Finite Group Databasebeta

← #13264292

Subgroups — #13264292

Order 1792.

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

normal subgroups only

This group has 484 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
1C7×#2598C211yesmaximal, characteristic
2#11729341C211yesmaximal, characteristic, complemented
3#11729326C211yesmaximal, characteristic, complemented
4#11725458C212yesmaximal, complemented
5#11725453C212yesmaximal, complemented
6C2×C4×C7×D4C411yescharacteristic
7C2×C7×#117C2211yescharacteristic
8C22×#1136—21no—
9C7×#400C2211yescharacteristic
10C7×#399C411yescharacteristic
11C7×#394C2211yescharacteristic
12C7×#392C411yescharacteristic
13C7×#388—21no—
14C7×#386—21no—
15C7×#386—21no—
16C7×#385—21no—
17C7×#383C411yescharacteristic
18#89698—21no—
19#89325—21no—
20#89325C2212yes—
21#89323C2212yes—
22#89320—21no—
23#11761—71nomaximal, Sylow
24C22×C7×D4—21no—
25C22×C7×D4C2×C411yescharacteristic
26C23×C4×C7—21no—
27C23×C4×C7D411yescharacteristic
28C4×C7×D4—41no—
29C4×C7×D4—41no—
30C7×#117—41no—
31C7×#117—41no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4C2×C411yescharacteristic
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C7×C4⋊C4C2311yescharacteristic
36C2×C7×C22⋊C4—21no—
37C2×C7×C22⋊C4—21no—
38C2×C7×C22⋊C4—21no—
39C2×C7×C22⋊C4—21no—
40C2×C7×C22⋊C4—21no—
41C2×C7×C22⋊C4C2×C411yescharacteristic
42C2×C7×C22⋊C4D411yescharacteristic
43C2×C42×C7C2×C411yescharacteristic
44C2×C42×C7D411yescharacteristic
45C2×#1136—24no—
46C2×#1136—22no—
47C2×#1136—41no—
48C2×#1136—42no—
49C22×C7⋊C8—41no—
50C7×#95—21no—
51C7×#95—21no—
52C7×#95—21no—
53C7×#95—21no—
54C7×#95C2×C411yescharacteristic
55C7×#95C2×C411yescharacteristic
56C22⋊(C7⋊C8)—22no—
57C4⋊(C7⋊C8)—41no—
58#6377—41no—
59#2598D711yescharacteristic
60#1742—71no—
61#1464—71no—
62#1353—72no—
63#1345—72no—
64C24×C7—21no—
65C24×C7C22⋊C411yescharacteristic
66C2×C7×D4—41no—
67C2×C7×D4—42no—
68C2×C7×D4—42no—
69C2×C7×D4—42no—
70C2×C7×D4—81no—
71C22×C4×C7—22no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—21no—
78C22×C4×C7—21no—
79C22×C4×C7—42no—
80C22×C4×C7—81no—
81C22×C4×C7—81no—
82C22×C4×C7C22⋊C411yescharacteristic
83C22×C4×C7C22⋊C411yescharacteristic
84C22×C4×C7C22⋊C411yescharacteristic
85C22×C4×C7C22×C411yescharacteristic
86C22×C4×C7C2×D411yescharacteristic
87C22×C4×C7C2×D411yescharacteristic
88C7×C4⋊C4—41no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—41no—
91C7×C4⋊C4—81no—
92C7×C22⋊C4—41no—
93C7×C22⋊C4—41no—
94C7×C22⋊C4—42no—
95C7×C22⋊C4—41no—
96C7×C22⋊C4—41no—
97C7×C22⋊C4—41no—
98C7×C22⋊C4—41no—
99C7×C22⋊C4—81no—
100C7×C22⋊C4—81no—
101C42×C7—21no—
102C42×C7—21no—
103C42×C7—21no—
104C42×C7—21no—
105#1136—24no—
106#1136—44no—
107#1136—42no—
108C2×C7⋊C8—44no—
109C2×C7⋊C8—42no—
110C2×C7⋊C8—42no—
111C22×M16—141no—
112C2×C4×D4Dic711yescharacteristic
113C2×#117C2×D711yescharacteristic
114#432—141no—
115#400C2×D711yescharacteristic
116#399Dic711yescharacteristic
117#394C2×D711yescharacteristic
118#392Dic711yescharacteristic
119#388—21no—
120#386—21no—
121#386—21no—
122#385—21no—
123#383Dic711yescharacteristic
124#343—72no—
125#343—141no—
126#324—72no—
127#323—141no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7—22no—
131C23×C7—41no—
132C23×C7—41no—
133C23×C7—41no—
134C23×C7—41no—
135C23×C7—41no—
136C23×C7—41no—
137C23×C7—41no—
138C23×C7—41no—
139C23×C7#10412yes—
140C23×C7C2×C22⋊C411yescharacteristic
141C7×D4—42no—
142C7×D4—42no—
143C7×D4—84no—
144C2×C4×C7—22no—
145C2×C4×C7—22no—
146C2×C4×C7—22no—
147C2×C4×C7—22no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—21no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7—41no—
161C2×C4×C7—41no—
162C2×C4×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—41no—
165C2×C4×C7—41no—
166C2×C4×C7—41no—
167C2×C4×C7—41no—
168C2×C4×C7—41no—
