Finite Group Databasebeta

← #13258522

Subgroups — #13258522

Order 1792.

418 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11728233C211yesmaximal, characteristic
2#11728224C211yesmaximal, characteristic
3#11727338C211yesmaximal, characteristic
4#11727330C211yesmaximal, characteristic, complemented
5C7×#1296C211yesmaximal, characteristic, complemented
6#11725509C211yesmaximal, characteristic, complemented
7#11725508C211yesmaximal, characteristic, complemented
8C2×C4×D28C2211yescharacteristic
9C2×C7×C4⋊C8C2211yescharacteristic
10C2×C7×C4⋊C8C2211yescharacteristic
11C7×#384C2211yescharacteristic
12C2×#6395—21no—
13C2×(C2×D7)⋊C8—21no—
14C2×(C2×D7)⋊C8—21no—
15C2×#6383—21no—
16C2×#6382—21no—
17C2×#6382—21no—
18#89707C2211yescharacteristic
19C2×C4⋊(C7⋊C8)C2211yescharacteristic
20C2×C4×C7⋊C8C2211yescharacteristic
21#89346—21no—
22#89324—21no—
23#10619—71nomaximal, Sylow
24C22×D28D411yescharacteristic
25C22×C4×D7—21no—
26C22×C7×C8—21no—
27C22×C7×C8—21no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C42×C7C2311yescharacteristic
32C2×(C2×D7)⋊C4—21no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7D411yescharacteristic
37C22×C7⋊C8—21no—
38C22×C7⋊C8D411yescharacteristic
39C22×C7⋊C8D411yescharacteristic
40C4×D28—21no—
41C4×D28—21no—
42C4×D28—21no—
43C4×D28—21no—
44C7×C4⋊C8—21no—
45C7×C4⋊C8—21no—
46C7×C4⋊C8—21no—
47C7×C4⋊C8—21no—
48#6395—42no—
49(C2×D7)⋊C8—42no—
50(C2×D7)⋊C8—42no—
51#6383—42no—
52#6382—42no—
53#6382—42no—
54C4⋊(C7⋊C8)—21no—
55C4⋊(C7⋊C8)—21no—
56C4×C7⋊C8—21no—
57C4×C7⋊C8—21no—
58#1954—71no—
59#1844—71no—
60#1802—71no—
61#1802—71no—
62#1296—71no—
63#1296D711yescharacteristic, complemented
64#1277—71no—
65C23×D7—21no—
66C22×C4×C7—41no—
67C22×C4×C7C2×D411yescharacteristic
68C22×C4×C7C2×D411yescharacteristic
69C22×C4×C7#4111yescharacteristic
70C22×Dic7—21no—
71C22×Dic7—41no—
72C2×D28—21no—
73C2×D28—21no—
74C2×D28—21no—
75C2×D28—21no—
76C2×D28—21no—
77C2×D28SD1612yes—
78C2×C4×D7—41no—
79C2×C4×D7—41no—
80C2×C4×D7—41no—
81C2×C4×D7—41no—
82C2×C4×D7—41no—
83C2×C4×D7—41no—
84C2×C7×C8—41no—
85C2×C7×C8—41no—
86C2×C7×C8—41no—
87C2×C7×C8—41no—
88C2×C7×C8—41no—
89C2×C7×C8—41no—
90C7×C4⋊C4—41no—
91C7×C4⋊C4—41no—
92C7×C4⋊C4—41no—
93C7×C4⋊C4—41no—
94C7×C4⋊C4—81no—
95C42×C7#4111yescharacteristic
96C42×C7#4111yescharacteristic
97C42×C7#4111yescharacteristic
98C42×C7#4111yescharacteristic
99(C2×D7)⋊C4—41no—
100(C2×D7)⋊C4—41no—
101C4⋊Dic7—21no—
102C4⋊Dic7—21no—
103C4⋊Dic7—41no—
104C4⋊Dic7—41no—
105C4⋊Dic7—41no—
106C4⋊Dic7—41no—
107C4⋊Dic7—81no—
108C2×C7⋊C8—21no—
109C2×C7⋊C8—21no—
110C2×C7⋊C8—21no—
111C2×C7⋊C8—21no—
112C2×C7⋊C8—41no—
113C2×C7⋊C8—41no—
114C2×C7⋊C8—41no—
115C2×C7⋊C8D812yes—
116C2×C7⋊C8SD1612yes—
117C2×C4×D4—71no—
118C2×#106—141no—
119C2×#106—141no—
120C2×C4⋊C8—71no—
121C2×C4⋊C8C2×D711yescharacteristic
122C2×C4⋊C8C2×D711yescharacteristic
123C2×#102—141no—
124C2×#102—141no—
125C2×C22⋊C8—141no—
126C2×C22⋊C8—141no—
127C2×C4×C8—71no—
