Finite Group Databasebeta

← #13058629

Subgroups — #13058629

Order 1344.

432 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10621377C211yesmaximal, characteristic, complemented
2C7×#896C211yesmaximal, characteristic, complemented
3C3×#6450C211yesmaximal, characteristic, complemented
4C4×#4247C211yesmaximal, characteristic, complemented
5#10620982C211yesmaximal, characteristic
6#10620973C211yesmaximal, characteristic, complemented
7#10620964C211yesmaximal, characteristic, complemented
8#10620949C211yesmaximal, characteristic, complemented
9#10620939C211yesmaximal, characteristic, complemented
10#10620937C211yesmaximal, characteristic, complemented
11#10620934C211yesmaximal, characteristic, complemented
12#10620913C211yesmaximal, characteristic, complemented
13#10620912C211yesmaximal, characteristic, complemented
14#10620891C211yesmaximal, characteristic, complemented
15#10620888C211yesmaximal, characteristic, complemented
16#90331—31nomaximal, Hall
17C2×D84C2211yescharacteristic
18C2×C4×D21C2211yescharacteristic
19C2×C4×D3×C7C2211yescharacteristic
20C2×C7×Dic6C2211yescharacteristic
21C2×C3×Dic14C2211yescharacteristic
22C2×#4248C2211yescharacteristic
23C2×#4247C2211yescharacteristic
24C2×#4247C2211yescharacteristic
25C2×D21⋊C4C2211yescharacteristic
26C3×C7×C4⋊C4C2211yescharacteristic
27#66631C2211yescharacteristic
28#66631C2211yescharacteristic
29#66631C2211yescharacteristic
30#66629C2211yescharacteristic
31C7×(C2×D3)⋊C4C2211yescharacteristic
32C7×(C2×D3)⋊C4C2211yescharacteristic
33C7×Dic3⋊C4C2211yescharacteristic
34C7×Dic3⋊C4C2211yescharacteristic
35C3×Dic7⋊C4C2211yescharacteristic
36C3×Dic7⋊C4C2211yescharacteristic
37C3×C4×Dic7C2211yescharacteristic
38C3×C4×Dic7C2211yescharacteristic
39C3×C4×Dic7C2211yescharacteristic
40Dic3⋊Dic7C2211yescharacteristic
41#66577C2211yescharacteristic
42#66577C2211yescharacteristic
43Dic7⋊Dic3C2211yescharacteristic
44#66575C2211yescharacteristic
45#66575C2211yescharacteristic
46#66575C2211yescharacteristic
47#66575C2211yescharacteristic
48#66575C2211yescharacteristic
49(C2×D3)⋊Dic7C2211yescharacteristic
50(C2×D3)⋊Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C7×C22⋊Q8—31no—
53#6510—31no—
54#6507—31no—
55#6492—31no—
56C4×C22⋊D7—31no—
57#6461—31no—
58#6459—31no—
59#6459—31no—
60#6457—31no—
61#6455—31no—
62#6450D311yescharacteristic, complemented
63#6448—31no—
64#6448—31no—
65#6447—31no—
66#6442—31no—
67#5582—71nomaximal, Hall
68C22×D21C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D3×C7C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×C3×C4×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74C2×Dic21C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76D84—41no—
77C4×D21—41no—
78C2×C7×Dic3C2311yescharacteristic
79C2×C7×Dic3C2311yescharacteristic
80C2×C7×Dic3C2311yescharacteristic
81C4×D3×C7—41no—
82C7×Dic6—41no—
83C2×C3×Dic7C2311yescharacteristic
84C2×C3×Dic7C2311yescharacteristic
85C2×C3×Dic7C2311yescharacteristic
86C2×C3×Dic7C2311yescharacteristic
87C3×Dic14—22no—
88#4248—41no—
89#4247—22no—
90#4247—41no—
91D21⋊C4—22no—
92C2×C7×Q8—31no—
93C22×C4×C7—31no—
94C2×C22⋊D7—31no—
95C2×C22⋊D7—31no—
96C2×D28—31no—
97C2×C4×D7—31no—
98C2×C4×D7—31no—
99C2×Dic14—31no—
100C2×Dic14C2×D311yescharacteristic
101C7×C4⋊C4—31no—
102C7×C4⋊C4—31no—
103C7×C4⋊C4C2×D311yescharacteristic
104C7×C22⋊C4—31no—
105C7×C22⋊C4—31no—
106C22⋊Dic7—31no—
107C22⋊Dic7—31no—
108(C2×D7)⋊C4—31no—
