Finite Group Databasebeta

← #13057798

Subgroups — #13057798

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#10621359C211yesmaximal, characteristic, complemented
2C4×C7×Dic6C211yesmaximal, characteristic, complemented
3C3×#6438C211yesmaximal, characteristic, complemented
4#10621017C211yesmaximal, characteristic, complemented
5#10620992C211yesmaximal, characteristic, complemented
6#10620983C211yesmaximal, characteristic, complemented
7#10620973C211yesmaximal, characteristic, complemented
8#10620971C211yesmaximal, characteristic
9#10620969C211yesmaximal, characteristic, complemented
10#10620957C211yesmaximal, characteristic, complemented
11#10620955C211yesmaximal, characteristic, complemented
12#10620925C211yesmaximal, characteristic, complemented
13#10620918C211yesmaximal, characteristic, complemented
14#10620915C211yesmaximal, characteristic, complemented
15#10620889C211yesmaximal, characteristic, complemented
16#90273—31nomaximal, Hall
17C2×C7×Dic6C2211yescharacteristic
18C2×C3×D28C2211yescharacteristic
19C2×C3×Dic14C2211yescharacteristic
20C2×#4248C2211yescharacteristic
21C2×#4246C2211yescharacteristic
22C2×#4246C2211yescharacteristic
23C2×D21⋊C4C2211yescharacteristic
24C2×Dic3×D7C2211yescharacteristic
25C2×Dic3×D7C2211yescharacteristic
26C3×C42×C7C2211yescharacteristic
27#66631C2211yescharacteristic
28#66631C2211yescharacteristic
29#66631C2211yescharacteristic
30#66629C2211yescharacteristic
31#66629C2211yescharacteristic
32#66629C2211yescharacteristic
33C7×C4⋊Dic3C2211yescharacteristic
34C7×Dic3⋊C4C2211yescharacteristic
35C7×Dic3⋊C4C2211yescharacteristic
36C4×C7×Dic3C2211yescharacteristic
37C4×C7×Dic3C2211yescharacteristic
38C3×(C2×D7)⋊C4C2211yescharacteristic
39C3×(C2×D7)⋊C4C2211yescharacteristic
40C3×(C2×D7)⋊C4C2211yescharacteristic
41C3×(C2×D7)⋊C4C2211yescharacteristic
42Dic3⋊Dic7C2211yescharacteristic
43#66577C2211yescharacteristic
44#66577C2211yescharacteristic
45Dic7⋊Dic3C2211yescharacteristic
46#66575C2211yescharacteristic
47(C2×D7)⋊Dic3C2211yescharacteristic
48(C2×D7)⋊Dic3C2211yescharacteristic
49(C2×D7)⋊Dic3C2211yescharacteristic
50(C2×D7)⋊Dic3C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C4×C7×Q8—31no—
53#6510—31no—
54#6509—31no—
55#6459—31no—
56#6459—31no—
57#6458—31no—
58#6457—31no—
59#6457—31no—
60#6451—31no—
61#6439—31no—
62#6439—31no—
63#6438—31no—
64#6438D311yescharacteristic, complemented
65C4×D28—31no—
66#6435—31no—
67#5669—71nomaximal, Hall
68C22×D21C2311yescharacteristic
69C22×C3×D7C2311yescharacteristic
70C22×C3×D7C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×C3×C4×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74C2×Dic21C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77C2×C7×Dic3C2311yescharacteristic
78C2×C7×Dic3C2311yescharacteristic
79C2×C7×Dic3C2311yescharacteristic
80C2×C7×Dic3C2311yescharacteristic
81C7×Dic6—22no—
82C2×C3×Dic7C2311yescharacteristic
83C2×C3×Dic7C2311yescharacteristic
84C3×D28—41no—
85C3×Dic14—41no—
86#4248—41no—
87#4246—22no—
88#4246—41no—
89D21⋊C4—41no—
90Dic3×D7—22no—
91Dic3×D7—41no—
92C2×C7×Q8—31no—
93C2×D28—31no—
94C2×D28—31no—
95C2×D28C2×D311yescharacteristic
96C2×C4×D7—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⋊C4—31no—
104C42×C7—31no—
105C42×C7—31no—
106C42×C7C2×D311yescharacteristic
