Finite Group Databasebeta

← #37545311

Subgroups — #37545311

Order 23168.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153849C211yesmaximal, characteristic, complemented
2C2×#19153838C211yesmaximal, characteristic, complemented
3#26041950C211yesmaximal, characteristic, complemented
4#26041938C211yesmaximal, characteristic, complemented
5#26041668C211yesmaximal, characteristic, complemented
6#26041532C211yesmaximal, characteristic, complemented
7#26041508C211yesmaximal, characteristic, complemented
8#26041502C211yesmaximal, characteristic, complemented
9#26041480C211yesmaximal, characteristic, complemented
10#26041443C211yesmaximal, characteristic, complemented
11#26041426C211yesmaximal, characteristic, complemented
12#26041426C211yesmaximal, characteristic, complemented
13#26041420C211yesmaximal, characteristic, complemented
14#26041387C211yesmaximal, characteristic, complemented
15#435×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668449C2211yescharacteristic
18C2×#15668449C2211yescharacteristic
19C22×Dic362C2211yescharacteristic
20#19153849—24no—
21#19153838—24no—
22C2×Dic724C2211yescharacteristic
23C2×Dic724C2211yescharacteristic
24C2×#15668438C2211yescharacteristic
25C2×#15668438C2211yescharacteristic
26C2×#15668438C2211yescharacteristic
27C2×#15668438C2211yescharacteristic
28C2×#15668438C2211yescharacteristic
29C2×D1448C2211yescharacteristic
30C2×D1448C2211yescharacteristic
31#19153813C2211yescharacteristic
32#19153812—21no—
33#19153804C2211yescharacteristic
34#19153802—21no—
35#19153795C2211yescharacteristic
36#19153794—21no—
37#19153790C2211yescharacteristic
38#19153790C2211yescharacteristic
39#19153790C2211yescharacteristic
40#19153789—21no—
41#19153789—21no—
42#19153788—21no—
43C4×Dic362C2211yescharacteristic
44C4×Dic362C2211yescharacteristic
45#19153778—21no—
46#19153776—21no—
47#19153748C2211yescharacteristic
48#19153741C2211yescharacteristic
49#19153741C2211yescharacteristic
50#19153741C2211yescharacteristic
51#19153738C2211yescharacteristic
52#19153738C2211yescharacteristic
53#19153738C2211yescharacteristic
54C2×M16×C181C2211yescharacteristic
55C22×C8×C181C2211yescharacteristic
56C4×D4×C181C2211yescharacteristic
57C4⋊C8×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C22⋊C8×C181C2211yescharacteristic
60#97×C181C2211yescharacteristic
61#15668449—22no—
62#15668449—22no—
63#15668449—22no—
64#15668449—41no—
65#15668449—41no—
66#15668449—41no—
67C2×Dic362—22no—
68C2×Dic362—21no—
69C2×Dic362—41no—
70C2×Dic362C2311yescharacteristic
71C2×Dic362C2311yescharacteristic
72C2×Dic362C2311yescharacteristic
73C2×D724—21no—
74C2×D724—21no—
75C2×D724C2311yescharacteristic
76C2×D724C2311yescharacteristic
77C2×D724C2311yescharacteristic
78C2×C22⋊D181—21no—
79C2×C22⋊D181—21no—
80C2×C22⋊D181—21no—
81C2×C22⋊D181—21no—
82C2×C22⋊D181—21no—
83C2×C22⋊D181—21no—
84C22×Dic181—21no—
85C2×C4×D181—21no—
86C2×C4×D181—21no—
87C2×C4×D181—21no—
88Dic724—22no—
89Dic724D414yescomplemented
90#15668438—22no—
91#15668438—22no—
92#15668438—22no—
93#15668438—22no—
94#15668438—41no—
95D1448—22no—
96D1448—41no—
97C4⋊Dic181C2311yescharacteristic
98C4⋊Dic181C2311yescharacteristic
99#15668428—21no—
100#15668428—21no—
101#15668428—21no—
102C22⋊Dic181—21no—
103#15668426—21no—
104#15668426—21no—
105#15668426—21no—
106#15668426—21no—
107#15668426—21no—
108C4×Dic181—21no—
109C4×Dic181—21no—
110C2×D4×C181D411yescharacteristic
