Finite Group Databasebeta

← #13264438

Subgroups — #13264438

Order 1792.

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

normal subgroups only

This group has 444 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#11739830C211yesmaximal, characteristic
2C4×C7×#100C211yesmaximal, characteristic
3#11729356C211yesmaximal, characteristic
4#11725302C212yesmaximal, complemented
5#11725300C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6487C411yescharacteristic
8C2×C7×#100—21no—
9C4×C7×M16—21no—
10#89992—21no—
11#89982—21no—
12C2×C7⋊#95C411yescharacteristic
13#89979—21no—
14#89758C2211yescharacteristic
15#89751C2211yescharacteristic
16#89721C411yescharacteristic
17#89719C411yescharacteristic
18#89714—21no—
19#89705—21no—
20C7×#343C2212yes—
21#89323C2212yes—
22#89320—21no—
23#11793—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C23×Dic7—21no—
28C22×Dic14C2×C411yescharacteristic
29C2×C7×M16—22no—
30C4×C7×D4—41no—
31C4×C7×D4—41no—
32C2×C7×C4⋊C4C2311yescharacteristic
33C2×C7×C22⋊C4C2×C411yescharacteristic
34C2×C7×C22⋊C4D411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C4⋊Dic7C2×C411yescharacteristic
40#6487—41no—
41#6487—41no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C2×#1136—41no—
46C7×#100—24no—
47C7×#97—41no—
48C4×C7×C8—41no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95C2×C411yescharacteristic
55C7⋊#95C2×C411yescharacteristic
56C22⋊(C7⋊C8)—22no—
57C22⋊(C7⋊C8)—41no—
58#2564—71no—
59C4×#100D711yescharacteristic
60#1465—71no—
61#1354—72no—
62#1353—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C22⋊C411yescharacteristic
65C2×C7×D4—22no—
66C2×C7×D4—22no—
67C2×C7×D4—41no—
68C22×C4×C7—21no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—81no—
73C22×C4×C7—81no—
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22×C411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—42no—
84C22×Dic7—42no—
85C22×Dic7—81no—
86C2×Dic14—41no—
87C2×Dic14—81no—
88C7×M16—24no—
89C7×M16—42no—
90C2×C7×C8—42no—
91C7×C4⋊C4—41no—
92C7×C22⋊C4—41no—
93C7×C22⋊C4—41no—
94C42×C7—21no—
95C42×C7—21no—
96C22⋊Dic7—42no—
97C22⋊Dic7—42no—
98C22⋊Dic7—81no—
99C4⋊Dic7—41no—
100Dic7⋊C4—42no—
101Dic7⋊C4—41no—
102Dic7⋊C4—41no—
103Dic7⋊C4—81no—
104#1136—82no—
105C2×C7⋊C8—42no—
106C2×C22⋊Q8—71no—
107C2×C4×D4C2×D711yescharacteristic
108C2×#100—21no—
109#407—141no—
110C4×M16—21no—
111#400—71no—
112#399—71no—
113#395—71no—
114#393—71no—
115#387—141no—
116#386—141no—
117#385—141no—
118#380—141no—
119C2×#95—71no—
120#343C2×D712yes—
121#324—72no—
122#323—141no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—41no—
129C23×C7—41no—
130C23×C7—41no—
131C23×C7—41no—
132C23×C7#10412yes—
133C23×C7C2×C22⋊C411yescharacteristic
134C7×D4—44no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—41no—
141C2×C4×C7—42no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—81no—
146C2×C4×C7—81no—
147C2×C4×C7—81no—
148C2×C4×C7#9911yescharacteristic
149C2×C4×C7#9911yescharacteristic
150C2×C4×C7#13712yes—
151C2×Dic7—22no—
152C2×Dic7—41no—
153C2×Dic7—41no—
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—84no—
164Dic14—82no—
165C7×C8—44no—
166C7⋊C8—82no—
167C22×Q8—71no—
168C22×D4C22⋊D711yescharacteristic
169C23×C4—141no—
170C23×C4C4×D711yescharacteristic
