Finite Group Databasebeta

← #11785553

Subgroups — #11785553

Order 1152.

645 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64110C211yesmaximal, characteristic
2C2×C3×#819C211yesmaximal, characteristic, complemented
3C3×#5106C211yesmaximal, characteristic, complemented
4#10591113C212yesmaximal
5#10589169C212yesmaximal, complemented
6#70719—31nomaximal
7#70665—31nomaximal
8C2×#3828C2211yescharacteristic
9C22×C32×C8C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11#64110—21no—
12#64110—21no—
13#64110C412yescomplemented
14#64110C412yescomplemented
15C2×#3743—21no—
16C2×C8×C3⋊D3—21no—
17C3×#926C2212yes—
18C2×C3×#208C2212yes—
19C3×#819—21no—
20C3×#819—21no—
21C3×#818—21no—
22C3×#817—21no—
23#63570—24no—
24C2×#901—31no—
25C2×#901—31no—
26C2×#901—61no—
27C2×C3×#108—31no—
28C3×#427—31no—
29#5139—32no—
30C2×#819D311yescharacteristic, complemented
31#5106D311yescharacteristic, complemented
32#5005—32no—
33#4556—32no—
34#4533—32no—
35C22×C32×C4C2311yescharacteristic
36C2×#638—21no—
37#3828—21no—
38#3828—21no—
39#3828C2×C412yes—
40#3828D412yes—
41C2×C4⋊(C3⋊D3)Q811yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×#634Q811yescharacteristic
44C2×C32×C8C2×C411yescharacteristic
45C2×C32×C8C2×C411yescharacteristic
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C2×C32×C8D411yescharacteristic
49C2×C32×C8D411yescharacteristic
50#3748—21no—
51#3748C2×C412yes—
52C2×C3⋊(C3⋊C8)—21no—
53#3743—22no—
54#3743—22no—
55C8×C3⋊D3—22no—
56C8×C3⋊D3—22no—
57C3×#217—22no—
58C3×C4⋊Dic3—22no—
59C3×C4×Dic3—22no—
60C3×#208—22no—
61C3×#208—22no—
62C2×C3×C3⋊C8—22no—
63#1814—91noSylow
64C2×#235—31no—
65C2×#235—31no—
66C2×#235—61no—
67C2×C3×M16—32no—
68C22×C3×C8—21no—
69C22×C3×C8C2×D311yescharacteristic
70C22×C3×C8C2×D311yescharacteristic
71C3×#117—32no—
72#926C2×D312yes—
73C2×#208—31no—
74C2×#208—31no—
75C2×#208—61no—
76C2×#208C2×D312yes—
77#901—32no—
78#901—32no—
79#901—32no—
80#901—32no—
81#901—62no—
82#901—62no—
83#901—62no—
84#901—62no—
85#901—61no—
86#901—61no—
87#901—61no—
88#901—61no—
89C2×ΓL(1,𝔽25)—62no—
90C2×ΓL(1,𝔽25)—61no—
91C2×ΓL(1,𝔽25)—61no—
92C2×D3×C8—62no—
93C2×D3×C8—61no—
94C2×D3×C8—61no—
95C3×#108—61no—
96C3×#108—61no—
97C3×#107—61no—
98C3×#106—61no—
99#825—64no—
100#819—21no—
101#819—21no—
102#818—21no—
103#817—21no—
104#805—64no—
105C23×C32#4111yescharacteristic
106C22×C3⋊D3—21no—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×Q811yescharacteristic
112C2×C32×C4#4111yescharacteristic
113#638—22no—
114#638—22no—
115C2×C3⋊Dic3—21no—
116C4⋊(C3⋊D3)—21no—
117C4⋊(C3⋊D3)C4⋊C412yes—
118C4×C3⋊D3—22no—
119C4×C3⋊D3—22no—
120#634—21no—
121#634C4⋊C412yes—
122C2×C3×Dic3—42no—
123C32×C8C22⋊C411yescharacteristic
124C32×C8C22⋊C411yescharacteristic
125C32×C8C22⋊C411yescharacteristic
126C32×C8C22⋊C411yescharacteristic
127C3⋊(C3⋊C8)—22no—
128C3×C3⋊C8—42no—
129C2×#131—91no—
130C2×#108—31no—
131#427—31no—
132#421—92no—
133#344—92no—
134C22×C3×C4—21no—
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C22×D311yescharacteristic
137C2×#67—62no—
138C2×#67—61no—
139C2×#67—61no—
140#235—32no—
141#235—32no—
142#235—32no—
143#235—32no—
144#235—62no—
145#235—62no—
146#235—62no—
147#235—62no—
148#235—61no—
149#235—61no—
150#235—61no—
151#235—61no—
