Finite Group Databasebeta

← #13253854

Subgroups — #13253854

Order 1792.

664 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#391C211yesmaximal, characteristic
2#11729284C211yesmaximal, characteristic
3#11729283C211yesmaximal, characteristic
4#11725419C214yesmaximal
5C23×C7×Q8C411yescharacteristic
6C22×C7×C4⋊C4C411yescharacteristic
7C22×C42×C7C2211yescharacteristic
8C7×#391—21no—
9C7×#391—21no—
10C7×#391—21no—
11C7×#391—21no—
12C2×C7×#95C412yes—
13C2×C7×#95C2212yes—
14C2×C22⋊(C7⋊C8)C2212yes—
15C2×C22⋊(C7⋊C8)C2212yes—
16C2×C4⋊(C7⋊C8)—21no—
17C2×#6377—21no—
18#89319—21no—
19#89319—21no—
20#9882—71nomaximal, Sylow
21C22×C7×Q8—21no—
22C22×C7×Q8—21no—
23C22×C7×Q8—24no—
24C22×C7×Q8—42no—
25C22×C7×Q8—42no—
26C23×C4×C7C2×C411yescharacteristic
27C23×C4×C7C2×C411yescharacteristic
28C23×C4×C7C2×C412yes—
29C23×C4×C7C2×C412yes—
30C23×C4×C7C2311yescharacteristic
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—42no—
34C2×C42×C7—42no—
35C2×C42×C7D411yescharacteristic
36C2×C42×C7D411yescharacteristic
37C2×C42×C7D411yescharacteristic
38C2×C42×C7D411yescharacteristic
39C22×C7⋊C8—22no—
40C22×C7⋊C8—22no—
41C7×#95—22no—
42C7×#95—22no—
43C7×#95—22no—
44C7×#95—22no—
45C22⋊(C7⋊C8)—22no—
46C22⋊(C7⋊C8)—24no—
47C22⋊(C7⋊C8)Q814yescomplemented
48C4⋊(C7⋊C8)—42no—
49#6377—42no—
50C2×#391D711yescharacteristic
51#1797—71no—
52#1749—71no—
53#1280—74no—
54C24×C7C22×C411yescharacteristic
55C2×C7×Q8—24no—
56C2×C7×Q8—24no—
57C2×C7×Q8—416no—
58C2×C7×Q8—42no—
59C2×C7×Q8—42no—
60C2×C7×Q8—42no—
61C2×C7×Q8—42no—
62C22×C4×C7—22no—
63C22×C4×C7—22no—
64C22×C4×C7—22no—
65C22×C4×C7—22no—
66C22×C4×C7—22no—
67C22×C4×C7—22no—
68C22×C4×C7—22no—
69C22×C4×C7—22no—
70C22×C4×C7—24no—
71C22×C4×C7—41no—
72C22×C4×C7—41no—
73C22×C4×C7—41no—
74C22×C4×C7—42no—
75C22×C4×C7—42no—
76C22×C4×C7—42no—
77C22×C4×C7—42no—
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7M1614yes—
83C22×C4×C7C2×D411yescharacteristic
84C22×C4×C7C2×D411yescharacteristic
85C22×C4×C7C2×Q812yes—
86C22×C4×C7#4112yes—
87C7×C4⋊C4—42no—
88C7×C4⋊C4—42no—
89C42×C7—22no—
90C42×C7—22no—
91C42×C7—41no—
92C42×C7—41no—
93C2×C7⋊C8—24no—
94C2×C7⋊C8—42no—
95C2×C7⋊C8—42no—
96C2×C7⋊C8—42no—
97C2×C7⋊C8—42no—
98C2×C7⋊C8—42no—
99C23×Q8Dic711yescharacteristic
100C22×C4⋊C4Dic711yescharacteristic
101C22×C42C2×D711yescharacteristic
102C2×C4⋊C8—141no—
103C2×C22⋊C8—72no—
104C2×C22⋊C8—72no—
105C2×#97—141no—
106#391—21no—
107#391—21no—
108#391—21no—
109#391—21no—
110C2×#95Dic712yes—
111C2×#95C2×D712yes—
112#336—141no—
113#336—141no—
114C23×C7—21no—
115C23×C7—21no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7C2×C22⋊C411yescharacteristic
119C23×C7C4×Q812yes—
120C23×C7C2×M1612yes—
121C23×C7#13112yes—
122C7×Q8—48no—
123C7×Q8—48no—
124C2×C4×C7—28no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—24no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—42no—
140C2×C4×C7—42no—
141C2×C4×C7—44no—
142C2×C4×C7—44no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7—44no—
146C2×C4×C7—42no—
147C2×C4×C7—42no—
148C2×C4×C7—42no—
149C2×C4×C7—84no—
150C2×C4×C7#9912yes—
151C2×C4×C7#10012yes—
152C2×C4×C7#10112yes—
153C2×C4×C7C22⋊Q812yes—
154C2×C4×C7#12411yescharacteristic
155C2×C4×C7C4⋊Q811yescharacteristic
156C7⋊C8—44no—
157C7⋊C8—82no—
158C22×Q8—24no—
159C22×Q8—21no—
160C22×Q8—21no—
161C22×Q8—42no—
162C22×Q8—42no—
163C23×C4C2×Dic711yescharacteristic
164C23×C4C2×Dic711yescharacteristic
165C23×C4C2×Dic712yes—
166C23×C4C2×Dic712yes—
167C23×C4C22×D711yescharacteristic
