Finite Group Databasebeta

← #13059586

Subgroups — #13059586

Order 1344.

468 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#10621412C211yesmaximal, characteristic, complemented
2C7×#929C211yesmaximal, characteristic, complemented
3C2×C3×C4×Dic7C211yesmaximal, characteristic, complemented
4#10621136C211yesmaximal, characteristic, complemented
5#10621128C211yesmaximal, characteristic
6#10621114C211yesmaximal, characteristic, complemented
7#67×Dic7C211yesmaximal, characteristic, complemented
8#10620967C211yesmaximal, characteristic, complemented
9#10620964C211yesmaximal, characteristic, complemented
10#10620960C211yesmaximal, characteristic, complemented
11#10620949C211yesmaximal, characteristic, complemented
12#10620940C211yesmaximal, characteristic, complemented
13#10620934C211yesmaximal, characteristic, complemented
14#10620912C211yesmaximal, characteristic, complemented
15#10620885C211yesmaximal, characteristic, complemented
16#90340—31nomaximal, Hall
17C22×C3×C4×C7C2211yescharacteristic
18C2×#4268C2211yescharacteristic
19C2×C7×#67C2211yescharacteristic
20C22×C3×Dic7C2211yescharacteristic
21C22×C3×Dic7C2211yescharacteristic
22C2×#4248C2211yescharacteristic
23C2×#4247C2211yescharacteristic
24C2×D21⋊C4C2211yescharacteristic
25C2×D3×Dic7C2211yescharacteristic
26#66636C2211yescharacteristic
27#66631C2211yescharacteristic
28#66631C2211yescharacteristic
29#66629C2211yescharacteristic
30#66629C2211yescharacteristic
31C7×#217C2211yescharacteristic
32C7×(C2×D3)⋊C4C2211yescharacteristic
33C7×(C2×D3)⋊C4C2211yescharacteristic
34C7×Dic3⋊C4C2211yescharacteristic
35C7×Dic3⋊C4C2211yescharacteristic
36C3×C4×Dic7C2211yescharacteristic
37C3×C4×Dic7C2211yescharacteristic
38C3×C4×Dic7C2211yescharacteristic
39C3×C4×Dic7C2211yescharacteristic
40Dic3⋊Dic7C2211yescharacteristic
41Dic3⋊Dic7C2211yescharacteristic
42#66577C2211yescharacteristic
43#66577C2211yescharacteristic
44Dic7⋊Dic3C2211yescharacteristic
45Dic7⋊Dic3C2211yescharacteristic
46#66575C2211yescharacteristic
47#66575C2211yescharacteristic
48(C2×D3)⋊Dic7C2211yescharacteristic
49(C2×D3)⋊Dic7C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C7×#123—31no—
53#6502—31no—
54D4×Dic7—31no—
55#6492—31no—
56C2×C4×Dic7D311yescharacteristic, complemented
57#6461—31no—
58#6455—31no—
59#6452—31no—
60#6450—31no—
61#6448—31no—
62(C22⋊D7)⋊C4—31no—
63(C22⋊D7)⋊C4—31no—
64#6442—31no—
65#6441—31no—
66#6440—31no—
67#5479—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D3×C7C2311yescharacteristic
71C2×C3×C4×C7—22no—
72C2×C3×C4×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74#4268—22no—
75C2×Dic21C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77C2×Dic21C2311yescharacteristic
78C7×#67—22no—
79C2×C7×Dic3C2311yescharacteristic
80C2×C7×Dic3C2311yescharacteristic
81C2×C7×Dic3C2311yescharacteristic
82C2×C3×Dic7—22no—
83C2×C3×Dic7—22no—
84C2×C3×Dic7C2311yescharacteristic
85C2×C3×Dic7C2311yescharacteristic
86C2×C3×Dic7C2311yescharacteristic
87C2×C3×Dic7C2311yescharacteristic
88#4248—22no—
89#4247—22no—
90D21⋊C4—22no—
91D3×Dic7—22no—
92C2×C7×D4—31no—
93C22×C4×C7C2×D311yescharacteristic
94C2×C22⋊D7—31no—
95C2×C22⋊D7—31no—
96C22×Dic7—31no—
97C22×Dic7C2×D311yescharacteristic
98C22×Dic7C2×D311yescharacteristic
99C2×C4×D7—31no—