107(C2×D7)⋊C4—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)⋊C4C2×D311yescharacteristic
116(C2×D7)⋊C4C2×D311yescharacteristic
117(C2×D7)⋊C4C2×D311yescharacteristic
118(C2×D7)⋊C4C2×D311yescharacteristic
119C4⋊Dic7—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4—31no—
122Dic7⋊C4—31no—
123Dic7⋊C4—31no—
124Dic7⋊C4—31no—
125Dic7⋊C4—31no—
126C4×Dic7—31no—
127C3×#124—71no—
128#946—71no—
129#944—71no—
130#939—71no—
131#935—71no—
132#885—71no—
133#885—71no—
134#883—71no—
135#67⋊C4—71no—
136#879—71no—
137#878—71no—
138#878—71no—
139#877—71no—
140#876—71no—
141C4×Dic6D711yescharacteristic, complemented
142C22×C3×C7C2411yescharacteristic
143C2×D21—21no—
144C2×D21—21no—
145C2×D21—21no—
146C2×C3×D7—21no—
147C2×C3×D7—21no—
148C2×C3×D7—21no—
149C2×C3×D7—21no—
150C2×C3×D7—21no—
151C2×C3×D7—21no—
152C3×C4×C7—21no—
153C3×C4×C7—21no—
154C3×C4×C7—21no—
155Dic21—21no—
156Dic21—21no—
157Dic21—21no—
158C3×Dic7—21no—
159C3×Dic7—21no—
160C7×Dic3—21no—
161C7×Dic3—21no—
162C7×Dic3—21no—
163C7×Dic3#4112yes—
164#542—211noSylow
165C22×D7—31no—
166C22×D7C22×D311yescharacteristic
167C22×D7C22×D311yescharacteristic
168C7×Q8—62no—
169C2×C4×C7—31no—
170C2×C4×C7—31no—
171C2×C4×C7—31no—
172C2×C4×C7—31no—
173C2×C4×C7C22×D311yescharacteristic
174C2×C4×C7C22×D311yescharacteristic
175C2×C4×C7C22×D311yescharacteristic
176C2×Dic7—31no—
177C2×Dic7—31no—
178C2×Dic7—31no—
179C2×Dic7C22×D311yescharacteristic
180C2×Dic7C22×D311yescharacteristic
181D28—41no—
182D28—62no—
183D28—121no—
184C4×D7—62no—
185C4×D7—121no—
186C4×D7—121no—
187Dic14—41no—
188Dic14—121no—
189C2×C3×Q8—71no—
190C2×C3×D4—71no—
191C2×#67—71no—
192C2×#67—71no—
193C22×Dic3—71no—
194C22×Dic3—71no—
195C2×C4×D3—71no—
196C2×Dic6—71no—
197C2×Dic6C2×D711yescharacteristic
198C3×C22⋊C4—71no—
199C3×C22⋊C4—71no—
200C3×C22⋊C4—71no—
201C3×C22⋊C4—71no—
202C3×C42C2×D711yescharacteristic
203#217—71no—
204#217—71no—
205#217—71no—
206#217—71no—
207(C2×D3)⋊C4—71no—
208(C2×D3)⋊C4—71no—
209(C2×D3)⋊C4—71no—
210(C2×D3)⋊C4—71no—
211C4⋊Dic3—71no—
212C4⋊Dic3C2×D711yescharacteristic
213Dic3⋊C4—71no—
214Dic3⋊C4—71no—
215Dic3⋊C4—71no—
216Dic3⋊C4—71no—
217Dic3⋊C4—71no—
218Dic3⋊C4—71no—
219Dic3⋊C4C2×D711yescharacteristic
220Dic3⋊C4C2×D711yescharacteristic
221C4×Dic3—71no—
222C4×Dic3C2×D711yescharacteristic
223C4×Dic3C2×D711yescharacteristic
224C2×C3×C7C2×#4111yescharacteristic
225C2×C3×C7H(5,𝔽2)11yescharacteristic
226C2×C3×C72−1+411yescharacteristic
227D21—41no—
228C3×D7—41no—
229C3×D7—41no—
230C4⋊Q8—211no—
231#126—211no—
232#126—211no—
233#124—71no—
234#124—211no—
235#124—211no—
236#123—211no—
237#123—211no—
238C22⋊Q8—211no—
239C22⋊Q8—211no—
240C22⋊Q8—211no—
241#121—211no—
242C4×Q8—31no—
243C4×D4—211no—
244#117—211no—
245C22×C7C23×D311yescharacteristic
246C2×D7—21no—
247C2×D7—21no—
248C2×D7—21no—
249C2×D7—21no—
250C2×D7—21no—
251C2×D7—21no—
252C2×D7—61no—
253C2×D7—61no—
254C2×D7—61no—
255C4×C7—21no—
256C4×C7—21no—
257C4×C7—21no—
258C4×C7—32no—
259C4×C7—61no—
260C4×C7—61no—
261C4×C7—61no—
262Dic7—21no—
263Dic7—21no—
264Dic7—61no—
265Dic7—61no—
266Dic7—61no—
267C23×C3—71no—
268C23×C3—71no—
269C22×D3—71no—
270C3×Q8—281no—
271C3×D4—281no—
272C2×C3×C4—71no—
273C2×C3×C4—71no—
274C2×C3×C4C22×D711yescharacteristic
275C2×C3×C4C22×D711yescharacteristic
276C2×C3×C4C22×D711yescharacteristic
277#67—142no—
278#67—281no—
279C2×Dic3—71no—
280C2×Dic3—71no—
281C2×Dic3—71no—
282C2×Dic3—142no—
