Finite Group Databasebeta

← #13337773

Subgroups — #13337773

Order 1792.

638 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#487C211yesmaximal, characteristic, complemented
2#11740657C211yesmaximal, characteristic
3#11740657C211yesmaximal, characteristic
4C8×#1157C211yesmaximal, characteristic
5#11729529C211yesmaximal, characteristic, complemented
6#11729528C211yesmaximal, characteristic, complemented
7#11728995C214yesmaximal, complemented
8#11728987C214yesmaximal, complemented
9#11727485C211yesmaximal, characteristic, complemented
10C2×C7×C4⋊Q8C2211yescharacteristic
11C2×C7×C4⋊Q8C2211yescharacteristic
12C4×#1157C2211yescharacteristic
13C7×#487—21no—
14C7×#487—21no—
15C7×#487C2214yes—
16C2×C7×#103—22no—
17C2×C4×C7×C8C2211yescharacteristic
18C8×C22⋊D7—22no—
19#89866—21no—
20#89866C2212yes—
21#89863—21no—
22#89863C2212yes—
23#89859—21no—
24#89859C2212yes—
25#89856—21no—
26#89856C2212yes—
27#89738—21no—
28#89738—21no—
29#89736—21no—
30#89736—21no—
31#89697C2211yescharacteristic
32#89696C2211yescharacteristic
33#89696C2211yescharacteristic
34C8×D28C2212yes—
35#89457—21no—
36C4×C8×D7—21no—
37C8×Dic14C2212yes—
38#89342C2214yes—
39#89341C2214yes—
40#89253C2214yes—
41#19277—71nomaximal, Sylow
42C22×C7×Q8—21no—
43C22×C7×Q8—21no—
44C2×#1157D411yescharacteristic
45C22×C7×C8D412yes—
46C7×C4⋊Q8—21no—
47C7×C4⋊Q8—21no—
48C7×C4⋊Q8—21no—
49C7×C4⋊Q8—21no—
50C7×C4⋊Q8—21no—
51C7×C4⋊Q8—21no—
52C7×C4⋊Q8C2312yes—
53C7×C4⋊Q8C2312yes—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4—21no—
56C2×C7×C4⋊C4—21no—
57C2×C7×C4⋊C4—21no—
58C2×C42×C7C2311yescharacteristic
59C4×C22⋊D7—21no—
60C4×C22⋊D7—21no—
61#6489D411yescharacteristic
62C2×#1136—21no—
63C2×#1136—21no—
64C2×C8×D7—22no—
65C4×D28D411yescharacteristic
66C4×D28C2311yescharacteristic
67#6435—21no—
68C42×D7—21no—
69C4×Dic14D411yescharacteristic
70C4×Dic14C2311yescharacteristic
71C7×#103—24no—
72C7×#103—24no—
73C4×C7×C8D411yescharacteristic
74C4×C7×C8D411yescharacteristic
75C4×C7×C8C2312yes—
76C22⋊(C7⋊C8)—21no—
77(C2×D7)⋊C8—22no—
78Dic7⋊C8—22no—
79C8×Dic7—22no—
80#6384—22no—
81#6384—22no—
82#6383—22no—
83#6383—22no—
84#6382—22no—
85#6382—22no—
86#6381—22no—
87#6381—22no—
88C4⋊(C7⋊C8)—21no—
89C4⋊(C7⋊C8)—21no—
90C4⋊(C7⋊C8)C2312yes—
91C4⋊(C7⋊C8)C2312yes—
92C4⋊(C7⋊C8)C2312yes—
93C4×C7⋊C8—21no—
94C2×#487D711yescharacteristic, complemented
95#3079—71no—
96#3079—71no—
97C8×#41—71no—
98#1684—74no—
99#1683—74no—
100#1567—71no—
101#1549—71no—
102#1548—71no—
103C2×C7×Q8—22no—
104C2×C7×Q8—22no—
105C2×C7×Q8—44no—
106C2×C7×Q8—41no—
107C2×C7×Q8—41no—
108C2×C7×Q8—82no—
109C22×C4×C7—41no—
110C22×C4×C7—41no—
111C22×C4×C7C2×D411yescharacteristic
112C22×C4×C7C2×D411yescharacteristic
113C22×C4×C7#4111yescharacteristic
114C2×C22⋊D7—21no—
115#1157—22no—
116#1157Q1614yes—
117C2×D28C2×D411yescharacteristic
118C2×C4×D7—21no—
119C2×C4×D7—21no—
120C2×C4×D7—21no—
121C2×Dic14C2×D411yescharacteristic
122C2×C7×C8—42no—
