Finite Group Databasebeta

← #13058602

Subgroups — #13058602

Order 1344.

412 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10621372C211yesmaximal, characteristic, complemented
2C7×#897C211yesmaximal, characteristic
3C3×#6452C211yesmaximal, characteristic, complemented
4#10621032C211yesmaximal, characteristic, complemented
5#10621030C211yesmaximal, characteristic, complemented
6#10620998C211yesmaximal, characteristic
7#10620979C211yesmaximal, characteristic
8#10620962C211yesmaximal, characteristic
9D3×Dic7⋊C4C211yesmaximal, characteristic
10#10620960C211yesmaximal, characteristic
11#10620914C211yesmaximal, characteristic
12#10620898C211yesmaximal, characteristic, complemented
13#10620897C211yesmaximal, characteristic, complemented
14#10620891C211yesmaximal, characteristic, complemented
15#10620891C211yesmaximal, characteristic, complemented
16#90314—31nomaximal, Hall
17C2×C4×D3×C7C2211yescharacteristic
18C2×C7×Dic6C2211yescharacteristic
19C2×#4248C2211yescharacteristic
20C2×#4248C2211yescharacteristic
21C2×#4248C2211yescharacteristic
22C2×D3×Dic7C2211yescharacteristic
23C2×D3×Dic7C2211yescharacteristic
24C3×C7×C4⋊C4C2211yescharacteristic
25C4⋊Dic21C2211yescharacteristic
26#66629C2211yescharacteristic
27#66629C2211yescharacteristic
28#66629C2211yescharacteristic
29#66629C2211yescharacteristic
30C4×Dic21C2211yescharacteristic
31C7×(C2×D3)⋊C4C2211yescharacteristic
32C7×(C2×D3)⋊C4C2211yescharacteristic
33C7×C4⋊Dic3C2211yescharacteristic
34C7×C4⋊Dic3C2211yescharacteristic
35C3×C4⋊Dic7C2211yescharacteristic
36C3×Dic7⋊C4C2211yescharacteristic
37C3×Dic7⋊C4C2211yescharacteristic
38C3×Dic7⋊C4C2211yescharacteristic
39C3×Dic7⋊C4C2211yescharacteristic
40C3×C4×Dic7C2211yescharacteristic
41Dic3⋊Dic7C2211yescharacteristic
42#66577C2211yescharacteristic
43#66577C2211yescharacteristic
44#66577C2211yescharacteristic
45Dic7⋊Dic3C2211yescharacteristic
46Dic7⋊Dic3C2211yescharacteristic
47Dic7⋊Dic3C2211yescharacteristic
48(C2×D3)⋊Dic7C2211yescharacteristic
49(C2×D3)⋊Dic7C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C7×C22⋊Q8—31no—
53#6507—31no—
54#6507—31no—
55#6487—31no—
56C2×Dic7⋊C4—31no—
57#6452—31no—
58#6452—31no—
59#6452—31no—
60#6452D311yescharacteristic, complemented
61#6451—31no—
62#6451—31no—
63#6441—31no—
64#6441—31no—
65#6440—31no—
66#6440—31no—
67#5689—71nomaximal, Hall
68C22×D3×C7C2311yescharacteristic
69C2×C3×C4×C7C2311yescharacteristic
70C2×C3×C4×C7C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×Dic21C2311yescharacteristic
73C2×Dic21C2311yescharacteristic
74C2×Dic21C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76C2×C7×Dic3C2311yescharacteristic
77C2×C7×Dic3C2311yescharacteristic
78C2×C7×Dic3C2311yescharacteristic
79C4×D3×C7—41no—
80C7×Dic6—41no—
81C2×C3×Dic7C2311yescharacteristic
82C2×C3×Dic7C2311yescharacteristic
83C2×C3×Dic7C2311yescharacteristic
84C2×C3×Dic7C2311yescharacteristic
85#4248—41no—
86#4248—41no—
87#4248—41no—
88D3×Dic7—41no—
89D3×Dic7Q814yescomplemented
90C2×C7×Q8—31no—
91C22×C4×C7—31no—
92C22×Dic7—31no—
93C22×Dic7—31no—
94C2×Dic14—31no—
95C2×Dic14—31no—
96C2×Dic14—31no—
97C7×C4⋊C4—31no—
98C7×C4⋊C4—31no—
