Finite Group Databasebeta

← #13248178

Subgroups — #13248178

Order 1792.

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

normal subgroups only

This group has 396 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#11727329C211yesmaximal, characteristic
6#11725465C211yesmaximal, characteristic
7#11725436C211yesmaximal, characteristic
8C2×#6433C2211yescharacteristic
9C2×C7×#97C2211yescharacteristic
10C7×#384C2211yescharacteristic
11C7×#382C2211yescharacteristic
12#89750—21no—
13#89744—21no—
14#89708C2211yescharacteristic
15C2×#6377C2211yescharacteristic
16C2×#6377C2211yescharacteristic
17#89427—21no—
18#89426—21no—
19#89425—21no—
20#89419—21no—
21C7×#340—21no—
22C7×#340—21no—
23#89324—21no—
24#89324—21no—
25#89324—21no—
26#89324—21no—
27#89260C414yescomplemented
28#8915—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#6377—21no—
63#6377—21no—
64#6377—21no—
65#6377C2×C412yes—
66#2382—71no—
67#1992—71no—
68#1836—71no—
69#1836D711yescharacteristic
70C2×#330—71no—
71#1295—71no—
72#1295—71no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—41no—
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C2×C7×C8—22no—
84C2×C7×C8—41no—
85C2×C7×C8—41no—
86C7×C4⋊C4—41no—
87C7×C4⋊C4—41no—
88C7×C4⋊C4—42no—
89C7×C4⋊C4—42no—
90C7×C4⋊C4—42no—
91C42×C7C22×C411yescharacteristic
92C42×C7C2×Q811yescharacteristic
93C42×C7#4111yescharacteristic
94C42×C7#4111yescharacteristic
95C4⋊Dic7—21no—
96C4⋊Dic7—21no—
97C4⋊Dic7—41no—
98C4⋊Dic7—41no—
99C4⋊Dic7C4⋊C412yes—
100C4⋊Dic7C4⋊C412yes—
101Dic7⋊C4—22no—
102Dic7⋊C4—22no—
103Dic7⋊C4—22no—
104Dic7⋊C4—22no—
105Dic7⋊C4—81no—
106Dic7⋊C4—81no—
107C4×Dic7—81no—
108C4×Dic7—81no—
109C2×C7⋊C8—22no—
110C2×C7⋊C8—22no—
111C2×C7⋊C8—41no—
112C2×C7⋊C8—41no—
113C2×C7⋊C8—41no—
114C2×C7⋊C8—41no—
115C2×#125—71no—
116C2×#97—71no—
117C2×#97—71no—
118C2×#97C2×D711yescharacteristic
119#389—141no—
120#389—141no—
121#387—141no—
122#387—141no—
123#387—141no—
124#387—141no—
125#384C2×D711yescharacteristic
126#382—71no—
127#382C2×D711yescharacteristic
128#340—21no—
129#340—21no—
130#340—141no—
131#340—141no—
132#340—141no—
133#340—141no—
134#330—74no—
135C23×C7#12011yescharacteristic
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7—81no—
149C2×C4×C7—81no—
150C2×C4×C7—81no—
151C2×C4×C7C2×C4⋊C411yescharacteristic
152C2×C4×C7C4×D411yescharacteristic
153C2×C4×C7C4×D411yescharacteristic
154C2×C4×C7C22⋊Q811yescharacteristic
155C2×C4×C7C22⋊Q811yescharacteristic
156C2×C4×C7#12311yescharacteristic
157C2×Dic7—22no—
158C2×Dic7—22no—
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—
169C7×C8—42no—
170C7⋊C8—42no—
171C7⋊C8—42no—
172C22×C8—21no—
173C22×C8—141no—
174C22×C8—141no—
175#125—72no—
176#125—72no—
177#125—141no—
178#125—141no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—71no—
183C2×C4⋊C4—71no—
184C2×C4⋊C4—71no—
185C2×C4⋊C4—71no—
186C2×C4⋊C4—141no—
187C2×C4⋊C4—141no—
188C2×C4⋊C4—141no—
189C2×C4⋊C4—141no—
190C2×C4⋊C4C22⋊D711yescharacteristic
191C2×C4⋊C4C22⋊D711yescharacteristic
192C2×C42—141no—
193C2×C42—141no—
194C2×C42C22×D711yescharacteristic
195#97—21no—
