Finite Group Databasebeta

← #11791406

Subgroups — #11791406

Order 1152.

743 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 743 conjugacy classes of subgroups — too many to draw. Only its 134 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
1#10595032C211yesmaximal, characteristic
2M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#825C212yesmaximal, complemented
4C4×#3724C211yesmaximal, characteristic, complemented
5C2×#63569C212yesmaximal, complemented
6#70358—32nomaximal
7C2×C3×#235C2212yes—
8C2×C32×M16C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C2×C3×C4×Dic3C2212yes—
12#63980—21no—
13#63980—21no—
14C2×#3724—21no—
15#63914C411yescharacteristic, complemented
16C4×#625—21no—
17C4×#625—21no—
18#63873C411yescharacteristic, complemented
19#63863C412yescomplemented
20#63642—21no—
21C8×C3⋊Dic3—21no—
22C3×#825—24no—
23#63579—21no—
24#63569—24no—
25#5832—32no—
26C2×C3×#104—32no—
27C2×#837—32no—
28C2×#825D312yescomplemented
29Dic3×M16—32no—
30Dic3×M16—61no—
31C4×Dic3⋊C4—32no—
32C2×#805—32no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×C3×#67—22no—
37C22×C3×Dic3—22no—
38C3×#235—22no—
39C3×#235—22no—
40C3×#235—22no—
41C3×#235—22no—
42C2×C3×D12C2×C412yes—
43C2×C3×C4×D3—22no—
44C2×C3×Dic6C2×C412yes—
45C2×#625—21no—
46C2×#625—21no—
47C32×M16—21no—
48C32×M16D412yescomplemented
49C2×C32×C8—21no—
50C4×C3⋊Dic3C2×C411yescharacteristic
51C4×C3⋊Dic3C2×C411yescharacteristic
52C4×C3⋊Dic3D411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54#3748—21no—
55#3748D412yescomplemented
56C2×C3⋊(C3⋊C8)—21no—
57C3×C4×Dic3—22no—
58C3×C4×Dic3—22no—
59#3724—24no—
60#3724—21no—
61#3724—21no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64#1980—91noSylow
65C2×C3×#41—32no—
66C2×#235C2×D312yes—
67C2×C3×M16—21no—
68C2×C3×M16C2×D312yes—
69C2×C3×C42—32no—
70#947—32no—
71#944—32no—
72#940—32no—
73#939—62no—
74#939—62no—
75#936—32no—
76C4×#67—62no—
77C4×#67—62no—
78C2×Dic3⋊C4—62no—
79C2×C4×Dic3—32no—
80C2×C4×Dic3—61no—
81C2×C4×Dic3C2×D312yes—
82C2×#208—32no—
83C2×#208—61no—
84C3×#104—64no—
85#837—64no—
86C3⋊#95—62no—
87#825—24no—
88#815—62no—
89#815—62no—
90C8×Dic3—62no—
91C8×Dic3—62no—
92#805—64no—
93C23×C32C2×D411yescharacteristic
94C22×C3×D3—22no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C3×#67—42no—
108C3×#67—42no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C3×D12—22no—
114C3×D12—22no—
115C3×C4×D3—42no—
116C3×C4×D3—42no—
117C3×Dic6—22no—
118C3×Dic6—22no—
119#625—42no—
120#625—42no—
121C32×C8—22no—
122C3⋊(C3⋊C8)—22no—
123#532—91no—
124C2×#104—32no—
125C2×#104—92no—
126C4×M16—91no—
127C4×C4⋊C4—91no—
128C3×#41—62no—
129C3×#41—62no—
130C3×#41—62no—
131C3×#41—62no—
132C2×C3×Q8—32no—
133C2×C3×D4—32no—
134C2×C3×D4—62no—
135C22×C3×C4—21no—
136C22×C3×C4—62no—
137C22×C3×C4—62no—
138C22×C3×C4C22×D312yes—
139C2×#67—22no—
