Finite Group Databasebeta

← #13058740

Subgroups — #13058740

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#10621378C211yesmaximal, characteristic
2C7×#889C211yesmaximal, characteristic, complemented
3C3×#6452C211yesmaximal, characteristic, complemented
4#10620995C211yesmaximal, characteristic, complemented
5#10620995C211yesmaximal, characteristic, complemented
6#10620995C211yesmaximal, characteristic, complemented
7#10620995C211yesmaximal, characteristic, complemented
8#10620991C211yesmaximal, characteristic, complemented
9#10620990C211yesmaximal, characteristic, complemented
10#10620981C211yesmaximal, characteristic, complemented
11#10620980C211yesmaximal, characteristic, complemented
12#10620966C211yesmaximal, characteristic, complemented
13#10620949C211yesmaximal, characteristic, complemented
14#10620942C211yesmaximal, characteristic, complemented
15#10620939C211yesmaximal, characteristic, complemented
16#90383—31nomaximal, Hall
17C2×D84C2211yescharacteristic
18C2×D84C2211yescharacteristic
19C2×D84C2211yescharacteristic
20C2×C4×D21C2211yescharacteristic
21C2×#4248C2211yescharacteristic
22C2×D21⋊C4C2211yescharacteristic
23C2×D21⋊C4C2211yescharacteristic
24C2×D21⋊C4C2211yescharacteristic
25C2×D21⋊C4C2211yescharacteristic
26C3×C7×C4⋊C4C2211yescharacteristic
27#66631C2211yescharacteristic
28#66631C2211yescharacteristic
29C7×C4⋊Dic3C2211yescharacteristic
30C7×Dic3⋊C4C2211yescharacteristic
31C7×Dic3⋊C4C2211yescharacteristic
32C7×Dic3⋊C4C2211yescharacteristic
33C7×Dic3⋊C4C2211yescharacteristic
34C4×C7×Dic3C2211yescharacteristic
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#66575C2211yescharacteristic
45#66575C2211yescharacteristic
46#66575C2211yescharacteristic
47#66575C2211yescharacteristic
48#66575C2211yescharacteristic
49#66575C2211yescharacteristic
50#66575C2211yescharacteristic
51#66575C2211yescharacteristic
52C7×#125—31no—
53#6461—31no—
54#6460—31no—
55#6459—31no—
56#6459—31no—
57#6458—31no—
58#6457—31no—
59#6457—31no—
60#6457—31no—
61#6457—31no—
62#6456—31no—
63D7×C4⋊C4—31no—
64#6452D311yescharacteristic, complemented
65#6439—31no—
66C4×D28—31no—
67#5692—71nomaximal, Hall
68C22×D21C2311yescharacteristic
69C22×D21C2311yescharacteristic
70C22×D21C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×C3×C4×C7C2311yescharacteristic
73C2×C3×C4×C7C2311yescharacteristic
74C2×Dic21C2311yescharacteristic
75D84—22no—
76D84—22no—
77D84—41no—
78C4×D21—41no—
79C2×C7×Dic3C2311yescharacteristic
80C2×C7×Dic3C2311yescharacteristic
81C2×C7×Dic3C2311yescharacteristic
82C2×C7×Dic3C2311yescharacteristic
83C2×C3×Dic7C2311yescharacteristic
84C2×C3×Dic7C2311yescharacteristic
85C2×C3×Dic7C2311yescharacteristic
86C2×C3×Dic7C2311yescharacteristic
87#4248—41no—
88D21⋊C4—22no—
89D21⋊C4—41no—
90D21⋊C4—41no—
91D21⋊C4—41no—
92C2×D28—31no—
93C2×D28—31no—
94C2×D28—31no—
95C2×C4×D7—31no—
96C2×C4×D7—31no—
97C2×C4×D7—31no—
98C2×C4×D7—31no—
99C2×C4×D7—31no—
100C2×Dic14—31no—
101C7×C4⋊C4—31no—
102C7×C4⋊C4—31no—
103C7×C4⋊C4—31no—
104C7×C4⋊C4—31no—