128#384—71no—
129#384C2×D711yescharacteristic
130#340—141no—
131#340—141no—
132C23×C7#12111yescharacteristic
133C22×D7—22no—
134C22×D7—41no—
135C22×D7—41no—
136C22×D7—41no—
137C22×D7—41no—
138C22×D7—41no—
139C22×D7—41no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—81no—
143C2×C4×C7—81no—
144C2×C4×C7—81no—
145C2×C4×C7#12311yescharacteristic
146C2×C4×C7#12311yescharacteristic
147C2×C4×C7#12311yescharacteristic
148C2×C4×C7#12411yescharacteristic
149C2×C4×C7#12611yescharacteristic
150C2×C4×C7#12611yescharacteristic
151C2×C4×C7C2×D811yescharacteristic
152C2×C4×C7C2×SD1611yescharacteristic
153C2×C4×C7C2×SD1611yescharacteristic
154C2×C4×C7#13511yescharacteristic
155C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C7#13711yescharacteristic
158C2×C4×C7#13711yescharacteristic
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—81no—
163C2×Dic7—81no—
164C2×Dic7—81no—
165D28—22no—
166D28—22no—
167D28—41no—
168D28—41no—
169C4×D7—81no—
170C4×D7—81no—
171C4×D7—81no—
172C4×D7—81no—
173C7×C8—81no—
174C7×C8—81no—
175C7⋊C8—22no—
176C7⋊C8—22no—
177C7⋊C8—81no—
178C22×D4—71no—
179C23×C4—141no—
180C22×C8—21no—
181C22×C8—21no—
182C22×C8—71no—
183C22×C8—71no—
184C22×C8—141no—
185C4×D4—141no—
186C4×D4—141no—
187C4×D4—141no—
188C4×D4—141no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—71no—
193C2×C4⋊C4—141no—
194C2×C4⋊C4—141no—
195C2×C4⋊C4—141no—
196C2×C22⋊C4—141no—
197C2×C42C22×D711yescharacteristic
198#106—282no—
199#106—282no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—141no—
205C4⋊C8—141no—
206#102—282no—
207#102—282no—
208C22⋊C8—282no—
209C22⋊C8—282no—
210C4×C8—141no—
211C4×C8—141no—
212C22×C7#39711yescharacteristic
213C22×C7#45911yescharacteristic
214C22×C7#46111yescharacteristic
215C22×C7#46511yescharacteristic
216C22×C7#46811yescharacteristic
217C22×C7#47111yescharacteristic
218C22×C7#47111yescharacteristic
219C2×D7—42no—
220C2×D7—42no—
221C2×D7—42no—
222C2×D7—81no—
223C2×D7—81no—
224C2×D7—81no—
225C2×D7—81no—
226C4×C7—21no—
227C4×C7—21no—
228C4×C7—161no—
229C4×C7#48011yescharacteristic
230C4×C7#48111yescharacteristic
231C4×C7#48111yescharacteristic
232C4×C7#48211yescharacteristic
233C4×C7#48311yescharacteristic
234C4×C7#48511yescharacteristic
235C4×C7#48611yescharacteristic
236C4×C7#48911yescharacteristic
237Dic7—81no—
238Dic7—161no—
239C24—141no—
240C2×D4—72no—
241C2×D4—141no—
242C2×D4—141no—
243C2×D4—141no—
244C2×D4—141no—
245C2×D4—141no—
246C22×C4—41no—
247C22×C4—141no—
248C22×C4—281no—
249C22×C4—281no—
250C22×C4—281no—
251C22×C4—281no—
252C22×C4—281no—
253C22×C4—281no—
254C22×C4—281no—
255C22×C4#115711yescharacteristic
256C22×C4D4×D711yescharacteristic
257C22×C4D4×D711yescharacteristic
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—72no—
265C2×C8—72no—
266C2×C8—141no—
267C2×C8—141no—
268C2×C8—141no—
269C2×C8—141no—
270C2×C8—281no—
271C2×C8—281no—
272C2×C8—281no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—81no—