140C2×#67—62no—
141C2×#67—62no—
142C22×Dic3—22no—
143C22×Dic3—32no—
144C22×Dic3—32no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147#235—22no—
148#235—22no—
149#235—22no—
150#235—22no—
151C2×D12C4×D312yes—
152C2×C4×D3—22no—
153C2×Dic6C4×D312yes—
154C3×M16—22no—
155C3×M16—22no—
156C3×M16—22no—
157C3×M16#6714yescomplemented
158C2×C3×C8—22no—
159C2×C3×C8—22no—
160C3×C42—62no—
161C3×C42—62no—
162#217—62no—
163#217—62no—
164(C2×D3)⋊C4—62no—
165(C2×D3)⋊C4—62no—
166Dic3⋊C4—62no—
167Dic3⋊C4—62no—
168Dic3⋊C4—68no—
169C4×Dic3—22no—
170C4×Dic3—22no—
171C4×Dic3—32no—
172C4×Dic3—32no—
173C4×Dic3—32no—
174C4×Dic3—32no—
175C4×Dic3—61no—
176C4×Dic3—61no—
177C4×Dic3—61no—
178C4×Dic3—61no—
179#208—34no—
180#208—62no—
181#208—62no—
182#208—62no—
183C2×C3⋊C8—62no—
184C2×C3⋊C8—62no—
185C22×C32—21no—
186C22×C32—21no—
187C22×C32C2×C22⋊C411yescharacteristic
188C22×C32#12411yescharacteristic
189C22×C32#12711yescharacteristic
190C2×C3×D3—42no—
191C2×C3×D3—42no—
192C2×C3×D3—42no—
193C32×C4C4×D411yescharacteristic
194C32×C4C4×D411yescharacteristic
195C32×C4#12111yescharacteristic
196C32×C4#12111yescharacteristic
197C3⋊Dic3—21no—
198C3⋊Dic3—21no—
199C3⋊Dic3—21no—
200C3⋊Dic3#10412yescomplemented
201C3×Dic3—44no—
202C3×Dic3—42no—
203C2×#41—32no—
204C2×M16—91no—
205C2×M16D3211yescharacteristic
206C4⋊Q8—91no—
207#127—91no—
208#124—92no—
209#121—181no—
210#121—181no—
211C4×D4—181no—
212C4×D4—181no—
213C2×C4⋊C4—181no—
214C2×C42—32no—
215C2×C42—91no—
216#104—64no—
217#104—184no—
218#97—181no—
219C4×C8—181no—
220#95—181no—
221C23×C3—21no—
222C23×C3—62no—
223C23×C3D3×D412yes—
224C22×D3—22no—
225C3×Q8—62no—
226C3×Q8—62no—
227C3×D4—62no—
228C3×D4—62no—
229C3×D4—122no—
230C3×D4—122no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—64no—
238C2×C3×C4—62no—
239C2×C3×C4—122no—
240C2×C3×C4—122no—
241C2×C3×C4—122no—
242C2×C3×C4—122no—
243C2×C3×C4C2×C4×D312yes—
244C2×C3×C4#23512yes—
245C2×C3×C4D3×D412yes—
246C2×C3×C4D3×D412yes—
247C2×C3×C4#23712yes—
248C2×C3×C4C2×#6712yes—
249#67—42no—
250#67—42no—
251#67—124no—
252#67—124no—
253C2×Dic3—24no—
254C2×Dic3—22no—
255C2×Dic3—32no—
256C2×Dic3—32no—
257C2×Dic3—32no—
258C2×Dic3—32no—
259C2×Dic3—42no—
260C2×Dic3—42no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—64no—
266C2×Dic3—122no—
267C2×Dic3—122no—
268C2×Dic3—122no—
269D12—22no—
270D12—22no—
271C4×D3—42no—
272C4×D3—42no—
273Dic6—22no—
274Dic6—22no—
275C3×C8—24no—
276C3×C8—24no—
277C3⋊C8—64no—
278C3⋊C8—64no—
279C2×C32—21no—
280C2×C32—21no—
281C2×C32#39011yescharacteristic
282C2×C32C2×#10411yescharacteristic
283C2×C32#42111yescharacteristic
284C3×D3—82no—
285#41—62no—
286#41—62no—
287#41—62no—
288#41—62no—
289C2×Q8—32no—
290C2×D4—32no—
291C2×D4—62no—
292C2×D4—181no—
293C2×D4—181no—
294C22×C4—62no—
295C22×C4—62no—
296C22×C4—91no—
297C22×C4—91no—
298C22×C4C2×D3211yescharacteristic