100C2×Dic14—31no—
101C7×C4⋊C4—31no—
102C7×C4⋊C4—31no—
103C7×C22⋊C4—31no—
104C7×C22⋊C4—31no—
105C7×C22⋊C4—31no—
106C22⋊Dic7—31no—
107C22⋊Dic7—31no—
108C22⋊Dic7—31no—
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—
115Dic7⋊C4—31no—
116Dic7⋊C4—31no—
117Dic7⋊C4—31no—
118Dic7⋊C4—31no—
119Dic7⋊C4—31no—
120Dic7⋊C4—31no—
121C4×Dic7—31no—
122C4×Dic7—31no—
123C4×Dic7C2×D311yescharacteristic
124C4×Dic7C2×D311yescharacteristic
125C4×Dic7C2×D311yescharacteristic
126C4×Dic7C2×D311yescharacteristic
127C2×C3×C42—71no—
128#930—71no—
129#929—71no—
130#929D711yescharacteristic, complemented
131C4×#67—71no—
132C4×#67—71no—
133#924—71no—
134#876—71no—
135#876—71no—
136#875—71no—
137C4×D12—71no—
138#872—71no—
139#872—71no—
140#870—71no—
141C4×Dic6—71no—
142C22×C3×C7—21no—
143C22×C3×C7—21no—
144C22×C3×C7#4112yes—
145C22×C3×C7C2411yescharacteristic
146C2×D21—21no—
147C2×D21—21no—
148C2×D21—21no—
149C2×D3×C7—21no—
150C2×D3×C7—21no—
151C2×D3×C7—21no—
152C3×C4×C7—21no—
153C3×C4×C7—21no—
154Dic21—21no—
155Dic21—21no—
156Dic21—21no—
157C3×Dic7—21no—
158C3×Dic7—21no—
159C3×Dic7#4112yes—
160C3×Dic7#4112yes—
161C7×Dic3—21no—
162C7×Dic3—21no—
163C7×Dic3—21no—
164#529—211noSylow
165C23×C7—31no—
166C23×C7C22×D311yescharacteristic
167C22×D7—31no—
168C7×D4—62no—
169C2×C4×C7—22no—
170C2×C4×C7—31no—
171C2×C4×C7—31no—
172C2×C4×C7—31no—
173C2×C4×C7C22×D311yescharacteristic
174C2×C4×C7C22×D311yescharacteristic
175C22⋊D7—62no—
176C22⋊D7—62no—
177C2×Dic7—22no—
178C2×Dic7—22no—
179C2×Dic7—31no—
180C2×Dic7—31no—
181C2×Dic7—31no—
182C2×Dic7—62no—
183C2×Dic7C22×D311yescharacteristic
184C2×Dic7C22×D311yescharacteristic
185C2×Dic7C22×D311yescharacteristic
186C2×Dic7C22×D311yescharacteristic
187C4×D7—62no—
188Dic14—62no—
189C22×C3×C4—71no—
190C22×C3×C4—71no—
191C22×C3×C4C2×D711yescharacteristic
192C2×#67—71no—
193C2×#67C2×D711yescharacteristic
194C2×D12—71no—
195C2×C4×D3—71no—
196C2×C4×D3—71no—
197C2×Dic6—71no—
198C3×C42—71no—
199C3×C42—71no—
200C3×C42—71no—
201C3×C42—71no—
202#217—71no—
203#217C2×D711yescharacteristic
204(C2×D3)⋊C4—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)⋊C4C2×D711yescharacteristic
211(C2×D3)⋊C4C2×D711yescharacteristic
212C4⋊Dic3—71no—
213C4⋊Dic3—71no—
214Dic3⋊C4—71no—
215Dic3⋊C4—71no—
216Dic3⋊C4—71no—
217Dic3⋊C4—71no—
218Dic3⋊C4—71no—
219Dic3⋊C4—71no—
220Dic3⋊C4C2×D711yescharacteristic
221Dic3⋊C4C2×D711yescharacteristic
222C4×Dic3—71no—
223C4×Dic3—71no—
224C2×C3×C7—22no—
225C2×C3×C7C2×#4111yescharacteristic
226C2×C3×C7C2×#4111yescharacteristic
227C2×C3×C7C2×#4111yescharacteristic
228D21—41no—
229D3×C7—41no—
230#126—211no—
231#126—211no—
232#125—211no—
233#124—211no—
234#123—31no—
235#123—211no—
236C22⋊Q8—211no—
237#121—211no—
238C4×Q8—211no—
239C4×D4—211no—
240C4×D4—211no—
241C4×D4—211no—
242#117—211no—
243#117—211no—
244C2×C42—71no—
245C22×C7—21no—
246C22×C7—21no—
247C22×C7—61no—
248C22×C7—61no—
249C22×C7—61no—
250C22×C7#23512yes—
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—61no—
263Dic7—61no—
264Dic7—61no—
265Dic7#23512yes—
266Dic7#23512yes—
267C23×C3C22×D711yescharacteristic
268C22×D3—71no—
269C22×D3C22×D711yescharacteristic
270C2×C3×C4—22no—
271C2×C3×C4—71no—
272C2×C3×C4—71no—
273C2×C3×C4—71no—
274C2×C3×C4—71no—
275C2×C3×C4—142no—
276C2×C3×C4—142no—