171C23×C4D2811yescharacteristic
172C2×M16—22no—
173C2×M16—281no—
174C22⋊Q8—281no—
175C22⋊Q8—281no—
176C4×D4—41no—
177C4×D4—41no—
178C2×C4⋊C4—71no—
179C2×C4⋊C4—141no—
180C2×C4⋊C4—141no—
181C2×C4⋊C4—141no—
182C2×C4⋊C4C22×D711yescharacteristic
183C2×C22⋊C4—141no—
184C2×C22⋊C4—141no—
185C2×C22⋊C4—141no—
186C2×C22⋊C4C4×D711yescharacteristic
187C2×C22⋊C4D2811yescharacteristic
188C2×C42C22⋊D711yescharacteristic
189#100—24no—
190C22⋊C8—142no—
191C22⋊C8—281no—
192#97—41no—
193C4×C8—41no—
194#95—71no—
195#95—71no—
196#95—141no—
197#95—141no—
198#95—141no—
199#95—141no—
200#95—141no—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—22no—
204C22×C7—42no—
205C22×C7—42no—
206C22×C7—42no—
207C22×C7—41no—
208C22×C7—41no—
209C22×C7—41no—
210C22×C7—41no—
211C22×C7—41no—
212C22×C7—81no—
213C22×C7C2×#9911yescharacteristic
214C22×C7#41911yescharacteristic
215C22×C7C2×#10411yescharacteristic
216C4×C7—21no—
217C4×C7—21no—
218C4×C7—22no—
219C4×C7—41no—
220C4×C7—41no—
221C4×C7—41no—
222Dic7—42no—
223Dic7—81no—
224Dic7—81no—
225Dic7—81no—
226C24(C2×D7)⋊C411yescharacteristic
227C24(C2×D7)⋊C411yescharacteristic
228C2×Q8—281no—
229C2×Q8—561no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4—141no—
240C22×C4—141no—
241C22×C4—141no—
242C22×C4—141no—
243C22×C4—282no—
244C22×C4—282no—
245C22×C4—561no—
246C22×C4(C2×D7)⋊C411yescharacteristic
247C22×C4(C2×D7)⋊C411yescharacteristic
248C22×C4C2×C4×D711yescharacteristic
249C22×C4C2×D2811yescharacteristic
250C22×C4C2×C22⋊D711yescharacteristic
251M16—24no—
252M16—42no—
253M16—562no—
254C2×C8—42no—
255C2×C8—282no—
256C4⋊C4—41no—
257C4⋊C4—281no—
258C4⋊C4—282no—
259C4⋊C4—281no—
260C4⋊C4—281no—
261C4⋊C4—561no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—282no—
265C22⋊C4—282no—
266C22⋊C4—561no—
267C42—21no—
268C42—21no—
269C2×C7—21no—
270C2×C7—21no—
271C2×C7—42no—
272C2×C7—81no—
273C2×C7#150811yescharacteristic
274C2×C7#212111yescharacteristic
275C2×C7#213211yescharacteristic
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23#637912yes—
286C23C2×(C2×D7)⋊C411yescharacteristic
287Q8—562no—
288D4—44no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—142no—
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×C4—281no—
313C2×C4—281no—
314C2×C4—564no—
315C2×C4#638011yescharacteristic
316C2×C4#638011yescharacteristic
317C2×C4#651412yes—
318C8—44no—
319C8—562no—
320C7#1179311yescharacteristic, complemented, Sylow
321C22—21no—
322C22—21no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22C2×#637911yescharacteristic
334C22C2×#638011yescharacteristic
335C22#8977611yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—282no—
343C4—561no—
344C4—561no—
345C4—561no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2#1172719911yescharacteristic
351C2#1172784811yescharacteristic
352C2#1172790211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC4×C7×#100C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C4⋊C4C23
hypercenterC4×#100D7
hypocenterC7#11793
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
4. #11725302C2semidirect
5. #11725300C2semidirect
320. C7#11793semidirect

Maximal subgroups

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

subgroupindex
#117398302
C4×C7×#1002
#117293562
#117253022
#117253002
#117937