Finite Group Databasebeta

← #13058140

Subgroups — #13058140

Order 1344.

436 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#10621366C211yesmaximal, characteristic, complemented
2C7×#67⋊C4C211yesmaximal, characteristic, complemented
3C3×#6442C211yesmaximal, characteristic, complemented
4#10621137C211yesmaximal, characteristic, complemented
5#10621120C211yesmaximal, characteristic
6#10621117C211yesmaximal, characteristic, complemented
7#10621104C211yesmaximal, characteristic, complemented
8C4×#4247C211yesmaximal, characteristic, complemented
9#10620989C211yesmaximal, characteristic, complemented
10#10620979C211yesmaximal, characteristic, complemented
11D3×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#10620943C211yesmaximal, characteristic, complemented
13#10620942C211yesmaximal, characteristic, complemented
14#10620940C211yesmaximal, characteristic, complemented
15#10620939C211yesmaximal, characteristic, complemented
16#90255—31nomaximal, Hall
17C2×#4268C2211yescharacteristic
18C2×C4×D21C2211yescharacteristic
19C2×C7×#67C2211yescharacteristic
20C22×C7×Dic3C2211yescharacteristic
21C2×C4×D3×C7C2211yescharacteristic
22C2×#4248C2211yescharacteristic
23C2×#4247C2211yescharacteristic
24C2×D3×Dic7C2211yescharacteristic
25C2×D3×Dic7C2211yescharacteristic
26C3×C7×C22⋊C4C2211yescharacteristic
27#66636C2211yescharacteristic
28#66631C2211yescharacteristic
29C4⋊Dic21C2211yescharacteristic
30#66629C2211yescharacteristic
31C7×(C2×D3)⋊C4C2211yescharacteristic
32C7×Dic3⋊C4C2211yescharacteristic
33C4×C7×Dic3C2211yescharacteristic
34C3×C22⋊Dic7C2211yescharacteristic
35C3×C22⋊Dic7C2211yescharacteristic
36C3×C4⋊Dic7C2211yescharacteristic
37C3×Dic7⋊C4C2211yescharacteristic
38C3×Dic7⋊C4C2211yescharacteristic
39C3×C4×Dic7C2211yescharacteristic
40Dic3⋊Dic7C2211yescharacteristic
41#66577C2211yescharacteristic
42#66577C2211yescharacteristic
43#66577C2211yescharacteristic
44Dic7⋊Dic3C2211yescharacteristic
45Dic7⋊Dic3C2211yescharacteristic
46Dic7⋊Dic3C2211yescharacteristic
47Dic7⋊Dic3C2211yescharacteristic
48#66575C2211yescharacteristic
49#66575C2211yescharacteristic
50#66575C2211yescharacteristic
51(C2×D3)⋊Dic7C2211yescharacteristic
52C4×C7×D4—31no—
53#6502—31no—
54#6498—31no—
55#6492—31no—
56C4×C22⋊D7—31no—
57#6487—31no—
58C2×Dic7⋊C4—31no—
59#6459—31no—
60#6452—31no—
61#6449—31no—
62#6446—31no—
63#6442D311yescharacteristic, complemented
64#6441—31no—
65#6439—31no—
66#6433—31no—
67#5707—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D3×C7C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×C3×C4×C7C2311yescharacteristic
73#4268—41no—
74C2×Dic21C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77C4×D21—41no—
78C7×#67—22no—
79C2×C7×Dic3—41no—
80C2×C7×Dic3C2311yescharacteristic
81C2×C7×Dic3C2311yescharacteristic
82C2×C7×Dic3C2311yescharacteristic
83C4×D3×C7—41no—
84C2×C3×Dic7C2311yescharacteristic
85C2×C3×Dic7C2311yescharacteristic
86C2×C3×Dic7C2311yescharacteristic
87C2×C3×Dic7C2311yescharacteristic
88#4248—41no—
89#4247—22no—
90D3×Dic7—22no—
91D3×Dic7—41no—
92C2×C7×D4—31no—
93C22×C4×C7—31no—
94C22×C4×C7—31no—
95C2×C22⋊D7—31no—
96C2×C22⋊D7—31no—
97C22×Dic7—31no—
98C22×Dic7—31no—
99C2×C4×D7—31no—
100C2×Dic14—31no—
101C7×C4⋊C4—31no—
102C7×C22⋊C4—31no—
103C7×C22⋊C4C2×D311yescharacteristic
104C42×C7—31no—
105C22⋊Dic7—31no—
106C22⋊Dic7—31no—
107C22⋊Dic7C2×D311yescharacteristic
108C22⋊Dic7C2×D311yescharacteristic
