Finite Group Databasebeta

← #13249254

Subgroups — #13249254

Order 1792.

488 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89798C211yesmaximal, characteristic
2#11739881C211yesmaximal, characteristic, complemented
3C7×#1479C211yesmaximal, characteristic, complemented
4#11728537C211yesmaximal, characteristic
5#11728510C211yesmaximal, characteristic
6#11725547C211yesmaximal, characteristic, complemented
7#11725546C211yesmaximal, characteristic, complemented
8C2×C4×C7×Q8C2211yescharacteristic
9C22×#1143C411yescharacteristic
10C2×C4×D28C2211yescharacteristic
11C7×#431C2211yescharacteristic
12C7×#431C2211yescharacteristic
13C2×#6409C411yescharacteristic
14#89798—22no—
15#89798—22no—
16#89796—22no—
17#89796—22no—
18C2×#6383C411yescharacteristic
19C2×#6381C411yescharacteristic
20#89698—22no—
21#89697C2211yescharacteristic
22#89697C2211yescharacteristic
23C2×#6377C2211yescharacteristic
24C7×Q8⋊C8—22no—
25#89278—22no—
26#89263—22no—
27#9094—71nomaximal, Sylow
28C22×C7×Q8C2×C411yescharacteristic
29C22×D28C2×C411yescharacteristic
30C22×C4×D7—21no—
31C4×C7×Q8—21no—
32C4×C7×Q8—21no—
33C4×C7×Q8D412yes—
34C4×C7×Q8D412yes—
35C2×C7×C4⋊C4—21no—
36C2×C7×C4⋊C4C2×C411yescharacteristic
37C2×C42×C7—21no—
38C2×C42×C7C2311yescharacteristic
39C2×#1143—22no—
40C2×#1143—22no—
41C2×#1143—22no—
42C2×(C2×D7)⋊C4—21no—
43C2×C4⋊Dic7C2×C411yescharacteristic
44C22×C7⋊C8C2×C411yescharacteristic
45C22×C7⋊C8C2×C411yescharacteristic
46C4×D28—21no—
47C4×D28—21no—
48C4×D28—21no—
49C4×D28—21no—
50C7×C4⋊C8—21no—
51C7×C4⋊C8—21no—
52C7×C22⋊C8—21no—
53C7×C22⋊C8—21no—
54C4×C7×C8—21no—
55C4×C7×C8—21no—
56#6409—22no—
57C22⋊(C7⋊C8)—21no—
58C22⋊(C7⋊C8)D412yes—
59#6383—22no—
60#6381—22no—
61C4⋊(C7⋊C8)—24no—
62C4⋊(C7⋊C8)—21no—
63C4⋊(C7⋊C8)—21no—
64#6377—24no—
65#6377—21no—
66#6377—21no—
67C4×C7⋊C8—21no—
68C4×C7⋊C8D412yes—
69#2983—71no—
70C2×#440—71no—
71#1479D711yescharacteristic, complemented
72#1478—71no—
73#1460—71no—
74#1281—71no—
75#1275—71no—
76C23×D7—21no—
77C2×C7×Q8—21no—
78C2×C7×Q8—21no—
79C2×C7×Q8—21no—
80C2×C7×Q8—21no—
81C2×C7×Q8—21no—
82C2×C7×Q8C22⋊C412yes—
83C22×C4×C7—21no—
84C22×C4×C7—21no—
85C22×C4×C7C22×C411yescharacteristic
86C22×C4×C7C2×D411yescharacteristic
87C22×C4×C7#4111yescharacteristic
88C22×Dic7—21no—
89C2×D28—21no—
90C2×D28—21no—
91C2×D28—21no—
92C2×D28—21no—
93C2×D28—21no—
94C2×D28M1612yes—
95C2×C4×D7—41no—
96C2×C4×D7—41no—
97C2×C4×D7—82no—
98C2×C7×C8—41no—
99C2×C7×C8—41no—
100C7×C4⋊C4—21no—
101C7×C4⋊C4—22no—
102C7×C4⋊C4—22no—
103C7×C4⋊C4C22⋊C412yes—
104C42×C7—22no—
105C42×C7—22no—
106C42×C7C2×D411yescharacteristic
107C42×C7C2×D411yescharacteristic
108C42×C7C2×D411yescharacteristic
109C42×C7#4111yescharacteristic
110#1143—28no—
111(C2×D7)⋊C4—41no—
112(C2×D7)⋊C4—41no—
113C4⋊Dic7—21no—
