Finite Group Databasebeta

← #11791201

Subgroups — #11791201

Order 1152.

876 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 876 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic, complemented
3#10592933C211yesmaximal, characteristic, complemented
4#10592828C211yesmaximal, characteristic, complemented
5C2×#63649C211yesmaximal, characteristic, complemented
6C2×#63632C211yesmaximal, characteristic, complemented
7C2×#63630C211yesmaximal, characteristic, complemented
8#70374—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64159—22no—
14#64159—22no—
15C2×#3756C411yescharacteristic, complemented
16C2×#3755C411yescharacteristic, complemented
17C2×#3754C411yescharacteristic, complemented
18C2×#3753C411yescharacteristic, complemented
19C2×#3748C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C32×#104—22no—
23#63657—22no—
24#63649—22no—
25#63647—22no—
26#63632—22no—
27#63630—22no—
28C2×#950—34no—
29C2×C3×#104D314yescomplemented
30#5234—34no—
31#5129—34no—
32C2×#822—34no—
33C2×#805—34no—
34C2×#803—34no—
35C32×#41—21no—
36C32×#41—21no—
37C32×#41—21no—
38C32×#41—21no—
39C2×C32×Q8C2×C411yescharacteristic
40C2×C32×D4—21no—
41C2×C32×D4C2×C411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634C2×C411yescharacteristic
53C32×M16—21no—
54C32×M16—21no—
55C2×C32×C8—21no—
56C32×C42—21no—
57C32×C42D412yes—
58#3756—22no—
59#3755—22no—
60#3754—22no—
61#3753—22no—
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
68C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
69C2×C3⋊(C3⋊C8)D412yes—
70C2×C3⋊(C3⋊C8)D412yes—
71C2×C3⋊(C3⋊C8)D412yes—
72#1975—91noSylow
73C2×C3×#41C2×D314yes—
74C2×#235—34no—
75C2×C3×M16C2×D314yes—
76C2×C3×C42C2×D314yes—
77#950—68no—
78#950—68no—
79C2×#216—34no—
80C2×#215—34no—
81C2×#214—34no—
82C2×#213—34no—
83C2×#208—34no—
84C22×C3⋊C8—34no—
85C22×C3⋊C8—34no—
86C3×#104—28no—
87#830—68no—
88#822—68no—
89(C2×D3)⋊C8—68no—
90#805—68no—
91#803—68no—
92C23×C32—21no—
93C23×C32#4111yescharacteristic
94C22×C3⋊D3—21no—
95C32×Q8—21no—
96C32×Q8—21no—
97C32×D4—21no—
98C32×D4—21no—
99C32×D4—41no—
100C32×D4—41no—
101C2×C32×C4—21no—
102C2×C32×C4—22no—
103C2×C32×C4—42no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112#638—41no—
113#638—41no—
114C2×C3⋊Dic3—21no—
115C4⋊(C3⋊D3)—21no—
116C4⋊(C3⋊D3)—21no—
117C4×C3⋊D3—41no—
118C4×C3⋊D3—41no—
119#634—21no—
120#634—21no—
121C32×C8—41no—
122C3⋊(C3⋊C8)—22no—
123C3⋊(C3⋊C8)—41no—
124C3⋊(C3⋊C8)C22⋊C412yes—
125C3⋊(C3⋊C8)C22⋊C412yes—
126C2×#135—91no—
127C2×#108—91no—
128C2×#104—91no—
129C2×#104C3⋊D311yescharacteristic, complemented
130#408—91no—
131#408—91no—
132C2×#97—91no—
133C3×#41—24no—
134C3×#41—24no—
135C3×#41—24no—
136C3×#41—24no—
137C2×C3×Q8C4×D314yes—
138C2×C3×D4—24no—
139C2×C3×D4C4×D314yes—
140C22×C3×C4—24no—
141C22×C3×C4—24no—
142C22×C3×C4C22×D314yes—
143C2×#67—64no—
144#235—64no—
145#235—64no—
146#235—64no—
147#235—64no—
148C2×D12—34no—
149C2×C4×D3—64no—
150C2×Dic6—34no—
151C3×M16—24no—
152C3×M16—24no—
153C2×C3×C8—24no—
154C3×C42—24no—
155C3×C42#6718yes—
156#216—68no—
157#215—68no—
158#214—68no—
159#213—68no—
160#208—64no—
161#208—64no—
162C2×C3⋊C8—34no—
163C2×C3⋊C8—34no—
164C2×C3⋊C8—38no—
165C2×C3⋊C8—38no—
166C2×C3⋊C8—38no—
167C2×C3⋊C8—64no—
168C2×C3⋊C8—64no—
169C2×C3⋊C8—64no—
170C22×C32—22no—
171C22×C32—41no—
172C22×C32—42no—
173C22×C32C4×D411yescharacteristic
174C22×C32#12111yescharacteristic
175C22×C32#12411yescharacteristic
176C2×C3⋊D3—41no—
177C2×C3⋊D3—42no—
178C32×C4—42no—
179C32×C4—41no—
180C32×C4C2×C22⋊C411yescharacteristic
181C32×C4C4×D411yescharacteristic
182C32×C4#12111yescharacteristic
183C32×C4#12711yescharacteristic
184C3⋊Dic3—41no—
185C2×#41—91no—
186C2×#41C2×C3⋊D311yescharacteristic
187#135—182no—
188#135—182no—
189C2×Q16—91no—
190C2×SD16—91no—
