Finite Group Databasebeta

← #46813791

Subgroups — #46813791

Order 34432.

704 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D269C211yesmaximal, characteristic
2C2×#22575413C211yesmaximal, characteristic
3C2×#22575413C211yesmaximal, characteristic
4#31770502C211yesmaximal, characteristic, complemented
5#31770500C211yesmaximal, characteristic, complemented
6#31770480C211yesmaximal, characteristic, complemented
7#31770479C211yesmaximal, characteristic, complemented
8#31770476C211yesmaximal, characteristic, complemented
9#31770469C211yesmaximal, characteristic, complemented
10#31770463C211yesmaximal, characteristic, complemented
11#31770462C211yesmaximal, characteristic, complemented
12C4⋊C4×Dic269C211yesmaximal, characteristic, complemented
13C2×#22575360C211yesmaximal, characteristic, complemented
14#95×D269C211yesmaximal, characteristic, complemented
15#385×C269C211yesmaximal, characteristic, complemented
16C22×C22⋊D269C2211yescharacteristic
17C23×Dic269C2211yescharacteristic
18C23×Dic269C2211yescharacteristic
19C22×C4×D269C2211yescharacteristic
20C22×C4×D269C2211yescharacteristic
21C22×C4×D269C2211yescharacteristic
22C4×C22⋊D269—24no—
23#22575413—24no—
24#22575413C418yescomplemented
25C2×C4⋊Dic269C2211yescharacteristic
26C2×C4⋊Dic269C2211yescharacteristic
27C2×#16864381C2211yescharacteristic
28C2×#16864381C2211yescharacteristic
29C2×#16864381C2211yescharacteristic
30C2×#16864381C2211yescharacteristic
31C2×#16864381C2211yescharacteristic
32C2×C22⋊Dic269C2211yescharacteristic
33C2×#16864379C2211yescharacteristic
34C2×#16864379C2211yescharacteristic
35C2×#16864379C2211yescharacteristic
36C2×C4×Dic269C2211yescharacteristic
37C2×C4×Dic269C2211yescharacteristic
38C2×C4×Dic269C2211yescharacteristic
39#22575360C2211yescharacteristic
40#22575360C2211yescharacteristic
41#22575360C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44#22575360C2211yescharacteristic
45#22575360C2211yescharacteristic
46#22575360C2211yescharacteristic
47C23×C4×C269C2211yescharacteristic
48C2×C4⋊C4×C269C2211yescharacteristic
49C2×C4⋊C4×C269C2211yescharacteristic
50C2×C22⋊C4×C269C2211yescharacteristic
51C2×C22⋊C4×C269C2211yescharacteristic
52#95×C269C2211yescharacteristic
53#95×C269C2211yescharacteristic
54C23×D269C2311yescharacteristic
55C2×C22⋊D269C2×C414yes—
56C2×C22⋊D269D414yes—
57C2×C22⋊D269Q814yes—
58C22×Dic269—22no—
59C22×Dic269—22no—
60C22×Dic269—41no—
61C22×Dic269—41no—
62C22×Dic269—41no—
63C22×Dic269C2×C414yescomplemented
64C22×Dic269C2311yescharacteristic
65C22×Dic269C2311yescharacteristic
66C22×Dic269C2311yescharacteristic
67C22×Dic269C2311yescharacteristic
68C22×Dic269C2311yescharacteristic
69C22×Dic269C2311yescharacteristic
70C22×Dic269C2311yescharacteristic
71C2×C4×D269—22no—
72C2×C4×D269—22no—
73C2×C4×D269—22no—
74C2×C4×D269—22no—
75C2×C4×D269—41no—
76C2×C4×D269—41no—
77C2×C4×D269—41no—
78C2×C4×D269—41no—
79C2×C4×D269C2×C414yescomplemented
80C4⋊Dic269—22no—
81C4⋊Dic269—41no—
82#16864381—22no—
83#16864381—22no—
84#16864381—41no—
85#16864381—41no—
86#16864381C2×C414yescomplemented
87C22⋊Dic269—22no—
88#16864379—22no—
89#16864379—22no—
90#16864379C2×C414yescomplemented
91C4×Dic269—22no—
92C4×Dic269—22no—
93C4×Dic269C2×C414yescomplemented
94C24×C269C2311yescharacteristic
95C22×C4×C269—22no—
96C22×C4×C269—22no—
97C22×C4×C269—41no—
98C22×C4×C269C2311yescharacteristic
99C22×C4×C269C2311yescharacteristic
100C22×C4×C269C2311yescharacteristic
101C22×C4×C269C2311yescharacteristic
102C22×C4×C269C2311yescharacteristic
103C22×C4×C269C2311yescharacteristic
104C4⋊C4×C269—22no—
105C4⋊C4×C269—41no—
106C22⋊C4×C269—22no—
