Finite Group Databasebeta

← #13264608

Subgroups — #13264608

Order 1792.

420 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 83 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#11739791C211yesmaximal, characteristic
2C7×#1465C211yesmaximal, characteristic
3#11729371C211yesmaximal, characteristic
4#11725265C212yesmaximal, complemented
5#11725264C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6489C411yescharacteristic
8C7×#407—21no—
9#89994—21no—
10C2×#6407—21no—
11C4×C22⋊Dic7—21no—
12C4×C22⋊Dic7C411yescharacteristic
13#89758C2211yescharacteristic
14#89755C2211yescharacteristic
15#89725C411yescharacteristic
16#89724—21no—
17#89721C411yescharacteristic
18C4×Dic7⋊C4—21no—
19#89696—21no—
20C7×#324C2212yes—
21C7×#323—21no—
22#89325C2212yes—
23#11830—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C2×C7×M16—41no—
28C4×C7×D4—41no—
29C4×C7×D4—41no—
30C2×C7×C4⋊C4C2311yescharacteristic
31C2×C7×C22⋊C4C2×C411yescharacteristic
32C2×C7×C22⋊C4D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C22⋊Dic7—21no—
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38#6489—41no—
39#6489—41no—
40C2×C4⋊Dic7C2×C411yescharacteristic
41C2×C4⋊Dic7C2×C411yescharacteristic
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×C4×Dic7—21no—
45C2×C4×Dic7—21no—
46C2×#1136—22no—
47C7×C22⋊C8—22no—
48C7×C22⋊C8—41no—
49#6407—42no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95C2×C411yescharacteristic
55C7⋊#95C2×C411yescharacteristic
56C4⋊(C7⋊C8)—41no—
57C4⋊(C7⋊C8)—41no—
58#2395—71no—
59#1800—71no—
60#1465D711yescharacteristic
61#1353—72no—
62#1346—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C22⋊C411yescharacteristic
65C2×C7×D4—21no—
66C2×C7×D4—21no—
67C2×C7×D4—41no—
68C2×C7×D4—41no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—42no—
74C22×C4×C7—42no—
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22×C411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—21no—
84C7×M16—82no—
85C2×C7×C8—42no—
86C7×C4⋊C4—41no—
87C7×C22⋊C4—41no—
88C7×C22⋊C4—41no—
89C42×C7—21no—
90C42×C7—21no—
91C22⋊Dic7—42no—
92C22⋊Dic7—42no—
93C22⋊Dic7—42no—
94C22⋊Dic7—42no—
95C4⋊Dic7—41no—
96C4⋊Dic7—41no—
97Dic7⋊C4—42no—
98Dic7⋊C4—41no—
99Dic7⋊C4—41no—
100C4×Dic7—42no—
101C4×Dic7—41no—
102C4×Dic7—41no—
103#1136—42no—
104#1136—42no—
105C2×C7⋊C8—42no—
106C2×C4×D4C2×D711yescharacteristic
107C2×#117—71no—
108#423—141no—
109C2×#100—141no—
110#407—21no—
111#400—71no—
112#399—71no—
113#398—71no—
114#397—71no—
115#397—141no—
116#394—141no—
117C4×C4⋊C4—141no—
118C4×C22⋊C4—71no—
119C4×C22⋊C4—141no—
120#343—72no—
121#324C2×D712yes—
122#323—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—41no—
130C23×C7—41no—
131C23×C7—41no—
132C23×C7—41no—
133C23×C7C2×C22⋊C411yescharacteristic
134C7×D4—42no—
135C7×D4—42no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—22no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—42no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7—81no—
149C2×C4×C7#9911yescharacteristic
150C2×C4×C7#9911yescharacteristic
151C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C7#13711yescharacteristic
153C2×Dic7—22no—
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—82no—
166C7⋊C8—82no—
167C22×D4D2811yescharacteristic
168C23×C4C4×D711yescharacteristic
169C23×C4C22⋊D711yescharacteristic
170C2×M16—41no—
171C2×M16—142no—
172C4×D4—41no—
