Finite Group Databasebeta

← #27198431

Subgroups — #27198431

Order 13184.

568 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic206C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D103C211yesmaximal, characteristic
3#20267733C211yesmaximal, characteristic, complemented
4#20267732C211yesmaximal, characteristic, complemented
5#20267720C211yesmaximal, characteristic, complemented
6#20267719C211yesmaximal, characteristic, complemented
7#20267707C211yesmaximal, characteristic
8#20267706C211yesmaximal, characteristic
9#20267704C211yesmaximal, characteristic, complemented
10#20267703C211yesmaximal, characteristic, complemented
11C4×(C2×D103)⋊C4C211yesmaximal, characteristic, complemented
12C4×(C2×D103)⋊C4C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic103C211yesmaximal, characteristic, complemented
14#20267637C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C103C211yesmaximal, characteristic, complemented
16C22×Dic206C2211yescharacteristic
17C22×C22⋊D103C2211yescharacteristic
18C22×C4×D103C2211yescharacteristic
19C4×Dic206—24no—
20C4×C22⋊D103—24no—
21C2×C4⋊Dic103C2211yescharacteristic
22C2×Dic103⋊C4C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×C22⋊Dic103C2211yescharacteristic
26C2×C22⋊Dic103C2211yescharacteristic
27C2×C22⋊Dic103C2211yescharacteristic
28C2×(C2×D103)⋊C4C2211yescharacteristic
29C2×(C2×D103)⋊C4C2211yescharacteristic
30C2×(C2×D103)⋊C4C2211yescharacteristic
31C2×(C2×D103)⋊C4C2211yescharacteristic
32C2×(C2×D103)⋊C4C2211yescharacteristic
33C2×C4×Dic103C2211yescharacteristic
34C2×C4×Dic103C2211yescharacteristic
35C2×C4×Dic103C2211yescharacteristic
36C103⋊#95C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C103⋊#95C2211yescharacteristic
46C23×C4×C103C2211yescharacteristic
47C2×C22⋊C4×C103C2211yescharacteristic
48C2×C22⋊C4×C103C2211yescharacteristic
49C2×C42×C103C2211yescharacteristic
50C2×C42×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52#95×C103C2211yescharacteristic
53C23×D103C2311yescharacteristic
54C2×Dic206—22no—
55C2×Dic206—22no—
56C2×Dic206—22no—
57C2×C22⋊D103—22no—
58C2×C22⋊D103—22no—
59C2×C22⋊D103—22no—
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C22×Dic103C2311yescharacteristic
64C22×Dic103C2311yescharacteristic
65C22×Dic103C2311yescharacteristic
66C22×Dic103C2311yescharacteristic
67C2×C4×D103—22no—
68C2×C4×D103—22no—
69C2×C4×D103—22no—
70C4⋊Dic103—22no—
71Dic103⋊C4—22no—
72Dic103⋊C4—22no—
73Dic103⋊C4—22no—
74C22⋊Dic103—22no—
75C22⋊Dic103—22no—
76C22⋊Dic103—22no—
77(C2×D103)⋊C4—22no—
78(C2×D103)⋊C4—22no—
79(C2×D103)⋊C4—22no—
80(C2×D103)⋊C4—22no—
81(C2×D103)⋊C4—22no—
82C4×Dic103—22no—
83C4×Dic103—22no—
84C4×Dic103D414yes—
85C24×C103C2311yescharacteristic
86C22×C4×C103—22no—
87C22×C4×C103—22no—
88C22×C4×C103—22no—
89C22×C4×C103C2311yescharacteristic
90C22×C4×C103C2311yescharacteristic
91C22×C4×C103C2311yescharacteristic
92C22×C4×C103C2311yescharacteristic
93C22×C4×C103C2311yescharacteristic
94C22×C4×C103C2311yescharacteristic
95C22⋊C4×C103—22no—
96C22⋊C4×C103—22no—
97C42×C103—22no—
98C42×C103—22no—
99C23×C103—21no—
100C23×C103—21no—
101C23×C103—21no—
102C23×C103—21no—
103C23×C103—21no—
104C23×C103—21no—
105C23×C103#4112yes—