168C22×C8—142no—
169C22×C8—142no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—42no—
173C2×C42—42no—
174C2×C42C22⋊D711yescharacteristic
175C2×C42C22⋊D711yescharacteristic
176C2×C42C22⋊D711yescharacteristic
177C2×C42C22⋊D711yescharacteristic
178C4⋊C8—282no—
179C22⋊C8—74no—
180C22⋊C8—142no—
181C22⋊C8—144no—
182#97—282no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—22no—
187C22×C7—22no—
188C22×C7—22no—
189C22×C7—22no—
190C22×C7—22no—
191C22×C7—22no—
192C22×C7—22no—
193C22×C7#39111yescharacteristic
194C22×C7#40711yescharacteristic
195C22×C7#40811yescharacteristic
196C22×C7C2×#9911yescharacteristic
197C22×C7#41011yescharacteristic
198C22×C7C2×#10011yescharacteristic
199C22×C7C2×#10111yescharacteristic
200C22×C7#44614yes—
201C4×C7—22no—
202C4×C7—22no—
203C4×C7—22no—
204C4×C7—22no—
205C4×C7—21no—
206C4×C7—21no—
207C4×C7—44no—
208C4×C7—41no—
209C4×C7—82no—
210C24C22×Dic711yescharacteristic
211C2×Q8—24no—
212C2×Q8—24no—
213C2×Q8—416no—
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—42no—
217C2×Q8—42no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—24no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4#113614yes—
235C22×C4C22⋊Dic711yescharacteristic
236C22×C4C22⋊Dic711yescharacteristic
237C22×C4C22⋊Dic711yescharacteristic
238C22×C4C22⋊Dic711yescharacteristic
239C22×C4Q8×D712yes—
240C22×C4#116112yes—
241C22×C4C2×C22⋊D711yescharacteristic
242C22×C4C2×C22⋊D711yescharacteristic
243C2×C8—144no—
244C2×C8—282no—
245C2×C8—282no—
246C2×C8—282no—
247C2×C8—282no—
248C2×C8—282no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C42—22no—
252C42—22no—
253C42—41no—
254C42—41no—
255C2×C7—24no—
256C2×C7#146211yescharacteristic
257C2×C7#146711yescharacteristic
258C2×C7#146911yescharacteristic
259C2×C7#147211yescharacteristic
260C2×C7#198511yescharacteristic
261C2×C7#199611yescharacteristic
262C2×C7#199711yescharacteristic
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23C2×#113612yes—
268C23Q8×Dic712yes—
269C23#651112yes—
270C23C2×C22⋊Dic711yescharacteristic
271Q8—48no—
272Q8—48no—
273C2×C4—28no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—84no—
299C2×C4#640712yes—
300C2×C4#640812yes—
301C2×C4#641012yes—
302C2×C4#650711yescharacteristic
303C2×C4#650912yes—
304C2×C4#651011yescharacteristic
305C8—284no—
306C8—562no—
307C7#988211yescharacteristic, complemented, Sylow
308C22—22no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22#8979614yes—
315C22#8997911yescharacteristic
316C22C2×#640711yescharacteristic
317C22C2×#640811yescharacteristic
318C22C2×#641011yescharacteristic
319C22#9000211yescharacteristic
320C22#9000611yescharacteristic
321C22#9001211yescharacteristic
322C4—22no—
323C4—22no—
324C4—21no—
325C4—21no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—44no—
330C4—82no—
331C2—24no—
332C2#1172929311yescharacteristic
333C2#1172937911yescharacteristic
334C2#1172938911yescharacteristic
335C2#1172944511yescharacteristic
336C2#1172945511yescharacteristic
337C2#1172947411yescharacteristic
338C2#1172954411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutator, prime radicalC24×C7C22×C4
FrattiniC23×C4C22×D7
FittingC2×C7×#391C2
socleC23×C7C2×C22⋊C4
cosocleC23×C4×C7C23
hypercenterC2×#391D7
hypocenterC7#9882
LCSG ▷ C24×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
47. C22⋊(C7⋊C8)Q8semidirect
307. C7#9882semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3912
#117292842
#117292832
#117254192
#98827