99C7×C4⋊C4C2×D311yescharacteristic
100C7×C22⋊C4—31no—
101C7×C22⋊C4—31no—
102C22⋊Dic7—31no—
103C22⋊Dic7—31no—
104C4⋊Dic7—31no—
105C4⋊Dic7—31no—
106C4⋊Dic7C2×D311yescharacteristic
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—
116Dic7⋊C4—31no—
117Dic7⋊C4C2×D311yescharacteristic
118Dic7⋊C4C2×D311yescharacteristic
119Dic7⋊C4C2×D311yescharacteristic
120Dic7⋊C4C2×D311yescharacteristic
121C4×Dic7—31no—
122C4×Dic7—31no—
123C4×Dic7—31no—
124C4×Dic7C2×D311yescharacteristic
125C3×#125—71no—
126#897—71no—
127#897D711yescharacteristic
128#896—71no—
129#896—71no—
130#892—71no—
131D3×C4⋊C4—71no—
132#890—71no—
133#889—71no—
134#889—71no—
135#888—71no—
136#888—71no—
137#888—71no—
138#872—71no—
139#869—71no—
140C22×C3×C7C2411yescharacteristic
141C2×D3×C7—21no—
142C2×D3×C7—21no—
143C2×D3×C7C2×Q812yes—
144C3×C4×C7—21no—
145C3×C4×C7—21no—
146C3×C4×C7—21no—
147Dic21—21no—
148Dic21—21no—
149Dic21—21no—
150Dic21C2×Q812yes—
151C3×Dic7—21no—
152C3×Dic7—21no—
153C3×Dic7—21no—
154C3×Dic7C2×Q812yes—
155C7×Dic3—21no—
156C7×Dic3—21no—
157C7×Dic3—21no—
158#544—211noSylow
159C23×C7—31no—
160C7×Q8—121no—
161C2×C4×C7—31no—
162C2×C4×C7—31no—
163C2×C4×C7—31no—
164C2×C4×C7—121no—
165C2×C4×C7C22×D311yescharacteristic
166C2×C4×C7C22×D311yescharacteristic
167C2×C4×C7C22×D311yescharacteristic
168C2×Dic7—31no—
169C2×Dic7—34no—
170C2×Dic7—31no—
171C2×Dic7—31no—
172C2×Dic7—31no—
173C2×Dic7—121no—
174C2×Dic7C22×D311yescharacteristic
175C2×Dic7C22×D311yescharacteristic
176C2×Dic7C22×D311yescharacteristic
177C2×Dic7C22×D311yescharacteristic
178Dic14—121no—
179Dic14—121no—
180Dic14—121no—
181C2×C4×D3—71no—
182C2×C4×D3—71no—
183C2×C4×D3C2×D711yescharacteristic
184C2×Dic6—71no—
185C2×Dic6—71no—
186C2×Dic6—71no—
187C2×Dic6C2×D711yescharacteristic
188C3×C4⋊C4—71no—
189C3×C4⋊C4—71no—
190C3×C4⋊C4—71no—
191C3×C4⋊C4—71no—
192C3×C4⋊C4—71no—
193C3×C4⋊C4C2×D711yescharacteristic
194C3×C42—71no—
195(C2×D3)⋊C4—71no—
196(C2×D3)⋊C4—71no—
197(C2×D3)⋊C4C2×D711yescharacteristic
198(C2×D3)⋊C4C2×D711yescharacteristic
199C4⋊Dic3—71no—
200C4⋊Dic3—71no—
201C4⋊Dic3—71no—
202C4⋊Dic3—71no—
203C4⋊Dic3C2×D711yescharacteristic
204C4⋊Dic3C2×D711yescharacteristic
205Dic3⋊C4—71no—
206Dic3⋊C4—71no—
207Dic3⋊C4—71no—
208Dic3⋊C4—71no—
209Dic3⋊C4—71no—
210Dic3⋊C4—71no—
211Dic3⋊C4—71no—
212Dic3⋊C4—71no—
213C4×Dic3—71no—
214C4×Dic3—71no—
215C4×Dic3—71no—
216C2×C3×C7C22×Q811yescharacteristic
217C2×C3×C7H(5,𝔽2)11yescharacteristic
218C2×C3×C72−1+411yescharacteristic
219D3×C7—22no—
220C4⋊Q8—211no—
221C4⋊Q8—211no—
222C4⋊Q8—211no—
223C4⋊Q8—211no—
224#125—71no—
225#125—211no—
226#125—211no—
227#125—211no—
228C22⋊Q8—31no—
229C22⋊Q8—211no—
230C22⋊Q8—211no—
231C22⋊Q8—211no—
232#117—211no—
233#117—211no—
234C2×C4⋊C4—211no—
235C22×C7—32no—
236C22×C7—61no—
237C22×C7—61no—
238C22×C7C23×D311yescharacteristic
239C4×C7—21no—
240C4×C7—21no—
241C4×C7—21no—
242C4×C7—61no—
243C4×C7—61no—
244C4×C7—61no—
245Dic7—21no—
246Dic7—21no—
247Dic7—21no—
248Dic7—32no—
249Dic7—61no—
250Dic7—61no—
251Dic7—61no—
252Dic7D3×Q812yes—
253C22×D3C22×D711yescharacteristic
254C2×C3×C4—71no—
255C2×C3×C4—71no—
256C2×C3×C4—71no—
257C2×C3×C4—71no—
258C2×C3×C4C22×D711yescharacteristic
