Finite Group Databasebeta

← #13248163

Subgroups — #13248163

Order 1792.

412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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#11731606C211yesmaximal, characteristic
2C7×#1836C211yesmaximal, characteristic
3C2×#89260C211yesmaximal, characteristic
4#11727337C211yesmaximal, characteristic
5#11727332C211yesmaximal, characteristic
6#11725465C211yesmaximal, characteristic
7#11725436C211yesmaximal, characteristic
8C2×#6433C2211yescharacteristic
9C2×C7×#97C2211yescharacteristic
10C7×#384C2211yescharacteristic
11C7×#382C2211yescharacteristic
12#89750—21no—
13#89744—21no—
14C2×#6382—21no—
15C2×#6381—21no—
16#89708C2211yescharacteristic
17C2×#6377C2211yescharacteristic
18C2×#6377C2211yescharacteristic
19#89427—21no—
20#89426—21no—
21#89425—21no—
22#89419—21no—
23C7×#340—21no—
24C7×#340—21no—
25#89324—21no—
26#89324—21no—
27#89260C414yescomplemented
28#8912—71nomaximal, Sylow
29C22×C7×C8—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C42×C7C2311yescharacteristic
36C2×C4⋊Dic7D411yescharacteristic
37C2×C4⋊Dic7D411yescharacteristic
38C2×C4⋊Dic7D411yescharacteristic
39C2×C4⋊Dic7D411yescharacteristic
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×C4×Dic7—21no—
45C2×C4×Dic7—21no—
46C22×C7⋊C8—21no—
47C22×C7⋊C8—21no—
48#6433—21no—
49#6433—21no—
50#6433C2×C412yes—
51#6433Q812yes—
52C7×#97—21no—
53C7×#97C2×C412yes—
54C7×#95—21no—
55C7×#95—21no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59C7⋊#95—21no—
60C7⋊#95—21no—
61C7⋊#95—21no—
62#6382—42no—
63#6381—42no—
64#6377—21no—
65#6377—21no—
66#6377—21no—
67#6377C2×C412yes—
68#2382—71no—
69#1992—71no—
70#1847—71no—
71#1836D711yescharacteristic
72C2×#330—71no—
73#1295—71no—
74#1295—71no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—41no—
78C22×C4×C7C2×D411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—21no—
84C22×Dic7—21no—
85C2×C7×C8—22no—
86C2×C7×C8—41no—
87C2×C7×C8—41no—
88C7×C4⋊C4—41no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—42no—
91C7×C4⋊C4—42no—
92C7×C4⋊C4—41no—
93C7×C4⋊C4—41no—
94C42×C7C22×C411yescharacteristic
95C42×C7C2×Q811yescharacteristic
96C42×C7#4111yescharacteristic
97C42×C7#4111yescharacteristic
98C4⋊Dic7—21no—
99C4⋊Dic7—21no—
100C4⋊Dic7—41no—
101C4⋊Dic7—41no—
102C4⋊Dic7C4⋊C412yes—
103C4⋊Dic7C4⋊C412yes—
104Dic7⋊C4—22no—
105Dic7⋊C4—22no—
106Dic7⋊C4—22no—
107Dic7⋊C4—22no—
108Dic7⋊C4—81no—
109Dic7⋊C4—81no—
110C4×Dic7—81no—
111C4×Dic7—81no—
112C2×C7⋊C8—22no—
113C2×C7⋊C8—22no—
114C2×C7⋊C8—22no—
115C2×C7⋊C8—22no—
116C2×C7⋊C8—41no—
117C2×C7⋊C8—41no—
118C2×#125—71no—
119C2×#107—141no—
120C2×#106—141no—
121C2×#97—71no—
122C2×#97—71no—
123C2×#97C2×D711yescharacteristic
124#389—141no—
125#389—141no—
126#387—141no—
127#387—141no—
128#387—141no—
129#387—141no—
130#384C2×D711yescharacteristic
131#382—71no—
132#382C2×D711yescharacteristic
133#340—21no—
134#340—21no—
135#340—141no—
136#340—141no—
137#330—74no—
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×C7—81no—
152C2×C4×C7—81no—
153C2×C4×C7—81no—
154C2×C4×C7C2×C4⋊C411yescharacteristic
155C2×C4×C7C4×D411yescharacteristic
156C2×C4×C7C4×D411yescharacteristic
157C2×C4×C7C22⋊Q811yescharacteristic
158C2×C4×C7C22⋊Q811yescharacteristic
159C2×C4×C7#12311yescharacteristic
160C2×Dic7—22no—
161C2×Dic7—22no—
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—41no—
171C2×Dic7—41no—
172C7×C8—42no—
173C7⋊C8—24no—
174C7⋊C8—42no—
175C22×C8—21no—
176C22×C8—141no—
177C22×C8—141no—
178#125—72no—
179#125—72no—
180#125—141no—
181#125—141no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—71no—
