Finite Group Databasebeta

← #13058115

Subgroups — #13058115

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#10621361C211yesmaximal, characteristic, complemented
2C7×#885C211yesmaximal, characteristic, complemented
3C3×#6448C211yesmaximal, characteristic, complemented
4#10621127C211yesmaximal, characteristic
5(C22⋊D7)⋊Dic3C211yesmaximal, characteristic, complemented
6#10621105C211yesmaximal, characteristic, complemented
7#10621092C211yesmaximal, characteristic, complemented
8#10621024C211yesmaximal, characteristic, complemented
9#10620983C211yesmaximal, characteristic, complemented
10#10620976C211yesmaximal, characteristic, complemented
11#10620972C211yesmaximal, characteristic, complemented
12#10620960C211yesmaximal, characteristic, complemented
13#10620938C211yesmaximal, characteristic, complemented
14#10620925C211yesmaximal, characteristic, complemented
15Dic3×Dic14C211yesmaximal, characteristic, complemented
16#90360—31nomaximal, Hall
17C22×Dic21C2211yescharacteristic
18C2×Dic42C2211yescharacteristic
19C2×C7×#67C2211yescharacteristic
20C2×C7×Dic6C2211yescharacteristic
21C2×C3×C22⋊D7C2211yescharacteristic
22C2×C3×Dic14C2211yescharacteristic
23C2×#4245C2211yescharacteristic
24C2×D3×Dic7C2211yescharacteristic
25C2×Dic3×D7C2211yescharacteristic
26C3×C7×C22⋊C4C2211yescharacteristic
27#66636C2211yescharacteristic
28C4⋊Dic21C2211yescharacteristic
29#66629C2211yescharacteristic
30#66629C2211yescharacteristic
31C7×#217C2211yescharacteristic
32C7×(C2×D3)⋊C4C2211yescharacteristic
33C7×(C2×D3)⋊C4C2211yescharacteristic
34C4×C7×Dic3C2211yescharacteristic
35C3×C22⋊Dic7C2211yescharacteristic
36C3×(C2×D7)⋊C4C2211yescharacteristic
37C3×(C2×D7)⋊C4C2211yescharacteristic
38C3×C4×Dic7C2211yescharacteristic
39Dic3⋊Dic7C2211yescharacteristic
40#66577C2211yescharacteristic
41Dic7⋊Dic3C2211yescharacteristic
42Dic7⋊Dic3C2211yescharacteristic
43Dic7⋊Dic3C2211yescharacteristic
44Dic7⋊Dic3C2211yescharacteristic
45Dic7⋊Dic3C2211yescharacteristic
46(C2×D3)⋊Dic7C2211yescharacteristic
47(C2×D3)⋊Dic7C2211yescharacteristic
48(C2×D7)⋊Dic3C2211yescharacteristic
49(C2×D7)⋊Dic3C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C7×#124—31no—
53#6509—31no—
54#6507—31no—
55#6502—31no—
56#6498—31no—
57#6448—31no—
58#6448D311yescharacteristic, complemented
59#6446—31no—
60(C22⋊D7)⋊C4—31no—
61#6442—31no—
62#6441—31no—
63#6441—31no—
64#6440—31no—
65#6439—31no—
66C4×Dic14—31no—
67#5682—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C22×D3×C7C2311yescharacteristic
70C22×C3×D7C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×C3×C4×C7C2311yescharacteristic
73C2×Dic21—41no—
74C2×Dic21C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77C2×Dic21C2311yescharacteristic
78Dic42—41no—
79C7×#67—41no—
80C2×C7×Dic3C2311yescharacteristic
81C2×C7×Dic3C2311yescharacteristic
82C2×C7×Dic3C2311yescharacteristic
83C7×Dic6—41no—
84C3×C22⋊D7—22no—
85C2×C3×Dic7C2311yescharacteristic
86C2×C3×Dic7C2311yescharacteristic
87C2×C3×Dic7C2311yescharacteristic
88C3×Dic14—22no—
89#4245—41no—
90D3×Dic7—22no—
91Dic3×D7—41no—
92C2×C7×Q8—31no—
93C2×C7×D4—31no—
94C2×C22⋊D7—31no—
95C2×C22⋊D7C2×D311yescharacteristic
96C22×Dic7—31no—
97C22×Dic7—31no—
98C2×C4×D7—31no—
99C2×Dic14—31no—
100C2×Dic14C2×D311yescharacteristic