283C2×Dic3—281no—
284C2×Dic3C22×D711yescharacteristic
285C2×Dic3C22×D711yescharacteristic
286C2×Dic3C22×D711yescharacteristic
287C2×Dic3C22×D711yescharacteristic
288C4×D3—281no—
289Dic6—22no—
290Dic6—281no—
291C3×C7#54211yescharacteristic, complemented, Hall
292C2×Q8—31no—
293C2×Q8—71no—
294C2×Q8—211no—
295C2×D4—71no—
296C2×D4—211no—
297C2×D4—211no—
298C22×C4—211no—
299C22×C4—211no—
300C22×C4—211no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—31no—
304C4⋊C4—211no—
305C4⋊C4—211no—
306C4⋊C4—211no—
307C4⋊C4—211no—
308C4⋊C4—211no—
309C4⋊C4—211no—
310C4⋊C4—211no—
311C22⋊C4—71no—
312C22⋊C4—71no—
313C22⋊C4—71no—
314C22⋊C4—71no—
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—31no—
324C42—31no—
325C42—211no—
326C42D3×D711yescharacteristic
327C2×C7#100411yescharacteristic
328C2×C7D3×#4111yescharacteristic
329C2×C7#101011yescharacteristic
330D7—41no—
331D7—41no—
332D7—121no—
333C22×C3—141no—
334C22×C3—141no—
335C22×C3—141no—
336C22×C3—141no—
337C22×C3—141no—
338C22×C3—141no—
339C22×C3C23×D711yescharacteristic
340C2×D3—141no—
341C2×D3—141no—
342C2×D3—141no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—141no—
347C3×C4—141no—
348Dic3—21no—
349Dic3—21no—
350Dic3—21no—
351Dic3—141no—
352Dic3—141no—
353Dic3—141no—
354Dic3#115712yes—
355C23—71no—
356C23—71no—
357C23—211no—
358Q8—62no—
359Q8—281no—
360Q8—841no—
361D4—281no—
362D4—422no—
363D4—841no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—31no—
367C2×C4—31no—
368C2×C4—71no—
369C2×C4—71no—
370C2×C4—211no—
371C2×C4—211no—
372C2×C4—211no—
373C2×C4—422no—
374C2×C4—841no—
375C2×C4—841no—
376C2×C4C2×D3×D711yescharacteristic
377C2×C4C2×D3×D711yescharacteristic
378C2×C4C2×D3×D711yescharacteristic
379C7#566911yescharacteristic, complemented, Sylow
380C2×C3—281no—
381C2×C3—281no—
382C2×C3C2×#115711yescharacteristic
383C2×C3#655111yescharacteristic
384C2×C3#655311yescharacteristic
385D3—281no—
386C22—141no—
387C22—141no—
388C22—141no—
389C22—141no—
390C22—141no—
391C22—141no—
392C22—421no—
393C22—421no—
394C22—421no—
395C22C22×D3×D711yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—32no—
400C4—61no—
401C4—61no—
402C4—61no—
403C4—141no—
404C4—141no—
405C4—421no—
406C4—421no—
407C4—421no—
408C3#9027311yescharacteristic, complemented, Sylow
409C2—281no—
410C2—281no—
411C2—841no—
412C2#1062154711yescharacteristic
413C2D3×#115711yescharacteristic
414C2#1062156411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C42×C7C22
prime radical#10620971C2
hypercenterC42D3×D7
hypocenterC3×C7#542
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #10621359C2semidirect
2. C4×C7×Dic6C2semidirect
3. C3×#6438C2semidirect
4. #10621017C2semidirect
5. #10620992C2semidirect
6. #10620983C2semidirect
7. #10620973C2semidirect
9. #10620969C2semidirect
10. #10620957C2semidirect
11. #10620955C2semidirect
12. #10620925C2semidirect
13. #10620918C2semidirect
14. #10620915C2semidirect
15. #10620889C2semidirect
64. #6438D3semidirect
141. C4×Dic6D7semidirect
291. C3×C7#542semidirect
379. C7#5669semidirect
408. C3#90273semidirect

Maximal subgroups

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

subgroupindex
#106213592
C4×C7×Dic62
C3×#64382
#106210172
#106209922
#106209832
#106209732
#106209712
#106209692
#106209572
#106209552
#106209252
#106209182
#106209152
#106208892
#902733
#56697