Finite Group Databasebeta

← #46847924

Subgroups — #46847924

Order 34688.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22576193C211yesmaximal, characteristic, complemented
2C2×#22576182C211yesmaximal, characteristic, complemented
3#31774556C211yesmaximal, characteristic, complemented
4#31774552C211yesmaximal, characteristic, complemented
5#31774291C211yesmaximal, characteristic, complemented
6#31774143C211yesmaximal, characteristic, complemented
7#31774138C211yesmaximal, characteristic, complemented
8#31774113C211yesmaximal, characteristic, complemented
9#31774108C211yesmaximal, characteristic, complemented
10#31774061C211yesmaximal, characteristic, complemented
11#31774061C211yesmaximal, characteristic, complemented
12#31774055C211yesmaximal, characteristic, complemented
13#31774044C211yesmaximal, characteristic, complemented
14#31773999C211yesmaximal, characteristic, complemented
15#435×C271C211yesmaximal, characteristic, complemented
16C2×#16864654C2211yescharacteristic
17C2×#16864654C2211yescharacteristic
18C2×#16864654C2211yescharacteristic
19C22×Dic542C2211yescharacteristic
20#22576193—24no—
21#22576182—24no—
22C2×Dic1084C2211yescharacteristic
23C2×Dic1084C2211yescharacteristic
24C2×Dic1084C2211yescharacteristic
25C2×Dic1084C2211yescharacteristic
26C2×#16864643C2211yescharacteristic
27C2×#16864643C2211yescharacteristic
28C2×#16864643C2211yescharacteristic
29C2×#16864643C2211yescharacteristic
30C2×D2168C2211yescharacteristic
31#22576160C2211yescharacteristic
32#22576148C2211yescharacteristic
33#22576146—21no—
34#22576142—21no—
35#22576142—21no—
36#22576139C2211yescharacteristic
37#22576139C2211yescharacteristic
38#22576139C2211yescharacteristic
39#22576138—21no—
40#22576134C2211yescharacteristic
41#22576132—21no—
42#22576131—21no—
43C4×Dic542C2211yescharacteristic
44C4×D1084C2211yescharacteristic
45(C22⋊D271)⋊C4—21no—
46C4⋊C4×D271—21no—
47#22576094C2211yescharacteristic
48#22576085C2211yescharacteristic
49#22576085C2211yescharacteristic
50#22576085C2211yescharacteristic
51#22576085C2211yescharacteristic
52#22576082C2211yescharacteristic
53#22576082C2211yescharacteristic
54C2×M16×C271C2211yescharacteristic
55C22×C8×C271C2211yescharacteristic
56C4×D4×C271C2211yescharacteristic
57C4⋊C8×C271C2211yescharacteristic
58C22⋊C8×C271C2211yescharacteristic
59C22⋊C8×C271C2211yescharacteristic
60#97×C271C2211yescharacteristic
61#16864654—22no—
62#16864654—22no—
63#16864654—22no—
64#16864654—41no—
65#16864654—41no—
66#16864654—41no—
67C2×Dic542—22no—
68C2×Dic542—21no—
69C2×Dic542—41no—
70C2×Dic542C2311yescharacteristic
71C2×Dic542C2311yescharacteristic
72C2×Dic542C2311yescharacteristic
73C2×Dic542C2311yescharacteristic
74C2×D1084C2311yescharacteristic
75C2×D1084C2311yescharacteristic
76C2×C22⋊D271—21no—
77C2×C22⋊D271—21no—
78C2×C22⋊D271—21no—
79C2×C22⋊D271—21no—
80C22×Dic271—21no—
81C2×C4×D271—21no—
82C2×C4×D271—21no—
83C2×C4×D271—21no—
84C2×C4×D271—21no—
85Dic1084—22no—
86Dic1084—22no—
87Dic1084—22no—
88Dic1084—41no—
89#16864643—22no—
90#16864643—22no—
91#16864643—41no—
92#16864643D414yescomplemented
93D2168—22no—
94C4⋊Dic271—21no—
95C4⋊Dic271—21no—
96C4⋊Dic271C2311yescharacteristic
97C4⋊Dic271C2311yescharacteristic
98Dic271⋊C4—21no—
99Dic271⋊C4—21no—
100Dic271⋊C4—21no—
101Dic271⋊C4—21no—
102C22⋊Dic271—21no—
103C22⋊Dic271—21no—
104C22⋊Dic271—21no—
105(C2×D271)⋊C4—21no—
106(C2×D271)⋊C4—21no—
107(C2×D271)⋊C4—21no—
108(C2×D271)⋊C4—21no—
