⋊C411yescharacteristic
340C22×C3D3×C4⋊C411yescharacteristic
341C22×C3#89611yescharacteristic
342C22×C3#89611yescharacteristic
343C22×C3#89711yescharacteristic
344C22×C3#94611yescharacteristic
345C2×D3—62no—
346C2×D3—62no—
347C2×D3—122no—
348C2×D3—122no—
349C2×D3—122no—
350C2×D3—242no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4C4×D1211yescharacteristic
356C3×C4#67⋊C411yescharacteristic
357C3×C4#88211yescharacteristic
358C3×C4#88311yescharacteristic
359C3×C4#89311yescharacteristic
360C3×C4#89411yescharacteristic
361C3×C4C4×#6711yescharacteristic
362C3×C4#93711yescharacteristic
363Dic3—62no—
364Dic3—62no—
365Dic3—122no—
366C32#185811yescharacteristic, complemented, Sylow
367C23—92no—
368C23#379711yescharacteristic
369Q8—181no—
370Q8—181no—
371D4—182no—
372D4—182no—
373D4—181no—
374D4—181no—
375C2×C4—92no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4#379911yescharacteristic
379C2×C4D3×D1211yescharacteristic
380C2×C4#380211yescharacteristic
381C2×C4#380411yescharacteristic
382C2×C4C2×#62411yescharacteristic
383C2×C4D3×#6711yescharacteristic
384C8—22no—
385C8—62no—
386C8—62no—
387C8—121no—
388C8—121no—
389C8—182no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—41no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3#466811yescharacteristic
401C2×C3#498911yescharacteristic
402D3—122no—
403D3—122no—
404D3—242no—
405C22—41no—
406C22—182no—
407C22—362no—
408C22#6388811yescharacteristic
409C22#6389511yescharacteristic
410C22#6390011yescharacteristic
411C4—182no—
412C4#6385411yescharacteristic
413C4#6389411yescharacteristic
414C4#6392211yescharacteristic
415C4#6395211yescharacteristic
416C3—21no—
417C3#6894511yescharacteristic, complemented
418C3#7073411yescharacteristic, complemented
419C2—21no—
420C2—21no—
421C2—21no—
422C2—362no—
423C2#1059137811yescharacteristic
subgroupG/H
centerC4#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#385
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1858
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#5125C2semidirect
4. #10591143C2semidirect
6. C3×#4558C2semidirect
7. #10589166C2semidirect
32. #5125D3semidirect
38. #4558D3semidirect
366. C32#1858semidirect
417. C3#68945semidirect
418. C3#70734semidirect

Maximal subgroups

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

subgroupindex
#105947802
#105928312
C3×#51252
#105911432
#105910732
C3×#45582
#105891662
#707343
#689453