278C4⋊C4—141no—
279C4⋊C4—141no—
280C4⋊C4—281no—
281C4⋊C4—281no—
282C4⋊C4—281no—
283C4⋊C4—281no—
284C4⋊C4—561no—
285C22⋊C4—281no—
286C22⋊C4—281no—
287C42#115711yescharacteristic
288C42#115711yescharacteristic
289C42#115911yescharacteristic
290C42#116111yescharacteristic
291C2×C7#166511yescharacteristic
292C2×C7#167111yescharacteristic
293C2×C7#168511yescharacteristic
294C2×C7#169111yescharacteristic
295C2×C7#207111yescharacteristic
296C2×C7#207711yescharacteristic
297C2×C7#207911yescharacteristic
298D7—82no—
299C23—142no—
300C23—281no—
301C23—281no—
302C23—281no—
303C23—281no—
304C23—281no—
305C23—281no—
306C23#644711yescharacteristic
307D4—142no—
308D4—142no—
309D4—281no—
310D4—281no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—281no—
317C2×C4—281no—
318C2×C4—281no—
319C2×C4—561no—
320C2×C4—561no—
321C2×C4—561no—
322C2×C4—561no—
323C2×C4—561no—
324C2×C4—561no—
325C2×C4—561no—
326C2×C4#643911yescharacteristic
327C2×C4#644611yescharacteristic
328C2×C4#644811yescharacteristic
329C2×C4#645711yescharacteristic
330C2×C4#645711yescharacteristic
331C2×C4#646111yescharacteristic
332C2×C4D7×D811yescharacteristic
333C2×C4#647411yescharacteristic
334C2×C4D7×SD1611yescharacteristic
335C2×C4D7×SD1611yescharacteristic
336C2×C4#647711yescharacteristic
337C2×C4#647811yescharacteristic
338C2×C4#648111yescharacteristic
339C2×C4#648211yescharacteristic
340C8—81no—
341C8—81no—
342C8—142no—
343C8—142no—
344C8—561no—
345C7#1061911yescharacteristic, complemented, Sylow
346C22—282no—
347C22—282no—
348C22—282no—
349C22—561no—
350C22—561no—
351C22—561no—
352C22—561no—
353C22#8944711yescharacteristic
354C22#8952011yescharacteristic
355C22#8952611yescharacteristic
356C22#8955211yescharacteristic
357C22#8955811yescharacteristic
358C22#8957911yescharacteristic
359C22#8959011yescharacteristic
360C4—21no—
361C4—21no—
362C4—161no—
363C4—561no—
364C4—1121no—
365C4#8953211yescharacteristic
366C4#8954911yescharacteristic
367C4#8956711yescharacteristic
368C4#8958611yescharacteristic
369C4#8963411yescharacteristic
370C4#8963511yescharacteristic
371C4#8965411yescharacteristic
372C4#8965711yescharacteristic
373C2—562no—
374C2#1172615211yescharacteristic
375C2#1172619411yescharacteristic
376C2#1172620411yescharacteristic
377C2#1172625011yescharacteristic
378C2#1172658711yescharacteristic
379C2#1172665611yescharacteristic
380C2#1172676511yescharacteristic
subgroupG/H
centerC23#6447
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1296C2
socleC23×C7#121
prime radicalC22×D28D4
hypercenter#1296D7
hypocenterC7#10619
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. #11727330C2semidirect
5. C7×#1296C2semidirect
6. #11725509C2semidirect
7. #11725508C2semidirect
63. #1296D7semidirect
345. C7#10619semidirect

Maximal subgroups

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

subgroupindex
#117282332
#117282242
#117273382
#117273302
C7×#12962
#117255092
#117255082
#106197