Finite Group Databasebeta

← #13058713

Subgroups — #13058713

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#10621381C211yesmaximal, characteristic, complemented
2C7×#888C211yesmaximal, characteristic, complemented
3C3×#6457C211yesmaximal, characteristic, complemented
4#10621017C211yesmaximal, characteristic, complemented
5#10621006C211yesmaximal, characteristic, complemented
6#10620986C211yesmaximal, characteristic, complemented
7#10620984C211yesmaximal, characteristic, complemented
8#10620971C211yesmaximal, characteristic
9#10620955C211yesmaximal, characteristic, complemented
10#10620930C211yesmaximal, characteristic, complemented
11#10620923C211yesmaximal, characteristic, complemented
12#10620921C211yesmaximal, characteristic, complemented
13#10620918C211yesmaximal, characteristic, complemented
14#10620915C211yesmaximal, characteristic, complemented
15#10620887C211yesmaximal, characteristic, complemented
16#90424—31nomaximal, Hall
17C2×C7×Dic6C2211yescharacteristic
18C2×C7×Dic6C2211yescharacteristic
19C2×C3×D28C2211yescharacteristic
20C2×C3×C4×D7C2211yescharacteristic
21C2×#4248C2211yescharacteristic
22C2×#4246C2211yescharacteristic
23C2×#4246C2211yescharacteristic
24C2×D21⋊C4C2211yescharacteristic
25C2×Dic3×D7C2211yescharacteristic
26C3×C7×C4⋊C4C2211yescharacteristic
27#66631C2211yescharacteristic
28#66631C2211yescharacteristic
29#66631C2211yescharacteristic
30C4⋊Dic21C2211yescharacteristic
31#66629C2211yescharacteristic
32C4×Dic21C2211yescharacteristic
33C7×C4⋊Dic3C2211yescharacteristic
34C7×Dic3⋊C4C2211yescharacteristic
35C7×Dic3⋊C4C2211yescharacteristic
36C4×C7×Dic3C2211yescharacteristic
37C3×(C2×D7)⋊C4C2211yescharacteristic
38C3×(C2×D7)⋊C4C2211yescharacteristic
39C3×(C2×D7)⋊C4C2211yescharacteristic
40C3×Dic7⋊C4C2211yescharacteristic
41Dic3⋊Dic7C2211yescharacteristic
42#66577C2211yescharacteristic
43#66577C2211yescharacteristic
44#66575C2211yescharacteristic
45(C2×D7)⋊Dic3C2211yescharacteristic
46(C2×D7)⋊Dic3C2211yescharacteristic
47(C2×D7)⋊Dic3C2211yescharacteristic
48(C2×D7)⋊Dic3C2211yescharacteristic
49(C2×D7)⋊Dic3C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C7×C4⋊Q8—31no—
53#6510—31no—
54#6510—31no—
55#6509—31no—
56#6509—31no—
57#6461—31no—
58#6461—31no—
59#6460—31no—
60#6458—31no—
61#6457—31no—
62#6457D311yescharacteristic, complemented
63#6456—31no—
64#6450—31no—
65#6438—31no—
66#6435—31no—
67#5662—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—41no—
82C7×Dic6—41no—
83C2×C3×Dic7C2311yescharacteristic
84C2×C3×Dic7C2311yescharacteristic
85C3×D28—41no—
86C3×C4×D7—41no—
87#4248—22no—
88#4246—22no—
89#4246—41no—
90D21⋊C4—41no—
91Dic3×D7—22no—
92C2×C7×Q8—31no—
93C2×C7×Q8—31no—
94C2×D28—31no—
95C2×D28—31no—
96C2×D28C2×D311yescharacteristic
97C2×C4×D7—31no—
98C2×C4×D7—31no—
99C2×C4×D7C2×D311yescharacteristic
100C2×Dic14—31no—
101C7×C4⋊C4—31no—
102C7×C4⋊C4—31no—
103C7×C4⋊C4—31no—
104C7×C4⋊C4C2×D311yescharacteristic
105C42×C7—31no—
106(C2×D7)⋊C4—31no—
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
118C4⋊Dic7—31no—
119C4⋊Dic7—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4—31no—
122Dic7⋊C4—31no—
123Dic7⋊C4C2×D311yescharacteristic
124C4×Dic7—31no—
125C4×Dic7—31no—
126C4×Dic7—31no—
127C3×#123—71no—
128#939—71no—
129#936—71no—
130C4×#67—71no—
131#924—71no—
132#898—71no—
133#896—71no—
134#888D711yescharacteristic, complemented
135#887—71no—
136#885—71no—
137#885—71no—
138#883—71no—
139#879—71no—
140#878—71no—
141#877—71no—
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—121no—
169C7×Q8—121no—
170C2×C4×C7—31no—
171C2×C4×C7—31no—
172C2×C4×C7—31no—
173C2×C4×C7—31no—
174C2×C4×C7C22×D311yescharacteristic
175C2×C4×C7C22×D311yescharacteristic
