Finite Group Databasebeta

← #27206700

Subgroups — #27206700

Order 13184.

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×#15693052C211yesmaximal, characteristic, complemented
2C2×#15693041C211yesmaximal, characteristic, complemented
3#20268446C211yesmaximal, characteristic, complemented
4#20268186C211yesmaximal, characteristic, complemented
5#20268035C211yesmaximal, characteristic, complemented
6#20268030C211yesmaximal, characteristic, complemented
7#20268003C211yesmaximal, characteristic, complemented
8#20268001C211yesmaximal, characteristic, complemented
9#20267953C211yesmaximal, characteristic, complemented
10#20267951C211yesmaximal, characteristic, complemented
11#20267947C211yesmaximal, characteristic, complemented
12#20267934C211yesmaximal, characteristic, complemented
13#20267889C211yesmaximal, characteristic, complemented
14#20267863C211yesmaximal, characteristic, complemented
15#548×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×#13110105C2211yescharacteristic
18#15693052—24no—
19#15693041—24no—
20C2×#13110095C2211yescharacteristic
21C2×#13110095C2211yescharacteristic
22C2×#13110095C2211yescharacteristic
23C2×#13110095C2211yescharacteristic
24C2×#13110093C2211yescharacteristic
25C2×#13110093C2211yescharacteristic
26C2×#13110092C2211yescharacteristic
27C2×#13110092C2211yescharacteristic
28C2×#13110090C2211yescharacteristic
29C2×#13110089C2211yescharacteristic
30C22×C103⋊C8C2211yescharacteristic
31#15693021C2211yescharacteristic
32#15693003—21no—
33#15693003—21no—
34#15693000C2211yescharacteristic
35#15693000C2211yescharacteristic
36#15692992—21no—
37C4×D412C2211yescharacteristic
38C4⋊C4×D103—21no—
39#15692954C2211yescharacteristic
40C4⋊(C103⋊C8)C2211yescharacteristic
41#15692945C2211yescharacteristic
42#15692945C2211yescharacteristic
43#15692944C2211yescharacteristic
44#15692944C2211yescharacteristic
45#15692942C2211yescharacteristic
46#15692941C2211yescharacteristic
47C22⋊(C103⋊C8)C2211yescharacteristic
48C22⋊(C103⋊C8)C2211yescharacteristic
49#15692932C2211yescharacteristic
50C2×#41×C103C2211yescharacteristic
51C22×Q8×C103C2211yescharacteristic
52#124×C103—21no—
53#124×C103C2211yescharacteristic
54C22⋊Q8×C103—21no—
55C22⋊Q8×C103C2211yescharacteristic
56#121×C103—21no—
57#121×C103C2211yescharacteristic
58C4×Q8×C103C2211yescharacteristic
59C4×D4×C103—21no—
60C4×D4×C103C2211yescharacteristic
61#13110105—22no—
62#13110105—22no—
63#13110105—41no—
64#13110105—41no—
65C2×Dic206C2311yescharacteristic
66C2×Dic206C2311yescharacteristic
67C2×D412C2311yescharacteristic
68C2×C22⋊D103—21no—
69C2×C22⋊D103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73#13110095—22no—
74#13110095—22no—
75#13110095—22no—
76#13110095—41no—
77#13110093—22no—
78#13110093—41no—
79#13110092—22no—
80#13110092D414yescomplemented
81#13110090—22no—
82#13110089—22no—
83C2×C103⋊C8—22no—
84C2×C103⋊C8C2311yescharacteristic
85C2×C103⋊C8C2311yescharacteristic
86C2×C103⋊C8C2311yescharacteristic
87C2×C103⋊C8C2311yescharacteristic
88C4⋊Dic103—21no—
89C4⋊Dic103—21no—
90C4⋊Dic103C2311yescharacteristic
91Dic103⋊C4—21no—
92Dic103⋊C4—21no—
93C22⋊Dic103—21no—
94C22⋊Dic103—21no—
95(C2×D103)⋊C4—21no—
96#41×C103—22no—
97#41×C103—41no—
98C2×Q8×C103—21no—
99C2×Q8×C103—22no—
100C2×Q8×C103—41no—
101C2×Q8×C103C2311yescharacteristic
102C2×Q8×C103C2311yescharacteristic