173C4×D4—41no—
174#117—281no—
175#117—281no—
176C2×C4⋊C4—71no—
177C2×C4⋊C4—71no—
178C2×C4⋊C4—141no—
179C2×C4⋊C4—141no—
180C2×C4⋊C4C22×D711yescharacteristic
181C2×C22⋊C4—141no—
182C2×C22⋊C4—141no—
183C2×C22⋊C4—141no—
184C2×C22⋊C4—141no—
185C2×C22⋊C4C4×D711yescharacteristic
186C2×C22⋊C4C22⋊D711yescharacteristic
187C2×C42—141no—
188C2×C42—141no—
189C2×C42D2811yescharacteristic
190C4⋊C8—281no—
191C4⋊C8—281no—
192#100—282no—
193C22⋊C8—22no—
194C22⋊C8—41no—
195#95—71no—
196#95—71no—
197#95—141no—
198#95—141no—
199#95—141no—
200#95—141no—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—42no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7—41no—
207C22×C7—41no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7—81no—
211C22×C7—81no—
212C22×C7—81no—
213C22×C7C2×#9911yescharacteristic
214C22×C7#41711yescharacteristic
215C22×C7#42111yescharacteristic
216C4×C7—21no—
217C4×C7—21no—
218C4×C7—21no—
219C4×C7—41no—
220C4×C7—41no—
221C4×C7—41no—
222C4×C7#35212yes—
223Dic7—42no—
224Dic7—81no—
225Dic7—81no—
226Dic7—81no—
227C24(C2×D7)⋊C411yescharacteristic
228C24(C2×D7)⋊C411yescharacteristic
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—41no—
232C2×D4—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—141no—
240C22×C4—141no—
241C22×C4—141no—
242C22×C4—141no—
243C22×C4(C2×D7)⋊C411yescharacteristic
244C22×C4(C2×D7)⋊C411yescharacteristic
245C22×C4C2×C4×D711yescharacteristic
246C22×C4C2×D2811yescharacteristic
247C22×C4C2×C22⋊D711yescharacteristic
248M16—82no—
249M16—282no—
250M16—282no—
251C2×C8—42no—
252C2×C8—282no—
253C4⋊C4—41no—
254C4⋊C4—281no—
255C4⋊C4—281no—
256C4⋊C4—282no—
257C4⋊C4—281no—
258C4⋊C4—281no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—282no—
262C22⋊C4—282no—
263C22⋊C4—282no—
264C22⋊C4—282no—
265C42—21no—
266C42—21no—
267C42—282no—
268C42—281no—
269C42—281no—
270C2×C7—21no—
271C2×C7—21no—
272C2×C7—81no—
273C2×C7—81no—
274C2×C7#151311yescharacteristic
275C2×C7C2×#35211yescharacteristic
276C2×C7#213211yescharacteristic
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23C2×(C2×D7)⋊C411yescharacteristic
288D4—42no—
289D4—42no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—142no—
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×C4—281no—
313C2×C4—281no—
314C2×C4—281no—
315C2×C4#638011yescharacteristic
316C2×C4#638011yescharacteristic
317C2×C4#647111yescharacteristic
318C2×C4#647211yescharacteristic
319C8—82no—
320C8—562no—
321C7#1183011yescharacteristic, complemented, Sylow
322C22—21no—
323C22—21no—
324C22—42no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22C2×#638011yescharacteristic
335C22#8990511yescharacteristic
336C22#8991111yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—282no—
344C4—561no—
345C4—561no—
346C4—561no—
347C4#8926712yes—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—81no—
352C2#1172773311yescharacteristic
353C2C2×#8926711yescharacteristic
354C2#1172790211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1465C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C4⋊C4C23
hypercenter#1465D7
hypocenterC7#11830
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
4. #11725265C2semidirect
5. #11725264C2semidirect
321. C7#11830semidirect

Maximal subgroups

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

subgroupindex
#117397912
C7×#14652
#117293712
#117252652
#117252642
#118307