169C2×C4×C7—84no—
170C2×C4×C7#9911yescharacteristic
171C2×C4×C7#9911yescharacteristic
172C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C7#13711yescharacteristic
174C7⋊C8—44no—
175C7⋊C8—82no—
176C22×D4—21no—
177C22×D4C2×Dic711yescharacteristic
178C23×C4—21no—
179C23×C4C22⋊D711yescharacteristic
180C2×M16—144no—
181C2×M16—142no—
182C2×M16—281no—
183C2×M16—282no—
184C22×C8—281no—
185C4×D4—41no—
186C4×D4—41no—
187#117—41no—
188#117—41no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×Dic711yescharacteristic
191C2×C4⋊C4C22⋊D711yescharacteristic
192C2×C4⋊C4C22×D711yescharacteristic
193C2×C22⋊C4—21no—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4C2×Dic711yescharacteristic
199C2×C22⋊C4C22⋊D711yescharacteristic
200C2×C42C2×Dic711yescharacteristic
201C2×C42C22⋊D711yescharacteristic
202C4⋊C8—281no—
203C22⋊C8—142no—
204#97—281no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95C2×Dic711yescharacteristic
210#95C2×Dic711yescharacteristic
211C22×C7—21no—
212C22×C7—21no—
213C22×C7—22no—
214C22×C7—42no—
215C22×C7—42no—
216C22×C7—42no—
217C22×C7—41no—
218C22×C7—41no—
219C22×C7—42no—
220C22×C7—81no—
221C22×C7—81no—
222C22×C7—81no—
223C22×C7—81no—
224C22×C7—81no—
225C22×C7C2×#9911yescharacteristic
226C22×C7#41711yescharacteristic
227C22×C7C2×#10411yescharacteristic
228C4×C7—21no—
229C4×C7—21no—
230C4×C7—21no—
231C4×C7—21no—
232C4×C7—41no—
233C4×C7—41no—
234C4×C7—41no—
235C4×C7—41no—
236C4×C7—81no—
237C4×C7—81no—
238C4×C7—81no—
239C24—21no—
240C24C22⋊Dic711yescharacteristic
241C2×D4—41no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—81no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4C22⋊Dic711yescharacteristic
258C22×C4C22⋊Dic711yescharacteristic
259C22×C4C22⋊Dic711yescharacteristic
260C22×C4C22×Dic711yescharacteristic
261C22×C4C2×C22⋊D711yescharacteristic
262C22×C4C2×C22⋊D711yescharacteristic
263M16—144no—
264M16—284no—
265M16—282no—
266C2×C8—284no—
267C2×C8—282no—
268C2×C8—282no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—81no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C42—21no—
283C42—21no—
284C42—21no—
285C42—21no—
286C2×C7—21no—
287C2×C7—21no—
288C2×C7—42no—
289C2×C7—82no—
290C2×C7#150411yescharacteristic
291C2×C7#212011yescharacteristic
292C2×C7#213411yescharacteristic
293C23—21no—
294C23—21no—
295C23—22no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23#641112yes—
305C23C2×C22⋊Dic711yescharacteristic
306D4—42no—
307D4—42no—
308D4—84no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—84no—
335C2×C4#640811yescharacteristic
336C2×C4#640811yescharacteristic
337C2×C4#651211yescharacteristic
338C2×C4#651411yescharacteristic
339C8—284no—
340C8—562no—
341C7#1176111yescharacteristic, complemented, Sylow
342C22—21no—
343C22—21no—
344C22—22no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—41no—
349C22—41no—
350C22—42no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C2×#640811yescharacteristic
357C22#9000411yescharacteristic
358C22C2×#641111yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—81no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—82no—
374C2#1172946211yescharacteristic
375C2#1172947011yescharacteristic
376C2#1172961611yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2598C2
socleC22×C7C2×#99
prime radicalC7×#392C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2598D7
hypocenterC7#11761
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2598

Complements

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

NH ≅ G/Ntype
2. #11729341C2semidirect
3. #11729326C2semidirect
4. #11725458C2semidirect
5. #11725453C2semidirect
341. C7#11761semidirect

Maximal subgroups

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

subgroupindex
C7×#25982
#117293412
#117293262
#117254582
#117254532
#117617