Finite Group Databasebeta

← #13258301

Subgroups — #13258301

Order 1792.

382 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 95 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#11731664C211yesmaximal, characteristic
2C7×#1847C211yesmaximal, characteristic
3#11727332C211yesmaximal, characteristic
4#11727329C211yesmaximal, characteristic
5#11725465C211yesmaximal, characteristic
6#11725465C211yesmaximal, characteristic
7#11725436C211yesmaximal, characteristic
8C2×C7×#107—21no—
9C2×C7×#106—21no—
10C2×C7×#97C2211yescharacteristic
11C7×#384C2211yescharacteristic
12C7×#382C2211yescharacteristic
13#89756—21no—
14#89756—21no—
15C2×#6382—21no—
16C2×#6381—21no—
17#89708C2211yescharacteristic
18#89708C2211yescharacteristic
19C2×#6377C2211yescharacteristic
20C2×#6377C2211yescharacteristic
21#89433—21no—
22#89433—21no—
23#89429—21no—
24#89429—21no—
25#89324—21no—
26#89324—21no—
27#10585—71nomaximal, Sylow
28C22×C7×C8—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C42×C7C2311yescharacteristic
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7D411yescharacteristic
38C2×C4⋊Dic7D411yescharacteristic
39C2×C4⋊Dic7D411yescharacteristic
40C2×C4⋊Dic7D411yescharacteristic
41C2×Dic7⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C22×C7⋊C8—21no—
46C22×C7⋊C8—21no—
47C7×#107—42no—
48C7×#106—42no—
49C7×#97—21no—
50C7×#97Q812yes—
51C7×#95—21no—
52C7×#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59#6382—42no—
60#6381—42no—
61#6377—21no—
62#6377—21no—
63#6377Q812yes—
64#6377Q812yes—
65#2845—71no—
66#1847—71no—
67#1847D711yescharacteristic
68#1836—71no—
69#1295—71no—
70#1295—71no—
71#1295—71no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—41no—
75C22×C4×C7C2×D411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×Dic7—21no—
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C2×C7×C8—22no—
83C2×C7×C8—22no—
84C2×C7×C8—22no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—41no—
87C7×C4⋊C4—41no—
88C7×C4⋊C4—41no—
89C7×C4⋊C4—42no—
90C7×C4⋊C4—41no—
91C7×C4⋊C4—41no—
92C42×C7C2×Q811yescharacteristic
93C42×C7C2×Q811yescharacteristic
94C42×C7C2×Q811yescharacteristic
95C42×C7#4111yescharacteristic
96C4⋊Dic7—41no—
97C4⋊Dic7—41no—
98C4⋊Dic7—41no—
99C4⋊Dic7—41no—
100C4⋊Dic7—81no—
101C4⋊Dic7—81no—
102Dic7⋊C4—81no—
103Dic7⋊C4—81no—
104Dic7⋊C4—81no—
105Dic7⋊C4—81no—
106C2×C7⋊C8—22no—
107C2×C7⋊C8—22no—
108C2×C7⋊C8—22no—
109C2×C7⋊C8—22no—
110C2×C7⋊C8—41no—
111C2×C7⋊C8—41no—
112C2×#107—21no—
113C2×#107—141no—
114C2×#106—21no—
115C2×#106—141no—
116C2×#97—71no—
117C2×#97—71no—
118C2×#97C2×D711yescharacteristic
119#398—141no—
120#398—141no—
121#398—141no—
122#398—141no—
123#398—141no—
124#398—141no—
125#384C2×D711yescharacteristic
126#382—71no—
127#382—71no—
128#382C2×D711yescharacteristic
129#340—141no—
130#340—141no—
131C23×C7#12011yescharacteristic
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7—41no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—81no—
145C2×C4×C7—81no—
146C2×C4×C7—81no—
147C2×C4×C7C22⋊Q811yescharacteristic
148C2×C4×C7C22⋊Q811yescharacteristic
149C2×C4×C7C22⋊Q811yescharacteristic
150C2×C4×C7C4⋊Q811yescharacteristic
151C2×C4×C7C4⋊Q811yescharacteristic
152C2×C4×C7C4⋊Q811yescharacteristic
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165C7×C8—24no—
166C7⋊C8—24no—
167C7⋊C8—42no—
168C22×C8—21no—
169C22×C8—141no—
170C22×C8—141no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—71no—
175C2×C4⋊C4—71no—
