Finite Group Databasebeta

← #13058704

Subgroups — #13058704

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#10621372C211yesmaximal, characteristic, complemented
2C7×#895C211yesmaximal, characteristic
3C3×#6452C211yesmaximal, characteristic, complemented
4#10620998C211yesmaximal, characteristic, complemented
5#10620997C211yesmaximal, characteristic, complemented
6#10620985C211yesmaximal, characteristic, complemented
7#10620985C211yesmaximal, characteristic, complemented
8#10620985C211yesmaximal, characteristic, complemented
9#10620985C211yesmaximal, characteristic, complemented
10#10620979C211yesmaximal, characteristic, complemented
11D12×Dic7C211yesmaximal, characteristic, complemented
12D3×Dic7⋊C4C211yesmaximal, characteristic, complemented
13#10620934C211yesmaximal, characteristic, complemented
14#10620929C211yesmaximal, characteristic, complemented
15#10620914C211yesmaximal, characteristic, complemented
16#90293—31nomaximal, Hall
17C2×C7×D12C2211yescharacteristic
18C2×C7×D12C2211yescharacteristic
19C2×C7×D12C2211yescharacteristic
20C2×C4×D3×C7C2211yescharacteristic
21C2×#4248C2211yescharacteristic
22C2×D3×Dic7C2211yescharacteristic
23C2×D3×Dic7C2211yescharacteristic
24C2×D3×Dic7C2211yescharacteristic
25C2×D3×Dic7C2211yescharacteristic
26C3×C7×C4⋊C4C2211yescharacteristic
27C4⋊Dic21C2211yescharacteristic
28#66629C2211yescharacteristic
29#66629C2211yescharacteristic
30#66629C2211yescharacteristic
31#66629C2211yescharacteristic
32C4×Dic21C2211yescharacteristic
33C7×(C2×D3)⋊C4C2211yescharacteristic
34C7×(C2×D3)⋊C4C2211yescharacteristic
35C3×C4⋊Dic7C2211yescharacteristic
36C3×Dic7⋊C4C2211yescharacteristic
37C3×Dic7⋊C4C2211yescharacteristic
38C3×Dic7⋊C4C2211yescharacteristic
39C3×Dic7⋊C4C2211yescharacteristic
40C3×C4×Dic7C2211yescharacteristic
41Dic3⋊Dic7C2211yescharacteristic
42#66577C2211yescharacteristic
43Dic7⋊Dic3C2211yescharacteristic
44(C2×D3)⋊Dic7C2211yescharacteristic
45(C2×D3)⋊Dic7C2211yescharacteristic
46(C2×D3)⋊Dic7C2211yescharacteristic
47(C2×D3)⋊Dic7C2211yescharacteristic
48(C2×D3)⋊Dic7C2211yescharacteristic
49(C2×D3)⋊Dic7C2211yescharacteristic
50(C2×D3)⋊Dic7C2211yescharacteristic
51(C2×D3)⋊Dic7C2211yescharacteristic
52C7×#121—31no—
53#6498—31no—
54#6498—31no—
55#6498—31no—
56#6498—31no—
57D4×Dic7—31no—
58D4×Dic7—31no—
59#6487—31no—
60C2×Dic7⋊C4—31no—
61#6452—31no—
62#6452D311yescharacteristic, complemented
63#6442—31no—
64#6442—31no—
65#6441—31no—
66#6441—31no—
67#5692—71nomaximal, Hall
68C22×D3×C7C2311yescharacteristic
69C22×D3×C7C2311yescharacteristic
70C22×D3×C7C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×C3×C4×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74C2×Dic21C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77C2×Dic21C2311yescharacteristic
78C2×C7×Dic3C2311yescharacteristic
79C7×D12—22no—
80C7×D12—22no—
81C7×D12—41no—
82C4×D3×C7—41no—
83C2×C3×Dic7C2311yescharacteristic
84C2×C3×Dic7C2311yescharacteristic
85C2×C3×Dic7C2311yescharacteristic
86C2×C3×Dic7C2311yescharacteristic
87#4248—41no—
88D3×Dic7—22no—
89D3×Dic7—41no—
90D3×Dic7—41no—
91D3×Dic7—41no—
92C2×C7×D4—31no—
93C2×C7×D4—31no—
94C2×C7×D4—31no—
95C22×C4×C7—31no—
96C22×Dic7—31no—
97C22×Dic7—31no—
98C22×Dic7—31no—