114C4⋊Dic7—21no—
115C2×C7⋊C8—21no—
116C2×C7⋊C8—21no—
117C2×C7⋊C8—21no—
118C2×C7⋊C8—22no—
119C2×C7⋊C8—22no—
120C2×C7⋊C8—21no—
121C2×C7⋊C8—21no—
122C2×C7⋊C8M1612yes—
123C22×SD16—71no—
124C2×C4×Q8C2×D711yescharacteristic
125C2×C4×D4—71no—
126#446—142no—
127#446—142no—
128#440—142no—
129#440—142no—
130#432—142no—
131#431—71no—
132#431—71no—
133#431C2×D711yescharacteristic
134#431C2×D711yescharacteristic
135C2×#107—71no—
136C2×#103—71no—
137C2×#102—71no—
138C2×#97—71no—
139Q8⋊C8—22no—
140D4⋊C8—142no—
141#323—142no—
142C23×C7C4×D411yescharacteristic
143C22×D7—22no—
144C22×D7—41no—
145C22×D7—41no—
146C22×D7—81no—
147C22×D7—81no—
148C7×Q8—22no—
149C7×Q8—22no—
150C7×Q8—41no—
151C7×Q8—41no—
152C2×C4×C7—22no—
153C2×C4×C7—22no—
154C2×C4×C7—41no—
155C2×C4×C7—41no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—81no—
159C2×C4×C7C2×C22⋊C411yescharacteristic
160C2×C4×C7C4×D411yescharacteristic
161C2×C4×C7#12011yescharacteristic
162C2×C4×C7#12111yescharacteristic
163C2×C4×C7#12111yescharacteristic
164C2×C4×C7#12311yescharacteristic
165C2×C4×C7C2×M1611yescharacteristic
166C2×C4×C7C2×M1611yescharacteristic
167C2×C4×C7#13111yescharacteristic
168C2×C4×C7#13111yescharacteristic
169C2×Dic7—41no—
170C2×Dic7—81no—
171D28—22no—
172D28—22no—
173D28—41no—
174D28—41no—
175C4×D7—82no—
176C4×D7—82no—
177C7×C8—81no—
178C7×C8—81no—
179C7⋊C8—22no—
180C7⋊C8—42no—
181C7⋊C8—42no—
182C7⋊C8—41no—
183C22×Q8C4×D711yescharacteristic
184C22×D4—71no—
185C23×C4—141no—
186C2×SD16—142no—
187C2×SD16—142no—
188C2×SD16—142no—
189C22×C8—71no—
190C22×C8—71no—
191C4×Q8—21no—
192C4×Q8—21no—
193C4×Q8D2812yes—
194C4×Q8C22⋊D712yes—
195C4×D4—141no—
196C4×D4—141no—
197C4×D4—141no—
198C4×D4—141no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—71no—
201C2×C4⋊C4C4×D711yescharacteristic
202C2×C22⋊C4—141no—
203C2×C42—21no—
204C2×C42C22×D711yescharacteristic
205#107—142no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—144no—
209C4⋊C8—141no—
210C4⋊C8—141no—
211#103—142no—
212#102—142no—
213C22⋊C8—21no—
214C22⋊C8—21no—
215C22⋊C8—72no—
216C22⋊C8—141no—
217#97—144no—
218#97—141no—
219#97—141no—
220C4×C8—21no—
221C4×C8—21no—
222C4×C8—72no—
223C4×C8—141no—
224C22×C7—21no—
225C22×C7—21no—
226C22×C7#38611yescharacteristic
227C22×C7#43511yescharacteristic
228C22×C7#43611yescharacteristic
229C2×D7—42no—
230C2×D7—82no—
231C2×D7—81no—
232C2×D7—81no—
233C2×D7—82no—
234C4×C7—21no—
235C4×C7—21no—
236C4×C7—21no—
237C4×C7—21no—
238C4×C7—42no—
239C4×C7—42no—
240C4×C7#40711yescharacteristic
241C4×C7#40811yescharacteristic
242C4×C7#43511yescharacteristic
243C4×C7#43611yescharacteristic
244Dic7—81no—
245C24—141no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8(C2×D7)⋊C412yes—
252C2×D4—72no—
253C2×D4—141no—
254C2×D4—141no—
255C2×D4—141no—
