Finite Group Databasebeta

← #13252625

Subgroups — #13252625

Order 1792.

656 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic
2C2×#89323C214yesmaximal
3#11729284C211yesmaximal, characteristic
4C4×C22⋊(C7⋊C8)C211yesmaximal, characteristic
5C22×C7×C4⋊C4C411yescharacteristic
6C22×C7×C4⋊C4C411yescharacteristic
7C22×C7×C4⋊C4C2212yes—
8C22×C42×C7C2211yescharacteristic
9C7×#389—21no—
10C7×#389—21no—
11C7×#389—21no—
12C7×#389—21no—
13C2×C7×#95C412yes—
14C2×C22⋊(C7⋊C8)C2212yes—
15C2×C22⋊(C7⋊C8)C2212yes—
16C2×C4⋊(C7⋊C8)—21no—
17C2×C4×C7⋊C8—21no—
18#89323—28no—
19#89319—21no—
20#89319—21no—
21#9650—71nomaximal, Sylow
22C23×C4×C7C2×C412yes—
23C23×C4×C7C2×C411yescharacteristic
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7C2×C412yes—
26C23×C4×C7C2311yescharacteristic
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—22no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—22no—
33C2×C7×C4⋊C4—22no—
34C2×C7×C4⋊C4—24no—
35C2×C7×C4⋊C4—24no—
36C2×C7×C4⋊C4—42no—
37C2×C7×C4⋊C4C814yescomplemented
38C2×C42×C7—42no—
39C2×C42×C7D411yescharacteristic
40C2×C42×C7D411yescharacteristic
41C2×C42×C7D411yescharacteristic
42C2×C42×C7D411yescharacteristic
43C22×C7⋊C8—22no—
44C22×C7⋊C8—22no—
45C7×#95—22no—
46C7×#95—22no—
47C22⋊(C7⋊C8)—22no—
48C22⋊(C7⋊C8)—24no—
49C22⋊(C7⋊C8)D414yes—
50C4⋊(C7⋊C8)—42no—
51C4×C7⋊C8—42no—
52C2×#389D711yescharacteristic
53#1797—71no—
54C4×C22⋊C8—71no—
55C2×#324—74no—
56C24×C7C22×C411yescharacteristic
57C22×C4×C7—22no—
58C22×C4×C7—22no—
59C22×C4×C7—22no—
60C22×C4×C7—24no—
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7—24no—
64C22×C4×C7—22no—
65C22×C4×C7—22no—
66C22×C4×C7—24no—
67C22×C4×C7—41no—
68C22×C4×C7—41no—
69C22×C4×C7—41no—
70C22×C4×C7—42no—
71C22×C4×C7—42no—
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C2×C814yes—
77C22×C4×C7C2×C812yes—
78C22×C4×C7M1612yes—
79C22×C4×C7C2×D411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×C4×C7C2×D412yes—
82C22×C4×C7#4112yes—
83C7×C4⋊C4—24no—
84C7×C4⋊C4—24no—
85C7×C4⋊C4—42no—
86C7×C4⋊C4—42no—
87C7×C4⋊C4—44no—
88C7×C4⋊C4—42no—
89C7×C4⋊C4—42no—
90C42×C7—22no—
91C42×C7—22no—
92C42×C7—41no—
93C42×C7—41no—
94C2×C7⋊C8—24no—
95C2×C7⋊C8—42no—
96C2×C7⋊C8—42no—
97C2×C7⋊C8—42no—
98C2×C7⋊C8—42no—
99C2×C7⋊C8—42no—
100C22×C4⋊C4Dic711yescharacteristic
101C22×C4⋊C4Dic711yescharacteristic
102C22×C4⋊C4C2×D712yes—
103C22×C42C2×D711yescharacteristic
104C2×C4⋊C8—141no—
105C2×C22⋊C8—72no—
106C2×C22⋊C8—72no—
107C2×C4×C8—141no—
108#389—21no—
109#389—21no—
110#389—21no—
111#389—21no—
112C2×#95Dic712yes—
113#336—141no—
114#336—141no—
115#324—148no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7C2×C22⋊C411yescharacteristic
121C23×C7C4×D412yes—
122C23×C7C22×C811yescharacteristic
123C23×C7C2×M1611yescharacteristic
124C23×C7#13112yes—
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—24no—
134C2×C4×C7—24no—
135C2×C4×C7—24no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—28no—
140C2×C4×C7—42no—
141C2×C4×C7—42no—
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×C7C22⋊C812yes—
151C2×C4×C7C22⋊C812yes—
152C2×C4×C7#9912yes—
153C2×C4×C7#10112yes—
154C2×C4×C7#10112yes—
155C2×C4×C7#12112yes—
156C2×C4×C7#12411yescharacteristic
157C2×C4×C7#12711yescharacteristic
158C7⋊C8—44no—
159C7⋊C8—82no—
160C23×C4C2×Dic712yes—
161C23×C4C2×Dic711yescharacteristic
162C23×C4C2×Dic711yescharacteristic
163C23×C4C2×Dic712yes—
164C23×C4C22×D711yescharacteristic
165C22×C8—142no—
166C22×C8—142no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4C7⋊C814yescomplemented
178C2×C42—42no—
179C2×C42C22⋊D711yescharacteristic
