Finite Group Databasebeta

← #13284848

Subgroups — #13284848

Order 1792.

1334 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6453C211yesmaximal, characteristic
2C2×#89422C211yesmaximal, characteristic
3C2×#89422C211yesmaximal, characteristic
4C7×#1445C211yesmaximal, characteristic
5#11729323C211yesmaximal, characteristic
6#11727177C211yesmaximal, characteristic
7#11727176C211yesmaximal, characteristic
8#11727165C214yesmaximal
9#11727163C214yesmaximal
10C22×C7×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic7C2212yes—
12C22×C4⋊Dic7C2211yescharacteristic
13C22×Dic7⋊C4C2212yes—
14C22×Dic7⋊C4C2212yes—
15C22×Dic7⋊C4C2212yes—
16C22×C4×Dic7C2211yescharacteristic
17C2×#6453—24no—
18C2×#6453—24no—
19C2×#6453C418yescomplemented
20C2×C7×#95C2211yescharacteristic
21C2×C7×#95C2211yescharacteristic
22C2×C7×#95C2214yes—
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2211yescharacteristic
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2214yes—
28C2×C7⋊#95C2214yes—
29C2×C7⋊#95C2214yes—
30#89422—24no—
31#89422—24no—
32#14664—71nomaximal, Sylow
33C23×C4×C7C2312yes—
34C23×C4×C7C2312yes—
35C23×C4×C7C2312yes—
36C23×C4×C7C2311yescharacteristic
37C23×Dic7C2312yes—
38C23×Dic7C2312yes—
39C23×Dic7C2312yes—
40C23×Dic7C2311yescharacteristic
41C23×Dic7C2311yescharacteristic
42C2×C7×C4⋊C4—22no—
43C2×C7×C4⋊C4—22no—
44C2×C7×C4⋊C4C2×C414yes—
45C2×C4⋊Dic7—22no—
46C2×C4⋊Dic7—22no—
47C2×C4⋊Dic7—24no—
48C2×C4⋊Dic7—24no—
49C2×C4⋊Dic7C2×C414yes—
50C2×C4⋊Dic7C2×C418yes—
51C2×Dic7⋊C4—24no—
52C2×Dic7⋊C4—24no—
53C2×Dic7⋊C4—24no—
54C2×Dic7⋊C4—24no—
55C2×Dic7⋊C4—44no—
56C2×Dic7⋊C4—44no—
57C2×Dic7⋊C4C2×C418yes—
58C2×C4×Dic7C2×C414yes—
59C2×C4×Dic7D414yes—
60C2×C4×Dic7D414yes—
61#6453—232no—
62C7×#95—22no—
63C7×#95—22no—
64C7×#95—44no—
65C7⋊#95—22no—
66C7⋊#95—22no—
67C7⋊#95—24no—
68C7⋊#95—24no—
69C7⋊#95—44no—
70C7⋊#95—44no—
71C7⋊#95—44no—
72C22×#125—71no—
73C2×#382—71no—
74C2×#382—71no—
75#1445—71no—
76#1445—71no—
77#1445—71no—
78#1445D711yescharacteristic
79#1441—74no—
80#1441—74no—
81C24×C7C2411yescharacteristic
82C22×C4×C7—24no—
83C22×C4×C7—22no—
84C22×C4×C7—22no—
85C22×C4×C7—24no—
86C22×C4×C7—24no—
87C22×C4×C7—22no—
88C22×C4×C7—22no—
89C22×C4×C7—22no—
90C22×C4×C7—24no—
91C22×C4×C7—22no—
92C22×C4×C7—24no—
93C22×C4×C7—24no—
94C22×C4×C7—24no—
95C22×C4×C7—22no—
96C22×C4×C7—22no—
97C22×C4×C7C22×C414yes—
98C22×C4×C7C22×C412yes—
99C22×C4×C7C2×D412yes—
100C22×C4×C7C2×D412yes—
101C22×Dic7—22no—
102C22×Dic7—22no—
103C22×Dic7—22no—
104C22×Dic7—22no—
105C22×Dic7—22no—
106C22×Dic7—22no—
107C22×Dic7—24no—
108C22×Dic7—24no—
109C22×Dic7—22no—
110C22×Dic7—22no—
111C22×Dic7—22no—
112C22×Dic7—22no—
113C22×Dic7—24no—
114C22×Dic7—24no—
115C22×Dic7—24no—
116C22×Dic7—24no—
117C22×Dic7—22no—
118C22×Dic7—22no—
119C22×Dic7C22×C414yes—
120C22×Dic7C22×C412yes—
121C22×Dic7C22×C412yes—
122C22×Dic7C2×D412yes—