256C2×D4—141no—
257C2×D4—141no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—141no—
261C22×C4—281no—
262C22×C4—281no—
263C22×C4—562no—
264C22×C4C2×C4×D711yescharacteristic
265C22×C4D4×D711yescharacteristic
266C22×C4#115911yescharacteristic
267SD16—148no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—72no—
271C2×C8—141no—
272C2×C8—141no—
273C2×C8—142no—
274C2×C8—142no—
275C2×C8—141no—
276C2×C8—141no—
277C2×C8—141no—
278C4⋊C4—21no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—141no—
282C4⋊C4—141no—
283C4⋊C4(C2×D7)⋊C412yes—
284C22⋊C4—281no—
285C22⋊C4—281no—
286C42—22no—
287C42—22no—
288C42C2×D2811yescharacteristic
289C42D4×D711yescharacteristic
290C42#115911yescharacteristic
291C42C2×C22⋊D711yescharacteristic
292C2×C7—21no—
293C2×C7—21no—
294C2×C7#187011yescharacteristic
295C2×C7#190311yescharacteristic
296C2×C7#190511yescharacteristic
297D7—82no—
298C23—142no—
299C23—281no—
300C23—281no—
301C23—561no—
302C23—561no—
303C23(C22⋊D7)⋊C411yescharacteristic
304Q8—22no—
305Q8—22no—
306Q8—41no—
307Q8—41no—
308D4—142no—
309D4—142no—
310D4—281no—
311D4—281no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—281no—
320C2×C4—562no—
321C2×C4—562no—
322C2×C4—561no—
323C2×C4(C22⋊D7)⋊C411yescharacteristic
324C2×C4#644511yescharacteristic
325C2×C4#644911yescharacteristic
326C2×C4#646411yescharacteristic
327C2×C4#646411yescharacteristic
328C2×C4D7×M1611yescharacteristic
329C2×C4D7×M1611yescharacteristic
330C2×C4C2×(C2×D7)⋊C411yescharacteristic
331C2×C4#650211yescharacteristic
332C2×C4#650211yescharacteristic
333C8—81no—
334C8—81no—
335C8—142no—
336C8—282no—
337C8—282no—
338C8—281no—
339C7#909411yescharacteristic, complemented, Sylow
340C22—21no—
341C22—21no—
342C22—282no—
343C22—562no—
344C22—562no—
345C22—561no—
346C22—561no—
347C22#8950011yescharacteristic
348C22#8950111yescharacteristic
349C22#8973011yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—561no—
357C4#8950011yescharacteristic
358C4#8950111yescharacteristic
359C4#8988211yescharacteristic
360C4#8989811yescharacteristic
361C2—21no—
362C2—21no—
363C2—562no—
364C2#1172770711yescharacteristic
365C2#1172808811yescharacteristic
366C2#1172815411yescharacteristic
subgroupG/H
centerC22#89730
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1479C2
socleC22×C7#386
prime radicalC22×D28C2×C4
cosocleC2×C42×C7C23
hypercenter#1479D7
hypocenterC7#9094
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #11739881C2semidirect
3. C7×#1479C2semidirect
6. #11725547C2semidirect
7. #11725546C2semidirect
71. #1479D7semidirect
339. C7#9094semidirect

Maximal subgroups

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

subgroupindex
C2×#897982
#117398812
C7×#14792
#117285372
#117285102
#117255472
#117255462
#90947