Finite Group Databasebeta

← #13358740

Subgroups — #13358740

Order 1792.

760 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#432C211yesmaximal, characteristic
2#11739494C211yesmaximal, characteristic
3C2×C4×#1136C211yesmaximal, characteristic
4#11728228C214yesmaximal, complemented
5#11727708C214yesmaximal
6#11727594C214yesmaximal, complemented
7C22×C42×C7C2211yescharacteristic
8C22×#1136C2212yes—
9C7×#432C412yes—
10C7×#432C412yes—
11C7×#432C412yes—
12C7×#432C412yes—
13C2×C7×C4⋊C8C2212yes—
14C2×C7×C22⋊C8C2212yes—
15C2×C7×#97C2212yes—
16#89979C2212yes—
17C2×#6393C2218yes—
18#89698—21no—
19#89698—21no—
20#89697—21no—
21#89697—21no—
22#89696C2212yes—
23C4×#1136—21no—
24C4×#1136—21no—
25C4×#1136C2212yes—
26C4×#1136C2212yes—
27C4×#1136C2212yes—
28C2×#6377—21no—
29C2×C4×C7⋊C8—21no—
30#89347C2218yes—
31#21371—71nomaximal, Sylow
32C23×C4×C7Q811yescharacteristic
33C23×C4×C7Q811yescharacteristic
34C23×C4×C7C2311yescharacteristic
35C22×C7×C8C2314yes—
36C2×C42×C7C2×C411yescharacteristic
37C2×C42×C7C2×C411yescharacteristic
38C2×C42×C7C2×C411yescharacteristic
39C2×C42×C7C2×C411yescharacteristic
40C2×C42×C7D411yescharacteristic
41C2×C42×C7D411yescharacteristic
42C2×C42×C7D411yescharacteristic
43C2×C42×C7D411yescharacteristic
44C2×C42×C7Q811yescharacteristic
45C2×C42×C7Q811yescharacteristic
46C2×C42×C7C2311yescharacteristic
47C2×C42×C7C2311yescharacteristic
48C2×#1136—22no—
49C2×#1136—28no—
50C2×#1136C2314yes—
51C2×#1136C2314yes—
52C22×C7⋊C8—22no—
53C7×C4⋊C8C2×C414yes—
54C7×C4⋊C8C2×C414yes—
55C7×C22⋊C8C2×C414yes—
56C7×C22⋊C8C2×C414yes—
57C7×#97C2×C414yes—
58C7×#97C2×C414yes—
59C22⋊(C7⋊C8)—22no—
60C22⋊(C7⋊C8)—22no—
61#6393—216no—
62C4⋊(C7⋊C8)—22no—
63C4⋊(C7⋊C8)—22no—
64#6377—22no—
65#6377—22no—
66#6377—22no—
67C4×C7⋊C8—22no—
68C4×C7⋊C8—22no—
69C4×C7⋊C8—22no—
70#2920—71no—
71C2×#432D711yescharacteristic
72C2×C4×M16—71no—
73#1950—74no—
74#1855—74no—
75#1778—74no—
76C24×C7C2×Q811yescharacteristic
77C22×C4×C7—24no—
78C22×C4×C7—42no—
79C22×C4×C7—42no—
80C22×C4×C7C4⋊C411yescharacteristic
81C22×C4×C7C4⋊C411yescharacteristic
82C22×C4×C7C4⋊C411yescharacteristic
83C22×C4×C7C4⋊C411yescharacteristic
84C22×C4×C7C4⋊C411yescharacteristic
85C22×C4×C7C4⋊C411yescharacteristic
86C22×C4×C7C4⋊C411yescharacteristic
87C22×C4×C7C4⋊C411yescharacteristic
88C22×C4×C7C22×C411yescharacteristic
89C22×C4×C7C22×C411yescharacteristic
90C22×C4×C7C2×D411yescharacteristic
91C22×C4×C7C2×D411yescharacteristic
92C22×C4×C7C2×Q811yescharacteristic
93C22×C4×C7C2×Q811yescharacteristic
94C22×C4×C7C2×Q811yescharacteristic
95C22×C4×C7C2×Q811yescharacteristic
96C22×C4×C7C2×Q811yescharacteristic
97C22×C4×C7C2411yescharacteristic
98C2×C7×C8—28no—
99C2×C7×C8C22×C418yes—
100C42×C7C4⋊C411yescharacteristic
101C42×C7C4⋊C411yescharacteristic
102C42×C7C4⋊C411yescharacteristic
103C42×C7C4⋊C411yescharacteristic
104C42×C7C4⋊C411yescharacteristic
105C42×C7C4⋊C411yescharacteristic
106C42×C7C4⋊C411yescharacteristic
107C42×C7C4⋊C411yescharacteristic
108C42×C7C22×C411yescharacteristic
109C42×C7C22×C411yescharacteristic
110C42×C7C22×C411yescharacteristic
