Finite Group Databasebeta

← #47986425

Subgroups — #47986425

Order 35456.

560 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22579840C211yesmaximal, characteristic
2C2×#22579836C211yesmaximal, characteristic, complemented
3#31799943C211yesmaximal, characteristic, complemented
4#31799937C211yesmaximal, characteristic, complemented
5#31799936C211yesmaximal, characteristic, complemented
6#31799931C211yesmaximal, characteristic, complemented
7#31799930C211yesmaximal, characteristic, complemented
8#31799918C211yesmaximal, characteristic
9#31799917C211yesmaximal, characteristic
10C4⋊C4×Dic277C211yesmaximal, characteristic, complemented
11#31799853C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic277C211yesmaximal, characteristic, complemented
13#31799849C211yesmaximal, characteristic, complemented
14#31799849C211yesmaximal, characteristic, complemented
15#397×C277C211yesmaximal, characteristic, complemented
16C22×C22⋊D277C2211yescharacteristic
17C23×Dic277C2211yescharacteristic
18C22×C4×D277C2211yescharacteristic
19#22579840—24no—
20#22579836—24no—
21C2×C4⋊Dic277C2211yescharacteristic
22C2×#17984542C2211yescharacteristic
23C2×#17984542C2211yescharacteristic
24C2×#17984542C2211yescharacteristic
25C2×#17984542C2211yescharacteristic
26C2×#17984542C2211yescharacteristic
27C2×C22⋊Dic277C2211yescharacteristic
28C2×C22⋊Dic277C2211yescharacteristic
29C2×#17984540C2211yescharacteristic
30C2×#17984540C2211yescharacteristic
31C2×#17984540C2211yescharacteristic
32C2×#17984540C2211yescharacteristic
33C2×#17984540C2211yescharacteristic
34C2×C4×Dic277C2211yescharacteristic
35C2×C4×Dic277C2211yescharacteristic
36C2×C4×Dic277C2211yescharacteristic
37C2×C4×Dic277C2211yescharacteristic
38C2×C4×Dic277C2211yescharacteristic
39#22579787C2211yescharacteristic
40#22579787C2211yescharacteristic
41#22579787C2211yescharacteristic
42#22579787C2211yescharacteristic
43#22579787C2211yescharacteristic
44#22579787C2211yescharacteristic
45#22579787C2211yescharacteristic
46C2×C4⋊C4×C277C2211yescharacteristic
47C2×C22⋊C4×C277C2211yescharacteristic
48C2×C22⋊C4×C277C2211yescharacteristic
49C2×C22⋊C4×C277C2211yescharacteristic
50#95×C277C2211yescharacteristic
51#95×C277C2211yescharacteristic
52#95×C277C2211yescharacteristic
53C23×D277C2311yescharacteristic
54C2×C22⋊D277—22no—
55C2×C22⋊D277—22no—
56C2×C22⋊D277—22no—
57C22×Dic277—22no—
58C22×Dic277—22no—
59C22×Dic277D414yes—
60C22×Dic277C2311yescharacteristic
61C22×Dic277C2311yescharacteristic
62C22×Dic277C2311yescharacteristic
63C22×Dic277C2311yescharacteristic
64C22×Dic277C2311yescharacteristic
65C22×Dic277C2311yescharacteristic
66C22×Dic277C2311yescharacteristic
67C2×C4×D277—22no—
68C2×C4×D277—22no—
69C2×C4×D277—22no—
70C4⋊Dic277—22no—
71#17984542—22no—
72#17984542—22no—
73#17984542—22no—
74#17984542—22no—
75#17984542—22no—
76C22⋊Dic277—22no—
77C22⋊Dic277—22no—
78#17984540—22no—
79#17984540—22no—
80#17984540—22no—
81#17984540—22no—
82#17984540—22no—
83C4×Dic277—22no—
84C4×Dic277—22no—
85C4×Dic277—22no—
86C4×Dic277—22no—
87C4×Dic277—22no—
88C24×C277C2311yescharacteristic
89C22×C4×C277C2311yescharacteristic
90C22×C4×C277C2311yescharacteristic
91C22×C4×C277C2311yescharacteristic
92C22×C4×C277C2311yescharacteristic
93C22×C4×C277C2311yescharacteristic
94C22×C4×C277C2311yescharacteristic
95C4⋊C4×C277—22no—