101C7×C22⋊C4—31no—
102C7×C22⋊C4—31no—
103C7×C22⋊C4—31no—
104C7×C22⋊C4C2×D311yescharacteristic
105C42×C7—31no—
106C22⋊Dic7—31no—
107C22⋊Dic7—31no—
108C22⋊Dic7—31no—
109C22⋊Dic7C2×D311yescharacteristic
110(C2×D7)⋊C4—31no—
111(C2×D7)⋊C4—31no—
112(C2×D7)⋊C4C2×D311yescharacteristic
113(C2×D7)⋊C4C2×D311yescharacteristic
114C4⋊Dic7—31no—
115C4⋊Dic7—31no—
116Dic7⋊C4—31no—
117Dic7⋊C4—31no—
118Dic7⋊C4—31no—
119Dic7⋊C4—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4—31no—
122Dic7⋊C4—31no—
123Dic7⋊C4—31no—
124C4×Dic7—31no—
125C4×Dic7—31no—
126C4×Dic7C2×D311yescharacteristic
127C3×#124—71no—
128#946—71no—
129Q8×Dic3—71no—
130#938—71no—
131D4×Dic3—71no—
132#886—71no—
133#886—71no—
134#885—71no—
135#885D711yescharacteristic, complemented
136#879—71no—
137#879—71no—
138#878—71no—
139#878—71no—
140#872—71no—
141#869—71no—
142C22×C3×C7—21no—
143C22×C3×C7—21no—
144C22×C3×C7—21no—
145C22×C3×C7C2411yescharacteristic
146C2×D3×C7—21no—
147C2×D3×C7—21no—
148C2×D3×C7—21no—
149C2×C3×D7—21no—
150C2×C3×D7—21no—
151C2×C3×D7—21no—
152C3×C4×C7—21no—
153C3×C4×C7—21no—
154Dic21—21no—
155Dic21—21no—
156Dic21—21no—
157Dic21—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—
166C23×C7C22×D311yescharacteristic
167C22×D7C22×D311yescharacteristic
168C7×Q8—121no—
169C7×D4—121no—
170C2×C4×C7—31no—
171C2×C4×C7—31no—
172C2×C4×C7—31no—
173C2×C4×C7C22×D311yescharacteristic
174C2×C4×C7C22×D311yescharacteristic
175C22⋊D7—22no—
176C22⋊D7—121no—
177C2×Dic7—31no—
178C2×Dic7—31no—
179C2×Dic7—31no—
180C2×Dic7—31no—
181C2×Dic7—62no—
182C2×Dic7—121no—
183C2×Dic7C22×D311yescharacteristic
184C2×Dic7C22×D311yescharacteristic
185C2×Dic7C22×D311yescharacteristic
186C4×D7—121no—
187Dic14—22no—
188Dic14—121no—
189C2×C3×Q8—71no—
190C2×C3×D4—71no—
191C2×#67—71no—
192C2×#67C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
202C3×C42—71no—
203#217—71no—
204#217—71no—
205#217—71no—
206#217C2×D711yescharacteristic
207(C2×D3)⋊C4—71no—
208(C2×D3)⋊C4—71no—
209(C2×D3)⋊C4C2×D711yescharacteristic
210(C2×D3)⋊C4C2×D711yescharacteristic
211C4⋊Dic3—71no—
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—
221C4×Dic3—71no—
222C4×Dic3—71no—
223C4×Dic3C2×D711yescharacteristic
224C2×C3×C7—41no—
225C2×C3×C7C2×#4111yescharacteristic
226C2×C3×C7H(5,𝔽2)11yescharacteristic
227C2×C3×C72−1+411yescharacteristic
228C3×D7—41no—
229D3×C7—41no—
230C4⋊Q8—211no—
231#126—211no—
232#126—211no—
233#124—31no—
234#124—71no—
235#124—211no—
236#123—211no—
237#123—211no—
238C22⋊Q8—211no—
239C22⋊Q8—211no—
240C22⋊Q8—211no—
241#121—211no—
242C4×Q8—211no—
243C4×D4—211no—
244#117—211no—
245C22×C7—21no—
246C22×C7—21no—
247C22×C7—21no—
248C22×C7—61no—
249C22×C7—61no—
250C22×C7—61no—
251C22×C7C23×D311yescharacteristic
252C2×D7—21no—
253C2×D7—21no—
254C2×D7—21no—
255C4×C7—21no—
256C4×C7—21no—
257C4×C7—61no—
258C4×C7—61no—
259C4×C7—61no—
260Dic7—21no—
261Dic7—21no—
262Dic7—61no—
263Dic7—61no—
264Dic7—61no—
265Dic7—61no—
266Dic7#23712yes—
267C23×C3—71no—
268C23×C3C22×D711yescharacteristic
269C22×D3C22×D711yescharacteristic
270C3×Q8—142no—
271C3×D4—142no—
272C2×C3×C4—71no—
273C2×C3×C4—71no—
274C2×C3×C4—71no—
275C2×C3×C4C22×D711yescharacteristic
276C2×C3×C4C22×D711yescharacteristic
277#67—41no—
278#67—281no—
279C2×Dic3—71no—
280C2×Dic3—71no—
281C2×Dic3—71no—
282C2×Dic3—71no—