109C4×Dic271—21no—
110C2×D4×C271D411yescharacteristic
111C22×C4×C271C2311yescharacteristic
112C22×C4×C271C2311yescharacteristic
113M16×C271—22no—
114C2×C8×C271—22no—
115C2×C8×C271C2311yescharacteristic
116C2×C8×C271C2311yescharacteristic
117C2×C8×C271C2311yescharacteristic
118C2×C8×C271C2311yescharacteristic
119C4⋊C4×C271D411yescharacteristic
120C22⋊C4×C271D411yescharacteristic
121C22⋊C4×C271D411yescharacteristic
122C42×C271C2311yescharacteristic
123C22×D271—21no—
124C22×D271—21no—
125Dic542—21no—
126Dic542—21no—
127Dic542—21no—
128Dic542—21no—
129Dic542—21no—
130Dic542—21no—
131Dic542—21no—
132Dic542—42no—
133Dic542C2×D412yes—
134D1084—21no—
135D1084—21no—
136D1084—21no—
137D1084C2×D412yes—
138C22⋊D271—42no—
139C22⋊D271—42no—
140C22⋊D271—42no—
141C22⋊D271—42no—
142C2×Dic271—21no—
143C2×Dic271—21no—
144C2×Dic271—21no—
145C2×Dic271—21no—
146C2×Dic271—21no—
147C2×Dic271—21no—
148C2×Dic271—42no—
149C4×D271—42no—
150C4×D271—42no—
151C4×D271—42no—
152C4×D271—42no—
153C23×C271C2×D411yescharacteristic
154C23×C271C2×D411yescharacteristic
155D4×C271—41no—
156C2×C4×C271—21no—
157C2×C4×C271—21no—
158C2×C4×C271—21no—
159C2×C4×C271—21no—
160C2×C4×C271C2×D411yescharacteristic
161C2×C4×C271C2×D411yescharacteristic
162C2×C4×C271C2×D411yescharacteristic
163C2×C4×C271C2×D411yescharacteristic
164C2×C4×C271C2411yescharacteristic
165C8×C271—21no—
166C8×C271—21no—
167C8×C271—21no—
168C8×C271C2×D412yes—
169C22×C271—21no—
170C22×C271—21no—
171C22×C271—21no—
172C22×C271—21no—
173C22×C271—21no—
174C22×C271—21no—
175C22×C271C22×D411yescharacteristic
176C2×D271—22no—
177C2×D271—41no—
178C2×D271—41no—
179C2×D271—41no—
180C2×D271—41no—
181C2×D271—41no—
182C4×C271—21no—
183C4×C271—21no—
184C4×C271—21no—
185C4×C271—21no—
186C4×C271C22×D411yescharacteristic
187C4×C271H(5,𝔽2)11yescharacteristic
188Dic271—22no—
189Dic271—41no—
190Dic271—41no—
191Dic271—41no—
192Dic271—41no—
193Dic271—41no—
194C2×C271—41no—
195C2×C271—41no—
196C2×C271D4211yescharacteristic
197C2×C271#57511yescharacteristic
198C2×C271#57811yescharacteristic
199D271—42no—
200D271—81no—
201C271#326911yescharacteristic, complemented, Sylow
202#3269—2711nomaximal, Sylow
203C2×#137—2711no—
204C2×#135—2711no—
205#548—2711no—
206#547—2711no—
207#497—2711no—
208#468—2711no—
209#467—2711no—
210#463—2711no—
211#462—2711no—
212#452—2711no—
213#452—2711no—
214#451—2711no—
215#449—2711no—
216#440—2711no—
217#435D27111yescharacteristic, complemented
218C2×#41—2711no—
219C2×#41—2711no—
220C2×#41—2711no—
221C22×Q8—2711no—
222#137—5424no—
223#135—5424no—
224C2×Q16—2711no—
225C2×Q16—2711no—
226C2×Q16—2711no—
227C2×Q16—2711no—
228C2×SD16—2711no—
229C2×SD16—2711no—
230C2×SD16—2711no—
231C2×SD16—2711no—
232C2×D8—2711no—
233C2×M16C2×D27111yescharacteristic
234C22×C8C2×D27111yescharacteristic
235C4⋊Q8—2711no—
236#124—2711no—
237#124—5421no—
238#123—5421no—
239#123—5421no—
240C22⋊Q8—2711no—
241C22⋊Q8—2711no—
242C22⋊Q8—2711no—
243C22⋊Q8—5421no—
244#121—2711no—
245#121—5421no—
246#121—5421no—
247C4×Q8—2711no—
248C4×D4—2711no—
249C4×D4—5421no—
250C4×D4C2×D27111yescharacteristic
251C2×C4⋊C4—5421no—
252#107—2711no—
253C4⋊C8C2×D27111yescharacteristic
254#103—2711no—
255#103—2711no—
256#103—2711no—
257#103—2711no—
258#102—2711no—
259#102—2711no—
260C22⋊C8C2×D27111yescharacteristic
261C22⋊C8C2×D27111yescharacteristic
262#97C2×D27111yescharacteristic
263#41—5422no—
264#41—5422no—
265#41—5422no—
266#41—10841no—
267#41—10841no—
268#41—10841no—