105C7×C4⋊C4—31no—
106C7×C4⋊C4C2×D311yescharacteristic
107C42×C7—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)⋊C4—31no—
116(C2×D7)⋊C4—31no—
117(C2×D7)⋊C4—31no—
118C4⋊Dic7—31no—
119C4⋊Dic7C2×D311yescharacteristic
120Dic7⋊C4—31no—
121Dic7⋊C4—31no—
122Dic7⋊C4C2×D311yescharacteristic
123Dic7⋊C4C2×D311yescharacteristic
124Dic7⋊C4C2×D311yescharacteristic
125Dic7⋊C4C2×D311yescharacteristic
126C4×Dic7C2×D311yescharacteristic
127C3×#125—71no—
128#898—71no—
129#897—71no—
130#896—71no—
131#896—71no—
132#895—71no—
133#894—71no—
134#894—71no—
135#894—71no—
136#894—71no—
137#893—71no—
138D3×C4⋊C4—71no—
139#889D711yescharacteristic, complemented
140#876—71no—
141C4×D12—71no—
142C22×C3×C7C2411yescharacteristic
143C2×D21—21no—
144C2×D21—21no—
145C2×D21—21no—
146C2×D21—21no—
147C2×D21—21no—
148C2×D21—21no—
149C2×D21—21no—
150C2×D21—21no—
151C2×D21#4112yes—
152C3×C4×C7—21no—
153C3×C4×C7—21no—
154C3×C4×C7—21no—
155Dic21—21no—
156C3×Dic7—21no—
157C3×Dic7—21no—
158C3×Dic7—21no—
159C3×Dic7—21no—
160C7×Dic3—21no—
161C7×Dic3—21no—
162C7×Dic3—21no—
163C7×Dic3—21no—
164#539—211noSylow
165C22×D7—31no—
166C22×D7—31no—
167C22×D7—31no—
168C2×C4×C7—31no—
169C2×C4×C7—31no—
170C2×C4×C7—31no—
171C2×C4×C7—31no—
172C2×C4×C7C22×D311yescharacteristic
173C2×C4×C7C22×D311yescharacteristic
174C2×C4×C7C22×D311yescharacteristic
175C2×Dic7—31no—
176C2×Dic7C22×D311yescharacteristic
177C2×Dic7C22×D311yescharacteristic
178C2×Dic7C22×D311yescharacteristic
179C2×Dic7C22×D311yescharacteristic
180D28—62no—
181D28—62no—
182D28—121no—
183C4×D7—62no—
184C4×D7—121no—
185C4×D7—121no—
186C4×D7—121no—
187C4×D7—121no—
188Dic14—121no—
189C2×D12—71no—
190C2×D12—71no—
191C2×D12—71no—
192C2×C4×D3—71no—
193C2×C4×D3—71no—
194C2×C4×D3—71no—
195C2×C4×D3—71no—
196C2×C4×D3—71no—
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)⋊C4—71no—
214(C2×D3)⋊C4—71no—
215C4⋊Dic3—71no—
216C4⋊Dic3C2×D711yescharacteristic
217Dic3⋊C4—71no—
218Dic3⋊C4—71no—
219Dic3⋊C4C2×D711yescharacteristic
220Dic3⋊C4C2×D711yescharacteristic
221Dic3⋊C4C2×D711yescharacteristic
222Dic3⋊C4C2×D711yescharacteristic
223C4×Dic3C2×D711yescharacteristic
224C2×C3×C7C2×#4111yescharacteristic
225C2×C3×C7H(5,𝔽2)11yescharacteristic
226C2×C3×C72−1+411yescharacteristic
227D21—22no—
228D21—41no—
229D21—41no—
230#126—211no—
231#126—211no—
232#125—31no—
233#125—71no—
234#123—211no—
235#123—211no—
236#123—211no—
237#123—211no—
238C22⋊Q8—211no—
239C22⋊Q8—211no—
240C22⋊Q8—211no—
241#121—211no—
242C4×D4—211no—
243C4×D4—211no—
244C2×C4⋊C4—211no—
245C22×C7C23×D311yescharacteristic
246C2×D7—32no—
247C2×D7—61no—
248C2×D7—61no—
249C2×D7—61no—
250C2×D7—61no—
251C2×D7—61no—
252C2×D7—61no—
253C2×D7—61no—
254C2×D7—61no—
255C4×C7—21no—
256C4×C7—21no—
257C4×C7—21no—
258C4×C7—61no—
259C4×C7—61no—
260C4×C7—61no—
261C4×C7—61no—
262Dic7—21no—
263Dic7—21no—
264Dic7—21no—
265Dic7—21no—
266Dic7—61no—
267C22×D3—71no—
268C22×D3—71no—
269C22×D3—71no—
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×Dic3C22×D711yescharacteristic
279C2×Dic3C22×D711yescharacteristic