123C22×Dic7C2×D412yes—
124C22×Dic7C2×D412yes—
125C22×Dic7C2×D412yes—
126C7×C4⋊C4—28no—
127C4⋊Dic7—28no—
128C4⋊Dic7—216no—
129Dic7⋊C4—216no—
130Dic7⋊C4—48no—
131Dic7⋊C4—48no—
132C4×Dic7C22⋊C4116yes—
133C2×#125—78no—
134C2×#125—144no—
135C2×#125—144no—
136C22×C4⋊C4—72no—
137C22×C4⋊C4—72no—
138C22×C4⋊C4—71no—
139C22×C4⋊C4—72no—
140C22×C4⋊C4—72no—
141C22×C4⋊C4C2×D711yescharacteristic
142C22×C42—71no—
143#382—144no—
144#382—144no—
145C2×#95—72no—
146C2×#95—72no—
147C2×#95—71no—
148C2×#95—71no—
149C2×#95—74no—
150C2×#95—74no—
151C2×#95—74no—
152C2×#95C2×D711yescharacteristic
153C2×#95C2×D711yescharacteristic
154C2×#95C2×D714yes—
155C23×C7C23×C411yescharacteristic
156C23×C7C22×D411yescharacteristic
157C23×C7C22×D411yescharacteristic
158C23×C7H(5,𝔽2)12yes—
159C23×C7H(5,𝔽2)12yes—
160C23×C72−1+412yes—
161C23×C72−1+414yes—
162C23×C72−1+412yes—
163C2×C4×C7—24no—
164C2×C4×C7—24no—
165C2×C4×C7—24no—
166C2×C4×C7—24no—
167C2×C4×C7—28no—
168C2×C4×C7—42no—
169C2×C4×C7—42no—
170C2×C4×C7—44no—
171C2×C4×C7—42no—
172C2×C4×C7—42no—
173C2×C4×C7—42no—
174C2×C4×C7—42no—
175C2×C4×C7—42no—
176C2×C4×C7—42no—
177C2×C4×C7—44no—
178C2×C4×C7—44no—
179C2×C4×C7—44no—
180C2×C4×C7—44no—
181C2×C4×C7C2×C22⋊C414yes—
182C2×Dic7—24no—
183C2×Dic7—24no—
184C2×Dic7—22no—
185C2×Dic7—22no—
186C2×Dic7—22no—
187C2×Dic7—22no—
188C2×Dic7—24no—
189C2×Dic7—24no—
190C2×Dic7—24no—
191C2×Dic7—28no—
192C2×Dic7—42no—
193C2×Dic7—42no—
194C2×Dic7—44no—
195C2×Dic7—42no—
196C2×Dic7—42no—
197C2×Dic7—42no—
198C2×Dic7—42no—
199C2×Dic7—42no—
200C2×Dic7—42no—
201C2×Dic7—44no—
202C2×Dic7—44no—
203C2×Dic7—44no—
204C2×Dic7—44no—
205C2×Dic7C2×C22⋊C414yes—
206C2×Dic7C2×C22⋊C414yes—
207C23×C4—71no—
208C23×C4—71no—
209C23×C4—72no—
210C23×C4—72no—
211C23×C4—72no—
212C23×C4C22×D712yes—
213C23×C4C22×D712yes—
214C23×C4C22×D712yes—
215C23×C4C22×D711yescharacteristic
216#125—1432no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—78no—
220C2×C4⋊C4—78no—
221C2×C4⋊C4—74no—
222C2×C4⋊C4—144no—
223C2×C4⋊C4—144no—
224C2×C4⋊C4—144no—
225C2×C4⋊C4—144no—
226C2×C4⋊C4—142no—
227C2×C4⋊C4—142no—
228C2×C4⋊C4—144no—
229C2×C4⋊C4—144no—
230C2×C4⋊C4—284no—
231C2×C4⋊C4—284no—
232C2×C4⋊C4C4×D714yes—
233C2×C42—74no—
234C2×C42—74no—
235C2×C42—74no—
236#95—22no—
237#95—22no—
238#95—44no—
239#95—144no—
240#95—144no—
241#95—142no—
242#95—142no—
243#95—284no—
244#95—284no—
245#95—284no—
246C22×C7C22×C22⋊C411yescharacteristic
247C22×C7#51912yes—
248C22×C7#52012yes—
249C22×C7#52012yes—
250C22×C7#53511yescharacteristic
251C22×C7#53511yescharacteristic
252C22×C7#53611yescharacteristic
253C22×C7#53612yes—
254C22×C7#53612yes—
255C22×C7#53611yescharacteristic
256C22×C7#53712yes—
257C22×C7#53712yes—
258C22×C7#56214yes—
259C22×C7#56314yes—
260C22×C7#56314yes—
261C22×C7#56414yes—
262C4×C7—24no—
263C4×C7—44no—
264C4×C7—82no—
265C4×C7—82no—
266Dic7—24no—
267Dic7—24no—
268Dic7—44no—