103C2×D4×C103—21no—
104C2×D4×C103—21no—
105C2×D4×C103D411yescharacteristic
106C2×D4×C103C2311yescharacteristic
107C22×C4×C103—21no—
108C22×C4×C103—21no—
109C22×C4×C103C2311yescharacteristic
110C22×C4×C103C2311yescharacteristic
111C4⋊C4×C103—21no—
112C4⋊C4×C103—21no—
113C4⋊C4×C103D411yescharacteristic
114C4⋊C4×C103C2311yescharacteristic
115C22⋊C4×C103—21no—
116C22⋊C4×C103—21no—
117C22⋊C4×C103—21no—
118C22⋊C4×C103—21no—
119C22⋊C4×C103D411yescharacteristic
120C22⋊C4×C103D411yescharacteristic
121C42×C103—21no—
122C42×C103C2311yescharacteristic
123C23×C103—21no—
124C23×C103C2×D411yescharacteristic
125C23×C103C2×D411yescharacteristic
126C22×D103—21no—
127Q8×C103—21no—
128Q8×C103—21no—
129Q8×C103—21no—
130Q8×C103—42no—
131Q8×C103C2×D412yes—
132D4×C103—21no—
133D4×C103—21no—
134D4×C103—41no—
135D4×C103—42no—
136D4×C103—42no—
137C2×C4×C103—21no—
138C2×C4×C103—21no—
139C2×C4×C103—21no—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103—21no—
143C2×C4×C103—21no—
144C2×C4×C103—42no—
145C2×C4×C103—42no—
146C2×C4×C103C2×D411yescharacteristic
147C2×C4×C103C2×D411yescharacteristic
148C2×C4×C103C2×D411yescharacteristic
149C2×C4×C103C2×D411yescharacteristic
150C2×C4×C103C2411yescharacteristic
151C22⋊D103—42no—
152C22⋊D103—42no—
153C2×Dic103—21no—
154C2×Dic103—21no—
155C2×Dic103—21no—
156D412—21no—
157D412C2×D412yes—
158C4×D103—42no—
159C4×D103—42no—
160C4×D103—42no—
161Dic206—21no—
162Dic206—21no—
163Dic206—21no—
164Dic206—21no—
165C103⋊C8—21no—
166C103⋊C8—21no—
167C103⋊C8—21no—
168C103⋊C8C2×D412yes—
169C22×C103—21no—
170C22×C103—21no—
171C22×C103—21no—
172C22×C103—21no—
173C22×C103—21no—
174C22×C103—21no—
175C22×C103—41no—
176C22×C103—41no—
177C22×C103—41no—
178C22×C103C22×D411yescharacteristic
179C2×D103—22no—
180C2×D103—41no—
181C2×D103—41no—
182C4×C103—21no—
183C4×C103—21no—
184C4×C103—22no—
185C4×C103—21no—
186C4×C103—21no—
187C4×C103—41no—
188C4×C103—41no—
189C4×C103C22×D411yescharacteristic
190C4×C103H(5,𝔽2)11yescharacteristic
191Dic103—41no—
192Dic103—41no—
193Dic103—41no—
194C2×C103—41no—
195C2×C103—41no—
196C2×C103—81no—
197C2×C103D4211yescharacteristic
198C2×C103#57511yescharacteristic
199C2×C103#57811yescharacteristic
200D103—42no—
201#3269—1031nomaximal, Sylow
202C103#326911yescharacteristic, complemented, Sylow
203C2×#137—1031no—
204C2×#135—1031no—
205#548D10311yescharacteristic, complemented
206#547—1031no—
207#497—1031no—
208#468—1031no—
209#467—1031no—
210#463—1031no—
211#462—1031no—
212#452—1031no—
213#452—1031no—
214#451—1031no—
215#449—1031no—
216#440—1031no—
217#435—1031no—
218C2×#41—1031no—
219C2×#41—1031no—
220C2×#41C2×D10311yescharacteristic
221C22×Q8C2×D10311yescharacteristic
222#137—2064no—
223#135—2064no—
224C2×Q16—1031no—
225C2×Q16—1031no—
226C2×Q16—1031no—
227C2×Q16—1031no—
228C2×SD16—1031no—
229C2×SD16—1031no—
230C2×SD16—1031no—
231C2×SD16—1031no—
232C2×D8—1031no—
233C2×M16—1031no—
234C22×C8—1031no—
235C4⋊Q8—1031no—
236#124—21no—
237#124C2×D10311yescharacteristic
238#123—2061no—
239#123—2061no—
240C22⋊Q8—21no—
241C22⋊Q8—1031no—
242C22⋊Q8—1031no—
243C22⋊Q8C2×D10311yescharacteristic
244#121—21no—
245#121—2061no—
246#121C2×D10311yescharacteristic
247C4×Q8C2×D10311yescharacteristic
248C4×D4—21no—
249C4×D4—1031no—
250C4×D4C2×D10311yescharacteristic
251C2×C4⋊C4—2061no—
252#107—1031no—
253C4⋊C8—1031no—
254#103—1031no—