123C2×C7×C8C2×D412yes—
124C2×C7×C8C2×D412yes—
125C7×C4⋊C4—22no—
126C7×C4⋊C4—22no—
127C7×C4⋊C4—22no—
128C7×C4⋊C4—22no—
129C7×C4⋊C4—41no—
130C7×C4⋊C4—41no—
131C7×C4⋊C4—41no—
132C7×C4⋊C4—41no—
133C42×C7C2×D411yescharacteristic
134C42×C7C2×D411yescharacteristic
135C42×C7#4111yescharacteristic
136C42×C7C2411yescharacteristic
137C22⋊Dic7—21no—
138(C2×D7)⋊C4—21no—
139(C2×D7)⋊C4—21no—
140C4⋊Dic7C2×D411yescharacteristic
141C4⋊Dic7C2×D411yescharacteristic
142Dic7⋊C4—21no—
143Dic7⋊C4—21no—
144C4×Dic7—21no—
145C4×Dic7—21no—
146C4×Dic7—21no—
147#1136—42no—
148#1136—42no—
149C2×C7⋊C8—22no—
150C2×C7⋊C8—22no—
151C2×C7⋊C8—22no—
152C8×D7—44no—
153C2×C4⋊Q8C2×D711yescharacteristic
154C2×C4⋊Q8C2×D711yescharacteristic
155C4×#41—71no—
156#487—21no—
157#487—21no—
158#487C2×D714yes—
159#477—72no—
160#477—141no—
161#476—72no—
162#476—141no—
163#475—72no—
164#475—141no—
165#474—72no—
166#474—141no—
167C8×Q8—72no—
168C8×D4—72no—
169C8×D4—142no—
170#431—71no—
171#431—141no—
172#428—141no—
173#428—141no—
174#423—71no—
175#423—71no—
176#417—141no—
177#417—141no—
178C2×#103—22no—
179C2×C4×C8—141no—
180C2×C4×C8C2×D711yescharacteristic
181#335—74no—
182#333—74no—
183#332—74no—
184C23×C7#12111yescharacteristic
185C22×D7—21no—
186C7×Q8—44no—
187C7×Q8—82no—
188C7×Q8—82no—
189C7×Q8—82no—
190C2×C4×C7—22no—
191C2×C4×C7—22no—
192C2×C4×C7—42no—
193C2×C4×C7—42no—
194C2×C4×C7—82no—
195C2×C4×C7—82no—
196C2×C4×C7#12111yescharacteristic
197C2×C4×C7#12111yescharacteristic
198C2×C4×C7#12111yescharacteristic
199C2×C4×C7C2×Q1612yes—
200C2×C4×C7#13512yes—
201C2×C4×C7C22×D411yescharacteristic
202C2×C4×C7C22×D411yescharacteristic
203C2×C4×C7C2×#4111yescharacteristic
204C22⋊D7—24no—
205C2×Dic7—21no—
206C2×Dic7—21no—
207C2×Dic7—21no—
208D28—21no—
209D28C2×Q1612yes—
210C4×D7—24no—
211C4×D7—42no—
212C4×D7—42no—
213Dic14—21no—
214Dic14C2×Q1612yes—
215C7×C8—22no—
216C7×C8—22no—
217C7⋊C8—42no—
218C7⋊C8—42no—
219C7⋊C8—42no—
220C2×#41—71no—
221C22×Q8—21no—
222C22×Q8—21no—
223C2×M16—141no—
224C2×M16—141no—
225C22×C8—142no—
226C22×C8C22⋊D712yes—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C22×D712yes—
234C4⋊Q8C22×D712yes—
235C4×Q8—71no—
236C4×Q8—71no—
237C4×D4—71no—
238C4×D4—71no—
239C4×D4—141no—
240C4×D4—141no—
241#117—71no—
242#117—141no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—141no—
248C2×C42C22×D711yescharacteristic
249#107—142no—
250#107—142no—
251#106—142no—
252#106—142no—
253C4⋊C8—72no—
254C4⋊C8—72no—
255C4⋊C8—72no—
256C4⋊C8—142no—
257C4⋊C8—141no—
258C4⋊C8—141no—
259#103—24no—
260#103—24no—
261#103—142no—
262#103—142no—
263#102—142no—
264#102—142no—
265C22⋊C8—141no—
266C22⋊C8—142no—
267C4×C8—142no—
268C4×C8—141no—
269C4×C8C22⋊D711yescharacteristic
270C4×C8C22⋊D711yescharacteristic
271C4×C8C22×D712yes—
272C22×C7—21no—
273C22×C7—21no—
274C22×C7#46712yes—
275C22×C7C2×#12111yescharacteristic
276C2×D7—22no—
277C2×D7—41no—
278C2×D7—41no—
279C4×C7—21no—
280C4×C7—21no—