283C2×Dic3—281no—
284C2×Dic3—281no—
285C2×Dic3C22×D711yescharacteristic
286C2×Dic3C22×D711yescharacteristic
287C2×Dic3C22×D711yescharacteristic
288C4×D3—142no—
289Dic6—41no—
290Dic6—281no—
291C3×C7#54211yescharacteristic, complemented, Hall
292C2×Q8—31no—
293C2×Q8—71no—
294C2×Q8—211no—
295C2×D4—31no—
296C2×D4—71no—
297C2×D4—211no—
298C22×C4—211no—
299C22×C4—211no—
300C22×C4—211no—
301C4⋊C4—211no—
302C4⋊C4—211no—
303C4⋊C4—211no—
304C4⋊C4—211no—
305C4⋊C4—211no—
306C4⋊C4—211no—
307C4⋊C4—211no—
308C4⋊C4—211no—
309C4⋊C4—211no—
310C4⋊C4—211no—
311C22⋊C4—31no—
312C22⋊C4—31no—
313C22⋊C4—31no—
314C22⋊C4—71no—
315C22⋊C4—71no—
316C22⋊C4—71no—
317C22⋊C4—211no—
318C22⋊C4—211no—
319C22⋊C4—211no—
320C22⋊C4—211no—
321C22⋊C4—211no—
322C22⋊C4D3×D711yescharacteristic
323C42—31no—
324C42—71no—
325C42—211no—
326C42—211no—
327C2×C7—41no—
328C2×C7—121no—
329C2×C7C2×#23711yescharacteristic
330C2×C7#100911yescharacteristic
331C2×C7#101011yescharacteristic
332D7—41no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—141no—
337C22×C3—141no—
338C22×C3—141no—
339C22×C3C23×D711yescharacteristic
340C2×D3—21no—
341C2×D3—21no—
342C2×D3—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—72no—
346C3×C4—141no—
347C3×C4—141no—
348Dic3—21no—
349Dic3—21no—
350Dic3—21no—
351Dic3—141no—
352Dic3—141no—
353Dic3—141no—
354Dic3—141no—
355C23—31no—
356C23—71no—
357C23C2×D3×D711yescharacteristic
358Q8—121no—
359Q8—142no—
360Q8—841no—
361D4—121no—
362D4—142no—
363D4—841no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—31no—
367C2×C4—71no—
368C2×C4—71no—
369C2×C4—71no—
370C2×C4—211no—
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#568211yescharacteristic, complemented, Sylow
380C2×C3—41no—
381C2×C3—281no—
382C2×C3#654811yescharacteristic
383C2×C3D7×#4111yescharacteristic
384C2×C3#655411yescharacteristic
385D3—41no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—61no—
390C22—61no—
391C22—61no—
392C22—141no—
393C22—141no—
394C22—141no—
395C22C22×D3×D711yescharacteristic
396C4—21no—
397C4—21no—
398C4—61no—
399C4—61no—
400C4—61no—
401C4—72no—
402C4—141no—
403C4—141no—
404C4—421no—
405C4—421no—
406C4—421no—
407C4—421no—
408C3#9036011yescharacteristic, complemented, Sylow
409C2—41no—
410C2—121no—
411C2—281no—
412C2#1062154811yescharacteristic
413C2D7×#23711yescharacteristic
414C2#1062157411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C22⋊C4C22
prime radical#10621127C2
hypercenterC22⋊C4D3×D7
hypocenterC3×C7#542
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. #10621361C2semidirect
2. C7×#885C2semidirect
3. C3×#6448C2semidirect
5. (C22⋊D7)⋊Dic3C2semidirect
6. #10621105C2semidirect
7. #10621092C2semidirect
8. #10621024C2semidirect
9. #10620983C2semidirect
10. #10620976C2semidirect
11. #10620972C2semidirect
12. #10620960C2semidirect
13. #10620938C2semidirect
14. #10620925C2semidirect
15. Dic3×Dic14C2semidirect
58. #6448D3semidirect
135. #885D7semidirect
291. C3×C7#542semidirect
379. C7#5682semidirect
408. C3#90360semidirect

Maximal subgroups

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

subgroupindex
#106213612
C7×#8852
C3×#64482
#106211272
(C22⋊D7)⋊Dic32
#106211052
#106210922
#106210242
#106209832
#106209762
#106209722
#106209602
#106209382
#106209252
Dic3×Dic142
#903603
#56827