Finite Group Databasebeta

← #27174393

Subgroups — #27174393

Order 12928.

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×C4×C22⋊D101C211yesmaximal, characteristic
2C2×#15692212C211yesmaximal, characteristic, complemented
3#20265118C211yesmaximal, characteristic, complemented
4#20265113C211yesmaximal, characteristic, complemented
5#20265111C211yesmaximal, characteristic, complemented
6#20265106C211yesmaximal, characteristic, complemented
7#20265105C211yesmaximal, characteristic, complemented
8#20265104C211yesmaximal, characteristic, complemented
9#20265093C211yesmaximal, characteristic
10#20265092C211yesmaximal, characteristic
11C4×#13108053C211yesmaximal, characteristic, complemented
12C4×C4⋊Dic101C211yesmaximal, characteristic, complemented
13C4×#13108051C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic101C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
16C22×C22⋊D101C2211yescharacteristic
17C22×C4×D101C2211yescharacteristic
18C4×C22⋊D101—24no—
19#15692212—24no—
20C2×C4⋊Dic101C2211yescharacteristic
21C2×C4⋊Dic101C2211yescharacteristic
22C2×#13108053C2211yescharacteristic
23C2×#13108053C2211yescharacteristic
24C2×#13108053C2211yescharacteristic
25C2×#13108053C2211yescharacteristic
26C2×#13108053C2211yescharacteristic
27C2×C22⋊Dic101C2211yescharacteristic
28C2×C22⋊Dic101C2211yescharacteristic
29C2×C22⋊Dic101C2211yescharacteristic
30C2×#13108051C2211yescharacteristic
31C2×#13108051C2211yescharacteristic
32C2×#13108051C2211yescharacteristic
33C2×#13108051C2211yescharacteristic
34C2×#13108051C2211yescharacteristic
35C2×C4×Dic101C2211yescharacteristic
36C2×C4×Dic101C2211yescharacteristic
37C2×C4×Dic101C2211yescharacteristic
38#15692162C2211yescharacteristic
39#15692162C2211yescharacteristic
40#15692162C2211yescharacteristic
41#15692162C2211yescharacteristic
42#15692162C2211yescharacteristic
43#15692162C2211yescharacteristic
44#15692162C2211yescharacteristic
45#15692162C2211yescharacteristic
46C23×C4×C101C2211yescharacteristic
47C2×C22⋊C4×C101C2211yescharacteristic
48C2×C22⋊C4×C101C2211yescharacteristic
49C2×C42×C101C2211yescharacteristic
50C2×C42×C101C2211yescharacteristic
51#95×C101C2211yescharacteristic
52#95×C101C2211yescharacteristic
53C23×D101C2311yescharacteristic
54C2×C22⋊D101—22no—
55C2×C22⋊D101—22no—
56C2×C22⋊D101—22no—
57C22×Dic101C2311yescharacteristic
58C22×Dic101C2311yescharacteristic
59C22×Dic101C2311yescharacteristic
60C22×Dic101C2311yescharacteristic
61C22×Dic101C2311yescharacteristic
62C22×Dic101C2311yescharacteristic
63C22×Dic101C2311yescharacteristic
64C2×C4×D101—22no—
65C2×C4×D101—22no—
66C2×C4×D101D414yes—
67C4⋊Dic101—22no—
68C4⋊Dic101—22no—
69#13108053—22no—
70#13108053—22no—
71#13108053—22no—
72#13108053—22no—
73#13108053—22no—
74C22⋊Dic101—22no—
75C22⋊Dic101—22no—
76C22⋊Dic101—22no—
77#13108051—22no—
78#13108051—22no—
79#13108051—22no—
80#13108051—22no—
81#13108051—22no—
82C4×Dic101—22no—
83C4×Dic101—22no—
84C4×Dic101—22no—
85C24×C101C2311yescharacteristic
86C22×C4×C101—22no—
87C22×C4×C101—22no—
88C22×C4×C101—22no—
89C22×C4×C101C2311yescharacteristic
90C22×C4×C101C2311yescharacteristic
91C22×C4×C101C2311yescharacteristic
92C22×C4×C101C2311yescharacteristic
93C22×C4×C101C2311yescharacteristic
94C22×C4×C101C2311yescharacteristic
95C22⋊C4×C101—22no—
96C22⋊C4×C101—22no—