259C2×C3×C4C22×D711yescharacteristic
260C2×C3×C4C22×D711yescharacteristic
261C2×Dic3—71no—
262C2×Dic3—71no—
263C2×Dic3—71no—
264C2×Dic3—71no—
265C2×Dic3C22×D711yescharacteristic
266C2×Dic3C22×D711yescharacteristic
267C2×Dic3C22×D711yescharacteristic
268C4×D3—41no—
269C4×D3—74no—
270C4×D3—281no—
271Dic6—41no—
272Dic6—281no—
273Dic6—281no—
274Dic6—281no—
275C3×C7#54411yescharacteristic, complemented, Hall
276C2×Q8—31no—
277C2×Q8—211no—
278C2×Q8—211no—
279C2×Q8—211no—
280C22×C4—31no—
281C22×C4—211no—
282C22×C4—211no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—71no—
286C4⋊C4—71no—
287C4⋊C4—71no—
288C4⋊C4—71no—
289C4⋊C4—71no—
290C4⋊C4—211no—
291C4⋊C4—211no—
292C4⋊C4—211no—
293C4⋊C4—211no—
294C4⋊C4—211no—
295C4⋊C4—211no—
296C4⋊C4—211no—
297C4⋊C4—211no—
298C4⋊C4—211no—
299C4⋊C4—211no—
300C4⋊C4—211no—
301C4⋊C4—211no—
302C4⋊C4D3×D711yescharacteristic
303C22⋊C4—31no—
304C22⋊C4—31no—
305C22⋊C4—211no—
306C22⋊C4—211no—
307C42—71no—
308C42—211no—
309C42—211no—
310C42—211no—
311C2×C7—62no—
312C2×C7C2×D3×Q811yescharacteristic
313C2×C7#100911yescharacteristic
314C2×C7#101011yescharacteristic
315C22×C3C23×D711yescharacteristic
316C2×D3—21no—
317C2×D3—21no—
318C2×D3Q8×D712yes—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—72no—
323C3×C4—141no—
324C3×C4—141no—
325C3×C4—141no—
326Dic3—21no—
327Dic3—21no—
328Dic3—21no—
329Dic3—72no—
330Dic3—141no—
331Dic3—141no—
332Dic3—141no—
333C23—31no—
334Q8—121no—
335Q8—841no—
336Q8—841no—
337Q8—841no—
338C2×C4—31no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—71no—
342C2×C4—71no—
343C2×C4—71no—
344C2×C4—71no—
345C2×C4—121no—
346C2×C4—214no—
347C2×C4—211no—
348C2×C4—211no—
349C2×C4—211no—
350C2×C4—211no—
351C2×C4—841no—
352C2×C4C2×D3×D711yescharacteristic
353C2×C4C2×D3×D711yescharacteristic
354C2×C4C2×D3×D711yescharacteristic
355C7#568911yescharacteristic, complemented, Sylow
356C2×C3#654811yescharacteristic
357C2×C3C2×Q8×D711yescharacteristic
358C2×C3#655411yescharacteristic
359D3—22no—
360C22—32no—
361C22—61no—
362C22—61no—
363C22C22×D3×D711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—61no—
368C4—61no—
369C4—61no—
370C4—72no—
371C4—141no—
372C4—141no—
373C4—141no—
374C4—212no—
375C4—421no—
376C4—421no—
377C4—421no—
378C3#9031411yescharacteristic, complemented, Sylow
379C2—62no—
380C2#1062156511yescharacteristic
381C2#1062156711yescharacteristic
382C2D3×Q8×D711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
prime radicalC22×D3×C7C23
hypercenterC4⋊C4D3×D7
hypocenterC3×C7#544
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10621372C2semidirect
3. C3×#6452C2semidirect
4. #10621032C2semidirect
5. #10621030C2semidirect
12. #10620898C2semidirect
13. #10620897C2semidirect
14. #10620891C2semidirect
15. #10620891C2semidirect
60. #6452D3semidirect
89. D3×Dic7Q8semidirect
275. C3×C7#544semidirect
355. C7#5689semidirect
378. C3#90314semidirect

Maximal subgroups

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

subgroupindex
#106213722
C7×#8972
C3×#64522
#106210322
#106210302
#106209982
#106209792
#106209622
D3×Dic7⋊C42
#106209602
#106209142
#106208982
#106208972
#106208912
#903143
#56897