191C2×SD16—91no—
192C2×D8—91no—
193C2×M16—91no—
194C2×M16C2×C3⋊D311yescharacteristic
195C22×C8—91no—
196C22×C8—91no—
197C2×C42C2×C3⋊D311yescharacteristic
198#108—182no—
199#104—22no—
200#104—182no—
201C22⋊C8—182no—
202C22⋊C8—182no—
203#97—182no—
204C23×C3—24no—
205C23×C3#23714yes—
206C22×D3—64no—
207C3×Q8—24no—
208C3×Q8—24no—
209C3×D4—24no—
210C3×D4—24no—
211C3×D4—44no—
212C3×D4—44no—
213C2×C3×C4—24no—
214C2×C3×C4—28no—
215C2×C3×C4—48no—
216C2×C3×C4—44no—
217C2×C3×C4—44no—
218C2×C3×C4C2×C4×D314yes—
219C2×C3×C4#23514yes—
220C2×C3×C4D3×D414yes—
221C2×C3×C4D3×D414yes—
222C2×C3×C4D3×D414yes—
223C2×C3×C4C2×#6714yes—
224#67—124no—
225#67—124no—
226C2×Dic3—64no—
227D12—64no—
228D12—64no—
229C4×D3—124no—
230C4×D3—124no—
231Dic6—64no—
232Dic6—64no—
233C3×C8—44no—
234C3⋊C8—38no—
235C3⋊C8—38no—
236C3⋊C8—68no—
237C3⋊C8—124no—
238C2×C32—21no—
239C2×C32—21no—
240C2×C32—81no—
241C2×C32#39011yescharacteristic
242C2×C32#44412yes—
243C3⋊D3—81no—
244#41—21no—
245#41—21no—
246#41—21no—
247#41—21no—
248#41—181no—
249#41—181no—
250#41—181no—
251#41—181no—
252C2×Q8—91no—
253C2×Q8C4×C3⋊D311yescharacteristic
254C2×D4—21no—
255C2×D4—91no—
256C2×D4—181no—
257C2×D4C4×C3⋊D311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—181no—
261C22×C4C22×C3⋊D311yescharacteristic
262Q16—182no—
263SD16—182no—
264SD16—182no—
265D8—182no—
266M16—21no—
267M16—21no—
268M16—181no—
269M16—181no—
270C2×C8—21no—
271C2×C8—91no—
272C2×C8—91no—
273C2×C8—92no—
274C2×C8—92no—
275C2×C8—92no—
276C2×C8—181no—
277C2×C8—181no—
278C2×C8—181no—
279C42—21no—
280C42#63812yes—
281C22×C3—28no—
282C22×C3—44no—
283C22×C3—48no—
284C22×C3#67⋊C414yes—
285C22×C3#88514yes—
286C22×C3#93914yes—
287C2×D3—124no—
288C2×D3—128no—
289C3×C4—48no—
290C3×C4—44no—
291C3×C4D3×C22⋊C414yes—
292C3×C4#88414yes—
293C3×C4C4×#6714yes—
294C3×C4#94014yes—
295Dic3—124no—
296C32#197511yescharacteristic, complemented, Sylow
297C23—21no—
298C23—181no—
299C23#383011yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—181no—
303Q8—181no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—41no—
308D4—181no—
309D4—181no—
310D4—361no—
311D4—361no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—181no—
318C2×C4—361no—
319C2×C4—361no—
320C2×C4C2×C4×C3⋊D311yescharacteristic
321C2×C4#382811yescharacteristic
322C2×C4D4×C3⋊D311yescharacteristic
323C2×C4D4×C3⋊D311yescharacteristic
324C2×C4D4×C3⋊D311yescharacteristic
325C2×C4C2×#63811yescharacteristic
326C8—41no—
327C8—92no—
328C8—92no—
329C8—182no—
330C8—361no—
331C2×C3—24no—
332C2×C3—24no—
333C2×C3—84no—
334C2×C3#482318yes—
335C2×C3#495714yes—
336D3—244no—
337C22—22no—
338C22—42no—
339C22—41no—
340C22—362no—
341C22—361no—
342C22#6409011yescharacteristic
343C22#6409411yescharacteristic
344C22#6414811yescharacteristic
345C4—42no—
346C4—41no—
347C4—361no—
348C4C22⋊C4×C3⋊D311yescharacteristic
349C4#6409311yescharacteristic
350C4C4×#63811yescharacteristic
351C4#6414911yescharacteristic
352C3#7037414yescomplemented
353C2—21no—
354C2—21no—
355C2—81no—
356C2—721no—
357C2#1059252212yes—
358C2#1059265611yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#104C2
socleC22×C32C4×D4
prime radicalC2×#64159C2
cosocleC22×C32×C4C23
hypercenterC2×#104C3⋊D3
hypocenterC32#1975
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C32×#104C2semidirect
3. #10592933C2semidirect
4. #10592828C2semidirect
5. C2×#63649C2semidirect
6. C2×#63632C2semidirect
7. C2×#63630C2semidirect
15. C2×#3756C4semidirect
16. C2×#3755C4semidirect
17. C2×#3754C4semidirect
18. C2×#3753C4semidirect
29. C2×C3×#104D3semidirect
129. C2×#104C3⋊D3semidirect
296. C32#1975semidirect
352. C3#70374semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C2×C32×#1042
#105929332
#105928282
C2×#636492
C2×#636322
C2×#636302
#703743