97C42×C101—22no—
98C42×C101—22no—
99C23×C101—21no—
100C23×C101—21no—
101C23×C101—21no—
102C23×C101—21no—
103C23×C101—21no—
104C23×C101—21no—
105C23×C101#4112yes—
106C23×C101C2411yescharacteristic
107C22×D101—21no—
108C22×D101—21no—
109C22×D101—21no—
110C22×D101—21no—
111C22×D101—21no—
112C22×D101—21no—
113C22×D101C2×D412yes—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C2×C4×C101—21no—
127C2×C4×C101—21no—
128C2×C4×C101—44no—
129C2×C4×C101C2×D412yes—
130C2×C4×C101#4112yes—
131C2×C4×C101#4112yes—
132C2×C4×C101#4112yes—
133C22⋊D101—28no—
134C2×Dic101—21no—
135C2×Dic101—21no—
136C2×Dic101—21no—
137C2×Dic101—21no—
138C2×Dic101—21no—
139C2×Dic101—21no—
140C2×Dic101—21no—
141C2×Dic101—21no—
142C2×Dic101—21no—
143C2×Dic101—21no—
144C2×Dic101—21no—
145C2×Dic101—21no—
146C2×Dic101—21no—
147C2×Dic101—21no—
148C2×Dic101—21no—
149C2×Dic101—21no—
150C2×Dic101—21no—
151C2×Dic101—21no—
152C2×Dic101C2×D412yes—
153C2×Dic101#4112yes—
154C2×Dic101#4112yes—
155C4×D101—28no—
156C22×C101—22no—
157C22×C101—22no—
158C22×C101—22no—
159C22×C101—41no—
160C22×C101—41no—
161C22×C101—41no—
162C22×C101—41no—
163C22×C101C22×D411yescharacteristic
164C22×C101C2×#4111yescharacteristic
165C22×C101C2×#4111yescharacteristic
166C22×C101C2×#4111yescharacteristic
167C22×C101C2×#4111yescharacteristic
168C22×C101C2×#4111yescharacteristic
169C22×C101C2×#4111yescharacteristic
170C2×D101—22no—
171C2×D101—22no—
172C2×D101—22no—
173C2×D101—41no—
174C2×D101—41no—
175C2×D101—41no—
176C2×D101—41no—
177C4×C101—22no—
178C4×C101—41no—
179C4×C101—41no—
180C4×C101—41no—
181C4×C101—41no—
182C4×C101#12314yes—
183Dic101—22no—
184Dic101—22no—
185Dic101—22no—
186Dic101—41no—
187Dic101—41no—
188Dic101—41no—
189Dic101—41no—
190C2×C101—42no—
191C2×C101C2×#12311yescharacteristic
192C2×C101#52511yescharacteristic
193C2×C101#52911yescharacteristic
194C2×C101#52911yescharacteristic
195C2×C101#52911yescharacteristic
196C2×C101#52911yescharacteristic
197C2×C101#53211yescharacteristic
198D101—42no—
199#2395—1011nomaximal, Sylow
200C101#239511yescharacteristic, complemented, Sylow
201C2×C4×D4—1011no—
202C2×#117—1011no—
203#400—1011no—
204#399—1011no—
205#398—1011no—
206#397—1011no—
207#397—1011no—
208#397—1011no—
209#394—1011no—
210#394—1011no—
211C4×C4⋊C4—1011no—
212C4×C4⋊C4—1011no—
213C4×C22⋊C4—1011no—
214C4×C22⋊C4—1011no—
215C4×C22⋊C4D10111yescharacteristic, complemented
216C22×D4—1011no—
217C23×C4—1011no—
218C23×C4C2×D10111yescharacteristic
219C4×D4—2024no—
220#117—2024no—
221C2×C4⋊C4—1011no—
222C2×C4⋊C4—1011no—
223C2×C4⋊C4—1011no—
224C2×C4⋊C4—1011no—
225C2×C4⋊C4—1011no—
226C2×C4⋊C4—1011no—
227C2×C4⋊C4—1011no—
228C2×C22⋊C4—1011no—
229C2×C22⋊C4—1011no—
230C2×C22⋊C4—1011no—
231C2×C22⋊C4—1011no—
232C2×C22⋊C4—1011no—
233C2×C22⋊C4—1011no—
234C2×C22⋊C4—1011no—
235C2×C22⋊C4—1011no—
236C2×C22⋊C4C2×D10111yescharacteristic
237C2×C22⋊C4C2×D10111yescharacteristic
238C2×C42—1011no—
239C2×C42—1011no—
240C2×C42—1011no—
241C2×C42C2×D10111yescharacteristic
242C2×C42C2×D10111yescharacteristic
243#95—1011no—
244#95—1011no—
245#95—1011no—
246#95—1011no—
247#95—1011no—
248#95—1011no—
249#95—1011no—
250#95—1011no—
251#95C2×D10111yescharacteristic
252#95C2×D10111yescharacteristic
253C24—1011no—
254C24C22×D10111yescharacteristic
255C2×D4—2022no—
256C2×D4—2022no—