176C2×C4×C7C22×D311yescharacteristic
177C2×Dic7—31no—
178C2×Dic7—31no—
179C2×Dic7—31no—
180C2×Dic7C22×D311yescharacteristic
181C2×Dic7C22×D311yescharacteristic
182D28—41no—
183D28—62no—
184D28—121no—
185C4×D7—41no—
186C4×D7—62no—
187C4×D7—121no—
188Dic14—62no—
189C2×C3×D4—71no—
190C22×C3×C4—71no—
191C2×#67—71no—
192C2×#67—71no—
193C22×Dic3—71no—
194C2×C4×D3—71no—
195C2×Dic6—71no—
196C2×Dic6C2×D711yescharacteristic
197C2×Dic6C2×D711yescharacteristic
198C3×C4⋊C4—71no—
199C3×C4⋊C4C2×D711yescharacteristic
200C3×C22⋊C4—71no—
201C3×C22⋊C4—71no—
202C3×C22⋊C4—71no—
203#217—71no—
204#217—71no—
205#217—71no—
206#217—71no—
207#217—71no—
208(C2×D3)⋊C4—71no—
209(C2×D3)⋊C4—71no—
210(C2×D3)⋊C4—71no—
211(C2×D3)⋊C4—71no—
212C4⋊Dic3—71no—
213C4⋊Dic3C2×D711yescharacteristic
214Dic3⋊C4—71no—
215Dic3⋊C4—71no—
216Dic3⋊C4—71no—
217Dic3⋊C4—71no—
218Dic3⋊C4C2×D711yescharacteristic
219Dic3⋊C4C2×D711yescharacteristic
220C4×Dic3—71no—
221C4×Dic3—71no—
222C4×Dic3—71no—
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—31no—
231#126—211no—
232#126—211no—
233#124—211no—
234#124—211no—
235#124—211no—
236#123—71no—
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×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×D4—281no—
271C2×C3×C4—71no—
272C2×C3×C4—71no—
273C2×C3×C4—281no—
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×Dic3C22×D711yescharacteristic
284C2×Dic3C22×D711yescharacteristic
285C2×Dic3C22×D711yescharacteristic
286C2×Dic3C22×D711yescharacteristic
287C4×D3—281no—
288Dic6—41no—
289Dic6—41no—
290Dic6—142no—
291C3×C7#54211yescharacteristic, complemented, Hall
292C2×Q8—31no—
293C2×Q8—31no—
294C2×Q8—211no—
295C2×D4—71no—
296C2×D4—211no—
297C2×D4—211no—
298C22×C4—71no—
299C22×C4—211no—
300C22×C4—211no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—31no—
304C4⋊C4—71no—
305C4⋊C4—211no—
306C4⋊C4—211no—
307C4⋊C4—211no—
308C4⋊C4—211no—
309C4⋊C4—211no—
310C4⋊C4D3×D711yescharacteristic
311C22⋊C4—71no—
312C22⋊C4—71no—
313C22⋊C4—71no—
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—31no—
324C42—211no—
325C42—211no—
326C42—211no—
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#116112yes—
355C23—71no—
356C23—71no—
357C23—211no—
358Q8—121no—
359Q8—121no—
360Q8—422no—
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—281no—
374C2×C4—422no—
375C2×C4—841no—
376C2×C4C2×D3×D711yescharacteristic
377C2×C4C2×D3×D711yescharacteristic
378C2×C4C2×D3×D711yescharacteristic
379C7#566211yescharacteristic, complemented, Sylow
380C2×C3—281no—
381C2×C3—281no—
382C2×C3#654811yescharacteristic
383C2×C3C2×#116111yescharacteristic
384C2×C3#655111yescharacteristic
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#9042411yescharacteristic, complemented, Sylow
409C2—281no—
410C2—281no—
411C2—841no—
412C2#1062154711yescharacteristic
413C2#1062157211yescharacteristic
414C2D3×#116111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
prime radical#10620971C2
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. #10621381C2semidirect
2. C7×#888C2semidirect
3. C3×#6457C2semidirect
4. #10621017C2semidirect
5. #10621006C2semidirect
6. #10620986C2semidirect
7. #10620984C2semidirect
9. #10620955C2semidirect
10. #10620930C2semidirect
11. #10620923C2semidirect
12. #10620921C2semidirect
13. #10620918C2semidirect
14. #10620915C2semidirect
15. #10620887C2semidirect
62. #6457D3semidirect
134. #888D7semidirect
291. C3×C7#542semidirect
379. C7#5662semidirect
408. C3#90424semidirect

Maximal subgroups

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

subgroupindex
#106213812
C7×#8882
C3×#64572
#106210172
#106210062
#106209862
#106209842
#106209712
#106209552
#106209302
#106209232
#106209212
#106209182
#106209152
#106208872
#904243
#56627