280C2×Dic3C22×D711yescharacteristic
281C2×Dic3C22×D711yescharacteristic
282D12—142no—
283D12—142no—
284D12—281no—
285C4×D3—142no—
286C4×D3—281no—
287C4×D3—281no—
288C4×D3—281no—
289C4×D3—281no—
290Dic6—281no—
291C3×C7#53911yescharacteristic, complemented, Hall
292C2×Q8—211no—
293C2×D4—211no—
294C2×D4—211no—
295C2×D4—211no—
296C22×C4—211no—
297C22×C4—211no—
298C22×C4—211no—
299C22×C4—211no—
300C22×C4—211no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—31no—
306C4⋊C4—71no—
307C4⋊C4—71no—
308C4⋊C4—71no—
309C4⋊C4—71no—
310C4⋊C4—71no—
311C4⋊C4—211no—
312C4⋊C4—211no—
313C4⋊C4—211no—
314C4⋊C4D3×D711yescharacteristic
315C22⋊C4—211no—
316C22⋊C4—211no—
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—31no—
326C42—71no—
327C2×C7#100711yescharacteristic
328C2×C7D3×#4111yescharacteristic
329C2×C7#100911yescharacteristic
330D7—62no—
331D7—121no—
332D7—121no—
333C22×C3C23×D711yescharacteristic
334C2×D3—72no—
335C2×D3—141no—
336C2×D3—141no—
337C2×D3—141no—
338C2×D3—141no—
339C2×D3—141no—
340C2×D3—141no—
341C2×D3—141no—
342C2×D3—141no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—141no—
347C3×C4—141no—
348C3×C4—141no—
349C3×C4—141no—
350Dic3—21no—
351Dic3—21no—
352Dic3—21no—
353Dic3—21no—
354Dic3—141no—
355C23—211no—
356C23—211no—
357C23—211no—
358Q8—841no—
359D4—422no—
360D4—422no—
361D4—841no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—71no—
367C2×C4—71no—
368C2×C4—71no—
369C2×C4—71no—
370C2×C4—211no—
371C2×C4—422no—
372C2×C4—841no—
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×C3#655111yescharacteristic
381C2×C3D7×#4111yescharacteristic
382C2×C3#655311yescharacteristic
383D3—142no—
384D3—281no—
385D3—281no—
386C22—212no—
387C22—421no—
388C22—421no—
389C22—421no—
390C22—421no—
391C22—421no—
392C22—421no—
393C22—421no—
394C22—421no—
395C22C22×D3×D711yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—61no—
400C4—61no—
401C4—61no—
402C4—61no—
403C4—141no—
404C4—141no—
405C4—141no—
406C4—141no—
407C4—421no—
408C3#9038311yescharacteristic, complemented, Sylow
409C2—422no—
410C2—841no—
411C2—841no—
412C2#1062156611yescharacteristic
413C2#1062157111yescharacteristic
414C2#1062157611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
prime radical#10621378C2
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
2. C7×#889C2semidirect
3. C3×#6452C2semidirect
4. #10620995C2semidirect
5. #10620995C2semidirect
6. #10620995C2semidirect
7. #10620995C2semidirect
8. #10620991C2semidirect
9. #10620990C2semidirect
10. #10620981C2semidirect
11. #10620980C2semidirect
12. #10620966C2semidirect
13. #10620949C2semidirect
14. #10620942C2semidirect
15. #10620939C2semidirect
64. #6452D3semidirect
139. #889D7semidirect
291. C3×C7#539semidirect
379. C7#5692semidirect
408. C3#90383semidirect

Maximal subgroups

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

subgroupindex
#106213782
C7×#8892
C3×#64522
#106209952
#106209912
#106209902
#106209812
#106209802
#106209662
#106209492
#106209422
#106209392
#903833
#56927