Finite Group Databasebeta

← #11785464

Subgroups — #11785464

Order 1152.

639 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3712C211yesmaximal, characteristic
2#10592825C211yesmaximal, characteristic
3C2×C3×#822C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591074C211yesmaximal, characteristic
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70712—31nomaximal
9#68940—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×C3×#208C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3712—22no—
18C2×#3712—22no—
19C2×#3712C414yes—
20#63647—22no—
21C3×#822—22no—
22#63577—22no—
23#63557—22no—
24C22×ΓL(1,𝔽25)—31no—
25C22×ΓL(1,𝔽25)—31no—
26C2×C3×#108—31no—
27#5126—31no—
28#5126—31no—
29#5126—31no—
30#5126—31no—
31#5126—61no—
32C2×#822—31no—
33C2×#822D311yescharacteristic, complemented
34C2×#819—31no—
35C3×#341—31no—
36#4558—31no—
37#4558D311yescharacteristic, complemented
38#4552—31no—
39C23×C3⋊D3Q811yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3Q811yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3C2×C412yes—
47C2×C4×C3⋊D3D412yes—
48C32×M16—21no—
49C32×M16—21no—
50C2×C32×C8—21no—
51#3748—21no—
52#3748—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×#208—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C2×C3×C3⋊C8—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8C2×C412yes—
63C2×C3×C3⋊C8C2×C412yes—
64C2×C3×C3⋊C8D412yes—
65C2×C3×C3⋊C8D412yes—
66#3712—28no—
67#1811—91noSylow
68C22×C4×D3—31no—
69C22×C4×D3—31no—
70C22×C4×D3—61no—
71C2×C3×M16—21no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C2×D311yescharacteristic
76C22×C3×C8—31no—
77C22×C3×C8—31no—
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—61no—
81C2×#208C2×D311yescharacteristic
82C2×#208C2×D311yescharacteristic
83C22×C3⋊C8C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C2×ΓL(1,𝔽25)—34no—
86C2×ΓL(1,𝔽25)—34no—
87C2×ΓL(1,𝔽25)—62no—
88C2×ΓL(1,𝔽25)—62no—
89C2×ΓL(1,𝔽25)—62no—
90C2×ΓL(1,𝔽25)—62no—
91C3×#108—62no—
92#822—22no—
93#822—62no—
94(C2×D3)⋊C8—62no—
95(C2×D3)⋊C8—62no—
96(C2×D3)⋊C8—62no—
97(C2×D3)⋊C8—62no—
98(C2×D3)⋊C8—64no—
99#819—62no—
100C23×C32C2×Q811yescharacteristic
101C22×C3⋊D3—21no—
102C22×C3⋊D3—21no—
103C22×C3⋊D3—42no—
104C22×C3⋊D3C4⋊C412yes—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3C4⋊C412yes—
114C4×C3⋊D3—22no—
115C4×C3⋊D3—22no—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—22no—
118C32×C8—41no—
119C3⋊(C3⋊C8)—41no—
120C3×C3⋊C8—22no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8—41no—
123C3×C3⋊C8C22⋊C414yes—
124C22×M16—91no—
125C2×#108—31no—
126C2×#108—91no—
127#407—91no—
128#407—91no—
129#341—31no—
130#341—91no—
131C23×D3—31no—
132C23×D3—31no—
133C23×D3—61no—
134C22×C3×C4—21no—
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C22×D311yescharacteristic
137C22×Dic3—31no—
138C22×Dic3—31no—
139C22×Dic3—61no—
140C2×C4×D3—32no—
141C2×C4×D3—32no—
142C2×C4×D3—32no—
143C2×C4×D3—32no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3—121no—
155C2×C4×D3—121no—
156C2×C4×D3—121no—
157C2×C4×D3—121no—
158C3×M16—21no—
159C3×M16—21no—
160C3×M16—21no—
161C3×M16—21no—
162C3×M16—41no—
163C3×M16—41no—
164C3×M16—61no—
165C3×M16—61no—
166C3×M16—61no—
167C3×M16—61no—
168C2×C3×C8—22no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—32no—
172C2×C3×C8—32no—
173C2×C3×C8—32no—
174C2×C3×C8—32no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179#208—21no—
180#208—21no—
181#208—21no—
182#208—21no—
183#208—61no—
184#208—61no—
185#208—61no—
186#208—61no—
187#208—121no—
188#208—121no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—62no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8C4×D312yes—
197C2×C3⋊C8C4×D312yes—
198C2×C3⋊C8D1212yes—
199C2×C3⋊C8#6712yes—
200ΓL(1,𝔽25)—68no—
201ΓL(1,𝔽25)—68no—
202C22×C32—22no—
203C22×C32C2×C4⋊C411yescharacteristic
204C22×C32C22⋊Q811yescharacteristic
205C22×C32C22⋊Q811yescharacteristic
206C2×C3⋊D3—22no—
207C2×C3⋊D3—22no—
208C2×C3⋊D3—22no—
209C2×C3⋊D3—42no—
210C2×C3⋊D3—42no—
211C32×C4C2×C22⋊C411yescharacteristic
212C32×C4#11711yescharacteristic
213C32×C4#12111yescharacteristic
214C32×C4#12111yescharacteristic
215C3⋊Dic3—22no—
216C23×C4—91no—
217C2×M16—31no—
218C2×M16—31no—
219C2×M16—94no—
220C2×M16—91no—
221C2×M16—182no—
222C2×M16—182no—
223C2×M16D3211yescharacteristic
224C22×C8—31no—
225C22×C8—31no—
226#108—62no—
227#108—182no—
228C22⋊C8—182no—
229C22⋊C8—182no—
230C23×C3—21no—