111C22×C4×C181C2311yescharacteristic
112C22×C4×C181C2311yescharacteristic
113M16×C181—22no—
114C2×C8×C181—22no—
115C2×C8×C181C2311yescharacteristic
116C2×C8×C181C2311yescharacteristic
117C2×C8×C181C2311yescharacteristic
118C2×C8×C181C2311yescharacteristic
119C4⋊C4×C181D411yescharacteristic
120C22⋊C4×C181D411yescharacteristic
121C22⋊C4×C181D411yescharacteristic
122C42×C181C2311yescharacteristic
123C22×D181—21no—
124C22×D181—21no—
125C22×D181—21no—
126Dic362—21no—
127Dic362—21no—
128Dic362—21no—
129Dic362—21no—
130Dic362—42no—
131Dic362C2×D412yes—
132Dic362C2×D412yes—
133D724—21no—
134D724—21no—
135D724—21no—
136D724—21no—
137D724—21no—
138D724—21no—
139D724—42no—
140D724—81no—
141C22⋊D181—42no—
142C22⋊D181—42no—
143C22⋊D181—42no—
144C22⋊D181—42no—
145C22⋊D181—81no—
146C22⋊D181—81no—
147C2×Dic181—21no—
148C2×Dic181—21no—
149C2×Dic181—21no—
150C2×Dic181—21no—
151C2×Dic181—21no—
152C2×Dic181—42no—
153C4×D181—42no—
154C4×D181—42no—
155C4×D181—42no—
156C23×C181C2×D411yescharacteristic
157C23×C181C2×D411yescharacteristic
158D4×C181—41no—
159C2×C4×C181—21no—
160C2×C4×C181—21no—
161C2×C4×C181—21no—
162C2×C4×C181—21no—
163C2×C4×C181C2×D411yescharacteristic
164C2×C4×C181C2×D411yescharacteristic
165C2×C4×C181C2×D411yescharacteristic
166C2×C4×C181C2×D411yescharacteristic
167C2×C4×C181C2411yescharacteristic
168C8×C181—21no—
169C8×C181—21no—
170C8×C181—21no—
171C8×C181C2×D412yes—
172C22×C181—21no—
173C22×C181—21no—
174C22×C181—21no—
175C22×C181—21no—
176C22×C181—21no—
177C22×C181—21no—
178C22×C181C22×D411yescharacteristic
179C2×D181—41no—
180C2×D181—41no—
181C2×D181—41no—
182C2×D181—41no—
183C2×D181—41no—
184C2×D181—41no—
185C2×D181—41no—
186C2×D181—41no—
187C2×D181—41no—
188C4×C181—21no—
189C4×C181—21no—
190C4×C181—21no—
191C4×C181—21no—
192C4×C181C22×D411yescharacteristic
193C4×C181H(5,𝔽2)11yescharacteristic
194Dic181—22no—
195Dic181—22no—
196Dic181—41no—
197Dic181—41no—
198Dic181—41no—
199C2×C181—41no—
200C2×C181—41no—
201C2×C181D4211yescharacteristic
202C2×C181#57511yescharacteristic
203C2×C181#57711yescharacteristic
204D181—81no—
205D181—81no—
206D181—81no—
207C181#327111yescharacteristic, complemented, Sylow
208#3271—1811nomaximal, Sylow
209C2×#137—1811no—
210C2×#135—1811no—
211#550—1811no—
212#548—1811no—
213#496—1811no—
214#469—1811no—
215#465—1811no—
216#464—1811no—
217#460—1811no—
218#452—1811no—
219#449—1811no—
220#449—1811no—
221#448—1811no—
222#441—1811no—
223#435D18111yescharacteristic, complemented
224C2×#41—1811no—
225C2×#41—1811no—
226C2×#41—1811no—
227C22×Q8—1811no—
228#137—3624no—
229#135—3624no—
230C2×Q16—1811no—
231C2×Q16—1811no—
232C2×SD16—1811no—
233C2×SD16—1811no—
234C2×SD16—1811no—
235C2×SD16—1811no—
236C2×SD16—1811no—
237C2×D8—1811no—
238C2×D8—1811no—
239C2×M16C2×D18111yescharacteristic
240C22×C8C2×D18111yescharacteristic
241#127—3621no—
242#127—1811no—
243#124—3621no—
244#124—1811no—
245C22⋊Q8—3621no—
246C22⋊Q8—1811no—
247#121—3621no—
248#121—3621no—
249#121—3621no—
250#121—1811no—
251#121—1811no—
252#121—1811no—
253C4×Q8—1811no—
254C4×Q8—1811no—
255C4×D4—3621no—
256C4×D4—3621no—
257C4×D4C2×D18111yescharacteristic
258#106—1811no—
259C4⋊C8C2×D18111yescharacteristic
260#103—1811no—
261#103—1811no—
262#103—1811no—
263#102—1811no—
264#102—1811no—
265#102—1811no—
266C22⋊C8C2×D18111yescharacteristic
267C22⋊C8C2×D18111yescharacteristic
268#97C2×D18111yescharacteristic
269#41—3622no—
270#41—3622no—
271#41—3622no—
