Finite Group Databasebeta

← #11789946

Subgroups — #11789946

Order 1152.

545 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63652C211yesmaximal, characteristic
2C3×#5119C211yesmaximal, characteristic, complemented
3#10591105C211yesmaximal, characteristic
4#10591073C211yesmaximal, characteristic
5C2×#63553C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70535—31nomaximal
9#68918—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63652—22no—
18C3×Dic3⋊C8—22no—
19#63567C412yescomplemented
20#63564C412yescomplemented
21#63557—22no—
22#63553—22no—
23C3×#424—31no—
24C2×#825—31no—
25C2×#825—31no—
26C2×#825—61no—
27#5129—31no—
28#5119D311yescharacteristic, complemented
29#5113—31no—
30#5110—31no—
31C2×C8×Dic3—31no—
32C2×C8×Dic3—31no—
33#5002—31no—
34C3×#341—31no—
35#4558D311yescharacteristic, complemented
36#4555—31no—
37#4532—31no—
38C22×C32×C4C2311yescharacteristic
39C2×#638—21no—
40C22×C3⋊Dic3—21no—
41#3828—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×#634C2×C411yescharacteristic
48C32×M16—21no—
49C32×M16—21no—
50C2×C32×C8—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3D412yes—
53C3×#217—21no—
54C3×C4⋊Dic3C2×C412yes—
55C3×C4×Dic3—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⋊C8—21no—
63C2×C3×C3⋊C8C2×C412yes—
64C2×C3×C3⋊C8D412yes—
65#1937—91noSylow
66C2×#235—31no—
67C2×#235—31no—
68C2×#235—61no—
69C2×C3×M16—21no—
70C2×C3×M16—31no—
71C2×C3×M16C2×D311yescharacteristic
72C2×C3×M16C2×D311yescharacteristic
73C22×C3×C8—31no—
74C22×C3×C8—31no—
75C3×#117—31no—
76#926C2×D311yescharacteristic
77C2×C4×Dic3—31no—
78C2×C4×Dic3—31no—
79C2×C4×Dic3—61no—
80C2×#208C2×D311yescharacteristic
81C22×C3⋊C8C2×D311yescharacteristic
82C22×C3⋊C8C2×D311yescharacteristic
83C3×C4⋊C8—62no—
84#825—62no—
85#825—62no—
86#825—64no—
87#821—32no—
88(C2×D3)⋊C8—62no—
89(C2×D3)⋊C8—62no—
90#816—32no—
91Dic3⋊C8—22no—
92C8×Dic3—62no—
93C8×Dic3—62no—
94#810—32no—
95#809—32no—
96C23×C32#4111yescharacteristic
97C22×C3⋊D3—21no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104#638—41no—
105#638—41no—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—21no—
109C4⋊(C3⋊D3)—21no—
110C4⋊(C3⋊D3)—21no—
111C4×C3⋊D3—41no—
112C4×C3⋊D3—41no—
113#634—21no—
114#634—21no—
115C2×C3×Dic3—22no—
116C32×C8—41no—
117C3×C3⋊C8—22no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120#424—31no—
121C2×#104—91no—
122#416—91no—
123#408—91no—
124C2×C4×C8—91no—
125#341—31no—
126#339—91no—
127C22×C3×C4—21no—
128C22×C3×C4C22×D311yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C2×#67—61no—
131C2×#67—61no—
132C2×#67—121no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—121no—
136#235—62no—
137#235—62no—
138#235—61no—
139#235—61no—
140#235—61no—
141#235—61no—
142#235—61no—
143#235—61no—
144#235—61no—
145#235—61no—
146#235—121no—
147#235—121no—
148C2×D12—31no—
149C2×D12—31no—
150C2×D12—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—121no—
154C2×Dic6—31no—
155C2×Dic6—31no—
156C2×Dic6—61no—
157C3×M16—22no—
158C3×M16—21no—
159C3×M16—21no—
160C3×M16—21no—
161C3×M16—21no—
162C3×M16—41no—
163C3×M16—61no—
164C3×M16—61no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—32no—
168C2×C3×C8—32no—
169C2×C3×C8—41no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—32no—
176C3×C22⋊C4—61no—
177C3×C42—61no—
178#217—21no—
179C4⋊Dic3C4×D312yes—
180C4×Dic3—21no—
181C4×Dic3—32no—
182C4×Dic3—32no—
183C4×Dic3—62no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—121no—
187#208—21no—
188#208—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8C4×D312yes—
195C2×C3⋊C8#6712yes—
196C22×C32—22no—
197C22×C32C4×D411yescharacteristic
198C22×C32#12311yescharacteristic
199C22×C32#12611yescharacteristic
200C2×C3⋊D3—41no—
201C2×C3⋊D3—42no—
202C32×C4#11711yescharacteristic
203C32×C4C4×D411yescharacteristic
204C32×C4#12111yescharacteristic
205C32×C4#12411yescharacteristic
206C3⋊Dic3—24no—
207C3⋊Dic3—41no—
208C3×Dic3—42no—
209C2×#41—91no—
210C2×M16—31no—
211C2×M16D3211yescharacteristic
212C22×C8—31no—
213C22×C8—31no—
214#117—31no—
215C2×C42—91no—
216C4⋊C8—62no—
217#104—182no—
218#103—92no—
219#102—92no—
220C22⋊C8—182no—
221C4×C8—182no—
222C23×C3—21no—
223C23×C3#23511yescharacteristic
224C23×C3#23911yescharacteristic