109(C2×D7)⋊C4—31no—
110(C2×D7)⋊C4—31no—
111(C2×D7)⋊C4—31no—
112(C2×D7)⋊C4—31no—
113C4⋊Dic7—31no—
114C4⋊Dic7—31no—
115C4⋊Dic7C2×D311yescharacteristic
116Dic7⋊C4—31no—
117Dic7⋊C4—31no—
118Dic7⋊C4—31no—
119Dic7⋊C4—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4—31no—
122Dic7⋊C4—31no—
123Dic7⋊C4—31no—
124Dic7⋊C4C2×D311yescharacteristic
125Dic7⋊C4C2×D311yescharacteristic
126C4×Dic7C2×D311yescharacteristic
127C3×#126—71no—
128#898—71no—
129#897—71no—
130#896—71no—
131#894—71no—
132D3×C4⋊C4—71no—
133#890—71no—
134#886—71no—
135#884—71no—
136#883—71no—
137#883—71no—
138#67⋊C4D711yescharacteristic, complemented
139#878—71no—
140C4×D12—71no—
141#870—71no—
142C22×C3×C7—21no—
143C22×C3×C7—21no—
144C22×C3×C7—21no—
145C22×C3×C7C2411yescharacteristic
146C2×D21—21no—
147C2×D21—21no—
148C2×D21—21no—
149C2×D3×C7—21no—
150C2×D3×C7—21no—
151C2×D3×C7#4112yes—
152C3×C4×C7—21no—
153C3×C4×C7—21no—
154Dic21—21no—
155Dic21—21no—
156Dic21—21no—
157C3×Dic7—21no—
158C3×Dic7—21no—
159C3×Dic7—21no—
160C3×Dic7—21no—
161C7×Dic3—21no—
162C7×Dic3—21no—
163C7×Dic3—21no—
164#539—211noSylow
165C23×C7—31no—
166C23×C7C22×D311yescharacteristic
167C22×D7—31no—
168C7×D4—62no—
169C2×C4×C7—31no—
170C2×C4×C7—31no—
171C2×C4×C7—31no—
172C2×C4×C7—121no—
173C2×C4×C7—121no—
174C2×C4×C7C22×D311yescharacteristic
175C2×C4×C7C22×D311yescharacteristic
176C22⋊D7—62no—
177C22⋊D7—121no—
178C2×Dic7—31no—
179C2×Dic7—31no—
180C2×Dic7—31no—
181C2×Dic7—62no—
182C2×Dic7—121no—
183C2×Dic7C22×D311yescharacteristic
184C2×Dic7C22×D311yescharacteristic
185C2×Dic7C22×D311yescharacteristic
186C2×Dic7C22×D311yescharacteristic
187C4×D7—121no—
188Dic14—121no—
189C2×#67—71no—
190C2×#67C2×D711yescharacteristic
191C22×Dic3C2×D711yescharacteristic
192C2×D12—71no—
193C2×C4×D3—71no—
194C2×C4×D3—71no—
195C2×C4×D3—71no—
196C2×C4×D3C2×D711yescharacteristic
197C2×Dic6—71no—
198C3×C4⋊C4—71no—
199C3×C4⋊C4—71no—
200C3×C4⋊C4—71no—
201C3×C22⋊C4—71no—
202C3×C22⋊C4—71no—
203C3×C22⋊C4C2×D711yescharacteristic
204C3×C42—71no—
205#217—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)⋊C4C2×D711yescharacteristic
212C4⋊Dic3—71no—
213C4⋊Dic3—71no—
214C4⋊Dic3—71no—
215C4⋊Dic3—71no—
216C4⋊Dic3—71no—
217Dic3⋊C4—71no—
218Dic3⋊C4—71no—
219Dic3⋊C4—71no—
220Dic3⋊C4—71no—
221Dic3⋊C4—71no—
222Dic3⋊C4C2×D711yescharacteristic
223C4×Dic3C2×D711yescharacteristic
224C2×C3×C7—41no—
225C2×C3×C7C2×#4111yescharacteristic
226C2×C3×C7H(5,𝔽2)11yescharacteristic
227C2×C3×C72−1+411yescharacteristic
228D21—41no—
229D3×C7—22no—
230#126—71no—
231#126—211no—
232#125—211no—
233#125—211no—
234#123—211no—
235#123—211no—
236#123—211no—
237#123—211no—
238C22⋊Q8—211no—
239C22⋊Q8—211no—
240C22⋊Q8—211no—
241#121—211no—
242C4×D4—31no—
243C4×D4—211no—
244C2×C4⋊C4—211no—
245C22×C7—21no—
246C22×C7—21no—
247C22×C7—21no—
248C22×C7—32no—
249C22×C7—61no—
250C22×C7—61no—
251C22×C7C23×D311yescharacteristic
252C2×D7—61no—
253C2×D7—61no—
254C2×D7—61no—
255C4×C7—21no—
256C4×C7—21no—
257C4×C7—61no—
258C4×C7—61no—
259C4×C7—61no—
260Dic7—21no—
261Dic7—21no—
262Dic7—21no—
263Dic7—21no—
264Dic7—61no—
265Dic7—61no—
266Dic7—61no—
267C23×C3C22×D711yescharacteristic
268C22×D3—71no—
269C22×D3C22×D711yescharacteristic
270C2×C3×C4—71no—
271C2×C3×C4—71no—
272C2×C3×C4—71no—
273C2×C3×C4—71no—
274C2×C3×C4C22×D711yescharacteristic
275C2×C3×C4C22×D711yescharacteristic
276#67—22no—
277#67—281no—
278C2×Dic3—41no—
279C2×Dic3—71no—
280C2×Dic3—71no—