111C42×C7C22×C411yescharacteristic
112C42×C7C2×D411yescharacteristic
113C42×C7C2×D411yescharacteristic
114C42×C7C2×D411yescharacteristic
115C42×C7C2×D411yescharacteristic
116#1136—28no—
117#1136—24no—
118#1136—28no—
119#1136#4118yes—
120C2×C7⋊C8—28no—
121C2×C7⋊C8—24no—
122C2×C7⋊C8—24no—
123C22×M16—72no—
124C22×C42C2×D711yescharacteristic
125#432—141no—
126#432—141no—
127#432Dic712yes—
128#432Dic712yes—
129#432Dic712yes—
130#432Dic712yes—
131#431—141no—
132#431—141no—
133C2×#108—78no—
134#423—72no—
135C2×C4⋊C8C2×D712yes—
136#407—72no—
137C2×C22⋊C8C2×D712yes—
138C4×M16—72no—
139C4×M16—72no—
140C4×M16—72no—
141C4×M16—141no—
142C4×M16—141no—
143C2×#97—141no—
144C2×#97C2×D712yes—
145C2×C4×C8—141no—
146#341—78no—
147C23×C7—22no—
148C23×C7—22no—
149C23×C7—41no—
150C23×C7C2×C4⋊C411yescharacteristic
151C23×C7C2×C4⋊C411yescharacteristic
152C23×C7C22×Q811yescharacteristic
153C2×C4×C7—22no—
154C2×C4×C7—22no—
155C2×C4×C7—22no—
156C2×C4×C7—22no—
157C2×C4×C7—22no—
158C2×C4×C7—22no—
159C2×C4×C7—22no—
160C2×C4×C7—22no—
161C2×C4×C7—22no—
162C2×C4×C7—22no—
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—41no—
170C2×C4×C7C2×C4⋊C411yescharacteristic
171C2×C4×C7C2×C4⋊C411yescharacteristic
172C2×C4×C7C2×C4⋊C411yescharacteristic
173C2×C4×C7C2×C4⋊C411yescharacteristic
174C2×C4×C7C2×C4⋊C411yescharacteristic
175C2×C4×C7C2×C4⋊C411yescharacteristic
176C2×C4×C7C2×C4⋊C411yescharacteristic
177C2×C4×C7C2×C4⋊C411yescharacteristic
178C2×C4×C7C2×C4⋊C411yescharacteristic
179C2×C4×C7C2×C4⋊C411yescharacteristic
180C2×C4×C7C23×C411yescharacteristic
181C2×C4×C7C22×D411yescharacteristic
182C2×C4×C7C2×#4114yes—
183C7×C8—28no—
184C7⋊C8—28no—
185C7⋊C8—44no—
186C23×C4Dic1411yescharacteristic
187C23×C4Dic1411yescharacteristic
188C23×C4C22×D711yescharacteristic
189C2×M16—74no—
190C2×M16—74no—
191C2×M16—148no—
192C2×M16—142no—
193C22×C8—142no—
194C22×C8C22×D714yes—
195C2×C42Dic1411yescharacteristic
196C2×C42Dic1411yescharacteristic
197C2×C42D2811yescharacteristic
198C2×C42D2811yescharacteristic
199C2×C42D2811yescharacteristic
200C2×C42D2811yescharacteristic
201C2×C42C2×Dic711yescharacteristic
202C2×C42C2×Dic711yescharacteristic
203C2×C42C2×Dic711yescharacteristic
204C2×C42C2×Dic711yescharacteristic
205C2×C42C22×D711yescharacteristic
206C2×C42C22×D711yescharacteristic
207#108—1416no—
208C4⋊C8—142no—
209C4⋊C8—142no—
210C4⋊C8C2×Dic714yes—
211C4⋊C8C2×Dic714yes—
212C22⋊C8—142no—
213C22⋊C8—142no—
214C22⋊C8C2×Dic714yes—
215C22⋊C8C2×Dic714yes—
216#97—142no—
217#97—142no—
218#97—142no—
219#97C2×Dic714yes—
220#97C2×Dic714yes—
221C4×C8—142no—
222C4×C8—142no—
223C4×C8—142no—
224C22×C7—21no—
225C22×C7—21no—
226C22×C7—21no—
227C22×C7—21no—
228C22×C7—21no—
229C22×C7—21no—
230C22×C7—21no—
231C22×C7—44no—
232C22×C7#43012yes—
233C22×C7C22×C4⋊C411yescharacteristic
234C22×C7#53312yes—
235C4×C7—21no—
236C4×C7—21no—
237C4×C7—21no—
238C4×C7—21no—
239C4×C7—21no—
240C4×C7—21no—
241C4×C7—21no—
242C4×C7—21no—
243C4×C7—21no—
244C4×C7#43012yes—
245C4×C7C4×#4112yes—
246C4×C7#52512yes—
247C24C2×Dic1411yescharacteristic
