Finite Group Databasebeta

← #13390084

Subgroups — #13390084

Order 1792.

930 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742871C211yesmaximal, characteristic
2C7×#2327C211yesmaximal, characteristic
3#11739876C212yesmaximal
4#11729538C212yesmaximal
5#11729391C211yesmaximal, characteristic
6#11727427C212yesmaximal
7#11727426C212yesmaximal
8#11727297C212yesmaximal
9#11727195C212yesmaximal
10C2×C7×C4⋊Q8C2211yescharacteristic
11C2×C4×C7×Q8C2211yescharacteristic
12C2×C4×C7×Q8C2211yescharacteristic
13#90503C2212yes—
14#90261—22no—
15#90260—24no—
16Q8×Dic14—22no—
17#90191—22no—
18#90191C2212yes—
19#90161—22no—
20#90161C2212yes—
21C7×#391C2211yescharacteristic
22C7×#391C2211yescharacteristic
23C7×#387—22no—
24C7×#387—22no—
25C7×#382C2211yescharacteristic
26C7×#376C2211yescharacteristic
27C2×#6410C2212yes—
28#89997C2214yes—
29#89794—24no—
30#89793—22no—
31#89792—22no—
32#89736C2214yes—
33#89696C2212yes—
34#89325C2212yes—
35#89318C2214yes—
36#89318C2214yes—
37#24319—71nomaximal, Sylow
38C22×C7×Q8C2311yescharacteristic
39C22×C7×Q8C2311yescharacteristic
40C7×C4⋊Q8—22no—
41C7×C4⋊Q8Q814yescomplemented
42C4×C7×Q8—22no—
43C4×C7×Q8—22no—
44C4×C7×Q8—22no—
45C4×C7×Q8—22no—
46C2×C7×C4⋊C4—22no—
47C2×C7×C4⋊C4—21no—
48C2×C7×C4⋊C4D412yes—
49C2×C7×C4⋊C4C2311yescharacteristic
50C2×C7×C4⋊C4C2311yescharacteristic
51C2×C42×C7—21no—
52C2×C42×C7D412yes—
53C2×C42×C7C2311yescharacteristic
54C2×C42×C7C2311yescharacteristic
55C2×C42×C7C2311yescharacteristic
56Q8×Dic7—24no—
57Q8×Dic7—24no—
58#6489—24no—
59#6489C2314yes—
60#6487—22no—
61#6487—24no—
62#6487—22no—
63C2×#1136C2314yes—
64#6453—28no—
65#6453—24no—
66#6451—28no—
67#6451—24no—
68#6433—24no—
69#6433D414yes—
70#6432—22no—
71#6432—22no—
72#6432D412yes—
73#6432D412yes—
74C4×Dic14—24no—
75C4×Dic14—24no—
76C4×Dic14—22no—
77C4×Dic14—22no—
78C7×#95—21no—
79C7×#95—21no—
80C7×#95—22no—
81C7×#95—22no—
82C7×#95—22no—
83#6410—24no—
84#6409—24no—
85#6409—24no—
86#6382—24no—
87#6381—24no—
88C4⋊(C7⋊C8)—22no—
89C4⋊(C7⋊C8)—22no—
90#3502—71no—
91#3078—72no—
92#2327D711yescharacteristic
93#2061—72no—
94#2028—72no—
95#1995—72no—
96#1886—72no—
97#1857—72no—
98#1801—71no—
99C2×C7×Q8—22no—
100C2×C7×Q8—21no—
101C2×C7×Q8—22no—
102C2×C7×Q8—22no—
103C2×C7×Q8—22no—
104C2×C7×Q8C2×Q812yes—
105C2×C7×Q8C2×Q812yes—
106C2×C7×Q8#4112yes—
107C22×C4×C7—21no—
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7C2×D412yes—
112C22×C4×C7C2×D412yes—
113C22×C4×C7C2×D411yescharacteristic
114C22×C4×C7C2×D411yescharacteristic
115C22×C4×C7C2411yescharacteristic
116C2×Dic14—22no—
117C2×Dic14—24no—
118C2×Dic14—22no—
119C7×C4⋊C4—24no—
120C7×C4⋊C4—28no—
121C7×C4⋊C4—22no—
122C7×C4⋊C4—22no—
123C7×C4⋊C4—41no—
124C7×C4⋊C4—41no—
125C42×C7—22no—
126C42×C7—22no—
127C42×C7—21no—