255#103—1031no—
256#103—1031no—
257#103—1031no—
258#102—1031no—
259#102—1031no—
260C22⋊C8—1031no—
261C22⋊C8—1031no—
262#97—1031no—
263#41—22no—
264#41—41no—
265#41—4121no—
266#41—4121no—
267#41—2062no—
268#41—2062no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—1031no—
273C2×Q8—1031no—
274C2×Q8C22×D10311yescharacteristic
275C2×Q8C22×D10311yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—1031no—
279C2×D4—2061no—
280C2×D4—2061no—
281C2×D4C22⋊D10311yescharacteristic
282C2×D4C22×D10311yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—2061no—
286C22×C4—2061no—
287C22×C4—2061no—
288C22×C4C22×D10311yescharacteristic
289C22×C4C22×D10311yescharacteristic
290Q16—4121no—
291Q16—2062no—
292Q16—2062no—
293Q16—2062no—
294SD16—1034no—
295SD16—4121no—
296SD16—2062no—
297SD16—2062no—
298D8—2062no—
299M16—2062no—
300C2×C8—1031no—
301C2×C8—1031no—
302C2×C8—1031no—
303C2×C8—1031no—
304C2×C8—2062no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—1031no—
308C4⋊C4—2061no—
309C4⋊C4—2061no—
310C4⋊C4—2061no—
311C4⋊C4—2061no—
312C4⋊C4C22⋊D10311yescharacteristic
313C4⋊C4C22×D10311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—21no—
318C22⋊C4—2061no—
319C22⋊C4—2061no—
320C22⋊C4—2061no—
321C22⋊C4C22⋊D10311yescharacteristic
322C22⋊C4C22⋊D10311yescharacteristic
323C42—21no—
324C42C22×D10311yescharacteristic
325C23—21no—
326C23—2061no—
327C23C2×C22⋊D10311yescharacteristic
328C23C2×C22⋊D10311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—2061no—
334Q8—2061no—
335Q8—2061no—
336Q8—2061no—
337Q8D4×D10312yes—
338D4—21no—
339D4—21no—
340D4—41no—
341D4—42no—
342D4—42no—
343D4—1032no—
344D4—4122no—
345D4—4122no—
346D4—2061no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—4122no—
357C2×C4—4122no—
358C2×C4—4122no—
359C2×C4—2061no—
360C2×C4—2061no—
361C2×C4—2061no—
362C2×C4C2×C22⋊D10311yescharacteristic
363C2×C4C2×C22⋊D10311yescharacteristic
364C2×C4C2×C22⋊D10311yescharacteristic
365C2×C4C2×C22⋊D10311yescharacteristic
366C2×C4C23×D10311yescharacteristic
367C8—1032no—
368C8—2061no—
369C8—2061no—
370C8—2061no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—4121no—
381C22—4121no—
382C22—2062no—
383C22C22×C22⋊D10311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—4121no—
392C4—4121no—
393C4—4121no—
394C4C2×D4×D10311yescharacteristic
395C4#1569306611yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—4122no—
400C2D4×C22⋊D10311yescharacteristic
401C2#2026858911yescharacteristic
402C2#2026860611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#548×C103C2
socleC22×C103C22×D4
hypercenter#548D103
hypocenterC103#3269
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#15693052C2semidirect
2. C2×#15693041C2semidirect
3. #20268446C2semidirect
4. #20268186C2semidirect
5. #20268035C2semidirect
6. #20268030C2semidirect
7. #20268003C2semidirect
8. #20268001C2semidirect
9. #20267953C2semidirect
10. #20267951C2semidirect
11. #20267947C2semidirect
12. #20267934C2semidirect
13. #20267889C2semidirect
14. #20267863C2semidirect
15. #548×C103C2semidirect
80. #13110092D4semidirect
202. C103#3269semidirect
205. #548D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930522
C2×#156930412
#202684462
#202681862
#202680352
#202680302
#202680032
#202680012
#202679532
#202679512
#202679472
#202679342
#202678892
#202678632
#548×C1032
#3269103