180C2×C42C22⋊D711yescharacteristic
181C2×C42C22⋊D711yescharacteristic
182C2×C42C22⋊D711yescharacteristic
183C4⋊C8—282no—
184C22⋊C8—74no—
185C22⋊C8—142no—
186C22⋊C8—144no—
187C4×C8—282no—
188#95—22no—
189#95—22no—
190C22×C7—22no—
191C22×C7—22no—
192C22×C7—21no—
193C22×C7—21no—
194C22×C7—21no—
195C22×C7—21no—
196C22×C7—22no—
197C22×C7—22no—
198C22×C7#39011yescharacteristic
199C22×C7C2×C22⋊C811yescharacteristic
200C22×C7#40811yescharacteristic
201C22×C7C2×#9911yescharacteristic
202C22×C7#41011yescharacteristic
203C22×C7C2×#10111yescharacteristic
204C22×C7C2×#10111yescharacteristic
205C22×C7C8×D412yes—
206C22×C7#43612yes—
207C4×C7—22no—
208C4×C7—21no—
209C4×C7—21no—
210C4×C7—22no—
211C4×C7—22no—
212C4×C7—44no—
213C4×C7—41no—
214C4×C7—82no—
215C4×C7#32414yescomplemented
216C24C22×Dic711yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—24no—
221C22×C4—22no—
222C22×C4—24no—
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×C4C2×C7⋊C814yes—
233C22×C4C2×C7⋊C812yes—
234C22×C4#113612yes—
235C22×C4C22⋊Dic711yescharacteristic
236C22×C4C22⋊Dic711yescharacteristic
237C22×C4C22⋊Dic711yescharacteristic
238C22×C4C22⋊Dic711yescharacteristic
239C22×C4D4×D712yes—
240C22×C4#115912yes—
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—24no—
250C4⋊C4—24no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—44no—
255C4⋊C4—42no—
256C42—22no—
257C42—22no—
258C42—41no—
259C42—41no—
260C2×C7—22no—
261C2×C7—22no—
262C2×C7C2×#32411yescharacteristic
263C2×C7#146111yescharacteristic
264C2×C7#147011yescharacteristic
265C2×C7#147211yescharacteristic
266C2×C7#195411yescharacteristic
267C2×C7#196411yescharacteristic
268C2×C7#196611yescharacteristic
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23C22×C7⋊C811yescharacteristic
274C23C2×#113611yescharacteristic
275C23D4×Dic712yes—
276C23#651112yes—
277C23C2×C22⋊Dic711yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—28no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—44no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—84no—
303C2×C4C22⋊(C7⋊C8)12yes—
304C2×C4C22⋊(C7⋊C8)12yes—
305C2×C4#640812yes—
306C2×C4#641012yes—
307C2×C4#641012yes—
308C2×C4#649911yescharacteristic
309C2×C4#650112yes—
310C2×C4#650311yescharacteristic
311C8—284no—
312C8—562no—
313C7#965011yescharacteristic, complemented, Sylow
314C22—22no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22D4×C7⋊C812yes—
323C22#8978412yes—
324C22C2×C22⋊(C7⋊C8)11yescharacteristic
325C22C2×#640811yescharacteristic
326C22#8999311yescharacteristic
327C22C2×#641011yescharacteristic
328C22C2×#641011yescharacteristic
329C22#9000611yescharacteristic
330C22#9001211yescharacteristic
331C4—22no—
332C4—21no—
333C4—21no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—44no—
338C4—82no—
339C4#8932314yescomplemented
340C2—22no—
341C2—22no—
342C2C2×#8932311yescharacteristic
343C2#1172936811yescharacteristic
344C2#1172937811yescharacteristic
345C2#1172944011yescharacteristic
346C2#1172944511yescharacteristic
347C2#1172949111yescharacteristic
348C2#1172954311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic7
commutatorC23×C7C22×C8
FrattiniC23×C4C22×D7
FittingC2×C7×#389C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22×C4
cosocleC23×C4×C7C23
hypercenterC2×#389D7
hypocenterC7#9650
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
37. C2×C7×C4⋊C4C8semidirect
177. C2×C4⋊C4C7⋊C8semidirect
215. C4×C7#324semidirect
313. C7#9650semidirect
339. C4#89323semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×#893232
#117292842
C4×C22⋊(C7⋊C8)2
#96507