248C22×C4—24no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4C4⋊Dic711yescharacteristic
252C22×C4C4⋊Dic711yescharacteristic
253C22×C4C4⋊Dic711yescharacteristic
254C22×C4C4⋊Dic711yescharacteristic
255C22×C4C4⋊Dic711yescharacteristic
256C22×C4C4⋊Dic711yescharacteristic
257C22×C4C4⋊Dic711yescharacteristic
258C22×C4C4⋊Dic711yescharacteristic
259C22×C4C2×Dic1411yescharacteristic
260C22×C4C2×Dic1411yescharacteristic
261C22×C4C2×Dic1411yescharacteristic
262C22×C4C2×Dic1411yescharacteristic
263C22×C4C2×Dic1411yescharacteristic
264C22×C4C2×D2811yescharacteristic
265C22×C4C2×D2811yescharacteristic
266C22×C4C22×Dic711yescharacteristic
267C22×C4C22×Dic711yescharacteristic
268C22×C4C23×D711yescharacteristic
269M16—78no—
270M16—148no—
271M16—144no—
272M16—148no—
273C2×C8—28no—
274C2×C8—148no—
275C2×C8—144no—
276C2×C8—144no—
277C2×C8C22×Dic718yes—
278C42C4⋊Dic711yescharacteristic
279C42C4⋊Dic711yescharacteristic
280C42C4⋊Dic711yescharacteristic
281C42C4⋊Dic711yescharacteristic
282C42C4⋊Dic711yescharacteristic
283C42C4⋊Dic711yescharacteristic
284C42C4⋊Dic711yescharacteristic
285C42C4⋊Dic711yescharacteristic
286C42C2×D2811yescharacteristic
287C42C2×D2811yescharacteristic
288C42C2×D2811yescharacteristic
289C42C2×D2811yescharacteristic
290C42C22×Dic711yescharacteristic
291C42C22×Dic711yescharacteristic
292C42C22×Dic711yescharacteristic
293C42C22×Dic711yescharacteristic
294C2×C7—22no—
295C2×C7—22no—
296C2×C7—41no—
297C2×C7#229611yescharacteristic
298C2×C7C2×#43011yescharacteristic
299C2×C7C2×#43011yescharacteristic
300C23—22no—
301C23—22no—
302C23—41no—
303C23C2×C4⋊Dic711yescharacteristic
304C23C2×C4⋊Dic711yescharacteristic
305C23C22×Dic1411yescharacteristic
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4C2×C4⋊Dic711yescharacteristic
324C2×C4C2×C4⋊Dic711yescharacteristic
325C2×C4C2×C4⋊Dic711yescharacteristic
326C2×C4C2×C4⋊Dic711yescharacteristic
327C2×C4C2×C4⋊Dic711yescharacteristic
328C2×C4C2×C4⋊Dic711yescharacteristic
329C2×C4C2×C4⋊Dic711yescharacteristic
330C2×C4C2×C4⋊Dic711yescharacteristic
331C2×C4C2×C4⋊Dic711yescharacteristic
332C2×C4C2×C4⋊Dic711yescharacteristic
333C2×C4C22×D2811yescharacteristic
334C2×C4D7×#4114yes—
335C2×C4C23×Dic711yescharacteristic
336C8—28no—
337C8—148no—
338C8—284no—
339C7#2137111yescharacteristic, complemented, Sylow
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22#8989712yes—
349C22#9020812yes—
350C22C22×C4⋊Dic711yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4#8989712yes—
361C4#9021512yes—
362C4#41×Dic712yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2#1173967211yescharacteristic
367C2C2×#8989711yescharacteristic
368C2C2×#8989711yescharacteristic
subgroupG/H
centerC2×C4C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#432C2
socleC22×C7C22×C4⋊C4
prime radicalC24×C7C2×Q8
cosocleC22×C4×C7C24
hypercenterC2×#432D7
hypocenterC7#21371
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
4. #11728228C2semidirect
6. #11727594C2semidirect
339. C7#21371semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4322
#117394942
C2×C4×#11362
#117282282
#117277082
#117275942
#213717