269C2×Q8—2711no—
270C2×Q8—2711no—
271C2×Q8—2711no—
272C2×Q8—2711no—
273C2×Q8—5422no—
274C2×Q8—5421no—
275C2×Q8—10841no—
276C2×D4—2711no—
277C2×D4—2711no—
278C2×D4—5421no—
279C2×D4—5421no—
280C2×D4—5421no—
281C2×D4—5421no—
282C2×D4D108411yescharacteristic
283C22×C4—5421no—
284C22×C4—5421no—
285C22×C4—5421no—
286C22×C4—5421no—
287C22×C4—5421no—
288C22×C4C22×D27111yescharacteristic
289C22×C4C22×D27111yescharacteristic
290Q16—5422no—
291Q16—5422no—
292Q16—5422no—
293Q16—10841no—
294SD16—2714no—
295SD16—5422no—
296SD16—5422no—
297SD16—10841no—
298D8—5422no—
299M16—22no—
300C2×C8—22no—
301C2×C8C22×D27111yescharacteristic
302C2×C8C22×D27111yescharacteristic
303C2×C8C22×D27111yescharacteristic
304C2×C8C22×D27111yescharacteristic
305C4⋊C4—2711no—
306C4⋊C4—2711no—
307C4⋊C4—5421no—
308C4⋊C4—5421no—
309C4⋊C4—5421no—
310C4⋊C4—5421no—
311C4⋊C4—5421no—
312C4⋊C4—5421no—
313C4⋊C4D108411yescharacteristic
314C22⋊C4—5421no—
315C22⋊C4—5421no—
316C22⋊C4—5421no—
317C22⋊C4—5421no—
318C22⋊C4—5421no—
319C22⋊C4—5421no—
320C22⋊C4—5421no—
321C22⋊C4D108411yescharacteristic
322C22⋊C4D108411yescharacteristic
323C42—5421no—
324C42C22×D27111yescharacteristic
325C23—5421no—
326C23—5421no—
327C23C2×D108411yescharacteristic
328C23C2×D108411yescharacteristic
329Q8—2712no—
330Q8—5421no—
331Q8—5421no—
332Q8—5421no—
333Q8—5421no—
334Q8—5421no—
335Q8—5421no—
336Q8—5421no—
337Q8—10842no—
338D4—41no—
339D4—2712no—
340D4—5421no—
341D4—5421no—
342D4—5421no—
343D4—10842no—
344D4—10842no—
345D4—10842no—
346D4—10842no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—5421no—
352C2×C4—5421no—
353C2×C4—5421no—
354C2×C4—5421no—
355C2×C4—5421no—
356C2×C4—5421no—
357C2×C4—10842no—
358C2×C4—10842no—
359C2×C4—10842no—
360C2×C4—10842no—
361C2×C4—10842no—
362C2×C4C2×D108411yescharacteristic
363C2×C4C2×D108411yescharacteristic
364C2×C4C2×D108411yescharacteristic
365C2×C4C2×D108411yescharacteristic
366C2×C4C23×D27111yescharacteristic
367C8—21no—
368C8—21no—
369C8—21no—
370C8D4×D27112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—5422no—
378C22—10841no—
379C22—10841no—
380C22—10841no—
381C22—10841no—
382C22—10841no—
383C22C22×D108411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—5422no—
389C4—10841no—
390C4—10841no—
391C4—10841no—
392C4—10841no—
393C4—10841no—
394C4C2×D4×D27111yescharacteristic
395C4#2257620611yescharacteristic
396C2—41no—
397C2—41no—
398C2—10842no—
399C2—21681no—
400C2D4×D108411yescharacteristic
401C2#3177469711yescharacteristic
402C2#3177471411yescharacteristic
subgroupG/H
centerC22C22×D1084
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#435×C271C2
socleC22×C271C22×D4
hypercenter#435D271
hypocenterC271#3269
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#22576193C2semidirect
2. C2×#22576182C2semidirect
3. #31774556C2semidirect
4. #31774552C2semidirect
5. #31774291C2semidirect
6. #31774143C2semidirect
7. #31774138C2semidirect
8. #31774113C2semidirect
9. #31774108C2semidirect
10. #31774061C2semidirect
11. #31774061C2semidirect
12. #31774055C2semidirect
13. #31774044C2semidirect
14. #31773999C2semidirect
15. #435×C271C2semidirect
92. #16864643D4semidirect
201. C271#3269semidirect
217. #435D271semidirect

Maximal subgroups

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

subgroupindex
C2×#225761932
C2×#225761822
#317745562
#317745522
#317742912
#317741432
#317741382
#317741132
#317741082
#317740612
#317740552
#317740442
#317739992
#435×C2712
#3269271