281C2×Dic3—71no—
282C2×Dic3C22×D711yescharacteristic
283C2×Dic3C22×D711yescharacteristic
284C2×Dic3C22×D711yescharacteristic
285D12—142no—
286C4×D3—41no—
287C4×D3—142no—
288C4×D3—281no—
289C4×D3—281no—
290Dic6—281no—
291C3×C7#53911yescharacteristic, complemented, Hall
292C2×Q8—211no—
293C2×D4—31no—
294C2×D4—211no—
295C2×D4—211no—
296C22×C4—31no—
297C22×C4—31no—
298C22×C4—211no—
299C22×C4—211no—
300C22×C4—211no—
301C4⋊C4—31no—
302C4⋊C4—71no—
303C4⋊C4—71no—
304C4⋊C4—71no—
305C4⋊C4—211no—
306C4⋊C4—211no—
307C4⋊C4—211no—
308C4⋊C4—211no—
309C4⋊C4—211no—
310C4⋊C4—211no—
311C4⋊C4—211no—
312C4⋊C4—211no—
313C4⋊C4—211no—
314C4⋊C4—211no—
315C22⋊C4—31no—
316C22⋊C4—71no—
317C22⋊C4—71no—
318C22⋊C4—211no—
319C22⋊C4—211no—
320C22⋊C4—211no—
321C22⋊C4—211no—
322C22⋊C4—211no—
323C22⋊C4—211no—
324C22⋊C4D3×D711yescharacteristic
325C42—31no—
326C42—71no—
327C2×C7—41no—
328C2×C7—62no—
329C2×C7D3×#4111yescharacteristic
330C2×C7#100911yescharacteristic
331C2×C7#101011yescharacteristic
332D7—121no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3C23×D711yescharacteristic
337C2×D3—21no—
338C2×D3—21no—
339C2×D3—141no—
340C2×D3—141no—
341C2×D3—141no—
342C2×D3#115712yes—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—141no—
346C3×C4—141no—
347C3×C4—141no—
348C3×C4—141no—
349Dic3—21no—
350Dic3—21no—
351Dic3—21no—
352Dic3—141no—
353Dic3—141no—
354Dic3—141no—
355C23—31no—
356C23—211no—
357C23C2×D3×D711yescharacteristic
358Q8—841no—
359D4—62no—
360D4—422no—
361D4—841no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—71no—
366C2×C4—71no—
367C2×C4—71no—
368C2×C4—71no—
369C2×C4—121no—
370C2×C4—121no—
371C2×C4—211no—
372C2×C4—211no—
373C2×C4—211no—
374C2×C4—422no—
375C2×C4—841no—
376C2×C4—841no—
377C2×C4C2×D3×D711yescharacteristic
378C2×C4C2×D3×D711yescharacteristic
379C7#570711yescharacteristic, complemented, Sylow
380C2×C3—41no—
381C2×C3C2×#115711yescharacteristic
382C2×C3#654811yescharacteristic
383C2×C3#655411yescharacteristic
384D3—22no—
385D3—281no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—32no—
390C22—61no—
391C22—61no—
392C22—421no—
393C22—421no—
394C22—421no—
395C22C22×D3×D711yescharacteristic
396C4—21no—
397C4—21no—
398C4—61no—
399C4—61no—
400C4—61no—
401C4—141no—
402C4—141no—
403C4—141no—
404C4—141no—
405C4—421no—
406C4—421no—
407C4—421no—
408C3#9025511yescharacteristic, complemented, Sylow
409C2—41no—
410C2—62no—
411C2—841no—
412C2D3×#115711yescharacteristic
413C2#1062156711yescharacteristic
414C2#1062157411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C22⋊C4C22
prime radical#10621120C2
hypercenterC22⋊C4D3×D7
hypocenterC3×C7#539
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10621366C2semidirect
2. C7×#67⋊C4C2semidirect
3. C3×#6442C2semidirect
4. #10621137C2semidirect
6. #10621117C2semidirect
7. #10621104C2semidirect
8. C4×#4247C2semidirect
9. #10620989C2semidirect
10. #10620979C2semidirect
11. D3×Dic7⋊C4C2semidirect
12. #10620943C2semidirect
13. #10620942C2semidirect
14. #10620940C2semidirect
15. #10620939C2semidirect
63. #6442D3semidirect
138. #67⋊C4D7semidirect
291. C3×C7#539semidirect
379. C7#5707semidirect
408. C3#90255semidirect

Maximal subgroups

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

subgroupindex
#106213662
C7×#67⋊C42
C3×#64422
#106211372
#106211202
#106211172
#106211042
C4×#42472
#106209892
#106209792
D3×Dic7⋊C42
#106209432
#106209422
#106209402
#106209392
#902553
#57077