Finite Group Databasebeta

← #13256983

Subgroups — #13256983

Order 1792.

390 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2606C211yesmaximal, characteristic, complemented
2#11727318C211yesmaximal, characteristic
3#11727246C211yesmaximal, characteristic
4#11727186C211yesmaximal, characteristic
5#11725439C211yesmaximal, characteristic, complemented
6#11725427C211yesmaximal, characteristic, complemented
7#11725421C211yesmaximal, characteristic, complemented
8#90168C2211yescharacteristic
9C7×#398—21no—
10C7×#398—21no—
11C7×#389—21no—
12C7×#389—21no—
13C7×#387—21no—
14C7×#387—21no—
15C7×#383C2211yescharacteristic
16C4×C7×C4⋊C4C2211yescharacteristic
17C7×#376C2211yescharacteristic
18C2×#6379—21no—
19C2×#6379—21no—
20#89698C2211yescharacteristic
21#89698C2211yescharacteristic
22C4×#1136C2211yescharacteristic
23#89246—21no—
24#89246—21no—
25#89246—21no—
26#89246—21no—
27#10380—71nomaximal, Sylow
28C2×#1157—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4—21no—
36C2×C42×C7—21no—
37C2×C42×C7D411yescharacteristic
38C2×C42×C7D411yescharacteristic
39C2×C42×C7C2311yescharacteristic
40#6493—21no—
41#6493—21no—
42C2×#1136—21no—
43#6438—21no—
44#6437Q811yescharacteristic
45C4×D28—21no—
46C4×D28—21no—
47#6432Q811yescharacteristic
48C7×#95—21no—
49C7×#95—21no—
50C7×#95—21no—
51C7×#95—21no—
52C7×#95—21no—
53C7×#95—21no—
54C7×#95D411yescharacteristic
55C7×#95D411yescharacteristic
56C7×#95D411yescharacteristic
57C7×#95D411yescharacteristic
58C22⋊(C7⋊C8)—21no—
59C22⋊(C7⋊C8)—21no—
60#6379—42no—
61#6379—42no—
62C4⋊(C7⋊C8)—21no—
63C4⋊(C7⋊C8)—21no—
64#6377—21no—
65#6377—21no—
66#6377—21no—
67C4×C7⋊C8—21no—
68#2606D711yescharacteristic, complemented
69#1980—71no—
70#1514—71no—
71#1505—71no—
72#1300—71no—
73#1288—71no—
74#1285—71no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—21no—
78C22×C4×C7—21no—
79C22×C4×C7—21no—
80C22×C4×C7—21no—
81C22×C4×C7C2×D411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C22×C4×C7C2×D411yescharacteristic
84C2×C22⋊D7—41no—
85#1157—41no—
86#1157—41no—
87#1157—41no—
88#1157—41no—
89C2×D28—21no—
90C2×D28—21no—
91C2×D28—21no—
92C2×C4×D7—41no—
93C2×Dic14—21no—
94C7×C4⋊C4—42no—
95C7×C4⋊C4—42no—
96C7×C4⋊C4—42no—
97C7×C4⋊C4—42no—
98C7×C4⋊C4—42no—
99C7×C4⋊C4—81no—
100C7×C4⋊C4—81no—
101C42×C7—41no—
102C42×C7—41no—
103C42×C7—42no—
104C42×C7C2×Q811yescharacteristic
105C42×C7#4111yescharacteristic
106C42×C7#4111yescharacteristic
107C42×C7#4111yescharacteristic
108(C2×D7)⋊C4—41no—
109(C2×D7)⋊C4—41no—
110C4⋊Dic7—21no—
111C4⋊Dic7—21no—
112#1136—22no—
113#1136—41no—
114C2×C7⋊C8—41no—
115C2×C7⋊C8—41no—
116C2×C7⋊C8—41no—
117#532—71no—
118#432—71no—
119#432—71no—
120C2×#104—141no—
121C2×#104—141no—
122C4×M16—71no—
123#398—21no—
124#398—21no—
125#389—21no—
126#389—21no—
127#387—21no—
128#387—21no—
129#383C2×D711yescharacteristic
130C4×C4⋊C4C2×D711yescharacteristic
131#376C2×D711yescharacteristic
132#327—141no—
133#327—141no—
134#327—141no—
135#327—141no—
136C23×C7#12011yescharacteristic
137C22×D7—41no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—22no—
141C2×C4×C7—22no—
142C2×C4×C7—41no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—41no—
148C2×C4×C7—41no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—41no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—41no—
155C2×C4×C7—41no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7C22⋊Q811yescharacteristic
161C2×C4×C7C22⋊Q811yescharacteristic
162C2×C4×C7C22⋊Q811yescharacteristic
163C2×C4×C7#12411yescharacteristic
164C2×C4×C7#12411yescharacteristic
165C2×C4×C7#12411yescharacteristic
166C22⋊D7—81no—
167C22⋊D7—81no—