281C4×C7—82no—
282C4×C7—82no—
283C4×C7#46712yes—
284C4×C7#47112yes—
285C4×C7C22×Q1611yescharacteristic
286C4×C7C2×#13511yescharacteristic
287C4×C7#57512yes—
288Dic7—22no—
289Dic7—41no—
290Dic7—41no—
291#41—74no—
292#41—142no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—44no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—71no—
299C2×Q8—82no—
300C2×D4—71no—
301C2×D4—141no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—141no—
305C22×C4—141no—
306C22×C4—141no—
307C22×C4D4×D711yescharacteristic
308C22×C4#115911yescharacteristic
309C22×C4C2×C22⋊D711yescharacteristic
310M16—282no—
311M16—282no—
312C2×C8—42no—
313C2×C8—142no—
314C2×C8—142no—
315C2×C8—142no—
316C2×C8—284no—
317C2×C8C2×C22⋊D712yes—
318C2×C8C2×C22⋊D712yes—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—71no—
328C4⋊C4—71no—
329C4⋊C4—141no—
330C4⋊C4—141no—
331C22⋊C4—141no—
332C22⋊C4—141no—
333C22⋊C4—141no—
334C42—141no—
335C42—141no—
336C42—141no—
337C42D4×D711yescharacteristic
338C42#115911yescharacteristic
339C42C2×C22⋊D711yescharacteristic
340C42C23×D711yescharacteristic
341C2×C7—22no—
342C2×C7#304011yescharacteristic
343C2×C7C2×#46711yescharacteristic
344C2×C7C2×#47111yescharacteristic
345D7—42no—
346C23—141no—
347C23#650111yescharacteristic
348Q8—44no—
349Q8—72no—
350Q8—82no—
351Q8—82no—
352Q8—82no—
353Q8—141no—
354D4—72no—
355D4—144no—
356D4—141no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—141no—
364C2×C4—144no—
365C2×C4—141no—
366C2×C4—141no—
367C2×C4—282no—
368C2×C4—282no—
369C2×C4D7×Q1612yes—
370C2×C4#648212yes—
371C2×C4#650111yescharacteristic
372C2×C4#650111yescharacteristic
373C2×C4#650111yescharacteristic
374C2×C4C2×D4×D711yescharacteristic
375C2×C4C2×#115911yescharacteristic
376C2×C4C22×C22⋊D711yescharacteristic
377C8—22no—
378C8—22no—
379C8—282no—
380C8—282no—
381C8—282no—
382C7#1927711yescharacteristic, complemented, Sylow
383C22—21no—
384C22—21no—
385C22—142no—
386C22—281no—
387C22—281no—
388C22#8996012yes—
389C22C2×#650111yescharacteristic
390C4—21no—
391C4—21no—
392C4—82no—
393C4—82no—
394C4—142no—
395C4—281no—
396C4—281no—
397C4#8994912yes—
398C4#8996012yes—
399C4C2×D7×Q1611yescharacteristic
400C4C2×#648211yescharacteristic
401C4#9051312yes—
402C2—22no—
403C2—282no—
404C2#1174039011yescharacteristic
405C2C2×#8994911yescharacteristic
406C2C2×#8996011yescharacteristic
subgroupG/H
centerC22C2×#6501
commutator, cosocleC42×C7C24
FrattiniC42C23×D7
FittingC2×C7×#487C2
socleC22×C7C2×#121
prime radicalC2×#1157D4
hypercenterC2×#487D7
hypocenterC7#19277
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C7×#487C2semidirect
5. #11729529C2semidirect
6. #11729528C2semidirect
7. #11728995C2semidirect
8. #11728987C2semidirect
9. #11727485C2semidirect
94. C2×#487D7semidirect
382. C7#19277semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4872
#117406572
C8×#11572
#117295292
#117295282
#117289952
#117289872
#117274852
#192777