107C22⋊C4×C269C2×C414yescomplemented
108C22×D269—21no—
109C22×D269—21no—
110C22×D269—21no—
111C22×D269—21no—
112C22×D269C22×C412yes—
113C22×D269C2×D412yes—
114C22×D269C2×Q812yes—
115C22⋊D269C4⋊C4116yescomplemented
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269—21no—
131C2×Dic269—44no—
132C2×Dic269—44no—
133C2×Dic269C22×C412yes—
134C2×Dic269C22×C412yes—
135C2×Dic269C22×C412yes—
136C2×Dic269C2×D412yes—
137C2×Dic269C2×Q812yes—
138C2×Dic269#4112yes—
139C4×D269—44no—
140C4×D269—44no—
141C4×D269—44no—
142C23×C269—21no—
143C23×C269—21no—
144C23×C269—21no—
145C23×C269—21no—
146C23×C269C22×C412yes—
147C23×C269C2×D412yes—
148C23×C269C2×Q812yes—
149C23×C269C2411yescharacteristic
150C2×C4×C269—21no—
151C2×C4×C269—21no—
152C2×C4×C269—21no—
153C2×C4×C269—21no—
154C2×C4×C269—21no—
155C2×C4×C269—21no—
156C2×C4×C269—21no—
157C2×C4×C269—21no—
158C2×C4×C269—21no—
159C2×C4×C269—21no—
160C2×C4×C269—21no—
161C2×C4×C269—21no—
162C2×C4×C269—21no—
163C2×C4×C269—21no—
164C2×C4×C269—21no—
165C2×C4×C269—44no—
166C2×C4×C269C22×C412yes—
167C2×C4×C269C22×C412yes—
168C2×C4×C269#4112yes—
169C22×C269—22no—
170C22×C269—22no—
171C22×C269—22no—
172C22×C269—22no—
173C22×C269—22no—
174C22×C269—22no—
175C22×C269C2×C4⋊C414yes—
176C22×C269C23×C411yescharacteristic
177C22×C269C22×D411yescharacteristic
178C22×C269C22×Q811yescharacteristic
179C22×C269C2×#4111yescharacteristic
180C22×C269C2×#4111yescharacteristic
181C22×C269H(5,𝔽2)11yescharacteristic
182C22×C269H(5,𝔽2)11yescharacteristic
183C2×D269—22no—
184C2×D269—22no—
185C2×D269—22no—
186C2×D269—22no—
187C2×D269—22no—
188C2×D269—22no—
189C2×D269C2×C4⋊C414yes—
190C4×C269—22no—
191C4×C269—22no—
192C4×C269—22no—
193C4×C269—41no—
194C4×C269—41no—
195C4×C269—41no—
196Dic269—22no—
197Dic269—22no—
198Dic269—22no—
199Dic269—41no—
200Dic269—41no—
201Dic269—41no—
202Dic269C2×C4⋊C414yes—
203C2×C269—24no—
204C2×C269C22×C4⋊C411yescharacteristic
205C2×C269C4×#4111yescharacteristic
206C2×C269#51811yescharacteristic
207C2×C269#54611yescharacteristic
208C2×C269#54611yescharacteristic
209C2×C269#55411yescharacteristic
210C2×C269#55411yescharacteristic
211D269—24no—
212C269#234911yescharacteristic, complemented, Sylow
213#2349—2691nomaximal, Sylow
214C2×C4×D4—2691no—
215C2×C4×D4—2691no—
216C2×C4×D4—2691no—
217#389—2691no—
218#389—2691no—
219#385—2691no—
220#385—2691no—
221#385—2691no—
222#385D26911yescharacteristic, complemented
223#382—2691no—
224#380—2691no—
225#380—2691no—
226C4×C4⋊C4—2691no—
227C2×#95—2691no—
228C2×#95—2691no—
229C22×D4—2691no—
230C23×C4—2691no—
231C23×C4—2691no—
232C23×C4—2691no—
233C23×C4—2691no—
234C23×C4—2691no—
235C23×C4C2×D26911yescharacteristic
236C4×D4—2698no—
237C4×D4—5384no—
238C4×D4—5384no—
239C2×C4⋊C4—2691no—
240C2×C4⋊C4—2691no—
241C2×C4⋊C4—2691no—
242C2×C4⋊C4—2691no—
243C2×C4⋊C4—2691no—
244C2×C4⋊C4—2691no—
245C2×C4⋊C4—2691no—
246C2×C4⋊C4C2×D26911yescharacteristic
247C2×C4⋊C4C2×D26911yescharacteristic
248C2×C22⋊C4—2691no—
249C2×C22⋊C4—2691no—
250C2×C22⋊C4—2691no—
251C2×C22⋊C4—2691no—
252C2×C22⋊C4C2×D26911yescharacteristic
253C2×C22⋊C4C2×D26911yescharacteristic
254C2×C42—2691no—
255C2×C42—2691no—
256C2×C42—2691no—
257#95—2691no—
258#95—2691no—
259#95—2691no—
260#95—2691no—
261#95—2691no—
262#95—2691no—
263#95—2691no—
264#95—2691no—
265#95C2×D26911yescharacteristic
266#95C2×D26911yescharacteristic
267C24—2691no—
268C24C22×D26911yescharacteristic
269C2×D4—2694no—
270C2×D4—2694no—
271C2×D4—2694no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—41no—
275C22×C4—2691no—
276C22×C4—2691no—
277C22×C4—2691no—
278C22×C4—2691no—
279C22×C4—2694no—
280C22×C4—2694no—
281C22×C4—2691no—