106C23×C103C2411yescharacteristic
107C22×D103—21no—
108C22×D103—21no—
109C22×D103—21no—
110C22×D103—21no—
111C22×D103—21no—
112C22×D103—21no—
113C22×D103#4112yes—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—44no—
129C2×C4×C103C2×D412yes—
130C2×C4×C103#4112yes—
131C2×C4×C103#4112yes—
132C2×C4×C103#4112yes—
133C22⋊D103—28no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—21no—
139C2×Dic103—21no—
140C2×Dic103—21no—
141C2×Dic103—21no—
142C2×Dic103—21no—
143C2×Dic103—21no—
144C2×Dic103—21no—
145C2×Dic103—21no—
146C2×Dic103—21no—
147C2×Dic103—21no—
148C2×Dic103—21no—
149C2×Dic103—21no—
150C2×Dic103—21no—
151C2×Dic103—21no—
152C2×Dic103C2×D412yes—
153C2×Dic103C2×D412yes—
154C2×Dic103#4112yes—
155C4×D103—44no—
156Dic206—28no—
157C22×C103—22no—
158C22×C103—22no—
159C22×C103—22no—
160C22×C103—41no—
161C22×C103—41no—
162C22×C103—41no—
163C22×C103—41no—
164C22×C103C22×D411yescharacteristic
165C22×C103C2×#4111yescharacteristic
166C22×C103C2×#4111yescharacteristic
167C22×C103C2×#4111yescharacteristic
168C22×C103C2×#4111yescharacteristic
169C22×C103C2×#4111yescharacteristic
170C22×C103C2×#4111yescharacteristic
171C2×D103—22no—
172C2×D103—22no—
173C2×D103—22no—
174C2×D103—41no—
175C2×D103—41no—
176C2×D103—41no—
177C2×D103—41no—
178C4×C103—22no—
179C4×C103—41no—
180C4×C103—41no—
181C4×C103—41no—
182C4×C103—41no—
183C4×C103#12414yes—
184Dic103—22no—
185Dic103—22no—
186Dic103—22no—
187Dic103—41no—
188Dic103—41no—
189Dic103—41no—
190Dic103—41no—
191C2×C103—42no—
192C2×C103#52511yescharacteristic
193C2×C103#52511yescharacteristic
194C2×C103C2×#12411yescharacteristic
195C2×C103#52911yescharacteristic
196C2×C103#52911yescharacteristic
197C2×C103#52911yescharacteristic
198C2×C103#52911yescharacteristic
199D103—42no—
200#2398—1031nomaximal, Sylow
201C103#239811yescharacteristic, complemented, Sylow
202C2×C4×Q8—1031no—
203C2×C4×D4—1031no—
204#400—1031no—
205#400—1031no—
206#397—1031no—
207#397—1031no—
208#394—1031no—
209#394—1031no—
210#393—1031no—
211#393—1031no—
212C4×C22⋊C4—1031no—
213C4×C22⋊C4—1031no—
214C4×C22⋊C4—1031no—
215C4×C22⋊C4D10311yescharacteristic, complemented
216#376—1031no—
217C22×Q8—1031no—
218C22×D4—1031no—
219C23×C4—1031no—
220C23×C4C2×D10311yescharacteristic
221C4×Q8—2064no—
222C4×D4—2064no—
223C2×C4⋊C4—1031no—
224C2×C4⋊C4—1031no—
225C2×C4⋊C4—1031no—
226C2×C4⋊C4—1031no—
227C2×C22⋊C4—1031no—
228C2×C22⋊C4—1031no—
229C2×C22⋊C4—1031no—
230C2×C22⋊C4—1031no—
231C2×C22⋊C4—1031no—
232C2×C22⋊C4—1031no—
233C2×C22⋊C4—1031no—
234C2×C22⋊C4—1031no—
235C2×C22⋊C4C2×D10311yescharacteristic
236C2×C22⋊C4C2×D10311yescharacteristic
237C2×C42—1031no—
238C2×C42—1031no—
239C2×C42—1031no—
240C2×C42C2×D10311yescharacteristic
241C2×C42C2×D10311yescharacteristic
242#95—1031no—
243#95—1031no—
244#95—1031no—
245#95—1031no—
246#95—1031no—
247#95—1031no—
248#95—1031no—
249#95—1031no—
250#95—1031no—
251#95—1031no—
252#95C2×D10311yescharacteristic
253#95C2×D10311yescharacteristic
254C24—1031no—
255C24C22×D10311yescharacteristic
256C2×Q8—2062no—
257C2×Q8—2062no—
258C2×Q8—2062no—
259C2×D4—2062no—
260C2×D4—2062no—
261C2×D4—2062no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—1031no—
266C22×C4—1031no—
