Finite Group Databasebeta

← #13247697

Subgroups — #13247697

Order 1792.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11736737C211yesmaximal, characteristic
2C7×#1565C211yesmaximal, characteristic, complemented
3#11728197C211yesmaximal, characteristic, complemented
4#11728179C211yesmaximal, characteristic
5C4×#6399C211yesmaximal, characteristic
6#11725542C211yesmaximal, characteristic, complemented
7#11725474C211yesmaximal, characteristic, complemented
8C4×#1157C2211yescharacteristic
9C7×#431C2211yescharacteristic
10C2×C7×C4⋊C8C2211yescharacteristic
11C4×C7×M16C2211yescharacteristic
12C2×#6399C411yescharacteristic
13C2×#6399C411yescharacteristic
14C42×Dic7C2211yescharacteristic
15#89697C2211yescharacteristic
16C2×C4⋊(C7⋊C8)C2211yescharacteristic
17#89609—21no—
18#89607—21no—
19#89502—22no—
20#89460—21no—
21#89451—21no—
22C7×#335—21no—
23C7×#334—21no—
24#89350C411yescharacteristic
25#89350C411yescharacteristic
26#89345—22no—
27#89279—21no—
28#89278—21no—
29#8842—71nomaximal, Sylow
30C2×#1157C2×C411yescharacteristic
31C2×C7×M16C2×C411yescharacteristic
32C2×C7×M16C2×C411yescharacteristic
33C22×C7×C8—21no—
34C2×C42×C7C2311yescharacteristic
35C4×C22⋊D7—21no—
36C4×C22⋊D7—21no—
37#6489C2×C411yescharacteristic
38C2×C4×Dic7—21no—
39C2×C4×Dic7—21no—
40C2×C4×Dic7C2×C411yescharacteristic
41C2×C4×Dic7C2×C411yescharacteristic
42C22×C7⋊C8D412yes—
43C2×#1131—22no—
44C4×D28D411yescharacteristic
45C4×D28Q811yescharacteristic
46#6435—21no—
47C42×D7—21no—
48C4×Dic14D411yescharacteristic
49C4×Dic14Q811yescharacteristic
50C7×C4⋊C8—21no—
51C7×C4⋊C8—21no—
52C7×C4⋊C8D411yescharacteristic
53C7×C4⋊C8D411yescharacteristic
54C7×C22⋊C8—21no—
55C7×#97—21no—
56C4×C7×C8—21no—
57C4×C7×C8—21no—
58C22⋊(C7⋊C8)—21no—
59#6399—22no—
60#6399—22no—
61(C2×D7)⋊C8—22no—
62#6389—22no—
63Dic7⋊C8—22no—
64C4⋊(C7⋊C8)—21no—
65C4⋊(C7⋊C8)—21no—
66C4⋊(C7⋊C8)—21no—
67C4×C7⋊C8—21no—
68#2989—71no—
69#1831—71no—
70C4×#104—71no—
71#1565D711yescharacteristic, complemented
72#1477—71no—
73#1283—71no—
74#1276—71no—
75C22×C4×C7C22×C411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7#4111yescharacteristic
78C2×C22⋊D7—21no—
79C22×Dic7—21no—
80C22×Dic7—21no—
81#1157—21no—
82#1157—21no—
83#1157—21no—
84#1157—21no—
85C2×D28C4⋊C411yescharacteristic
86C2×C4×D7—21no—
87C2×C4×D7—21no—
88C2×C4×D7—21no—
89C2×Dic14C4⋊C411yescharacteristic
90C7×M16—21no—
91C7×M16—21no—
92C7×M16—21no—
93C7×M16M1612yescomplemented
94C2×C7×C8—21no—
95C2×C7×C8—21no—
96C2×C7×C8—21no—
97C2×C7×C8—21no—
98C2×C7×C8—42no—
99C2×C7×C8—41no—
100C42×C7C2×D411yescharacteristic
101C42×C7C2×D411yescharacteristic
102C42×C7C2×Q811yescharacteristic
103C42×C7#4111yescharacteristic
104C22⋊Dic7—21no—
105(C2×D7)⋊C4—21no—
106(C2×D7)⋊C4—21no—
107C4⋊Dic7C4⋊C411yescharacteristic
108C4⋊Dic7C4⋊C411yescharacteristic
109Dic7⋊C4—21no—
110Dic7⋊C4—21no—
111C4×Dic7—21no—
112C4×Dic7—21no—
113C4×Dic7—21no—
114C4×Dic7—21no—
