Finite Group Databasebeta

← #13256871

Subgroups — #13256871

Order 1792.

400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11731663C211yesmaximal, characteristic
2C7×#1993C211yesmaximal, characteristic
3#11729542C211yesmaximal, characteristic
4#11729540C211yesmaximal, characteristic
5#11725465C211yesmaximal, characteristic
6#11725465C211yesmaximal, characteristic
7#11725436C211yesmaximal, characteristic
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×C7×#97C2211yescharacteristic
10C7×#382C2211yescharacteristic
11C2×#6409—21no—
12C2×#6409—21no—
13#89758—21no—
14#89751—21no—
15#89708C2211yescharacteristic
16#89708C2211yescharacteristic
17C2×#6377C2211yescharacteristic
18C2×#6377C2211yescharacteristic
19#89432—21no—
20#89432—21no—
21#89428—21no—
22#89428—21no—
23C7×#340—21no—
24C7×#340—21no—
25#89324—21no—
26#89324—21no—
27#10359—71nomaximal, Sylow
28C22×C7×Q8—21no—
29C22×Dic14—21no—
30C22×C7×C8—21no—
31C7×C4⋊Q8—21no—
32C7×C4⋊Q8—21no—
33C7×C4⋊Q8—21no—
34C7×C4⋊Q8Q812yescomplemented
35C2×C7×C4⋊C4—21no—
36C2×C7×C4⋊C4—21no—
37C2×C7×C4⋊C4D411yescharacteristic
38C2×C7×C4⋊C4D411yescharacteristic
39C2×C42×C7C2311yescharacteristic
40C2×C4⋊Dic7—21no—
41C2×C4⋊Dic7D411yescharacteristic
42C2×C4⋊Dic7D411yescharacteristic
43C2×C4⋊Dic7D411yescharacteristic
44C2×C4⋊Dic7D411yescharacteristic
45C2×Dic7⋊C4—21no—
46C2×Dic7⋊C4—21no—
47C22×C7⋊C8—21no—
48C22×C7⋊C8—21no—
49C7×#97—21no—
50C7×#97—21no—
51C7×#95—21no—
52C7×#95—21no—
53#6409—42no—
54#6409—42no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59C7⋊#95—21no—
60C7⋊#95—21no—
61C7⋊#95—21no—
62C7⋊#95—21no—
63#6377—21no—
64#6377—21no—
65#6377—21no—
66#6377—21no—
67#2844—71no—
68#1993—71no—
69#1993D711yescharacteristic
70#1960—71no—
71#1295—71no—
72#1295—71no—
73#1295—71no—
74C2×C7×Q8—22no—
75C2×C7×Q8—41no—
76C2×C7×Q8—41no—
77C2×C7×Q8—41no—
78C2×C7×Q8—41no—
79C2×C7×Q8—41no—
80C22×C4×C7—21no—
81C22×C4×C7—21no—
82C22×C4×C7—41no—
83C22×C4×C7C2×D411yescharacteristic
84C22×C4×C7C2×D411yescharacteristic
85C22×C4×C7C2×D411yescharacteristic
86C22×Dic7—21no—
87C22×Dic7—21no—
88C22×Dic7—21no—
89C22×Dic7—21no—
90C2×Dic14—81no—
91C2×Dic14—81no—
92C2×Dic14—81no—
93C2×C7×C8—22no—
94C2×C7×C8—41no—
95C2×C7×C8—41no—
96C7×C4⋊C4—22no—
97C7×C4⋊C4—22no—
98C7×C4⋊C4—41no—
99C7×C4⋊C4—41no—
100C7×C4⋊C4—41no—
101C7×C4⋊C4—41no—
102C42×C7C2×Q811yescharacteristic
103C42×C7#4111yescharacteristic
104C42×C7#4111yescharacteristic
105C42×C7#4111yescharacteristic
106C4⋊Dic7—41no—
107C4⋊Dic7—41no—
108C4⋊Dic7—41no—
109C4⋊Dic7—41no—
110C4⋊Dic7—81no—
111Dic7⋊C4—81no—
112Dic7⋊C4—81no—
113C2×C7⋊C8—22no—
114C2×C7⋊C8—22no—
115C2×C7⋊C8—41no—
116C2×C7⋊C8—41no—
117C2×C7⋊C8—41no—
118C2×C7⋊C8—41no—
119C2×C4⋊Q8C2×D711yescharacteristic
120C2×#103—141no—
121C2×#103—141no—
122C2×#97—71no—
123C2×#97—71no—
124C2×#97C2×D711yescharacteristic
125#400—141no—
126#400—141no—
127#400—141no—
128#395—141no—
129#395—141no—
130#395—141no—
131#382—71no—
132#382—71no—
133#382C2×D711yescharacteristic
134#340—21no—
135#340—21no—
136#340—141no—
137#340—141no—
138C23×C7#12011yescharacteristic
139C7×Q8—42no—
140C7×Q8—42no—
141C7×Q8—81no—
142C7×Q8—81no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—42no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—41no—
155C2×C4×C7—41no—
156C2×C4×C7—81no—
157C2×C4×C7—81no—
158C2×C4×C7C22⋊Q811yescharacteristic
159C2×C4×C7C22⋊Q811yescharacteristic
160C2×C4×C7C22⋊Q811yescharacteristic
161C2×C4×C7#12411yescharacteristic
162C2×C4×C7#12411yescharacteristic
163C2×C4×C7#12411yescharacteristic
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—41no—
167C2×Dic7—41no—
168C2×Dic7—41no—
169C2×Dic7—41no—
170C2×Dic7—41no—
171C2×Dic7—41no—
172C2×Dic7—41no—
173C2×Dic7—41no—
174C2×Dic7—41no—
175C2×Dic7—41no—
176Dic14—84no—
177C7×C8—42no—
178C7⋊C8—42no—