128C42×C7—22no—
129C42×C7—42no—
130C42×C7C2×D412yes—
131C42×C7C2×D412yes—
132C42×C7C2×Q812yes—
133C22⋊Dic7—24no—
134C4⋊Dic7—24no—
135C4⋊Dic7—24no—
136C4⋊Dic7—24no—
137C4⋊Dic7—22no—
138C4⋊Dic7—22no—
139C4⋊Dic7C2×D414yes—
140C4⋊Dic7C2×D414yes—
141Dic7⋊C4—28no—
142Dic7⋊C4—24no—
143Dic7⋊C4—24no—
144C4×Dic7—28no—
145C4×Dic7—24no—
146#1136—24no—
147#1136—24no—
148C2×C7⋊C8—24no—
149Q82—142no—
150#557—144no—
151#557—142no—
152#544—72no—
153#544—142no—
154#533—72no—
155#533—142no—
156C2×C4⋊Q8C2×D711yescharacteristic
157#519—72no—
158C2×C4×Q8C2×D711yescharacteristic
159C2×C4×Q8C2×D711yescharacteristic
160#479—144no—
161#477—142no—
162#475—142no—
163#428—74no—
164#423—72no—
165#419—74no—
166C2×#101—72no—
167#391C2×D711yescharacteristic
168#391C2×D711yescharacteristic
169#387—22no—
170#387—22no—
171#382C2×D711yescharacteristic
172#376C2×D711yescharacteristic
173#343—72no—
174#339—74no—
175#339—74no—
176C23×C7C22×D411yescharacteristic
177C7×Q8—24no—
178C7×Q8—24no—
179C7×Q8—24no—
180C7×Q8—42no—
181C2×C4×C7—22no—
182C2×C4×C7—22no—
183C2×C4×C7—22no—
184C2×C4×C7—22no—
185C2×C4×C7—22no—
186C2×C4×C7—41no—
187C2×C4×C7—41no—
188C2×C4×C7—41no—
189C2×C4×C7—41no—
190C2×C4×C7—41no—
191C2×C4×C7—41no—
192C2×C4×C7—42no—
193C2×C4×C7—41no—
194C2×C4×C7—41no—
195C2×C4×C7—42no—
196C2×C4×C7—41no—
197C2×C4×C7—41no—
198C2×C4×C7#12011yescharacteristic
199C2×C4×C7#12012yes—
200C2×C4×C7#12011yescharacteristic
201C2×C4×C7C22⋊Q814yes—
202C2×C4×C7C22×D412yes—
203C2×C4×C7C22×Q811yescharacteristic
204C2×C4×C7C2×#4111yescharacteristic
205C2×C4×C72−1+412yes—
206C2×Dic7—24no—
207C2×Dic7—24no—
208Dic14—44no—
209Dic14—82no—
210Dic14—84no—
211C7⋊C8—44no—
212C22×Q8C22×D711yescharacteristic
213C22×Q8C22×D711yescharacteristic
214C2×M16—74no—
215C4⋊Q8—22no—
216C4⋊Q8—72no—
217C4⋊Q8—72no—
218C4⋊Q8—142no—
219C4⋊Q8—142no—
220C4⋊Q8—144no—
221C4⋊Q8—148no—
222C4⋊Q8Dic1414yescomplemented
223#125—74no—
224#125—144no—
225#125—144no—
226#125—148no—
227C22⋊Q8—142no—
228C22⋊Q8—142no—
229C22⋊Q8—144no—
230C4×Q8—22no—
231C4×Q8—22no—
232C4×Q8—22no—
233C4×Q8—22no—
234C4×Q8—144no—
235C4×Q8—144no—
236C4×Q8—144no—
237C4×Q8—144no—
238C4×Q8—142no—
239C4×Q8—142no—
240#117—74no—
241#117—144no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4C22⋊D712yes—
245C2×C4⋊C4C22×D711yescharacteristic
246C2×C4⋊C4C22×D711yescharacteristic
247C2×C42—21no—
248C2×C42C22⋊D712yes—
249C2×C42C22×D711yescharacteristic
250C2×C42C22×D711yescharacteristic
251C2×C42C22×D711yescharacteristic
252#107—144no—
253#106—144no—
254C4⋊C8—142no—
255C4⋊C8—142no—
256#103—144no—
257#103—144no—
258#101—144no—
259#95—21no—
260#95—21no—
261#95—22no—
262#95—22no—
263#95—22no—
264C22×C7—21no—
265C22×C7—21no—
266C22×C7C2×#12011yescharacteristic