176C2×C4⋊C4—71no—
177C2×C4⋊C4—71no—
178C2×C4⋊C4—141no—
179C2×C4⋊C4—141no—
180C2×C4⋊C4—141no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4—141no—
183C2×C4⋊C4—141no—
184C2×C4⋊C4C22⋊D711yescharacteristic
185C2×C4⋊C4C22⋊D711yescharacteristic
186C2×C42C22×D711yescharacteristic
187#107—42no—
188#107—282no—
189#106—42no—
190#106—282no—
191#97—21no—
192#97—72no—
193#97—72no—
194#97—141no—
195#97—141no—
196#97Dic1412yes—
197#95—21no—
198#95—21no—
199#95—141no—
200#95—141no—
201#95—141no—
202#95—141no—
203#95—141no—
204#95—141no—
205C22×C7#39511yescharacteristic
206C22×C7#45311yescharacteristic
207C22×C7#45311yescharacteristic
208C22×C7#45411yescharacteristic
209C22×C7#45511yescharacteristic
210C22×C7#45611yescharacteristic
211C22×C7#45611yescharacteristic
212C4×C7—21no—
213C4×C7—21no—
214C4×C7—21no—
215C4×C7—21no—
216C4×C7—21no—
217C4×C7—21no—
218C4×C7—81no—
219C4×C7—81no—
220C4×C7—161no—
221Dic7—81no—
222Dic7—81no—
223Dic7—81no—
224Dic7—81no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—141no—
229C22×C4—141no—
230C22×C4—141no—
231C22×C4—141no—
232C22×C4D4×D711yescharacteristic
233C22×C4D4×D711yescharacteristic
234C22×C4C2×C22⋊D711yescharacteristic
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—142no—
239C2×C8—142no—
240C2×C8—142no—
241C2×C8—142no—
242C2×C8—281no—
243C2×C8—281no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—42no—
251C4⋊C4—281no—
252C4⋊C4—281no—
253C4⋊C4—281no—
254C4⋊C4—281no—
255C4⋊C4—561no—
256C4⋊C4—561no—
257C4⋊C4—561no—
258C4⋊C4—561no—
259C4⋊C4—561no—
260C4⋊C4—561no—
261C42C2×Dic1411yescharacteristic
262C42#115711yescharacteristic
263C42Q8×D711yescharacteristic
264C42Q8×D711yescharacteristic
265C2×C7#165611yescharacteristic
266C2×C7#166111yescharacteristic
267C2×C7#166111yescharacteristic
268C2×C7#166311yescharacteristic
269C2×C7#206011yescharacteristic
270C2×C7#206011yescharacteristic
271C2×C7#206111yescharacteristic
272C23#650011yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—281no—
289C2×C4—281no—
290C2×C4—281no—
291C2×C4—281no—
292C2×C4—281no—
293C2×C4—281no—
294C2×C4—281no—
295C2×C4—281no—
296C2×C4—281no—
297C2×C4—281no—
298C2×C4—281no—
299C2×C4—281no—
300C2×C4#645111yescharacteristic
301C2×C4#645111yescharacteristic
302C2×C4#645911yescharacteristic
303C2×C4#645911yescharacteristic
304C2×C4#648711yescharacteristic
305C2×C4#650711yescharacteristic
306C8—24no—
307C8—144no—
308C8—282no—
309C7#1058511yescharacteristic, complemented, Sylow
310C22#8975111yescharacteristic
311C22#8984911yescharacteristic
312C22#8986711yescharacteristic
313C22#8997011yescharacteristic
314C22#8997311yescharacteristic
315C22#8997411yescharacteristic
316C22#8997711yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—161no—
326C4—561no—
327C4—561no—
328C4—561no—
329C4—561no—
330C2#1172732711yescharacteristic
331C2#1172842011yescharacteristic
332C2#1172842111yescharacteristic
333C2#1172908111yescharacteristic
334C2#1172908511yescharacteristic
335C2#1172914611yescharacteristic
336C2#1172914711yescharacteristic
subgroupG/H
centerC23#6500
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1847C2
socle, prime radicalC23×C7#120
hypercenter#1847D7
hypocenterC7#10585
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
309. C7#10585semidirect

Maximal subgroups

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

subgroupindex
#117316642
C7×#18472
#117273322
#117273292
#117254652
#117254362
#105857