225C22×D3—61no—
226C22×D3—61no—
227C22×D3—121no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—62no—
235C2×C3×C4C2×C4×D311yescharacteristic
236C2×C3×C4C2×C4×D311yescharacteristic
237C2×C3×C4#23511yescharacteristic
238C2×C3×C4#23511yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4#23711yescharacteristic
243C2×C3×C4#23711yescharacteristic
244C2×C3×C4#23911yescharacteristic
245C2×C3×C4#23911yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247#67—122no—
248#67—122no—
249#67—121no—
250#67—121no—
251#67—121no—
252#67—121no—
253C2×Dic3—22no—
254C2×Dic3—64no—
255C2×Dic3—64no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—122no—
261C2×Dic3—121no—
262C2×Dic3—124no—
263D12—62no—
264D12—61no—
265D12—61no—
266D12—61no—
267D12—61no—
268D12—121no—
269C4×D3—122no—
270C4×D3—122no—
271C4×D3—121no—
272C4×D3—121no—
273C4×D3—121no—
274C4×D3—121no—
275Dic6—62no—
276Dic6—61no—
277Dic6—61no—
278Dic6—61no—
279Dic6—61no—
280Dic6—121no—
281C3×C8—42no—
282C3×C8—41no—
283C3×C8—41no—
284C3×C8—62no—
285C3×C8—62no—
286C3×C8—121no—
287C3⋊C8—22no—
288C3⋊C8—22no—
289C3⋊C8—41no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32#38811yescharacteristic
293C2×C32#44312yes—
294C3⋊D3—81no—
295#41—181no—
296#41—181no—
297#41—181no—
298#41—181no—
299C2×Q8—91no—
300C2×D4—91no—
301C2×D4—181no—
302C22×C4—181no—
303C22×C4—181no—
304C22×C4C2×D3211yescharacteristic
305M16—21no—
306M16—21no—
307M16—61no—
308M16—61no—
309C2×C8—21no—
310C2×C8—32no—
311C2×C8—32no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—61no—
317C4⋊C4—32no—
318C22⋊C4—61no—
319C42—61no—
320C42—92no—
321C42—181no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—42no—
328C22×C3#89311yescharacteristic
329C22×C3#89411yescharacteristic
330C22×C3#89411yescharacteristic
331C22×C3#89811yescharacteristic
332C22×C3#89811yescharacteristic
333C22×C3C4×#6711yescharacteristic
334C2×D3—122no—
335C2×D3—122no—
336C2×D3—122no—
337C2×D3—121no—
338C2×D3—121no—
339C2×D3—242no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—122no—
345C3×C4#87211yescharacteristic
346C3×C4#67⋊C411yescharacteristic
347C3×C4#88411yescharacteristic
348C3×C4#88511yescharacteristic
349C3×C4#89211yescharacteristic
350C3×C4#89311yescharacteristic
351C3×C4#93911yescharacteristic
352C3×C4#94711yescharacteristic
353Dic3—42no—
354Dic3—64no—
355Dic3—64no—
356Dic3—124no—
357Dic3—122no—
358Dic3—121no—
359Dic3—121no—
360C32#193711yescharacteristic, complemented, Sylow
361C23—181no—
362C23#379911yescharacteristic
363Q8—181no—
364Q8—181no—
365D4—181no—
366D4—181no—
367D4—361no—
368D4—361no—
369C2×C4—62no—
370C2×C4—184no—
371C2×C4—182no—
372C2×C4—181no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4#379611yescharacteristic
376C2×C4#379911yescharacteristic
377C2×C4C4×D3211yescharacteristic
378C2×C4#380411yescharacteristic
379C2×C4D3×#6711yescharacteristic
380C2×C4#381111yescharacteristic
381C8—41no—
382C8—62no—
383C8—62no—
384C8—121no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—22no—
390C2×C3—21no—
391C2×C3—41no—
392C2×C3—41no—
393C2×C3#466911yescharacteristic
394C2×C3#489512yes—
395C2×C3#499011yescharacteristic
396C2×C3#514412yes—
397D3—242no—
398D3—241no—
399D3—241no—
400C22—22no—
401C22—362no—
402C22—361no—
403C22#6384811yescharacteristic
404C22#6389711yescharacteristic
405C22#6390411yescharacteristic
406C4—122no—
407C4—184no—
408C4—361no—
409C4#6383611yescharacteristic
410C4#6388111yescharacteristic
411C4#6390711yescharacteristic
412C4#6397111yescharacteristic
413C3—21no—
414C3#6891811yescharacteristic, complemented
415C3#7053511yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—721no—
419C2#1059099512yes—
420C2#1059125811yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1937
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
2. C3×#5119C2semidirect
5. C2×#63553C2semidirect
6. C3×#4558C2semidirect
7. #10589160C2semidirect
19. #63567C4semidirect
20. #63564C4semidirect
28. #5119D3semidirect
35. #4558D3semidirect
360. C32#1937semidirect
414. C3#68918semidirect
415. C3#70535semidirect

Maximal subgroups

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

subgroupindex
C2×#636522
C3×#51192
#105911052
#105910732
C2×#635532
C3×#45582
#105891602
#705353
#689183