272#41—7241no—
273#41—7241no—
274#41—7241no—
275C2×Q8—3622no—
276C2×Q8—3621no—
277C2×Q8—1811no—
278C2×Q8—1811no—
279C2×Q8—1811no—
280C2×Q8—7241no—
281C2×D4—3621no—
282C2×D4—3621no—
283C2×D4—3621no—
284C2×D4—3621no—
285C2×D4—3621no—
286C2×D4—3621no—
287C2×D4—3621no—
288C2×D4—3621no—
289C2×D4—1811no—
290C2×D4—1811no—
291C2×D4—1811no—
292C2×D4D72411yescharacteristic
293C22×C4—3621no—
294C22×C4—3621no—
295C22×C4—3621no—
296C22×C4—3621no—
297C22×C4C22×D18111yescharacteristic
298C22×C4C22×D18111yescharacteristic
299Q16—3622no—
300Q16—1814no—
301SD16—3622no—
302SD16—3622no—
303SD16—3622no—
304SD16—3622no—
305SD16—7241no—
306D8—3622no—
307D8—7241no—
308M16—22no—
309C2×C8—22no—
310C2×C8C22×D18111yescharacteristic
311C2×C8C22×D18111yescharacteristic
312C2×C8C22×D18111yescharacteristic
313C2×C8C22×D18111yescharacteristic
314C4⋊C4—3621no—
315C4⋊C4—3621no—
316C4⋊C4—3621no—
317C4⋊C4—1811no—
318C4⋊C4—1811no—
319C4⋊C4D72411yescharacteristic
320C22⋊C4—3621no—
321C22⋊C4—3621no—
322C22⋊C4—3621no—
323C22⋊C4—3621no—
324C22⋊C4—3621no—
325C22⋊C4—3621no—
326C22⋊C4D72411yescharacteristic
327C22⋊C4D72411yescharacteristic
328C42—3621no—
329C42—3621no—
330C42C22×D18111yescharacteristic
331C23—3621no—
332C23—3621no—
333C23—3621no—
334C23C2×D72411yescharacteristic
335C23C2×D72411yescharacteristic
336Q8—3621no—
337Q8—3621no—
338Q8—3621no—
339Q8—3621no—
340Q8—1812no—
341Q8—1812no—
342Q8—7242no—
343D4—41no—
344D4—3621no—
345D4—3621no—
346D4—3621no—
347D4—3621no—
348D4—3621no—
349D4—3621no—
350D4—14481no—
351D4—14481no—
352D4—14481no—
353D4—7242no—
354D4—7242no—
355D4—7242no—
356D4—7242no—
357D4—7242no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—3621no—
363C2×C4—3621no—
364C2×C4—3621no—
365C2×C4—3621no—
366C2×C4—3621no—
367C2×C4—7242no—
368C2×C4—7242no—
369C2×C4—7242no—
370C2×C4—7242no—
371C2×C4C2×D72411yescharacteristic
372C2×C4C2×D72411yescharacteristic
373C2×C4C2×D72411yescharacteristic
374C2×C4C2×D72411yescharacteristic
375C2×C4C23×D18111yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8D4×D18112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—7241no—
387C22—7241no—
388C22—7241no—
389C22—7241no—
390C22—7241no—
391C22—7241no—
392C22—7241no—
393C22—7241no—
394C22—7241no—
395C22C22×D72411yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—3622no—
401C4—3622no—
402C4—7241no—
403C4—7241no—
404C4—7241no—
405C4C2×D4×D18111yescharacteristic
406C4#1915386211yescharacteristic
407C2—41no—
408C2—41no—
409C2—14481no—
410C2—14481no—
411C2—14481no—
412C2D4×D72411yescharacteristic
413C2#2604207911yescharacteristic
414C2#2604209111yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#435×C181C2
socleC22×C181C22×D4
hypercenter#435D181
hypocenterC181#3271
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#19153849C2semidirect
2. C2×#19153838C2semidirect
3. #26041950C2semidirect
4. #26041938C2semidirect
5. #26041668C2semidirect
6. #26041532C2semidirect
7. #26041508C2semidirect
8. #26041502C2semidirect
9. #26041480C2semidirect
10. #26041443C2semidirect
11. #26041426C2semidirect
12. #26041426C2semidirect
13. #26041420C2semidirect
14. #26041387C2semidirect
15. #435×C181C2semidirect
89. Dic724D4semidirect
207. C181#3271semidirect
223. #435D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538492
C2×#191538382
#260419502
#260419382
#260416682
#260415322
#260415082
#260415022
#260414802
#260414432
#260414262
#260414202
#260413872
#435×C1812
#3271181