179C7⋊C8—42no—
180C22×Q8—21no—
181C22×Q8—141no—
182C22×C8—21no—
183C22×C8—141no—
184C22×C8—141no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8Dic1412yescomplemented
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—71no—
192C2×C4⋊C4—71no—
193C2×C4⋊C4—71no—
194C2×C4⋊C4—71no—
195C2×C4⋊C4—141no—
196C2×C4⋊C4—141no—
197C2×C4⋊C4—141no—
198C2×C4⋊C4C22⋊D711yescharacteristic
199C2×C4⋊C4C22⋊D711yescharacteristic
200C2×C42C22×D711yescharacteristic
201#103—282no—
202#103—282no—
203#97—21no—
204#97—21no—
205#97—141no—
206#97—141no—
207#97—141no—
208#97—141no—
209#95—21no—
210#95—21no—
211#95—141no—
212#95—141no—
213#95—141no—
214#95—141no—
215#95—141no—
216#95—141no—
217#95—141no—
218#95—141no—
219C22×C7#39311yescharacteristic
220C22×C7#45311yescharacteristic
221C22×C7#45411yescharacteristic
222C22×C7#45511yescharacteristic
223C22×C7#45511yescharacteristic
224C22×C7#45611yescharacteristic
225C22×C7#45611yescharacteristic
226C4×C7—21no—
227C4×C7—21no—
228C4×C7—21no—
229C4×C7—21no—
230C4×C7—21no—
231C4×C7—21no—
232C4×C7—81no—
233C4×C7—81no—
234C4×C7—82no—
235Dic7—81no—
236Dic7—81no—
237Dic7—81no—
238Dic7—81no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—561no—
246C2×Q8—561no—
247C2×Q8—561no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—141no—
252C22×C4—141no—
253C22×C4—141no—
254C22×C4—141no—
255C22×C4D4×D711yescharacteristic
256C22×C4D4×D711yescharacteristic
257C22×C4C2×C22⋊D711yescharacteristic
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—142no—
262C2×C8—142no—
263C2×C8—281no—
264C2×C8—281no—
265C2×C8—281no—
266C2×C8—281no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—281no—
274C4⋊C4—281no—
275C4⋊C4—281no—
276C4⋊C4—281no—
277C4⋊C4—561no—
278C4⋊C4—561no—
279C4⋊C4—561no—
280C42C2×Dic1411yescharacteristic
281C42#115711yescharacteristic
282C42#115911yescharacteristic
283C42#115911yescharacteristic
284C2×C7#165911yescharacteristic
285C2×C7#166011yescharacteristic
286C2×C7#166411yescharacteristic
287C2×C7#166411yescharacteristic
288C2×C7#202711yescharacteristic
289C2×C7#202811yescharacteristic
290C2×C7#202811yescharacteristic
291C23#650011yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296Q8—564no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—281no—
313C2×C4—281no—
314C2×C4—281no—
315C2×C4—281no—
316C2×C4—281no—
317C2×C4—281no—
318C2×C4—281no—
319C2×C4—281no—
320C2×C4—281no—
321C2×C4—281no—
322C2×C4—281no—
323C2×C4—281no—
324C2×C4#644111yescharacteristic
325C2×C4#644111yescharacteristic
326C2×C4#644811yescharacteristic
327C2×C4#644811yescharacteristic
328C2×C4#648711yescharacteristic
329C2×C4#649911yescharacteristic
330C8—42no—
331C8—282no—
332C8—282no—
333C7#1035911yescharacteristic, complemented, Sylow
334C22#8971911yescharacteristic
335C22#8983311yescharacteristic
336C22#8986711yescharacteristic
337C22#8997011yescharacteristic
338C22#8997311yescharacteristic
339C22#8997411yescharacteristic
340C22#8997711yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—81no—
348C4—81no—
349C4—82no—
350C4—561no—
351C4—561no—
352C4—561no—
353C4—561no—
354C2#1172742711yescharacteristic
355C2#1172806711yescharacteristic
356C2#1172808711yescharacteristic
357C2#1172899811yescharacteristic
358C2#1172900111yescharacteristic
359C2#1172914511yescharacteristic
360C2#1172914811yescharacteristic
subgroupG/H
centerC23#6500
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1993C2
socle, prime radicalC23×C7#120
hypercenter#1993D7
hypocenterC7#10359
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
34. C7×C4⋊Q8Q8semidirect
188. C4⋊Q8Dic14semidirect
333. C7#10359semidirect

Maximal subgroups

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

subgroupindex
#117316632
C7×#19932
#117295422
#117295402
#117254652
#117254362
#103597