Finite Group Databasebeta

← #13256880

Subgroups — #13256880

Order 1792.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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
2#11727582C211yesmaximal, characteristic
3#11727576C211yesmaximal, characteristic
4#11727309C211yesmaximal, characteristic
5C7×#1295C211yesmaximal, characteristic
6#11725465C211yesmaximal, characteristic
7#11725465C211yesmaximal, characteristic
8C2×#6432C2211yescharacteristic
9C2×C7×#97C2211yescharacteristic
10C2×C7×#97C2211yescharacteristic
11C7×#382C2211yescharacteristic
12C2×#6390—21no—
13C2×#6390—21no—
14#89756—21no—
15#89756—21no—
16#89708C2211yescharacteristic
17#89708C2211yescharacteristic
18C2×#6377C2211yescharacteristic
19#89433—21no—
20#89433—21no—
21#89429—21no—
22#89429—21no—
23#89346—21no—
24#89346—21no—
25#89324—21no—
26#89324—21no—
27#10361—71nomaximal, Sylow
28C22×Dic14—21no—
29C22×C7×C8—21no—
30C22×C7×C8—21no—
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C42×C7C2311yescharacteristic
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7D411yescharacteristic
39C2×C4⋊Dic7D411yescharacteristic
40C2×C4⋊Dic7D411yescharacteristic
41C2×C4⋊Dic7D411yescharacteristic
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—21no—
46C22×C7⋊C8—21no—
47#6432—21no—
48#6432—21no—
49#6432—21no—
50#6432Q812yes—
51C7×#97—21no—
52C7×#97—21no—
53C7×#97—21no—
54C7×#97—21no—
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#6390—42no—
64#6390—42no—
65#6377—21no—
66#6377—21no—
67#2845—71no—
68#1993—71no—
69#1993—71no—
70#1960—71no—
71#1295—71no—
72#1295—71no—
73#1295D711yescharacteristic
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—41no—
84C2×Dic14—22no—
85C2×Dic14—41no—
86C2×Dic14—41no—
87C2×Dic14—41no—
88C2×Dic14—41no—
89C2×Dic14—41no—
90C2×C7×C8—22no—
91C2×C7×C8—22no—
92C2×C7×C8—41no—
93C2×C7×C8—41no—
94C2×C7×C8—41no—
95C2×C7×C8—41no—
96C7×C4⋊C4—41no—
97C7×C4⋊C4—41no—
98C42×C7C2×Q811yescharacteristic
99C42×C7#4111yescharacteristic
100C42×C7#4111yescharacteristic
101C42×C7#4111yescharacteristic
102C4⋊Dic7—22no—
103C4⋊Dic7—22no—
104C4⋊Dic7—41no—
105C4⋊Dic7—41no—
106C4⋊Dic7—41no—
107C4⋊Dic7—41no—
108C4⋊Dic7—41no—
109C4⋊Dic7—41no—
110C4⋊Dic7—81no—
111C4⋊Dic7—81no—
112Dic7⋊C4—81no—
113Dic7⋊C4—81no—
114Dic7⋊C4—81no—
115Dic7⋊C4—81no—
116C2×C7⋊C8—22no—
117C2×C7⋊C8—41no—
118C2×C7⋊C8—41no—
119C2×C4⋊Q8—71no—
120C2×#103—141no—
121C2×#103—141no—
122C2×#97—71no—
123C2×#97C2×D711yescharacteristic
124C2×#97C2×D711yescharacteristic
125#398—141no—
126#398—141no—
127#398—141no—
128#398—141no—
129#398—141no—
130#398—141no—
131#382—71no—
132#382—71no—
133#382C2×D711yescharacteristic
134#340—141no—
135#340—141no—
136#340—141no—
137#340—141no—
138C23×C7#12011yescharacteristic
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7C22⋊Q811yescharacteristic
152C2×C4×C7C22⋊Q811yescharacteristic
153C2×C4×C7C22⋊Q811yescharacteristic
154C2×C4×C7#12411yescharacteristic
155C2×C4×C7#12411yescharacteristic
156C2×C4×C7#12411yescharacteristic
157C2×Dic7—42no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—41no—
167C2×Dic7—41no—
168C2×Dic7—41no—
169C2×Dic7—41no—
170C2×Dic7—81no—
171C2×Dic7—81no—
172Dic14—42no—
173Dic14—42no—
174Dic14—81no—
175Dic14—81no—
176C7×C8—42no—
177C7×C8—42no—
178C7⋊C8—42no—
179C22×Q8—141no—
180C22×C8—21no—
181C22×C8—21no—
182C22×C8—141no—
183C4⋊Q8—72no—
184C4⋊Q8—141no—
185C4⋊Q8—141no—
186C4⋊Q8—141no—
187C2×C4⋊C4—71no—
188C2×C4⋊C4—71no—
189C2×C4⋊C4—71no—
190C2×C4⋊C4—71no—
191C2×C4⋊C4—141no—
192C2×C4⋊C4—141no—