186C2×C4⋊C4—71no—
187C2×C4⋊C4—71no—
188C2×C4⋊C4—71no—
189C2×C4⋊C4—141no—
190C2×C4⋊C4—141no—
191C2×C4⋊C4—141no—
192C2×C4⋊C4—141no—
193C2×C4⋊C4C22⋊D711yescharacteristic
194C2×C4⋊C4C22⋊D711yescharacteristic
195C2×C42—141no—
196C2×C42—141no—
197C2×C42C22×D711yescharacteristic
198#107—282no—
199#106—282no—
200#97—21no—
201#97—72no—
202#97—141no—
203#97—141no—
204#97—141no—
205#97C4×D712yes—
206#95—21no—
207#95—21no—
208#95—141no—
209#95—141no—
210#95—141no—
211#95—141no—
212#95—141no—
213#95—141no—
214C22×C7#38511yescharacteristic
215C22×C7#45311yescharacteristic
216C22×C7#45411yescharacteristic
217C22×C7#45411yescharacteristic
218C22×C7#45511yescharacteristic
219C22×C7#45611yescharacteristic
220C22×C7#45611yescharacteristic
221C4×C7—21no—
222C4×C7—21no—
223C4×C7—21no—
224C4×C7—21no—
225C4×C7—21no—
226C4×C7—21no—
227C4×C7—81no—
228C4×C7—81no—
229C4×C7—161no—
230Dic7—42no—
231Dic7—42no—
232Dic7—81no—
233Dic7—81no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—141no—
238C22×C4—141no—
239C22×C4—141no—
240C22×C4—141no—
241C22×C4D4×D711yescharacteristic
242C22×C4D4×D711yescharacteristic
243C22×C4C2×C22⋊D711yescharacteristic
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—142no—
248C2×C8—142no—
249C2×C8—142no—
250C2×C8—142no—
251C2×C8—281no—
252C2×C8—281no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—72no—
260C4⋊C4—72no—
261C4⋊C4—142no—
262C4⋊C4—141no—
263C4⋊C4—141no—
264C4⋊C4—142no—
265C4⋊C4—142no—
266C4⋊C4—142no—
267C4⋊C4—281no—
268C4⋊C4—281no—
269C4⋊C4—561no—
270C4⋊C4—561no—
271C42—561no—
272C42—561no—
273C42C2×C4×D711yescharacteristic
274C42#115711yescharacteristic
275C42Q8×D711yescharacteristic
276C42#116111yescharacteristic
277C2×C7#165711yescharacteristic
278C2×C7#166111yescharacteristic
279C2×C7#166311yescharacteristic
280C2×C7#166411yescharacteristic
281C2×C7#185711yescharacteristic
282C2×C7#185911yescharacteristic
283C2×C7#186011yescharacteristic
284C23#650011yescharacteristic
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—142no—
301C2×C4—142no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4—281no—
306C2×C4—281no—
307C2×C4—281no—
308C2×C4—281no—
309C2×C4—281no—
310C2×C4—281no—
311C2×C4—281no—
312C2×C4D7×C4⋊C411yescharacteristic
313C2×C4#645611yescharacteristic
314C2×C4#645711yescharacteristic
315C2×C4#645911yescharacteristic
316C2×C4C4×C22⋊D711yescharacteristic
317C2×C4#650911yescharacteristic
318C8—42no—
319C8—144no—
320C8—282no—
321C7#891211yescharacteristic, complemented, Sylow
322C22#8976111yescharacteristic
323C22#8983311yescharacteristic
324C22#8983411yescharacteristic
325C22#8997011yescharacteristic
326C22#8997311yescharacteristic
327C22#8997711yescharacteristic
328C22#8997711yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—81no—
336C4—81no—
337C4—161no—
338C4—282no—
339C4—282no—
340C4—561no—
341C4—561no—
342C2#1172731611yescharacteristic
343C2#1172843111yescharacteristic
344C2#1172843411yescharacteristic
345C2#1172899911yescharacteristic
346C2#1172900111yescharacteristic
347C2#1172900311yescharacteristic
348C2#1172900611yescharacteristic
subgroupG/H
centerC23#6500
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1836C2
socle, prime radicalC23×C7#120
cosocleC2×C42×C7C23
hypercenter#1836D7
hypocenterC7#8912
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
27. #89260C4semidirect
321. C7#8912semidirect

Maximal subgroups

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

subgroupindex
#117316062
C7×#18362
C2×#892602
#117273372
#117273322
#117254652
#117254362
#89127