282C22×C4—2691no—
283C22×C4—2691no—
284C22×C4—5382no—
285C22×C4—5382no—
286C22×C4—5382no—
287C22×C4—5382no—
288C22×C4—5382no—
289C22×C4—5382no—
290C22×C4—10761no—
291C22×C4—10761no—
292C22×C4—10761no—
293C22×C4—10761no—
294C22×C4—10761no—
295C22×C4—10761no—
296C22×C4—10761no—
297C22×C4C22×D26911yescharacteristic
298C22×C4C22×D26911yescharacteristic
299C22×C4C22×D26911yescharacteristic
300C22×C4C22×D26911yescharacteristic
301C22×C4C22×D26911yescharacteristic
302C22×C4C22×D26911yescharacteristic
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—2694no—
306C4⋊C4—5382no—
307C4⋊C4—5382no—
308C4⋊C4—5382no—
309C4⋊C4—10761no—
310C4⋊C4—10761no—
311C4⋊C4—10761no—
312C22⋊C4—22no—
313C22⋊C4—2694no—
314C22⋊C4—5382no—
315C22⋊C4—5382no—
316C22⋊C4—5382no—
317C22⋊C4C4×D26914yescomplemented
318C42—2694no—
319C42—5382no—
320C42—5382no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—2692no—
326C23—2692no—
327C23—2692no—
328C23—5381no—
329C23—5381no—
330C23—5381no—
331C23—5381no—
332C23C2×C4×D26912yes—
333C23D4×D26912yes—
334C23Q8×D26912yes—
335C23C23×D26911yescharacteristic
336D4—26916no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—44no—
353C2×C4—2692no—
354C2×C4—2692no—
355C2×C4—2692no—
356C2×C4—2692no—
357C2×C4—2692no—
358C2×C4—2692no—
359C2×C4—5381no—
360C2×C4—5381no—
361C2×C4—5381no—
362C2×C4—5381no—
363C2×C4—5381no—
364C2×C4—5381no—
365C2×C4—5381no—
366C2×C4—5381no—
367C2×C4—5381no—
368C2×C4—5381no—
369C2×C4—5381no—
370C2×C4—5381no—
371C2×C4—5381no—
372C2×C4—5381no—
373C2×C4—5381no—
374C2×C4—10764no—
375C2×C4—10764no—
376C2×C4—10764no—
377C2×C4—10764no—
378C2×C4—10764no—
379C2×C4C2×C4×D26912yes—
380C2×C4C2×C4×D26912yes—
381C2×C4#1686440112yes—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—2694no—
389C22—5382no—
390C22—5382no—
391C22—5382no—
392C22—5382no—
393C22—5382no—
394C22—5382no—
395C22C4⋊C4×D26914yes—
396C22C22×C4×D26911yescharacteristic
397C22C2×D4×D26911yescharacteristic
398C22C2×Q8×D26911yescharacteristic
399C22#41×D26911yescharacteristic
400C22C2×#1686440111yescharacteristic
401C22#2257549811yescharacteristic
402C22#2257549911yescharacteristic
403C4—22no—
404C4—22no—
405C4—22no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—2694no—
410C4—5382no—
411C4—5382no—
412C4—5382no—
413C4—10761no—
414C4—10761no—
415C4—10761no—
416C2—24no—
417C2—5384no—
418C2C2×C4⋊C4×D26911yescharacteristic
419C2C4×#1686440111yescharacteristic
420C2#3177107711yescharacteristic
421C2#3177124211yescharacteristic
422C2#3177124711yescharacteristic
423C2#3177130911yescharacteristic
424C2#3177131311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#385×C269C2
socle, cosocleC23×C269C24
prime radicalC22×C22⋊D269C22
hypercenter#385D269
hypocenterC269#2349
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
4. #31770502C2semidirect
5. #31770500C2semidirect
6. #31770480C2semidirect
7. #31770479C2semidirect
8. #31770476C2semidirect
9. #31770469C2semidirect
10. #31770463C2semidirect
11. #31770462C2semidirect
12. C4⋊C4×Dic269C2semidirect
13. C2×#22575360C2semidirect
14. #95×D269C2semidirect
15. #385×C269C2semidirect
24. #22575413C4semidirect
63. C22×Dic269C2×C4semidirect
79. C2×C4×D269C2×C4semidirect
86. #16864381C2×C4semidirect
90. #16864379C2×C4semidirect
93. C4×Dic269C2×C4semidirect
107. C22⋊C4×C269C2×C4semidirect
115. C22⋊D269C4⋊C4semidirect
212. C269#2349semidirect
222. #385D269semidirect
317. C22⋊C4C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D2692
C2×#225754132
#317705022
#317705002
#317704802
#317704792
#317704762
#317704692
#317704632
#317704622
C4⋊C4×Dic2692
C2×#225753602
#95×D2692
#385×C2692
#2349269