152C2×D12—31no—
153C2×D12—31no—
154C2×D12—61no—
155C2×C4×D3—62no—
156C2×C4×D3—61no—
157C2×C4×D3—61no—
158C2×Dic6—31no—
159C2×Dic6—31no—
160C2×Dic6—61no—
161C3×M16—62no—
162C3×M16—62no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—62no—
170C2×C3×C8C4×D311yescharacteristic
171C2×C3×C8C4×D311yescharacteristic
172C2×C3×C8C4×D311yescharacteristic
173C2×C3×C8C4×D311yescharacteristic
174C2×C3×C8D1211yescharacteristic
175C2×C3×C8D1211yescharacteristic
176C2×C3×C8D1211yescharacteristic
177C2×C3×C8D1211yescharacteristic
178C2×C3×C8#6711yescharacteristic
179C2×C3×C8#6711yescharacteristic
180C2×C3×C8#6711yescharacteristic
181C2×C3×C8#6711yescharacteristic
182C3×C4⋊C4—62no—
183C3×C22⋊C4—62no—
184C3×C42—62no—
185#217—22no—
186C4⋊Dic3—22no—
187C4×Dic3—22no—
188#208—22no—
189#208—22no—
190#208—32no—
191#208—32no—
192#208—62no—
193#208—62no—
194#208—61no—
195#208—61no—
196C2×C3⋊C8—22no—
197C2×C3⋊C8—62no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—61no—
200ΓL(1,𝔽25)—64no—
201ΓL(1,𝔽25)—64no—
202ΓL(1,𝔽25)—62no—
203ΓL(1,𝔽25)—62no—
204ΓL(1,𝔽25)—62no—
205ΓL(1,𝔽25)—62no—
206D3×C8—64no—
207D3×C8—64no—
208D3×C8—62no—
209D3×C8—62no—
210D3×C8—62no—
211D3×C8—62no—
212C22×C32—41no—
213C22×C32#11711yescharacteristic
214C22×C32#12111yescharacteristic
215C22×C32C22⋊Q811yescharacteristic
216C2×C3⋊D3—22no—
217C2×C3⋊D3—42no—
218C32×C4C2×C22⋊C411yescharacteristic
219C32×C4C2×C4⋊C411yescharacteristic
220C32×C4#12111yescharacteristic
221C32×C4C22⋊Q811yescharacteristic
222C3⋊Dic3—22no—
223C3×Dic3—82no—
224C2×#41—91no—
225#131—92no—
226#131—92no—
227#131—181no—
228#131—181no—
229C2×M16—32no—
230C2×M16—91no—
231C2×M16—181no—
232C22×C8—181no—
233C22×C8D3211yescharacteristic
234#117—32no—
235#108—61no—
236#108—61no—
237#107—61no—
238#106—61no—
239#104—184no—
240C23×C3—21no—
241C23×C3#23711yescharacteristic
242C23×C3#23911yescharacteristic
243C22×D3—62no—
244C22×D3—61no—
245C22×D3—61no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—122no—
253C2×C3×C4C2×C4×D311yescharacteristic
254C2×C3×C4C2×C4×D311yescharacteristic
255C2×C3×C4C2×D1211yescharacteristic
256C2×C3×C4C2×D1211yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4#23711yescharacteristic
260C2×C3×C4D3×Q811yescharacteristic
261C2×C3×C4D3×Q811yescharacteristic
262C2×C3×C4#23911yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265#67—64no—
266#67—64no—
267#67—62no—
268#67—62no—
269#67—62no—
270#67—62no—
271C2×Dic3—42no—
272C2×Dic3—62no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275D12—32no—
276D12—32no—
277D12—62no—
278D12—62no—
279D12—61no—
280D12—61no—
281C4×D3—64no—
282C4×D3—64no—
283C4×D3—62no—
284C4×D3—62no—
285C4×D3—62no—
286C4×D3—62no—
287Dic6—32no—
288Dic6—32no—
289Dic6—62no—
290Dic6—62no—
291Dic6—61no—
292Dic6—61no—
293C3×C8—21no—
294C3×C8—21no—
295C3×C8—21no—
296C3×C8—21no—
297C3×C8—122no—
298C3×C8(C2×D3)⋊C411yescharacteristic
299C3×C8(C2×D3)⋊C411yescharacteristic
300C3×C8(C2×D3)⋊C411yescharacteristic
301C3×C8(C2×D3)⋊C411yescharacteristic
302C3×C8(C2×D3)⋊C411yescharacteristic
303C3×C8(C2×D3)⋊C411yescharacteristic
304C3×C8(C2×D3)⋊C411yescharacteristic
305C3×C8(C2×D3)⋊C411yescharacteristic
306C3⋊C8—42no—
307C3⋊C8—64no—
308C3⋊C8—62no—
309C3⋊C8—62no—
310C2×C32—21no—