96C22⋊C4×C277—22no—
97C22⋊C4×C277—22no—
98C22⋊C4×C277—22no—
99C22×D277—21no—
100C22×D277—21no—
101C22×D277—21no—
102C22×D277—21no—
103C22×D277—21no—
104C22×D277—21no—
105C22×D277#4112yes—
106C22⋊D277—28no—
107C2×Dic277—21no—
108C2×Dic277—21no—
109C2×Dic277—21no—
110C2×Dic277—21no—
111C2×Dic277—21no—
112C2×Dic277—21no—
113C2×Dic277—28no—
114C2×Dic277—21no—
115C2×Dic277—21no—
116C2×Dic277—21no—
117C2×Dic277—21no—
118C2×Dic277—21no—
119C2×Dic277—21no—
120C2×Dic277—21no—
121C2×Dic277—21no—
122C2×Dic277—21no—
123C2×Dic277C2×D412yes—
124C2×Dic277C2×D412yes—
125C2×Dic277#4112yes—
126C2×Dic277#4112yes—
127C2×Dic277#4112yes—
128C2×Dic277#4112yes—
129C4×D277—44no—
130C23×C277—21no—
131C23×C277—21no—
132C23×C277—21no—
133C23×C277—21no—
134C23×C277—21no—
135C23×C277—21no—
136C23×C277C2×D412yes—
137C23×C277C2411yescharacteristic
138C2×C4×C277—21no—
139C2×C4×C277—21no—
140C2×C4×C277—21no—
141C2×C4×C277—21no—
142C2×C4×C277—21no—
143C2×C4×C277—21no—
144C2×C4×C277—21no—
145C2×C4×C277—21no—
146C2×C4×C277—21no—
147C2×C4×C277—21no—
148C2×C4×C277—21no—
149C2×C4×C277—21no—
150C2×C4×C277—21no—
151C2×C4×C277—21no—
152C2×C4×C277—21no—
153C2×C4×C277—21no—
154C2×C4×C277—21no—
155C2×C4×C277#4112yes—
156C22×C277—22no—
157C22×C277—22no—
158C22×C277—22no—
159C22×C277—41no—
160C22×C277—41no—
161C22×C277—41no—
162C22×C277—41no—
163C22×C277C22×D411yescharacteristic
164C22×C277C2×#4111yescharacteristic
165C22×C277C2×#4111yescharacteristic
166C22×C277C2×#4111yescharacteristic
167C22×C277C2×#4111yescharacteristic
168C22×C277C2×#4111yescharacteristic
169C22×C277C2×#4111yescharacteristic
170C2×D277—22no—
171C2×D277—22no—
172C2×D277—22no—
173C2×D277—41no—
174C2×D277—41no—
175C2×D277—41no—
176C2×D277—41no—
177C4×C277—22no—
178C4×C277—41no—
179C4×C277—41no—
180C4×C277—41no—
181C4×C277—41no—
182C4×C277—41no—
183Dic277—22no—
184Dic277—22no—
185Dic277—22no—
186Dic277—41no—
187Dic277—41no—
188Dic277—41no—
189Dic277#12314yes—
190C2×C277—42no—
191C2×C277C2×#12311yescharacteristic
192C2×C277#52511yescharacteristic
193C2×C277#52911yescharacteristic
194C2×C277#52911yescharacteristic
195C2×C277#52911yescharacteristic
196C2×C277#52911yescharacteristic
197C2×C277#53211yescharacteristic
198D277—42no—
199C277#239511yescharacteristic, complemented, Sylow
200#2395—2771nomaximal, Sylow
201C2×C4×D4—2771no—
202C2×#117—2771no—
203#400—2771no—
204#399—2771no—
205#398—2771no—
206#397—2771no—
207#397—2771no—
208#397D27711yescharacteristic, complemented
209#394—2771no—
210#394—2771no—
211C4×C4⋊C4—2771no—
212C4×C4⋊C4—2771no—
213C4×C22⋊C4—2771no—
214C4×C22⋊C4—2771no—
215C4×C22⋊C4—2771no—
216C22×D4—2771no—
217C23×C4—2771no—
218C23×C4—2771no—
219C4×D4—5544no—
220#117—5544no—
221C2×C4⋊C4—2771no—
222C2×C4⋊C4—2771no—
223C2×C4⋊C4—2771no—
224C2×C4⋊C4—2771no—
225C2×C4⋊C4—2771no—
226C2×C4⋊C4—2771no—
227C2×C4⋊C4C2×D27711yescharacteristic
228C2×C22⋊C4—2771no—
229C2×C22⋊C4—2771no—
230C2×C22⋊C4—2771no—
231C2×C22⋊C4—2771no—
232C2×C22⋊C4—2771no—
233C2×C22⋊C4—2771no—
234C2×C22⋊C4—2771no—
235C2×C22⋊C4C2×D27711yescharacteristic
236C2×C22⋊C4C2×D27711yescharacteristic
237C2×C22⋊C4C2×D27711yescharacteristic
238C2×C42—2771no—
239C2×C42—2771no—
240C2×C42—2771no—
241C2×C42—2771no—
242C2×C42—2771no—
243#95—2771no—
244#95—2771no—
245#95—2771no—
246#95—2771no—
247#95—2771no—
248#95—2771no—
249#95—2771no—
250#95C2×D27711yescharacteristic
