Finite Group Databasebeta

← #13257018

Subgroups — #13257018

Order 1792.

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

normal subgroups only

This group has 396 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×#2667C211yesmaximal, characteristic
2#11727287C211yesmaximal, characteristic
3#11727283C211yesmaximal, characteristic
4#11727199C211yesmaximal, characteristic
5#11725434C211yesmaximal, characteristic
6#11725432C211yesmaximal, characteristic
7#11725424C211yesmaximal, characteristic
8C2×#6487C2211yescharacteristic
9C7×#399—21no—
10C7×#398—21no—
11C7×#398—21no—
12C7×#396—21no—
13C7×#389—21no—
14C7×#387—21no—
15C7×#381C2211yescharacteristic
16C7×#380C2211yescharacteristic
17C4×C7×C22⋊C4C2211yescharacteristic
18C4×C22⋊Dic7C2211yescharacteristic
19#89979C2211yescharacteristic
20#89979C2211yescharacteristic
21#89322—21no—
22#89322—21no—
23#89247—21no—
24#89247—21no—
25#89247—21no—
26#89247—21no—
27#10385—71nomaximal, Sylow
28C23×C4×C7C2311yescharacteristic
29C22×Dic14Q811yescharacteristic
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×C7×C4⋊C4—21no—
37C2×C7×C22⋊C4—21no—
38C2×C7×C22⋊C4—21no—
39C2×C7×C22⋊C4D411yescharacteristic
40C2×C7×C22⋊C4D411yescharacteristic
41C2×C42×C7—21no—
42C2×C22⋊Dic7—21no—
43C2×C22⋊Dic7—21no—
44C2×C4⋊Dic7Q811yescharacteristic
45#6487—21no—
46#6487—21no—
47#6487—21no—
48#6487—21no—
49C2×Dic7⋊C4—21no—
50C2×C4×Dic7—21no—
51C2×#1136—21no—
52C2×#1136—21no—
53C7×#95—21no—
54C7×#95—21no—
55C7×#95—21no—
56C7×#95—21no—
57C7×#95D411yescharacteristic
58C7×#95D411yescharacteristic
59C7×#95D411yescharacteristic
60C7×#95D411yescharacteristic
61C7⋊#95—21no—
62C22⋊(C7⋊C8)—21no—
63C22⋊(C7⋊C8)—21no—
64C22⋊(C7⋊C8)—21no—
65C22⋊(C7⋊C8)—21no—
66#2667D711yescharacteristic
67#1996—71no—
68#1511—71no—
69#1508—71no—
70#1305—71no—
71#1297—71no—
72#1284—71no—
73C24×C7C2×D411yescharacteristic
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—21no—
78C22×C4×C7—21no—
79C22×C4×C7—21no—
80C22×C4×C7—81no—
81C22×C4×C7C2×D411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C22×C4×C7C2×Q811yescharacteristic
84C22×C4×C7#4111yescharacteristic
85C22×C4×C7#4111yescharacteristic
86C22×C4×C7#4111yescharacteristic
87C22×Dic7—21no—
88C22×Dic7—21no—
89C22×Dic7—41no—
90C2×Dic14—21no—
91C2×Dic14—21no—
92C2×Dic14—81no—
93C7×C4⋊C4—42no—
94C7×C4⋊C4—42no—
95C7×C4⋊C4—81no—
96C7×C4⋊C4—81no—
97C7×C4⋊C4—81no—
98C7×C4⋊C4—81no—
99C7×C4⋊C4—81no—
100C7×C22⋊C4—42no—
101C7×C22⋊C4—41no—
102C7×C22⋊C4—41no—
103C7×C22⋊C4—81no—
104C42×C7—81no—
105C22⋊Dic7—22no—
106C22⋊Dic7—41no—
107C22⋊Dic7—41no—
108C22⋊Dic7—41no—
109C4⋊Dic7—21no—
110C4⋊Dic7—21no—
111Dic7⋊C4—41no—
112Dic7⋊C4—41no—
113C4×Dic7—81no—
114#1136—81no—
115#1136—81no—
116C2×C7⋊C8—41no—
117C2×C7⋊C8—41no—
118C2×C22⋊Q8—71no—
119#407—71no—
120#407—71no—
121#399—21no—
122#398—21no—
123#398—21no—
124#396—21no—
125#389—21no—
126#387—21no—
127#381C2×D711yescharacteristic
128#380C2×D711yescharacteristic
129C4×C22⋊C4—71no—
130C4×C22⋊C4C2×D711yescharacteristic
131#342—141no—
132#342—141no—
133#328—141no—
134#328—141no—
135#328—141no—
136#328—141no—
137C23×C7—21no—
138C23×C7—21no—
139C23×C7—41no—
140C23×C7—41no—
141C23×C7#12011yescharacteristic
142C23×C7C22⋊Q811yescharacteristic
143C23×C7#12411yescharacteristic
144C2×C4×C7—22no—
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×C7—41no—
161C2×C4×C7—41no—
162C2×C4×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—41no—
165C2×C4×C7—41no—
166C2×C4×C7—41no—
167C2×C4×C7—41no—
168C2×C4×C7C22⋊Q811yescharacteristic
169C2×C4×C7C22⋊Q811yescharacteristic
170C2×C4×C7#12411yescharacteristic
171C2×C4×C7#12411yescharacteristic
172C2×Dic7—42no—
173C2×Dic7—41no—
174C2×Dic7—41no—
175C2×Dic7—81no—
176C2×Dic7—81no—
177C2×Dic7—81no—
178C2×Dic7—81no—