99C22×Dic7—31no—
100C2×Dic14—31no—
101C7×C4⋊C4C2×D311yescharacteristic
102C7×C22⋊C4—31no—
103C7×C22⋊C4—31no—
104C22⋊Dic7—31no—
105C22⋊Dic7—31no—
106C22⋊Dic7—31no—
107C22⋊Dic7—31no—
108C22⋊Dic7—31no—
109C22⋊Dic7—31no—
110C22⋊Dic7—31no—
111C22⋊Dic7—31no—
112C4⋊Dic7—31no—
113C4⋊Dic7—31no—
114C4⋊Dic7C2×D311yescharacteristic
115Dic7⋊C4—31no—
116Dic7⋊C4—31no—
117Dic7⋊C4—31no—
118Dic7⋊C4—31no—
119Dic7⋊C4—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4C2×D311yescharacteristic
122Dic7⋊C4C2×D311yescharacteristic
123Dic7⋊C4C2×D311yescharacteristic
124Dic7⋊C4C2×D311yescharacteristic
125C4×Dic7—31no—
126C4×Dic7C2×D311yescharacteristic
127C3×#125—71no—
128#898—71no—
129#897—71no—
130#896—71no—
131#896—71no—
132#895D711yescharacteristic
133#894—71no—
134#894—71no—
135#894—71no—
136#894—71no—
137#893—71no—
138D3×C4⋊C4—71no—
139#889—71no—
140#876—71no—
141C4×D12—71no—
142C22×C3×C7C2411yescharacteristic
143C2×D3×C7—21no—
144C2×D3×C7—21no—
145C2×D3×C7—21no—
146C2×D3×C7—21no—
147C2×D3×C7—21no—
148C2×D3×C7—21no—
149C2×D3×C7—21no—
150C2×D3×C7—21no—
151C2×D3×C7#4112yes—
152C3×C4×C7—21no—
153C3×C4×C7—21no—
154C3×C4×C7—21no—
155Dic21—21no—
156Dic21—21no—
157Dic21—21no—
158Dic21—21no—
159C3×Dic7—21no—
160C3×Dic7—21no—
161C3×Dic7—21no—
162C3×Dic7—21no—
163C7×Dic3—21no—
164#539—211noSylow
165C23×C7—31no—
166C23×C7—31no—
167C23×C7—31no—
168C7×D4—62no—
169C7×D4—62no—
170C7×D4—121no—
171C2×C4×C7—31no—
172C2×C4×C7—121no—
173C2×C4×C7C22×D311yescharacteristic
174C2×C4×C7C22×D311yescharacteristic
175C2×C4×C7C22×D311yescharacteristic
176C2×Dic7—31no—
177C2×Dic7—31no—
178C2×Dic7—31no—
179C2×Dic7—31no—
180C2×Dic7—62no—
181C2×Dic7—121no—
182C2×Dic7—121no—
183C2×Dic7—121no—
184C2×Dic7C22×D311yescharacteristic
185C2×Dic7C22×D311yescharacteristic
186C2×Dic7C22×D311yescharacteristic
187C2×Dic7C22×D311yescharacteristic
188Dic14—121no—
189C2×D12C2×D711yescharacteristic
190C2×D12C2×D711yescharacteristic
191C2×D12C2×D711yescharacteristic
192C2×C4×D3—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×C4⋊C4—71no—
202C3×C4⋊C4—71no—
203C3×C4⋊C4C2×D711yescharacteristic
204C3×C42—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)⋊C4C2×D711yescharacteristic
214(C2×D3)⋊C4C2×D711yescharacteristic
215C4⋊Dic3—71no—
216C4⋊Dic3—71no—
217Dic3⋊C4—71no—
218Dic3⋊C4—71no—
219Dic3⋊C4—71no—
220Dic3⋊C4—71no—
221Dic3⋊C4—71no—
222Dic3⋊C4—71no—
223C4×Dic3—71no—
224C2×C3×C7C2×#4111yescharacteristic
225C2×C3×C7H(5,𝔽2)11yescharacteristic
226C2×C3×C72−1+411yescharacteristic
227D3×C7—22no—
228D3×C7—41no—
229D3×C7—41no—
230#126—211no—
231#126—211no—
232#125—71no—
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—31no—
242C4×D4—211no—
243C4×D4—211no—
244C2×C4⋊C4—211no—
245C22×C7—32no—
246C22×C7—61no—
247C22×C7—61no—
248C22×C7—61no—
249C22×C7—61no—
250C22×C7—61no—
251C22×C7—61no—
252C22×C7—61no—
253C22×C7—61no—
254C22×C7C23×D311yescharacteristic
255C4×C7—21no—
256C4×C7—21no—
257C4×C7—21no—
258C4×C7—61no—
259Dic7—21no—
260Dic7—21no—
261Dic7—21no—
262Dic7—21no—
263Dic7—61no—
264Dic7—61no—
265Dic7—61no—
266Dic7—61no—
267C22×D3C22×D711yescharacteristic
268C22×D3C22×D711yescharacteristic
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
276C2×C3×C4C22×D711yescharacteristic