196#97—72no—
197#97—141no—
198#97—141no—
199#97—141no—
200#97C4×D712yes—
201#95—21no—
202#95—21no—
203#95—141no—
204#95—141no—
205#95—141no—
206#95—141no—
207#95—141no—
208#95—141no—
209C22×C7#38511yescharacteristic
210C22×C7#45411yescharacteristic
211C22×C7#45411yescharacteristic
212C22×C7#45411yescharacteristic
213C22×C7#45511yescharacteristic
214C22×C7#45511yescharacteristic
215C22×C7#45611yescharacteristic
216C4×C7—21no—
217C4×C7—21no—
218C4×C7—21no—
219C4×C7—21no—
220C4×C7—21no—
221C4×C7—21no—
222C4×C7—81no—
223C4×C7—81no—
224C4×C7—161no—
225Dic7—42no—
226Dic7—42no—
227Dic7—81no—
228Dic7—81no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4—141no—
233C22×C4—141no—
234C22×C4—141no—
235C22×C4—141no—
236C22×C4D4×D711yescharacteristic
237C22×C4D4×D711yescharacteristic
238C22×C4C2×C22⋊D711yescharacteristic
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—142no—
243C2×C8—142no—
244C2×C8—281no—
245C2×C8—281no—
246C2×C8—281no—
247C2×C8—281no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—72no—
254C4⋊C4—72no—
255C4⋊C4—142no—
256C4⋊C4—141no—
257C4⋊C4—141no—
258C4⋊C4—142no—
259C4⋊C4—142no—
260C4⋊C4—142no—
261C4⋊C4—281no—
262C4⋊C4—281no—
263C4⋊C4—561no—
264C4⋊C4—561no—
265C42—561no—
266C42—561no—
267C42C2×C4×D711yescharacteristic
268C42#115711yescharacteristic
269C42Q8×D711yescharacteristic
270C42#116111yescharacteristic
271C2×C7#165811yescharacteristic
272C2×C7#166211yescharacteristic
273C2×C7#166411yescharacteristic
274C2×C7#166411yescharacteristic
275C2×C7#185711yescharacteristic
276C2×C7#186011yescharacteristic
277C2×C7#186011yescharacteristic
278C23#650011yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—142no—
295C2×C4—142no—
296C2×C4—281no—
297C2×C4—281no—
298C2×C4—281no—
299C2×C4—281no—
300C2×C4—281no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4—281no—
306C2×C4D7×C4⋊C411yescharacteristic
307C2×C4#645611yescharacteristic
308C2×C4#645711yescharacteristic
309C2×C4#645911yescharacteristic
310C2×C4C4×C22⋊D711yescharacteristic
311C2×C4#650911yescharacteristic
312C8—42no—
313C8—282no—
314C8—282no—
315C7#891511yescharacteristic, complemented, Sylow
316C22#8976111yescharacteristic
317C22#8983311yescharacteristic
318C22#8983411yescharacteristic
319C22#8997311yescharacteristic
320C22#8997311yescharacteristic
321C22#8997411yescharacteristic
322C22#8997711yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—81no—
330C4—81no—
331C4—161no—
332C4—282no—
333C4—282no—
334C4—561no—
335C4—561no—
336C2#1172731611yescharacteristic
337C2#1172843111yescharacteristic
338C2#1172843511yescharacteristic
339C2#1172900011yescharacteristic
340C2#1172900111yescharacteristic
341C2#1172900411yescharacteristic
342C2#1172900711yescharacteristic
subgroupG/H
centerC23#6500
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1836C2
socle, prime radicalC23×C7#120
cosocleC2×C42×C7C23
hypercenter#1836D7
hypocenterC7#8915
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
315. C7#8915semidirect

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
#117273292
#117254652
#117254362
#89157