257C2×D4—2022no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—1011no—
262C22×C4—1011no—
263C22×C4—1011no—
264C22×C4—1014no—
265C22×C4—1011no—
266C22×C4—1011no—
267C22×C4—1011no—
268C22×C4—1011no—
269C22×C4—2022no—
270C22×C4—2022no—
271C22×C4C22×D10111yescharacteristic
272C22×C4C22×D10111yescharacteristic
273C22×C4C22×D10111yescharacteristic
274C22×C4C22×D10111yescharacteristic
275C22×C4C22×D10111yescharacteristic
276C22×C4C22×D10111yescharacteristic
277C4⋊C4—2022no—
278C4⋊C4—2022no—
279C4⋊C4—2022no—
280C4⋊C4—2022no—
281C4⋊C4—2022no—
282C4⋊C4—2022no—
283C4⋊C4—2022no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—2022no—
287C22⋊C4—2022no—
288C22⋊C4—2022no—
289C22⋊C4—2022no—
290C22⋊C4—2022no—
291C22⋊C4—2022no—
292C22⋊C4—2022no—
293C22⋊C4—2022no—
294C42—22no—
295C42—22no—
296C42—2022no—
297C42—2022no—
298C42—2022no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—1012no—
306C23—2021no—
307C23—2021no—
308C23—2021no—
309C23—2021no—
310C23—2021no—
311C23—2021no—
312C23#1310807412yes—
313C23C23×D10111yescharacteristic
314D4—2028no—
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—44no—
330C2×C4—1012no—
331C2×C4—1012no—
332C2×C4—1012no—
333C2×C4—2021no—
334C2×C4—2021no—
335C2×C4—2021no—
336C2×C4—2021no—
337C2×C4—2021no—
338C2×C4—2021no—
339C2×C4—2021no—
340C2×C4—2021no—
341C2×C4—2021no—
342C2×C4—2021no—
343C2×C4—2021no—
344C2×C4—2021no—
345C2×C4—2021no—
346C2×C4—2021no—
347C2×C4—2021no—
348C2×C4—2021no—
349C2×C4—2021no—
350C2×C4—2021no—
351C2×C4—2028no—
352C2×C4D4×D10112yes—
353C2×C4#1310807312yes—
354C2×C4#1310807412yes—
355C2×C4#1310807412yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—4041no—
364C22—4041no—
365C22—4041no—
366C22—4041no—
367C22—2022no—
368C22—2022no—
369C22—2022no—
370C22C2×D4×D10111yescharacteristic
371C22#41×D10111yescharacteristic
372C22#41×D10111yescharacteristic
373C22C2×#1310807311yescharacteristic
374C22C2×#1310807411yescharacteristic
375C22C2×#1310807411yescharacteristic
376C22C2×#1310807411yescharacteristic
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—4041no—
383C4—4041no—
384C4—4041no—
385C4—4041no—
386C4—2022no—
387C4—2022no—
388C4—2022no—
389C4#1569223714yes—
390C2—42no—
391C2—4042no—
392C2C2×#1569223711yescharacteristic
393C2#2026568611yescharacteristic
394C2#2026570511yescharacteristic
395C2#2026570711yescharacteristic
396C2#2026570711yescharacteristic
397C2#2026571111yescharacteristic
398C2#2026572411yescharacteristic
subgroupG/H
centerC22×C4C22×D101
commutator, socle, cosocleC23×C101C24
FrattiniC23C23×D101
FittingC4×C22⋊C4×C101C2
prime radicalC22×C22⋊D101C22
hypercenterC4×C22⋊C4D101
hypocenterC101#2395
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15692212C2semidirect
3. #20265118C2semidirect
4. #20265113C2semidirect
5. #20265111C2semidirect
6. #20265106C2semidirect
7. #20265105C2semidirect
8. #20265104C2semidirect
11. C4×#13108053C2semidirect
12. C4×C4⋊Dic101C2semidirect
13. C4×#13108051C2semidirect
14. C4×C22⋊Dic101C2semidirect
15. C4×C22⋊C4×C101C2semidirect
200. C101#2395semidirect
215. C4×C22⋊C4D101semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1012
C2×#156922122
#202651182
#202651132
#202651112
#202651062
#202651052
#202651042
#202650932
#202650922
C4×#131080532
C4×C4⋊Dic1012
C4×#131080512
C4×C22⋊Dic1012
C4×C22⋊C4×C1012
#2395101