299M16—21no—
300M16—92no—
301M16—181no—
302M16#62512yescomplemented
303C2×C8—21no—
304C2×C8—181no—
305C4⋊C4—181no—
306C4⋊C4—181no—
307C4⋊C4—184no—
308C22⋊C4—182no—
309C22⋊C4—182no—
310C42—62no—
311C42—62no—
312C42—91no—
313C42—91no—
314C42—91no—
315C42—91no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—122no—
324C22×C3—122no—
325C22×C3—122no—
326C22×C3D3×C22⋊C412yes—
327C22×C3#88512yes—
328C22×C3#94012yes—
329C2×D3—42no—
330C2×D3—42no—
331C2×D3—42no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—124no—
337C3×C4—122no—
338C3×C4#67⋊C412yes—
339C3×C4#88412yes—
340C3×C4C4×#6712yes—
341C3×C4#93912yes—
342Dic3—34no—
343Dic3—44no—
344Dic3—42no—
345Dic3—62no—
346Dic3—62no—
347Dic3—62no—
348Dic3—62no—
349Dic3—62no—
350Dic3—121no—
351Dic3—121no—
352C32#198011yescharacteristic, complemented, Sylow
353C23—62no—
354C23#380211yescharacteristic
355Q8—62no—
356Q8—62no—
357D4—62no—
358D4—62no—
359D4—122no—
360D4—122no—
361D4—362no—
362D4—362no—
363C2×C4—64no—
364C2×C4—62no—
365C2×C4—91no—
366C2×C4—91no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—122no—
370C2×C4—122no—
371C2×C4—122no—
372C2×C4—122no—
373C2×C4—182no—
374C2×C4—361no—
375C2×C4#379811yescharacteristic
376C2×C4C4×D3211yescharacteristic
377C2×C4#380211yescharacteristic
378C2×C4#380511yescharacteristic
379C2×C4C2×#62511yescharacteristic
380C2×C4#381111yescharacteristic
381C8—22no—
382C8—182no—
383C2×C3—22no—
384C2×C3—22no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—41no—
389C2×C3—41no—
390C2×C3—242no—
391C2×C3D3×#10412yes—
392C2×C3#482112yes—
393C2×C3#495712yes—
394D3—82no—
395C22—21no—
396C22—21no—
397C22—122no—
398C22—122no—
399C22—122no—
400C22#6391411yescharacteristic
401C22#6391511yescharacteristic
402C22#6392111yescharacteristic
403C4—92no—
404C4—124no—
405C4—122no—
406C4—181no—
407C4—181no—
408C4—181no—
409C4C4×#62511yescharacteristic
410C4#6390211yescharacteristic
411C4#6391211yescharacteristic
412C4#6398011yescharacteristic
413C3—21no—
414C3#7035812yescomplemented
415C2—21no—
416C2—21no—
417C2—242no—
418C2#1059100811yescharacteristic
419C2#1059100911yescharacteristic
420C2#1059138511yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595032C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1980
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. M16×C3⋊Dic3C2semidirect
3. C2×C3×#825C2semidirect
4. C4×#3724C2semidirect
5. C2×#63569C2semidirect
15. #63914C4semidirect
18. #63873C4semidirect
19. #63863C4semidirect
28. C2×#825D3semidirect
48. C32×M16D4semidirect
55. #3748D4semidirect
157. C3×M16#67semidirect
200. C3⋊Dic3#104semidirect
302. M16#625semidirect
352. C32#1980semidirect
414. C3#70358semidirect

Maximal subgroups

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

subgroupindex
#105950322
M16×C3⋊Dic32
C2×C3×#8252
C4×#37242
C2×#635692
#703583