251#95C2×D27711yescharacteristic
252#95C2×D27711yescharacteristic
253C24—2771no—
254C24C22×D27711yescharacteristic
255C2×D4—5542no—
256C2×D4—5542no—
257C2×D4—5542no—
258C22×C4—2771no—
259C22×C4—2774no—
260C22×C4—2771no—
261C22×C4—2771no—
262C22×C4—2771no—
263C22×C4—2771no—
264C22×C4—2771no—
265C22×C4—2771no—
266C22×C4—5542no—
267C22×C4—5542no—
268C22×C4—5542no—
269C22×C4—5542no—
270C22×C4—5542no—
271C22×C4C22×D27711yescharacteristic
272C22×C4C22×D27711yescharacteristic
273C22×C4C22×D27711yescharacteristic
274C22×C4C22×D27711yescharacteristic
275C22×C4C22×D27711yescharacteristic
276C22×C4C22×D27711yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—5542no—
279C4⋊C4—5542no—
280C4⋊C4—5542no—
281C4⋊C4—5542no—
282C4⋊C4—5542no—
283C4⋊C4—5542no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—5542no—
288C22⋊C4—5542no—
289C22⋊C4—5542no—
290C22⋊C4—5542no—
291C22⋊C4—5542no—
292C22⋊C4—5542no—
293C22⋊C4—5542no—
294C42—5542no—
295C42—5542no—
296C42—5542no—
297C42—5542no—
298C42—5542no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—2772no—
306C23—5541no—
307C23—5541no—
308C23—5541no—
309C23—5541no—
310C23—5541no—
311C23—5541no—
312C23D4×D27712yes—
313C23C23×D27711yescharacteristic
314D4—5548no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—2772no—
333C2×C4—2772no—
334C2×C4—2772no—
335C2×C4—2772no—
336C2×C4—2772no—
337C2×C4—2772no—
338C2×C4—5548no—
339C2×C4—5541no—
340C2×C4—5541no—
341C2×C4—5541no—
342C2×C4—5541no—
343C2×C4—5541no—
344C2×C4—5541no—
345C2×C4—5541no—
346C2×C4—5541no—
347C2×C4—5541no—
348C2×C4—5541no—
349C2×C4—5541no—
350C2×C4—5541no—
351C2×C4—5541no—
352C2×C4—5541no—
353C2×C4—5541no—
354C2×C4—11084no—
355C2×C4#1798456212yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—5542no—
364C22—5542no—
365C22—5542no—
366C22—11081no—
367C22—11081no—
368C22—11081no—
369C22—11081no—
370C22C2×D4×D27711yescharacteristic
371C22#41×D27711yescharacteristic
372C22#41×D27711yescharacteristic
373C22#41×D27711yescharacteristic
374C22#41×D27711yescharacteristic
375C22#41×D27711yescharacteristic
376C22C2×#1798456211yescharacteristic
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—2774no—
384C4—5542no—
385C4—5542no—
386C4—5542no—
387C4—11081no—
388C4—11081no—
389C4—11081no—
390C2—42no—
391C2—11082no—
392C2#123×D27711yescharacteristic
393C2#3180051011yescharacteristic
394C2#3180052911yescharacteristic
395C2#3180053111yescharacteristic
396C2#3180053511yescharacteristic
397C2#3180053511yescharacteristic
398C2#3180054711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutator, socle, cosocleC23×C277C24
Fitting#397×C277C2
prime radicalC22×C22⋊D277C22
hypercenter#397D277
hypocenterC277#2395
LCSG ▷ C23×C277 ▷ C277
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#22579836C2semidirect
3. #31799943C2semidirect
4. #31799937C2semidirect
5. #31799936C2semidirect
6. #31799931C2semidirect
7. #31799930C2semidirect
10. C4⋊C4×Dic277C2semidirect
11. #31799853C2semidirect
12. C22⋊C4×Dic277C2semidirect
13. #31799849C2semidirect
14. #31799849C2semidirect
15. #397×C277C2semidirect
199. C277#2395semidirect
208. #397D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798402
C2×#225798362
#317999432
#317999372
#317999362
#317999312
#317999302
#317999182
#317999172
C4⋊C4×Dic2772
#317998532
C22⋊C4×Dic2772
#317998492
#397×C2772
#2395277