277C2×C3×C4C22×D711yescharacteristic
278C2×C3×C4C22×D711yescharacteristic
279#67—22no—
280#67—142no—
281C2×Dic3—71no—
282C2×Dic3—71no—
283C2×Dic3—71no—
284C2×Dic3C22×D711yescharacteristic
285C2×Dic3C22×D711yescharacteristic
286C2×Dic3C22×D711yescharacteristic
287D12—142no—
288C4×D3—142no—
289C4×D3—142no—
290Dic6—142no—
291C3×C7#52911yescharacteristic, complemented, Hall
292C2×Q8—211no—
293C2×D4—31no—
294C2×D4—211no—
295C2×D4—211no—
296C22×C4—71no—
297C22×C4—71no—
298C22×C4—211no—
299C22×C4—211no—
300C22×C4D3×D711yescharacteristic
301C4⋊C4—31no—
302C4⋊C4—31no—
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—211no—
315C22⋊C4—211no—
316C22⋊C4—211no—
317C22⋊C4—211no—
318C22⋊C4—211no—
319C22⋊C4—211no—
320C22⋊C4—211no—
321C42—71no—
322C42—71no—
323C42—71no—
324C42—71no—
325C42—211no—
326C42—211no—
327C2×C7—22no—
328C2×C7—121no—
329C2×C7C2×#23511yescharacteristic
330C2×C7C2×#23511yescharacteristic
331C2×C7C2×#23511yescharacteristic
332D7—121no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3#115912yes—
336C22×C3C23×D711yescharacteristic
337C2×D3—21no—
338C2×D3—21no—
339C2×D3—21no—
340C2×D3—141no—
341C2×D3—141no—
342C2×D3—141no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—72no—
346C3×C4—72no—
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—422no—
359D4—62no—
360D4—422no—
361D4—422no—
362C2×C4—22no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—71no—
367C2×C4—71no—
368C2×C4—71no—
369C2×C4—71no—
370C2×C4—142no—
371C2×C4—142no—
372C2×C4—211no—
373C2×C4—211no—
374C2×C4—211no—
375C2×C4—422no—
376C2×C4—422no—
377C2×C4C2×D3×D711yescharacteristic
378C2×C4C2×D3×D711yescharacteristic
379C7#547911yescharacteristic, complemented, Sylow
380C2×C3—22no—
381C2×C3C2×#115911yescharacteristic
382C2×C3D7×#4111yescharacteristic
383C2×C3D7×#4111yescharacteristic
384D3—41no—
385D3—281no—
386C22—21no—
387C22—21no—
388C22—61no—
389C22—61no—
390C22—61no—
391C22—421no—
392C22—421no—
393C22—421no—
394C22#6668612yes—
395C22C22×D3×D711yescharacteristic
396C4—21no—
397C4—21no—
398C4—61no—
399C4—61no—
400C4—61no—
401C4—72no—
402C4—72no—
403C4—141no—
404C4—141no—
405C4—421no—
406C4—421no—
407C4—421no—
408C3#9034011yescharacteristic, complemented, Sylow
409C2—22no—
410C2—121no—
411C2—841no—
412C2D7×#23511yescharacteristic
413C2D7×#23511yescharacteristic
414C2C2×#6668611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC22×C3×C4×C7C22
prime radical#10621128C2
hypercenterC22×C4D3×D7
hypocenterC3×C7#529
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. #10621412C2semidirect
2. C7×#929C2semidirect
3. C2×C3×C4×Dic7C2semidirect
4. #10621136C2semidirect
6. #10621114C2semidirect
7. #67×Dic7C2semidirect
8. #10620967C2semidirect
9. #10620964C2semidirect
10. #10620960C2semidirect
11. #10620949C2semidirect
12. #10620940C2semidirect
13. #10620934C2semidirect
14. #10620912C2semidirect
15. #10620885C2semidirect
56. C2×C4×Dic7D3semidirect
130. #929D7semidirect
291. C3×C7#529semidirect
379. C7#5479semidirect
408. C3#90340semidirect

Maximal subgroups

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

subgroupindex
#106214122
C7×#9292
C2×C3×C4×Dic72
#106211362
#106211282
#106211142
#67×Dic72
#106209672
#106209642
#106209602
#106209492
#106209402
#106209342
#106209122
#106208852
#903403
#54797