Finite Group Databasebeta

← #13061791

Subgroups — #13061791

Order 1344.

384 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×#126C211yesmaximal, characteristic
2#10621373C211yesmaximal, characteristic, complemented
3#10621372C211yesmaximal, characteristic, complemented
4#10621372C211yesmaximal, characteristic, complemented
5#10621372C211yesmaximal, characteristic, complemented
6#10621371C211yesmaximal, characteristic, complemented
7#10621370C211yesmaximal, characteristic, complemented
8#10621362C211yesmaximal, characteristic
9#10621362C211yesmaximal, characteristic
10#10621362C211yesmaximal, characteristic
11#10621361C211yesmaximal, characteristic
12#10621361C211yesmaximal, characteristic
13#10621360C211yesmaximal, characteristic
14#10621353C211yesmaximal, characteristic, complemented
15C4×Dic42C211yesmaximal, characteristic, complemented
16#90392—31nomaximal, Hall
17C22×Dic21C2211yescharacteristic
18C2×Dic42C2211yescharacteristic
19C2×Dic42C2211yescharacteristic
20C3×C7×C4⋊C4C2211yescharacteristic
21C3×C7×C4⋊C4C2211yescharacteristic
22C3×C7×C4⋊C4C2211yescharacteristic
23C3×C7×C22⋊C4C2211yescharacteristic
24C3×C7×C22⋊C4C2211yescharacteristic
25C3×C7×C22⋊C4C2211yescharacteristic
26C3×C42×C7C2211yescharacteristic
27#66636C2211yescharacteristic
28#66636C2211yescharacteristic
29#66636C2211yescharacteristic
30C4⋊Dic21C2211yescharacteristic
31C4⋊Dic21C2211yescharacteristic
32C4⋊Dic21C2211yescharacteristic
33C4⋊Dic21C2211yescharacteristic
34C4⋊Dic21C2211yescharacteristic
35#66629C2211yescharacteristic
36#66629C2211yescharacteristic
37#66629C2211yescharacteristic
38#66629C2211yescharacteristic
39#66629C2211yescharacteristic
40#66629C2211yescharacteristic
41#66629C2211yescharacteristic
42#66629C2211yescharacteristic
43#66629C2211yescharacteristic
44#66629C2211yescharacteristic
45#66629C2211yescharacteristic
46#66629C2211yescharacteristic
47C4×Dic21C2211yescharacteristic
48C4×Dic21C2211yescharacteristic
49C4×Dic21C2211yescharacteristic
50C4×Dic21C2211yescharacteristic
51C4×Dic21C2211yescharacteristic
52C7×#126D311yescharacteristic
53#6453—31no—
54#6452—31no—
55#6452—31no—
56#6452—31no—
57#6451—31no—
58#6450—31no—
59#6442—31no—
60#6442—31no—
61#6442—31no—
62#6441—31no—
63#6441—31no—
64#6440—31no—
65#6433—31no—
66C4×Dic14—31no—
67#5701—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C2×C3×C4×C7C2311yescharacteristic
70C2×C3×C4×C7C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×C3×C4×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74C2×C3×C4×C7C2311yescharacteristic
75C2×Dic21—22no—
76C2×Dic21C2311yescharacteristic
77C2×Dic21C2311yescharacteristic
78C2×Dic21C2311yescharacteristic
79C2×Dic21C2311yescharacteristic
80C2×Dic21C2311yescharacteristic
81C2×Dic21C2311yescharacteristic
82C2×Dic21C2311yescharacteristic
83C2×Dic21C2311yescharacteristic
84Dic42—22no—
85Dic42—22no—
86C22×Dic7—31no—
87C2×Dic14—31no—
88C2×Dic14—31no—
89C7×C4⋊C4C2×D311yescharacteristic
90C7×C4⋊C4C2×D311yescharacteristic
91C7×C4⋊C4C2×D311yescharacteristic
92C7×C22⋊C4C2×D311yescharacteristic
93C7×C22⋊C4C2×D311yescharacteristic