109(C2×D7)⋊C4—31no—
110(C2×D7)⋊C4—31no—
111(C2×D7)⋊C4—31no—
112(C2×D7)⋊C4—31no—
113(C2×D7)⋊C4—31no—
114(C2×D7)⋊C4—31no—
115(C2×D7)⋊C4—31no—
116C4⋊Dic7—31no—
117Dic7⋊C4—31no—
118Dic7⋊C4—31no—
119Dic7⋊C4—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4C2×D311yescharacteristic
122Dic7⋊C4C2×D311yescharacteristic
123C4×Dic7—31no—
124C4×Dic7C2×D311yescharacteristic
125C4×Dic7C2×D311yescharacteristic
126C4×Dic7C2×D311yescharacteristic
127C3×C4×Q8—71no—
128#947—71no—
129#946—71no—
130#896—71no—
131#896D711yescharacteristic, complemented
132#895—71no—
133#894—71no—
134#894—71no—
135#888—71no—
136#876—71no—
137#876—71no—
138#875—71no—
139#875—71no—
140C4×D12—71no—
141#872—71no—
142C22×C3×C7C2411yescharacteristic
143C2×D21—21no—
144C2×D21—21no—
145C2×D21—21no—
146C2×D21—21no—
147C2×D21—21no—
148C2×D21—21no—
149C2×D3×C7—21no—
150C2×D3×C7—21no—
151C2×D3×C7—21no—
152C3×C4×C7—21no—
153C3×C4×C7—21no—
154C3×C4×C7—21no—
155Dic21—21no—
156Dic21—21no—
157C3×Dic7—21no—
158C3×Dic7—21no—
159C3×Dic7—21no—
160C3×Dic7#4112yes—
161C7×Dic3—21no—
162C7×Dic3—21no—
163C7×Dic3—21no—
164#542—211noSylow
165C23×C7—31no—
166C22×D7—31no—
167C22×D7—31no—
168C7×Q8—121no—
169C2×C4×C7—31no—
170C2×C4×C7—31no—
171C2×C4×C7—31no—
172C2×C4×C7—121no—
173C2×C4×C7C22×D311yescharacteristic
174C2×C4×C7C22×D311yescharacteristic
175C2×C4×C7C22×D311yescharacteristic
176C22⋊D7—62no—
177C22⋊D7—121no—
178C2×Dic7—31no—
179C2×Dic7—31no—
180C2×Dic7C22×D311yescharacteristic
181C2×Dic7C22×D311yescharacteristic
182C2×Dic7C22×D311yescharacteristic
183C2×Dic7C22×D311yescharacteristic
184D28—121no—
185C4×D7—62no—
186C4×D7—121no—
187Dic14—22no—
188Dic14—121no—
189C2×C3×Q8—71no—
190C2×D12—71no—
191C2×D12—71no—
192C2×D12—71no—
193C2×C4×D3—71no—
194C2×C4×D3—71no—
195C2×C4×D3C2×D711yescharacteristic
196C2×Dic6—71no—
197C2×Dic6C2×D711yescharacteristic
198C3×C4⋊C4—71no—
199C3×C4⋊C4—71no—
200C3×C4⋊C4C2×D711yescharacteristic
201C3×C42—71no—
202C3×C42—71no—
203C3×C42—71no—
204(C2×D3)⋊C4—71no—
205(C2×D3)⋊C4—71no—
206(C2×D3)⋊C4—71no—
207(C2×D3)⋊C4—71no—
208(C2×D3)⋊C4—71no—
209(C2×D3)⋊C4—71no—
210(C2×D3)⋊C4—71no—
211(C2×D3)⋊C4—71no—
212(C2×D3)⋊C4—71no—
213(C2×D3)⋊C4—71no—
214(C2×D3)⋊C4C2×D711yescharacteristic
215(C2×D3)⋊C4C2×D711yescharacteristic
216C4⋊Dic3—71no—
217Dic3⋊C4—71no—
218Dic3⋊C4—71no—
219Dic3⋊C4—71no—
220Dic3⋊C4—71no—
221Dic3⋊C4C2×D711yescharacteristic
222Dic3⋊C4C2×D711yescharacteristic
223C4×Dic3—71no—
224C2×C3×C7C2×#4111yescharacteristic
225C2×C3×C7H(5,𝔽2)11yescharacteristic
226C2×C3×C72−1+411yescharacteristic
227D21—41no—
228D21—41no—
229D3×C7—41no—
230C4⋊Q8—211no—
231#126—211no—
232#126—211no—
233#124—211no—
234#124—211no—
235#124—211no—
236#123—211no—
237#123—211no—
238C22⋊Q8—31no—
239C22⋊Q8—211no—
240C22⋊Q8—211no—
241#121—211no—
242C4×Q8—71no—
243C4×D4—211no—
244#117—211no—
245C22×C7—61no—
246C22×C7—61no—
247C22×C7—61no—
248C22×C7C23×D311yescharacteristic
249C2×D7—61no—
250C2×D7—61no—
251C2×D7—61no—
252C2×D7—61no—
253C2×D7—61no—
254C2×D7—61no—
255C4×C7—21no—
256C4×C7—21no—
257C4×C7—21no—
258C4×C7—61no—
259C4×C7—61no—
260C4×C7—61no—
261Dic7—21no—
262Dic7—21no—
263Dic7—21no—
264Dic7—61no—
265Dic7—61no—
266Dic7#23512yes—
267C22×D3—71no—
268C22×D3—71no—
269C22×D3C22×D711yescharacteristic
270C3×Q8—142no—
271C2×C3×C4—71no—
272C2×C3×C4—71no—
273C2×C3×C4—71no—
274C2×C3×C4—71no—
275C2×C3×C4C22×D711yescharacteristic
276C2×C3×C4C22×D711yescharacteristic
277C2×C3×C4C22×D711yescharacteristic