179Dic14—81no—
180Dic14—81no—
181C7⋊C8—81no—
182C7⋊C8—81no—
183C22×Q8—71no—
184C23×C4C22×D711yescharacteristic
185C2×M16—141no—
186C2×M16—141no—
187C22⋊Q8—141no—
188C22⋊Q8—141no—
189C22⋊Q8—141no—
190C22⋊Q8—141no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—71no—
199C2×C4⋊C4—141no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—141no—
203C2×C22⋊C4—141no—
204C2×C22⋊C4C22⋊D711yescharacteristic
205C2×C22⋊C4C22⋊D711yescharacteristic
206C2×C42—21no—
207C2×C42—141no—
208C22⋊C8—141no—
209C22⋊C8—141no—
210C22⋊C8—141no—
211C22⋊C8—141no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—141no—
217#95C22⋊D711yescharacteristic
218#95C22⋊D711yescharacteristic
219#95C22⋊D711yescharacteristic
220#95C22⋊D711yescharacteristic
221C22×C7—21no—
222C22×C7—21no—
223C22×C7—21no—
224C22×C7—21no—
225C22×C7—21no—
226C22×C7—21no—
227C22×C7—21no—
228C22×C7—21no—
229C22×C7—81no—
230C22×C7—81no—
231C22×C7#39311yescharacteristic
232C22×C7#45511yescharacteristic
233C22×C7#45611yescharacteristic
234C4×C7—21no—
235C4×C7—21no—
236C4×C7—21no—
237C4×C7—21no—
238C4×C7—42no—
239C4×C7—81no—
240C4×C7—81no—
241C4×C7—81no—
242C4×C7—81no—
243C4×C7—81no—
244Dic7—82no—
245Dic7—81no—
246Dic7—81no—
247C24C2×C22⋊D711yescharacteristic
248C2×Q8—141no—
249C2×Q8—141no—
250C2×Q8—561no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—81no—
258C22×C4—141no—
259C22×C4—141no—
260C22×C4—281no—
261C22×C4Q8×D711yescharacteristic
262C22×C4#116111yescharacteristic
263C22×C4#116111yescharacteristic
264C22×C4#116111yescharacteristic
265C22×C4C2×C22⋊D711yescharacteristic
266C22×C4C2×C22⋊D711yescharacteristic
267M16—561no—
268M16—561no—
269C2×C8—281no—
270C2×C8—281no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—81no—
274C4⋊C4—81no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—141no—
279C4⋊C4—141no—
280C4⋊C4—281no—
281C4⋊C4—281no—
282C22⋊C4—42no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—81no—
286C22⋊C4—142no—
287C22⋊C4—281no—
288C22⋊C4—281no—
289C22⋊C4—281no—
290C42—81no—
291C42—561no—
292C2×C7—21no—
293C2×C7—21no—
294C2×C7—41no—
295C2×C7—41no—
296C2×C7#202811yescharacteristic
297C2×C7#203111yescharacteristic
298C2×C7#203211yescharacteristic
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23#650911yescharacteristic
304C23#651011yescharacteristic
305C23#651611yescharacteristic
306Q8—561no—
307Q8—561no—
308C2×C4—22no—
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—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—282no—
333C2×C4—281no—
334C2×C4—281no—
335C2×C4—561no—
336C2×C4—561no—
337C2×C4—561no—
338C2×C4—561no—
339C2×C4#650911yescharacteristic
340C2×C4#650911yescharacteristic
341C2×C4#651011yescharacteristic
342C2×C4#651011yescharacteristic
343C8—561no—
344C8—561no—
345C7#1038511yescharacteristic, complemented, Sylow
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22#9000311yescharacteristic
357C22#9001411yescharacteristic
358C22#9001811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—42no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—562no—
370C4—561no—
371C4—561no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2#1172959611yescharacteristic
377C2#1172965011yescharacteristic
378C2#1172965911yescharacteristic
subgroupG/H
centerC22#90003
commutator, cosocleC23×C4×C7C23
FrattiniC23×C4C22×D7
FittingC7×#2667C2
socleC22×C7#393
prime radicalC24×C7C2×D4
hypercenter#2667D7
hypocenterC7#10385
LCSG ▷ C23×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2667

Complements

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

NH ≅ G/Ntype
345. C7#10385semidirect

Maximal subgroups

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

subgroupindex
C7×#26672
#117272872
#117272832
#117271992
#117254342
#117254322
#117254242
#103857