231C23×C3D3×Q811yescharacteristic
232C23×C3D3×Q811yescharacteristic
233C22×D3—32no—
234C22×D3—32no—
235C22×D3—62no—
236C22×D3—61no—
237C22×D3—61no—
238C22×D3—61no—
239C22×D3—61no—
240C22×D3—121no—
241C22×D3—121no—
242C22×D3—122no—
243C22×D3—122no—
244C22×D3—124no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4C2×C4×D311yescharacteristic
252C2×C3×C4C2×C4×D311yescharacteristic
253C2×C3×C4C2×D1211yescharacteristic
254C2×C3×C4#23511yescharacteristic
255C2×C3×C4#23511yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4#23711yescharacteristic
261C2×C3×C4#23911yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263C2×Dic3—32no—
264C2×Dic3—32no—
265C2×Dic3—62no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—121no—
271C2×Dic3—121no—
272C4×D3—62no—
273C4×D3—62no—
274C4×D3—62no—
275C4×D3—62no—
276C4×D3—62no—
277C4×D3—62no—
278C4×D3—62no—
279C4×D3—62no—
280C4×D3—122no—
281C4×D3—122no—
282C4×D3—122no—
283C4×D3—122no—
284C3×C8—34no—
285C3×C8—42no—
286C3×C8—41no—
287C3×C8—41no—
288C3×C8—62no—
289C3×C8—121no—
290C3×C8—121no—
291C3⋊C8—22no—
292C3⋊C8—41no—
293C3⋊C8—41no—
294C3⋊C8—122no—
295C3⋊C8—121no—
296C3⋊C8—121no—
297C3⋊C8(C2×D3)⋊C414yes—
298C2×C32—21no—
299C2×C32—21no—
300C2×C32#38011yescharacteristic
301C2×C32#43012yes—
302C3⋊D3—42no—
303C24—91no—
304C22×C4—91no—
305C22×C4—92no—
306C22×C4—92no—
307C22×C4—181no—
308C22×C4—181no—
309C22×C4—181no—
310C22×C4—181no—
311C22×C4C2×D3211yescharacteristic
312M16—21no—
313M16—21no—
314M16—61no—
315M16—61no—
316M16—61no—
317M16—61no—
318M16—188no—
319M16—181no—
320M16—181no—
321C2×C8—21no—
322C2×C8—32no—
323C2×C8—32no—
324C2×C8—32no—
325C2×C8—32no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—61no—
329C2×C8—61no—
330C2×C8—181no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—42no—
337C22×C3D3×C4⋊C411yescharacteristic
338C22×C3D3×C4⋊C411yescharacteristic
339C22×C3#89611yescharacteristic
340C22×C3#89611yescharacteristic
341C22×C3#89711yescharacteristic
342C22×C3#94611yescharacteristic
343C2×D3—64no—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—62no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—122no—
351C2×D3—122no—
352C2×D3—122no—
353C2×D3—122no—
354C2×D3—122no—
355C2×D3—122no—
356C2×D3—124no—
357C2×D3—124no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4#87211yescharacteristic
363C3×C4D3×C22⋊C411yescharacteristic
364C3×C4#88411yescharacteristic
365C3×C4#88411yescharacteristic
366C3×C4#89211yescharacteristic
367C3×C4#89511yescharacteristic
368C3×C4C2×(C2×D3)⋊C411yescharacteristic
369C3×C4#93811yescharacteristic
370Dic3—62no—
371Dic3—62no—
372Dic3—122no—
373C32#181111yescharacteristic, complemented, Sylow
374C23—92no—
375C23—181no—
376C23—181no—
377C23—362no—
378C23#379711yescharacteristic
379C2×C4—92no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4—182no—
385C2×C4—182no—
386C2×C4#379911yescharacteristic
387C2×C4C4×D3211yescharacteristic
388C2×C4D3×D1211yescharacteristic
389C2×C4#380411yescharacteristic
390C2×C4D3×#6711yescharacteristic
391C2×C4#381111yescharacteristic
392C8—34no—
393C8—41no—
394C8—62no—
395C8—121no—
396C8—121no—
397C8—361no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—22no—
404C2×C3—41no—
405C2×C3—41no—
406C2×C3#466711yescharacteristic
407C2×C3#489312yes—
408C2×C3#489312yes—
409C2×C3#498711yescharacteristic
410D3—124no—
411D3—122no—
412D3—122no—
413C22—22no—
414C22—182no—
415C22—182no—
416C22—182no—
417C22—362no—
418C22—362no—
419C22#6388311yescharacteristic
420C22#6388811yescharacteristic
421C22#6389511yescharacteristic
422C4—182no—
423C4#6383611yescharacteristic
424C4#6391011yescharacteristic
425C4D3×(C2×D3)⋊C411yescharacteristic
426C4#6395811yescharacteristic
427C3—21no—
428C3#6894011yescharacteristic, complemented
429C3#7071211yescharacteristic, complemented
430C2—21no—
431C2—21no—
432C2—362no—
433C2#1059097412yes—
434C2#1059136711yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1811
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×C3×#822C2semidirect
4. C2×#63577C2semidirect
6. C3×#4558C2semidirect
7. #10589166C2semidirect
33. C2×#822D3semidirect
37. #4558D3semidirect
373. C32#1811semidirect
428. C3#68940semidirect
429. C3#70712semidirect

Maximal subgroups

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

subgroupindex
C22×#37122
#105928252
C2×C3×#8222
C2×#635772
#105910742
C3×#45582
#105891662
#707123
#689403