94C7×C22⋊C4C2×D311yescharacteristic
95C42×C7C2×D311yescharacteristic
96C22⋊Dic7—31no—
97C22⋊Dic7—31no—
98C22⋊Dic7—31no—
99C4⋊Dic7—31no—
100C4⋊Dic7—31no—
101C4⋊Dic7—31no—
102C4⋊Dic7—31no—
103C4⋊Dic7—31no—
104Dic7⋊C4—31no—
105Dic7⋊C4—31no—
106Dic7⋊C4—31no—
107Dic7⋊C4—31no—
108Dic7⋊C4—31no—
109Dic7⋊C4—31no—
110Dic7⋊C4—31no—
111Dic7⋊C4—31no—
112Dic7⋊C4—31no—
113Dic7⋊C4—31no—
114Dic7⋊C4—31no—
115Dic7⋊C4—31no—
116C4×Dic7—31no—
117C4×Dic7—31no—
118C4×Dic7—31no—
119C4×Dic7—31no—
120C4×Dic7—31no—
121C3×#126D711yescharacteristic
122#890—71no—
123#889—71no—
124#889—71no—
125#889—71no—
126#888—71no—
127#887—71no—
128#879—71no—
129#879—71no—
130#879—71no—
131#878—71no—
132#878—71no—
133#877—71no—
134#870—71no—
135C4×Dic6—71no—
136C22×C3×C7—21no—
137C22×C3×C7—21no—
138C22×C3×C7—21no—
139C22×C3×C7C2411yescharacteristic
140C3×C4×C7—21no—
141C3×C4×C7—21no—
142C3×C4×C7—21no—
143C3×C4×C7—21no—
144C3×C4×C7—21no—
145C3×C4×C7—21no—
146Dic21—21no—
147Dic21—21no—
148Dic21—21no—
149Dic21—21no—
150Dic21—21no—
151Dic21—21no—
152Dic21—21no—
153Dic21#4112yes—
154#541—211noSylow
155C23×C7C22×D311yescharacteristic
156C2×C4×C7C22×D311yescharacteristic
157C2×C4×C7C22×D311yescharacteristic
158C2×C4×C7C22×D311yescharacteristic
159C2×C4×C7C22×D311yescharacteristic
160C2×C4×C7C22×D311yescharacteristic
161C2×C4×C7C22×D311yescharacteristic
162C2×Dic7—31no—
163C2×Dic7—31no—
164C2×Dic7—31no—
165C2×Dic7—31no—
166C2×Dic7—31no—
167C2×Dic7—31no—
168C2×Dic7—31no—
169C2×Dic7—31no—
170C2×Dic7—62no—
171Dic14—62no—
172Dic14—62no—
173C22×Dic3—71no—
174C2×Dic6—71no—
175C2×Dic6—71no—
176C3×C4⋊C4C2×D711yescharacteristic
177C3×C4⋊C4C2×D711yescharacteristic
178C3×C4⋊C4C2×D711yescharacteristic
179C3×C22⋊C4C2×D711yescharacteristic
180C3×C22⋊C4C2×D711yescharacteristic
181C3×C22⋊C4C2×D711yescharacteristic
182C3×C42C2×D711yescharacteristic
183#217—71no—
184#217—71no—
185#217—71no—
186C4⋊Dic3—71no—
187C4⋊Dic3—71no—
188C4⋊Dic3—71no—
189C4⋊Dic3—71no—
190C4⋊Dic3—71no—
191Dic3⋊C4—71no—
192Dic3⋊C4—71no—
193Dic3⋊C4—71no—
194Dic3⋊C4—71no—
195Dic3⋊C4—71no—
196Dic3⋊C4—71no—
197Dic3⋊C4—71no—
198Dic3⋊C4—71no—
199Dic3⋊C4—71no—
200Dic3⋊C4—71no—
201Dic3⋊C4—71no—
202Dic3⋊C4—71no—
203C4×Dic3—71no—
204C4×Dic3—71no—
205C4×Dic3—71no—
206C4×Dic3—71no—
207C4×Dic3—71no—
208C2×C3×C7—41no—
209C2×C3×C7C2×#4111yescharacteristic
210C2×C3×C72−1+411yescharacteristic
211C2×C3×C72−1+411yescharacteristic
212C4⋊Q8—211no—
213#126—211no—
214#126—211no—
215#126—211no—
216#126D2111yescharacteristic
217#125—211no—
218#125—211no—
219#125—211no—
220#125—211no—
221#125—211no—
222C22⋊Q8—211no—
223C22⋊Q8—211no—
224C4×Q8—211no—
225C4×Q8—211no—
226#117—211no—
227C22×C7—21no—
228C22×C7—21no—
229C22×C7—21no—
230C22×C7C23×D311yescharacteristic
231C4×C7—21no—
232C4×C7—21no—
233C4×C7—21no—
234C4×C7—21no—
235C4×C7—21no—
236C4×C7—21no—
237Dic7—32no—
238Dic7—61no—
239Dic7—61no—
240Dic7—61no—
241Dic7—61no—
242Dic7—61no—
243Dic7—61no—
244Dic7—61no—
245C23×C3C22×D711yescharacteristic
246C2×C3×C4C22×D711yescharacteristic
247C2×C3×C4C22×D711yescharacteristic
248C2×C3×C4C22×D711yescharacteristic