115C4×Dic7—21no—
116C4×Dic7—21no—
117C4×Dic7—42no—
118C4×Dic7—41no—
119C4×Dic7—41no—
120C4×Dic7M1612yescomplemented
121C2×C7⋊C8—22no—
122C2×C7⋊C8—42no—
123C2×C7⋊C8—41no—
124#1131—82no—
125C4×#41—71no—
126#446—141no—
127#436—141no—
128#435—142no—
129#432—141no—
130#431—71no—
131#431C2×D711yescharacteristic
132#423—141no—
133C2×C4⋊C8—71no—
134C2×C4⋊C8C2×D711yescharacteristic
135C2×#104—71no—
136C2×#104—71no—
137C4×M16C2×D711yescharacteristic
138C43—71no—
139#339—71no—
140#339—71no—
141#336—142no—
142#335—21no—
143#334—21no—
144Q8⋊C8—141no—
145D4⋊C8—141no—
146C23×C7C4×D411yescharacteristic
147C22×D7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—41no—
151C2×C4×C7C2×C4⋊C411yescharacteristic
152C2×C4×C7C4×D411yescharacteristic
153C2×C4×C7#12011yescharacteristic
154C2×C4×C7C22⋊Q811yescharacteristic
155C2×C4×C7C22⋊Q811yescharacteristic
156C2×C4×C7#12311yescharacteristic
157C2×C4×C7C2×M1611yescharacteristic
158C2×C4×C7C2×M1611yescharacteristic
159C2×C4×C7#13111yescharacteristic
160C2×C4×C7#13111yescharacteristic
161C22⋊D7—41no—
162C22⋊D7—41no—
163C2×Dic7—22no—
164C2×Dic7—21no—
165C2×Dic7—21no—
166C2×Dic7—21no—
167C2×Dic7—22no—
168C2×Dic7—41no—
169C2×Dic7—41no—
170C2×Dic7—41no—
171C2×Dic7—41no—
172D28—21no—
173D28—21no—
174C4×D7—41no—
175C4×D7—41no—
176C4×D7—41no—
177C4×D7—41no—
178C4×D7—81no—
179Dic14—21no—
180Dic14—21no—
181C7×C8—22no—
182C7×C8—41no—
183C7×C8—41no—
184C7×C8—41no—
185C7×C8—81no—
186C7⋊C8—42no—
187C7⋊C8—81no—
188C2×#41—71no—
189C2×M16—142no—
190C2×M16C4×D711yescharacteristic
191C2×M16C4×D711yescharacteristic
192C22×C8—21no—
193C22×C8—72no—
194C4×Q8—71no—
195C4×Q8—71no—
196C4×D4—71no—
197C4×D4—71no—
198C4×D4—141no—
199C4×D4—141no—
200#117—71no—
201#117—141no—
202C2×C42—71no—
203C2×C42—71no—
204C2×C42—141no—
205C2×C42—141no—
206C2×C42—141no—
207C2×C42C22×D711yescharacteristic
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—142no—
211C4⋊C8—141no—
212C4⋊C8—141no—
213C4⋊C8—141no—
214C4⋊C8C22⋊D711yescharacteristic
215C4⋊C8C22⋊D711yescharacteristic
216#104—142no—
217#104—142no—
218C22⋊C8—21no—
219C22⋊C8—142no—
220C22⋊C8—141no—
221#97—21no—
222#97—142no—
223C4×C8—21no—
224C4×C8—21no—
225C4×C8—141no—
226C22×C7—21no—
227C22×C7—21no—
228C22×C7#38511yescharacteristic
229C22×C7#43511yescharacteristic
230C22×C7#43611yescharacteristic
231C2×D7—41no—
232C2×D7—41no—
233C2×D7—41no—
234C4×C7—21no—
235C4×C7—21no—
236C4×C7—21no—
237C4×C7#42311yescharacteristic
238C4×C7#42411yescharacteristic
239C4×C7#43511yescharacteristic
240C4×C7#43611yescharacteristic
241C4×C7#45411yescharacteristic
242C4×C7#45511yescharacteristic
243Dic7—42no—
244Dic7—42no—
245Dic7—41no—
246Dic7—41no—
247Dic7—41no—
248#41—141no—
249#41—141no—
250#41—141no—
251#41—141no—
252C2×Q8—71no—
253C2×D4—71no—
254C2×D4—141no—
255C22×C4—141no—
256C22×C4—141no—
257C22×C4—141no—
258C22×C4—141no—
259C22×C4—141no—
260C22×C4C2×C4×D711yescharacteristic