311C2×C32—21no—
312C2×C32—21no—
313C2×C32#38011yescharacteristic
314C3⋊D3—42no—
315#41—92no—
316#41—92no—
317#41—181no—
318#41—181no—
319C2×Q8—91no—
320C2×D4—91no—
321C2×D4—181no—
322C22×C4—181no—
323C22×C4C2×D3211yescharacteristic
324M16—62no—
325M16—62no—
326M16—92no—
327M16—181no—
328M16—182no—
329M16—182no—
330C2×C8—62no—
331C2×C8—181no—
332C2×C8—182no—
333C2×C8—182no—
334C2×C8#62411yescharacteristic
335C2×C8#62411yescharacteristic
336C2×C8#62611yescharacteristic
337C2×C8#62611yescharacteristic
338C2×C8#62611yescharacteristic
339C2×C8#62611yescharacteristic
340C4⋊C4—62no—
341C22⋊C4—62no—
342C42—62no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—42no—
349C22×C3#89211yescharacteristic
350C22×C3#89211yescharacteristic
351C22×C3#89511yescharacteristic
352C22×C3#89711yescharacteristic
353C22×C3#93811yescharacteristic
354C22×C3#94611yescharacteristic
355C2×D3—64no—
356C2×D3—62no—
357C2×D3—62no—
358C2×D3—124no—
359C2×D3—122no—
360C2×D3—122no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—242no—
366C3×C4D3×C4⋊C411yescharacteristic
367C3×C4D3×C4⋊C411yescharacteristic
368C3×C4#89511yescharacteristic
369C3×C4#89711yescharacteristic
370C3×C4C2×(C2×D3)⋊C411yescharacteristic
371C3×C4C2×(C2×D3)⋊C411yescharacteristic
372C3×C4#93811yescharacteristic
373C3×C4#94611yescharacteristic
374Dic3—64no—
375Dic3—62no—
376Dic3—62no—
377Dic3—82no—
378C32#181411yescharacteristic, complemented, Sylow
379C23—181no—
380C23#379611yescharacteristic
381Q8—92no—
382Q8—181no—
383D4—92no—
384D4—182no—
385D4—182no—
386D4—181no—
387C2×C4—122no—
388C2×C4—181no—
389C2×C4—182no—
390C2×C4—182no—
391C2×C4#379611yescharacteristic
392C2×C4#379711yescharacteristic
393C2×C4#380211yescharacteristic
394C2×C4C2×#62411yescharacteristic
395C2×C4C2×#62611yescharacteristic
396C2×C4C2×#62611yescharacteristic
397C8—122no—
398C8—182no—
399C8#372211yescharacteristic
400C8#372211yescharacteristic
401C8#372211yescharacteristic
402C8#372211yescharacteristic
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—41no—
412C2×C3—41no—
413C2×C3#498711yescharacteristic
414C2×C3#498711yescharacteristic
415D3—124no—
416D3—122no—
417D3—122no—
418C22—41no—
419C22—182no—
420C22—362no—
421C22#6384911yescharacteristic
422C22#6387111yescharacteristic
423C22#6391611yescharacteristic
424C4—182no—
425C4—242no—
426C4#6387111yescharacteristic
427C4#6390011yescharacteristic
428C4#6391611yescharacteristic
429C4C2×#372211yescharacteristic
430C3—21no—
431C3#7066511yescharacteristic, complemented
432C3#7071911yescharacteristic, complemented
433C2—21no—
434C2—21no—
435C2—21no—
436C2—362no—
437C2#1059132511yescharacteristic
subgroupG/H
centerC4#63916
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC2×C32#380
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1814
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#819C2semidirect
3. C3×#5106C2semidirect
5. #10589169C2semidirect
13. #64110C4semidirect
14. #64110C4semidirect
30. C2×#819D3semidirect
31. #5106D3semidirect
378. C32#1814semidirect
431. C3#70665semidirect
432. C3#70719semidirect

Maximal subgroups

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

subgroupindex
C2×#641102
C2×C3×#8192
C3×#51062
#105911132
#105891692
#707193
#706653