277C2×Dic3—71no—
278C2×Dic3—71no—
279C2×Dic3—71no—
280C2×Dic3—71no—
281C2×Dic3C22×D711yescharacteristic
282D12—22no—
283D12—22no—
284D12—41no—
285C4×D3—41no—
286C4×D3—142no—
287C4×D3—281no—
288C4×D3—281no—
289C4×D3—281no—
290Dic6—281no—
291C3×C7#53911yescharacteristic, complemented, Hall
292C2×Q8—211no—
293C2×D4—31no—
294C2×D4—31no—
295C2×D4—31no—
296C22×C4—31no—
297C22×C4—211no—
298C22×C4—211no—
299C22×C4—211no—
300C22×C4—211no—
301C4⋊C4—71no—
302C4⋊C4—71no—
303C4⋊C4—71no—
304C4⋊C4—71no—
305C4⋊C4—71no—
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⋊C4D3×D711yescharacteristic
315C22⋊C4—31no—
316C22⋊C4—31no—
317C22⋊C4—211no—
318C22⋊C4—211no—
319C22⋊C4—211no—
320C22⋊C4—211no—
321C22⋊C4—211no—
322C22⋊C4—211no—
323C22⋊C4—211no—
324C22⋊C4—211no—
325C42—71no—
326C42—211no—
327C2×C7—62no—
328C2×C7—121no—
329C2×C7—121no—
330C2×C7#100711yescharacteristic
331C2×C7D3×#4111yescharacteristic
332C2×C7#100911yescharacteristic
333C22×C3C23×D711yescharacteristic
334C2×D3—21no—
335C2×D3—21no—
336C2×D3—21no—
337C2×D3—21no—
338C2×D3—21no—
339C2×D3—21no—
340C2×D3—21no—
341C2×D3—21no—
342C2×D3#115912yes—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—141no—
347C3×C4—141no—
348C3×C4—141no—
349C3×C4—141no—
350Dic3—21no—
351Dic3—141no—
352Dic3—141no—
353Dic3—141no—
354Dic3—141no—
355C23—31no—
356C23—31no—
357C23—31no—
358Q8—841no—
359D4—62no—
360D4—62no—
361D4—121no—
362C2×C4—31no—
363C2×C4—71no—
364C2×C4—71no—
365C2×C4—71no—
366C2×C4—71no—
367C2×C4—121no—
368C2×C4—211no—
369C2×C4—211no—
370C2×C4—211no—
371C2×C4—211no—
372C2×C4—422no—
373C2×C4—841no—
374C2×C4—841no—
375C2×C4—841no—
376C2×C4C2×D3×D711yescharacteristic
377C2×C4C2×D3×D711yescharacteristic
378C2×C4C2×D3×D711yescharacteristic
379C7#569211yescharacteristic, complemented, Sylow
380C2×C3C2×#115911yescharacteristic
381C2×C3#654811yescharacteristic
382C2×C3#655411yescharacteristic
383D3—22no—
384D3—41no—
385D3—41no—
386C22—32no—
387C22—61no—
388C22—61no—
389C22—61no—
390C22—61no—
391C22—61no—
392C22—61no—
393C22—61no—
394C22—61no—
395C22C22×D3×D711yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—61no—
400C4—141no—
401C4—141no—
402C4—141no—
403C4—141no—
404C4—421no—
405C4—421no—
406C4—421no—
407C4—421no—
408C3#9029311yescharacteristic, complemented, Sylow
409C2—62no—
410C2—121no—
411C2—121no—
412C2#1062156511yescharacteristic
413C2D3×#115911yescharacteristic
414C2#1062157711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
prime radicalC7×#895C2
hypercenterC4⋊C4D3×D7
hypocenterC3×C7#539
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. #10620998C2semidirect
5. #10620997C2semidirect
6. #10620985C2semidirect
7. #10620985C2semidirect
8. #10620985C2semidirect
9. #10620985C2semidirect
10. #10620979C2semidirect
11. D12×Dic7C2semidirect
12. D3×Dic7⋊C4C2semidirect
13. #10620934C2semidirect
14. #10620929C2semidirect
15. #10620914C2semidirect
62. #6452D3semidirect
291. C3×C7#539semidirect
379. C7#5692semidirect
408. C3#90293semidirect

Maximal subgroups

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

subgroupindex
#106213722
C7×#8952
C3×#64522
#106209982
#106209972
#106209852
#106209792
D12×Dic72
D3×Dic7⋊C42
#106209342
#106209292
#106209142
#902933
#56927