267C22×C4—1031no—
268C22×C4—1031no—
269C22×C4—1031no—
270C22×C4—1031no—
271C22×C4—1031no—
272C22×C4—2062no—
273C22×C4—2062no—
274C22×C4—2062no—
275C22×C4C22×D10311yescharacteristic
276C22×C4C22×D10311yescharacteristic
277C22×C4C22×D10311yescharacteristic
278C22×C4C22×D10311yescharacteristic
279C22×C4C22×D10311yescharacteristic
280C22×C4C22×D10311yescharacteristic
281C4⋊C4—2062no—
282C4⋊C4—2062no—
283C4⋊C4—2062no—
284C4⋊C4—2062no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—2062no—
288C22⋊C4—2062no—
289C22⋊C4—2062no—
290C22⋊C4—2062no—
291C22⋊C4—2062no—
292C22⋊C4—2062no—
293C22⋊C4—2062no—
294C22⋊C4—2062no—
295C42—22no—
296C42—22no—
297C42—1034no—
298C42—2062no—
299C42—2062no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—1032no—
307C23—2061no—
308C23—2061no—
309C23—2061no—
310C23—2061no—
311C23—2061no—
312C23—2061no—
313C23#1311010512yes—
314C23C23×D10311yescharacteristic
315Q8—2068no—
316D4—2068no—
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—44no—
332C2×C4—1032no—
333C2×C4—1032no—
334C2×C4—1032no—
335C2×C4—4124no—
336C2×C4—2061no—
337C2×C4—2061no—
338C2×C4—2061no—
339C2×C4—2061no—
340C2×C4—2061no—
341C2×C4—2061no—
342C2×C4—2061no—
343C2×C4—2061no—
344C2×C4—2061no—
345C2×C4—2061no—
346C2×C4—2061no—
347C2×C4—2061no—
348C2×C4—2061no—
349C2×C4—2061no—
350C2×C4—2061no—
351C2×C4—2061no—
352C2×C4—2061no—
353C2×C4—2061no—
354C2×C4D4×D10312yes—
355C2×C4#1311010412yes—
356C2×C4#1311010512yes—
357C2×C4#1311010512yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—4121no—
366C22—4121no—
367C22—4121no—
368C22—4121no—
369C22—2062no—
370C22—2062no—
371C22—2062no—
372C22C2×D4×D10311yescharacteristic
373C22#41×D10311yescharacteristic
374C22#41×D10311yescharacteristic
375C22C2×#1311010411yescharacteristic
376C22C2×#1311010511yescharacteristic
377C22C2×#1311010511yescharacteristic
378C22C2×#1311010511yescharacteristic
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—4121no—
385C4—4121no—
386C4—4121no—
387C4—4121no—
388C4—2062no—
389C4—2062no—
390C4—2062no—
391C4#1569300714yes—
392C2—42no—
393C2—4122no—
394C2#2026830011yescharacteristic
395C2#2026830011yescharacteristic
396C2C2×#1569300711yescharacteristic
397C2#2026831911yescharacteristic
398C2#2026832111yescharacteristic
399C2#2026832311yescharacteristic
400C2#2026832511yescharacteristic
subgroupG/H
centerC22×C4C22×D103
commutator, socle, cosocleC23×C103C24
FrattiniC23C23×D103
FittingC4×C22⋊C4×C103C2
prime radicalC22×C22⋊D103C22
hypercenterC4×C22⋊C4D103
hypocenterC103#2398
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic206C2semidirect
3. #20267733C2semidirect
4. #20267732C2semidirect
5. #20267720C2semidirect
6. #20267719C2semidirect
9. #20267704C2semidirect
10. #20267703C2semidirect
11. C4×(C2×D103)⋊C4C2semidirect
12. C4×(C2×D103)⋊C4C2semidirect
13. C4×C22⋊Dic103C2semidirect
14. #20267637C2semidirect
15. C4×C22⋊C4×C103C2semidirect
201. C103#2398semidirect
215. C4×C22⋊C4D103semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic2062
C2×C4×C22⋊D1032
#202677332
#202677322
#202677202
#202677192
#202677072
#202677062
#202677042
#202677032
C4×(C2×D103)⋊C42
C4×C22⋊Dic1032
#202676372
C4×C22⋊C4×C1032
#2398103