278C2×Dic3—71no—
279C2×Dic3—71no—
280C2×Dic3C22×D711yescharacteristic
281C2×Dic3C22×D711yescharacteristic
282C2×Dic3C22×D711yescharacteristic
283D12—142no—
284D12—281no—
285D12—281no—
286C4×D3—41no—
287C4×D3—142no—
288C4×D3—281no—
289Dic6—41no—
290Dic6—281no—
291C3×C7#54211yescharacteristic, complemented, Hall
292C2×Q8—31no—
293C2×Q8—71no—
294C2×Q8—211no—
295C2×D4—211no—
296C2×D4—211no—
297C2×D4—211no—
298C22×C4—31no—
299C22×C4—211no—
300C22×C4—211no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—71no—
304C4⋊C4—71no—
305C4⋊C4—211no—
306C4⋊C4—211no—
307C4⋊C4—211no—
308C4⋊C4—211no—
309C4⋊C4—211no—
310C4⋊C4D3×D711yescharacteristic
311C22⋊C4—31no—
312C22⋊C4—31no—
313C22⋊C4—211no—
314C22⋊C4—211no—
315C22⋊C4—211no—
316C22⋊C4—211no—
317C22⋊C4—211no—
318C22⋊C4—211no—
319C22⋊C4—211no—
320C22⋊C4—211no—
321C22⋊C4—211no—
322C22⋊C4—211no—
323C42—71no—
324C42—71no—
325C42—71no—
326C42—211no—
327C2×C7—121no—
328C2×C7C2×#23511yescharacteristic
329C2×C7#100711yescharacteristic
330C2×C7#100911yescharacteristic
331D7—121no—
332D7—121no—
333C22×C3C23×D711yescharacteristic
334C2×D3—21no—
335C2×D3—21no—
336C2×D3—21no—
337C2×D3—141no—
338C2×D3—141no—
339C2×D3—141no—
340C2×D3—141no—
341C2×D3—141no—
342C2×D3—141no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—72no—
347C3×C4—141no—
348C3×C4—141no—
349C3×C4—141no—
350Dic3—21no—
351Dic3—21no—
352Dic3—21no—
353Dic3—141no—
354Dic3—141no—
355C23—31no—
356C23—211no—
357C23—211no—
358Q8—121no—
359Q8—142no—
360Q8—841no—
361D4—422no—
362D4—841no—
363D4—841no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—31no—
367C2×C4—71no—
368C2×C4—71no—
369C2×C4—71no—
370C2×C4—71no—
371C2×C4—121no—
372C2×C4—211no—
373C2×C4—211no—
374C2×C4—422no—
375C2×C4—841no—
376C2×C4C2×D3×D711yescharacteristic
377C2×C4C2×D3×D711yescharacteristic
378C2×C4C2×D3×D711yescharacteristic
379C7#558211yescharacteristic, complemented, Sylow
380C2×C3#654811yescharacteristic
381C2×C3#655111yescharacteristic
382C2×C3D7×#4111yescharacteristic
383D3—41no—
384D3—281no—
385D3—281no—
386C22—61no—
387C22—61no—
388C22—61no—
389C22—421no—
390C22—421no—
391C22—421no—
392C22—421no—
393C22—421no—
394C22—421no—
395C22C22×D3×D711yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—61no—
400C4—61no—
401C4—61no—
402C4—72no—
403C4—141no—
404C4—141no—
405C4—141no—
406C4—421no—
407C4—421no—
408C3#9033111yescharacteristic, complemented, Sylow
409C2—121no—
410C2—841no—
411C2—841no—
412C2D7×#23511yescharacteristic
413C2#1062157411yescharacteristic
414C2#1062157611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
prime radical#10620982C2
hypercenterC4⋊C4D3×D7
hypocenterC3×C7#542
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. #10621377C2semidirect
2. C7×#896C2semidirect
3. C3×#6450C2semidirect
4. C4×#4247C2semidirect
6. #10620973C2semidirect
7. #10620964C2semidirect
8. #10620949C2semidirect
9. #10620939C2semidirect
10. #10620937C2semidirect
11. #10620934C2semidirect
12. #10620913C2semidirect
13. #10620912C2semidirect
14. #10620891C2semidirect
15. #10620888C2semidirect
62. #6450D3semidirect
131. #896D7semidirect
291. C3×C7#542semidirect
379. C7#5582semidirect
408. C3#90331semidirect

Maximal subgroups

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

subgroupindex
#106213772
C7×#8962
C3×#64502
C4×#42472
#106209822
#106209732
#106209642
#106209492
#106209392
#106209372
#106209342
#106209132
#106209122
#106208912
#106208882
#903313
#55827