249C2×C3×C4C22×D711yescharacteristic
250C2×C3×C4C22×D711yescharacteristic
251C2×C3×C4C22×D711yescharacteristic
252C2×Dic3—71no—
253C2×Dic3—71no—
254C2×Dic3—71no—
255C2×Dic3—71no—
256C2×Dic3—71no—
257C2×Dic3—71no—
258C2×Dic3—71no—
259C2×Dic3—71no—
260C2×Dic3—142no—
261Dic6—142no—
262Dic6—142no—
263C3×C7#54111yescharacteristic, complemented, Hall
264C2×Q8—211no—
265C2×Q8—211no—
266C22×C4—211no—
267C4⋊C4—211no—
268C4⋊C4—211no—
269C4⋊C4—211no—
270C4⋊C4—211no—
271C4⋊C4—211no—
272C4⋊C4—211no—
273C4⋊C4—211no—
274C4⋊C4—211no—
275C4⋊C4—211no—
276C4⋊C4—211no—
277C4⋊C4—211no—
278C4⋊C4—211no—
279C4⋊C4—211no—
280C4⋊C4—211no—
281C4⋊C4—211no—
282C4⋊C4—211no—
283C4⋊C4—211no—
284C4⋊C4C2×D2111yescharacteristic
285C4⋊C4C2×D2111yescharacteristic
286C4⋊C4C2×D2111yescharacteristic
287C22⋊C4—211no—
288C22⋊C4—211no—
289C22⋊C4—211no—
290C22⋊C4C2×D2111yescharacteristic
291C22⋊C4C2×D2111yescharacteristic
292C22⋊C4C2×D2111yescharacteristic
293C42—211no—
294C42—211no—
295C42—211no—
296C42—211no—
297C42—211no—
298C42C2×D2111yescharacteristic
299C2×C7—41no—
300C2×C7D3×#4111yescharacteristic
301C2×C7#101011yescharacteristic
302C2×C7#101011yescharacteristic
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3C23×D711yescharacteristic
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313Dic3—72no—
314Dic3—141no—
315Dic3—141no—
316Dic3—141no—
317Dic3—141no—
318Dic3—141no—
319Dic3—141no—
320Dic3—141no—
321C23C22×D2111yescharacteristic
322Q8—422no—
323Q8—422no—
324C2×C4—211no—
325C2×C4—211no—
326C2×C4—211no—
327C2×C4—211no—
328C2×C4—211no—
329C2×C4—211no—
330C2×C4—211no—
331C2×C4—211no—
332C2×C4—422no—
333C2×C4C22×D2111yescharacteristic
334C2×C4C22×D2111yescharacteristic
335C2×C4C22×D2111yescharacteristic
336C2×C4C22×D2111yescharacteristic
337C2×C4C22×D2111yescharacteristic
338C2×C4C22×D2111yescharacteristic
339C7#570111yescharacteristic, complemented, Sylow
340C2×C3—41no—
341C2×C3D7×#4111yescharacteristic
342C2×C3#655411yescharacteristic
343C2×C3#655411yescharacteristic
344C22—21no—
345C22—21no—
346C22—21no—
347C22C23×D2111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—212no—
355C4—421no—
356C4—421no—
357C4—421no—
358C4—421no—
359C4—421no—
360C4—421no—
361C4—421no—
362C3#9039211yescharacteristic, complemented, Sylow
363C2—41no—
364C2#41×D2111yescharacteristic
365C2#1062166311yescharacteristic
366C2#1062166311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D21
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×#126C2
prime radicalC23×C3×C7C23
hypercenter#126D21
hypocenterC3×C7#541
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
2. #10621373C2semidirect
3. #10621372C2semidirect
4. #10621372C2semidirect
5. #10621372C2semidirect
6. #10621371C2semidirect
7. #10621370C2semidirect
14. #10621353C2semidirect
15. C4×Dic42C2semidirect
263. C3×C7#541semidirect
339. C7#5701semidirect
362. C3#90392semidirect

Maximal subgroups

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

subgroupindex
C3×C7×#1262
#106213732
#106213722
#106213712
#106213702
#106213622
#106213612
#106213602
#106213532
C4×Dic422
#903923
#57017