269Dic7—82no—
270Dic7—82no—
271C24C23×D711yescharacteristic
272C22×C4—24no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—72no—
288C22×C4—72no—
289C22×C4—72no—
290C22×C4—72no—
291C22×C4—72no—
292C22×C4—72no—
293C22×C4—74no—
294C22×C4—142no—
295C22×C4—142no—
296C22×C4—142no—
297C22×C4—142no—
298C22×C4—142no—
299C22×C4—142no—
300C22×C4—144no—
301C22×C4—144no—
302C22×C4—142no—
303C22×C4—142no—
304C22×C4—142no—
305C22×C4—144no—
306C22×C4—142no—
307C22×C4—142no—
308C22×C4—144no—
309C22×C4—142no—
310C22×C4—144no—
311C22×C4—144no—
312C22×C4C2×C4×D714yes—
313C22×C4C2×C4×D712yes—
314C22×C4D4×D712yes—
315C22×C4D4×D712yes—
316C4⋊C4—28no—
317C4⋊C4—1416no—
318C4⋊C4—1416no—
319C4⋊C4—148no—
320C4⋊C4—288no—
321C4⋊C4—288no—
322C42—716no—
323C2×C7#231011yescharacteristic
324C2×C7#231111yescharacteristic
325C2×C7#231111yescharacteristic
326C2×C7#238214yes—
327C2×C7#282012yes—
328C2×C7#282012yes—
329C2×C7#282212yes—
330C2×C7#282212yes—
331C23C22×C4×D711yescharacteristic
332C23C2×D4×D711yescharacteristic
333C23C2×D4×D711yescharacteristic
334C23#654812yes—
335C23#655112yes—
336C23#655312yes—
337C23#655412yes—
338C23#655414yes—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—28no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—74no—
358C2×C4—74no—
359C2×C4—142no—
360C2×C4—142no—
361C2×C4—144no—
362C2×C4—144no—
363C2×C4—144no—
364C2×C4—144no—
365C2×C4—142no—
366C2×C4—142no—
367C2×C4—144no—
368C2×C4—148no—
369C2×C4—282no—
370C2×C4—284no—
371C2×C4—282no—
372C2×C4—284no—
373C2×C4—282no—
374C2×C4—282no—
375C2×C4—282no—
376C2×C4—284no—
377C2×C4—282no—
378C2×C4—282no—
379C2×C4—284no—
380C2×C4—284no—
381C2×C4—282no—
382C2×C4D7×C22⋊C414yes—
383C7#1466411yescharacteristic, complemented, Sylow
384C22C2×D7×C22⋊C411yescharacteristic
385C22#9020712yes—
386C22#9023712yes—
387C22#9026512yes—
388C22#9029912yes—
389C22#9032012yes—
390C22#9033714yes—
391C22#9033912yes—
392C22#9033912yes—
393C22#9035814yes—
394C22#9036511yescharacteristic
395C22#9036611yescharacteristic
396C22C7⋊#56414yes—
397C22#9040314yes—
398C22#9040611yescharacteristic
399C22#9041511yescharacteristic
400C4—24no—
401C4—44no—
402C4—82no—
403C4—82no—
404C4—144no—
405C4—144no—
406C4—284no—
407C4—562no—
408C4—562no—
409C2#1173149811yescharacteristic
410C2#1173242314yes—
411C2#1173373911yescharacteristic
412C2#1173392711yescharacteristic
413C2#1173509212yes—
414C2#1173537112yes—
415C2#1173553612yes—
416C2#1173576312yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1445C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1445D7
hypocenterC7#14664
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
19. C2×#6453C4semidirect
383. C7#14664semidirect

Maximal subgroups

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

subgroupindex
C22×#64532
C2×#894222
C7×#14452
#117293232
#117271772
#117271762
#117271652
#117271632
#146647