267C22×C7C2×C22⋊Q811yescharacteristic
268C22×C7#53611yescharacteristic
269C4×C7—24no—
270C4×C7—21no—
271C4×C7—21no—
272C4×C7—22no—
273C4×C7—42no—
274C4×C7—42no—
275C4×C7—42no—
276C4×C7—81no—
277C4×C7—81no—
278C4×C7#54812yes—
279C4×C7D4×Q812yes—
280Dic7—44no—
281Dic7—44no—
282C2×Q8—21no—
283C2×Q8—22no—
284C2×Q8—22no—
285C2×Q8—22no—
286C2×Q8—22no—
287C2×Q8—144no—
288C2×Q8—142no—
289C2×Q8—142no—
290C2×Q8C2×Dic1412yes—
291C2×Q8C2×Dic1412yes—
292C2×Q8#115712yes—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4C2×C22⋊D712yes—
298C22×C4C2×C22⋊D712yes—
299C22×C4C2×C22⋊D711yescharacteristic
300C22×C4C2×C22⋊D711yescharacteristic
301C22×C4C23×D711yescharacteristic
302M16—144no—
303M16—144no—
304C2×C8—144no—
305C4⋊C4—28no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—74no—
312C4⋊C4—74no—
313C4⋊C4—148no—
314C4⋊C4—144no—
315C4⋊C4—144no—
316C4⋊C4—144no—
317C4⋊C4—144no—
318C4⋊C4—144no—
319C4⋊C4—142no—
320C4⋊C4—142no—
321C22⋊C4—144no—
322C42—22no—
323C42—22no—
324C42—21no—
325C42—22no—
326C42—42no—
327C42—148no—
328C42—144no—
329C42C2×Dic1412yes—
330C42D4×D712yes—
331C42D4×D712yes—
332C2×C7—21no—
333C2×C7—21no—
334C2×C7#240911yescharacteristic
335C2×C7#302011yescharacteristic
336C2×C7#302211yescharacteristic
337C23C22×C22⋊D711yescharacteristic
338Q8—24no—
339Q8—24no—
340Q8—24no—
341Q8—42no—
342Q8—284no—
343Q8—562no—
344Q8—564no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—144no—
363C2×C4—144no—
364C2×C4#648714yes—
365C2×C4#650011yescharacteristic
366C2×C4#650011yescharacteristic
367C2×C4#650012yes—
368C2×C4C22×Dic1411yescharacteristic
369C2×C4C2×#115711yescharacteristic
370C2×C4C2×D4×D712yes—
371C2×C4#655412yes—
372C8—284no—
373C7#2431911yescharacteristic, complemented, Sylow
374C22—21no—
375C22—21no—
376C22C2×#648711yescharacteristic
377C22C2×#650011yescharacteristic
378C22#9051611yescharacteristic
379C4—24no—
380C4—21no—
381C4—21no—
382C4—22no—
383C4—42no—
384C4—42no—
385C4—42no—
386C4—81no—
387C4—81no—
388C4—284no—
389C4—284no—
390C4D4×Dic1412yes—
391C4#9024312yes—
392C2—21no—
393C2—21no—
394C2#1173979411yescharacteristic
395C2#1174086011yescharacteristic
396C2#1174086111yescharacteristic
subgroupG/H
centerC22C2×#6500
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2327C2
socleC22×C7C2×#120
prime radicalC23×C7C22×D4
hypercenter#2327D7
hypocenterC7#24319
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2327

Complements

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

NH ≅ G/Ntype
41. C7×C4⋊Q8Q8semidirect
222. C4⋊Q8Dic14semidirect
373. C7#24319semidirect

Maximal subgroups

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

subgroupindex
#117428712
C7×#23272
#117398762
#117295382
#117293912
#117274272
#117274262
#117272972
#117271952
#243197