168C2×Dic7—41no—
169D28—41no—
170D28—41no—
171D28—81no—
172D28—81no—
173C4×D7—81no—
174C4×D7—81no—
175Dic14—41no—
176Dic14—41no—
177C7⋊C8—42no—
178C7⋊C8—81no—
179C7⋊C8—81no—
180C2×#41—141no—
181C2×M16—141no—
182C4⋊Q8—71no—
183#127—71no—
184#124—141no—
185#121—141no—
186#121—141no—
187C4×D4—141no—
188C4×D4—141no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C42—21no—
197C2×C42C22⋊D711yescharacteristic
198C2×C42C22⋊D711yescharacteristic
199C2×C42C22×D711yescharacteristic
200C4⋊C8—141no—
201C4⋊C8—141no—
202#104—282no—
203#104—282no—
204C22⋊C8—141no—
205C22⋊C8—141no—
206#97—141no—
207#97—141no—
208#97—141no—
209C4×C8—141no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95C22⋊D711yescharacteristic
217#95C22⋊D711yescharacteristic
218#95C22⋊D711yescharacteristic
219#95C22⋊D711yescharacteristic
220C22×C7—21no—
221C22×C7—21no—
222C22×C7#39311yescharacteristic
223C22×C7#45311yescharacteristic
224C22×C7#45411yescharacteristic
225C2×D7—81no—
226C2×D7—81no—
227C2×D7—81no—
228C4×C7—21no—
229C4×C7—21no—
230C4×C7—21no—
231C4×C7—21no—
232C4×C7—21no—
233C4×C7—21no—
234C4×C7—42no—
235C4×C7—42no—
236C4×C7—81no—
237C4×C7—81no—
238C4×C7—81no—
239C4×C7—81no—
240Dic7—81no—
241#41—281no—
242#41—281no—
243#41—281no—
244#41—281no—
245C2×Q8—141no—
246C2×D4—141no—
247C2×D4—141no—
248C2×D4—141no—
249C2×D4—281no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—281no—
257C22×C4C2×C22⋊D711yescharacteristic
258C22×C4C2×C22⋊D711yescharacteristic
259C22×C4C2×C22⋊D711yescharacteristic
260M16—142no—
261M16—281no—
262C2×C8—281no—
263C2×C8—281no—
264C2×C8—281no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—141no—
273C4⋊C4—141no—
274C22⋊C4—281no—
275C22⋊C4—281no—
276C42—41no—
277C42—41no—
278C42—42no—
279C42Q8×D711yescharacteristic
280C42#116111yescharacteristic
281C42#116111yescharacteristic
282C42#116111yescharacteristic
283C2×C7—21no—
284C2×C7—21no—
285C2×C7#202711yescharacteristic
286C2×C7#203111yescharacteristic
287C2×C7#203111yescharacteristic
288D7—161no—
289C23—281no—
290C23#651611yescharacteristic
291Q8—281no—
292Q8—281no—
293D4—281no—
294D4—281no—
295D4—561no—
296D4—561no—
297D4—561no—
298D4—561no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—281no—
322C2×C4—561no—
323C2×C4—561no—
324C2×C4#650911yescharacteristic
325C2×C4#650911yescharacteristic
326C2×C4#650911yescharacteristic
327C2×C4#651011yescharacteristic
328C2×C4#651011yescharacteristic
329C2×C4#651011yescharacteristic
330C8—282no—
331C8—561no—
332C8—561no—
333C7#1038011yescharacteristic, complemented, Sylow
334C22—21no—
335C22—21no—
336C22—561no—
337C22—561no—
338C22—561no—
339C22#9000311yescharacteristic
340C22#9001311yescharacteristic
341C22#9001711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—42no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—81no—
354C4—561no—
355C2—21no—
356C2—21no—
357C2—1121no—
358C2#1172959611yescharacteristic
359C2#1172959611yescharacteristic
360C2#1172965711yescharacteristic
subgroupG/H
centerC22#90003
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#2606C2
socleC22×C7#393
prime radical#90168C22
hypercenter#2606D7
hypocenterC7#10380
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2606

Complements

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

NH ≅ G/Ntype
1. C7×#2606C2semidirect
5. #11725439C2semidirect
6. #11725427C2semidirect
7. #11725421C2semidirect
68. #2606D7semidirect
333. C7#10380semidirect

Maximal subgroups

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

subgroupindex
C7×#26062
#117273182
#117272462
#117271862
#117254392
#117254272
#117254212
#103807