261C22×C4D4×D711yescharacteristic
262C22×C4#116111yescharacteristic
263M16—21no—
264M16—21no—
265M16—21no—
266M16—562no—
267M16#113112yescomplemented
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—42no—
273C2×C8—41no—
274C2×C8—142no—
275C2×C8—282no—
276C2×C8—281no—
277C4⋊C4—71no—
278C4⋊C4—71no—
279C4⋊C4—141no—
280C4⋊C4—141no—
281C22⋊C4—141no—
282C22⋊C4—141no—
283C22⋊C4—141no—
284C42—72no—
285C42—141no—
286C42—141no—
287C42—141no—
288C42—141no—
289C42—141no—
290C42—141no—
291C42—281no—
292C42—281no—
293C42—282no—
294C42#115711yescharacteristic
295C42D4×D711yescharacteristic
296C42Q8×D711yescharacteristic
297C42C2×C22⋊D711yescharacteristic
298C2×C7—21no—
299C2×C7—21no—
300C2×C7#185111yescharacteristic
301C2×C7#186011yescharacteristic
302C2×C7#186111yescharacteristic
303D7—81no—
304C23—141no—
305C23#645611yescharacteristic
306Q8—141no—
307Q8—141no—
308D4—141no—
309D4—141no—
310D4—281no—
311D4—281no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—142no—
316C2×C4—142no—
317C2×C4—141no—
318C2×C4—141no—
319C2×C4—141no—
320C2×C4—281no—
321C2×C4—281no—
322C2×C4—281no—
323C2×C4—281no—
324C2×C4—281no—
325C2×C4—281no—
326C2×C4—281no—
327C2×C4—281no—
328C2×C4—561no—
329C2×C4D7×C4⋊C411yescharacteristic
330C2×C4#645711yescharacteristic
331C2×C4#645911yescharacteristic
332C2×C4C2×#113111yescharacteristic
333C2×C4#646411yescharacteristic
334C2×C4D7×M1611yescharacteristic
335C2×C4#647011yescharacteristic
336C2×C4C4×C22⋊D711yescharacteristic
337C2×C4#650011yescharacteristic
338C2×C4#650911yescharacteristic
339C8—22no—
340C8—41no—
341C8—41no—
342C8—41no—
343C8—81no—
344C8—282no—
345C8—561no—
346C7#884211yescharacteristic, complemented, Sylow
347C22—21no—
348C22—21no—
349C22—281no—
350C22—281no—
351C22—281no—
352C22#8960811yescharacteristic
353C22#8961011yescharacteristic
354C22#8976111yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—282no—
359C4—282no—
360C4—281no—
361C4—281no—
362C4—281no—
363C4#8960911yescharacteristic
364C4#8961111yescharacteristic
365C4#8988311yescharacteristic
366C4#8990011yescharacteristic
367C4#8997311yescharacteristic
368C4#8997411yescharacteristic
369C2—21no—
370C2—21no—
371C2—561no—
372C2#1172823211yescharacteristic
373C2#1172843511yescharacteristic
374C2#1172848911yescharacteristic
subgroupG/H
centerC2×C4#6500
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1565C2
socleC22×C7#385
prime radicalC2×#1157C2×C4
cosocleC2×C42×C7C23
hypercenter#1565D7
hypocenterC7#8842
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
2. C7×#1565C2semidirect
3. #11728197C2semidirect
6. #11725542C2semidirect
7. #11725474C2semidirect
71. #1565D7semidirect
93. C7×M16M16semidirect
120. C4×Dic7M16semidirect
267. M16#1131semidirect
346. C7#8842semidirect

Maximal subgroups

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

subgroupindex
#117367372
C7×#15652
#117281972
#117281792
C4×#63992
#117255422
#117254742
#88427