193C2×C4⋊C4—141no—
194C2×C4⋊C4—141no—
195C2×C4⋊C4—141no—
196C2×C4⋊C4—141no—
197C2×C4⋊C4—141no—
198C2×C4⋊C4—141no—
199C2×C4⋊C4D2811yescharacteristic
200C2×C4⋊C4D2811yescharacteristic
201C2×C42C22×D711yescharacteristic
202#103—282no—
203#103—282no—
204#97—21no—
205#97—21no—
206#97—21no—
207#97—21no—
208#97—141no—
209#97—141no—
210#95—21no—
211#95—21no—
212#95—141no—
213#95—141no—
214#95—141no—
215#95—141no—
216#95—141no—
217#95—141no—
218C22×C7#39311yescharacteristic
219C22×C7#45311yescharacteristic
220C22×C7#45411yescharacteristic
221C22×C7#45511yescharacteristic
222C22×C7#45511yescharacteristic
223C22×C7#45611yescharacteristic
224C22×C7#45611yescharacteristic
225C4×C7—21no—
226C4×C7—21no—
227C4×C7—21no—
228C4×C7—21no—
229C4×C7—21no—
230C4×C7—21no—
231C4×C7—81no—
232C4×C7—81no—
233Dic7—81no—
234Dic7—81no—
235Dic7—81no—
236Dic7—81no—
237Dic7—82no—
238C2×Q8—142no—
239C2×Q8—281no—
240C2×Q8—281no—
241C2×Q8—281no—
242C2×Q8—281no—
243C2×Q8—281no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—141no—
247C22×C4—141no—
248C22×C4—141no—
249C22×C4—141no—
250C22×C4—281no—
251C22×C4C2×D2811yescharacteristic
252C22×C4D4×D711yescharacteristic
253C22×C4D4×D711yescharacteristic
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—142no—
261C2×C8—281no—
262C2×C8—281no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—142no—
266C4⋊C4—142no—
267C4⋊C4—281no—
268C4⋊C4—281no—
269C4⋊C4—281no—
270C4⋊C4—281no—
271C4⋊C4—281no—
272C4⋊C4—281no—
273C4⋊C4—561no—
274C4⋊C4—561no—
275C4⋊C4—561no—
276C4⋊C4—561no—
277C4⋊C4—561no—
278C4⋊C4—561no—
279C42#115711yescharacteristic
280C42#115711yescharacteristic
281C42#115911yescharacteristic
282C42Q8×D711yescharacteristic
283C2×C7#166111yescharacteristic
284C2×C7#166111yescharacteristic
285C2×C7#166211yescharacteristic
286C2×C7#166311yescharacteristic
287C2×C7#202711yescharacteristic
288C2×C7#202811yescharacteristic
289C2×C7#202811yescharacteristic
290C23#644511yescharacteristic
291Q8—282no—
292Q8—282no—
293Q8—561no—
294Q8—561no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—282no—
308C2×C4—281no—
309C2×C4—281no—
310C2×C4—281no—
311C2×C4—281no—
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—561no—
321C2×C4—561no—
322C2×C4#643811yescharacteristic
323C2×C4#644811yescharacteristic
324C2×C4#644811yescharacteristic
325C2×C4#645911yescharacteristic
326C2×C4#645911yescharacteristic
327C2×C4#646011yescharacteristic
328C8—42no—
329C8—42no—
330C8—282no—
331C7#1036111yescharacteristic, complemented, Sylow
332C22#8944511yescharacteristic
333C22#8951811yescharacteristic
334C22#8952411yescharacteristic
335C22#8959411yescharacteristic
336C22#8959711yescharacteristic
337C22#8959811yescharacteristic
338C22#8959911yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—81no—
346C4—81no—
347C4—561no—
348C4—561no—
349C4—561no—
350C4—561no—
351C4—562no—
352C2#1172611111yescharacteristic
353C2#1172611211yescharacteristic
354C2#1172612711yescharacteristic
355C2#1172613011yescharacteristic
356C2#1172651711yescharacteristic
357C2#1172652311yescharacteristic
358C2#1172675211yescharacteristic
subgroupG/H
centerC23#6445
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1295C2
socle, prime radicalC23×C7#120
hypercenter#1295D7
hypocenterC7#10361
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
331. C7#10361semidirect

Maximal subgroups

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

subgroupindex
#117316642
#117275822
#117275762
#117273092
C7×#12952
#117254652
#103617