Finite Group Databasebeta

← #13255130

Subgroups — #13255130

Order 1792.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×C7×#501C211yesmaximal, characteristic
2C2×#89852C211yesmaximal, characteristic
3#11740500C211yesmaximal, characteristic
4#11729540C211yesmaximal, characteristic
5C2×#89338C211yesmaximal, characteristic
6C2×#89260C211yesmaximal, characteristic
7#11725465C211yesmaximal, characteristic
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×C7×#125C2211yescharacteristic
10C2×#6433C2211yescharacteristic
11C7×#501—22no—
12C7×#501—22no—
13C2×C7×#107—21no—
14C2×C7×#106—21no—
15C2×C7×#97C2211yescharacteristic
16C2×#6409—22no—
17#89852—22no—
18#89852—22no—
19#89758—21no—
20#89756—22no—
21#89755—21no—
22#89754—21no—
23#89752—21no—
24C2×#6382—21no—
25C2×#6381—21no—
26#89708C2211yescharacteristic
27C2×#6377C2211yescharacteristic
28C2×#6377C2211yescharacteristic
29#89338—22no—
30#89260—22no—
31#10087—71nomaximal, Sylow
32C22×C7×Q8—21no—
33C22×C7×C8—21no—
34C7×C4⋊Q8—21no—
35C7×C4⋊Q8—21no—
36C7×C4⋊Q8—21no—
37C7×C4⋊Q8D412yes—
38C7×#125—21no—
39C7×#125—21no—
40C7×#125—21no—
41C7×#125—21no—
42C2×C7×C4⋊C4—21no—
43C2×C7×C4⋊C4—21no—
44C2×C7×C4⋊C4—21no—
45C2×C7×C4⋊C4—21no—
46C2×C7×C4⋊C4D411yescharacteristic
47C2×C7×C4⋊C4D411yescharacteristic
48C2×C42×C7C2311yescharacteristic
49C2×C4⋊Dic7D411yescharacteristic
50C2×C4⋊Dic7D411yescharacteristic
51C2×C4⋊Dic7D412yes—
52C2×Dic7⋊C4—21no—
53C2×Dic7⋊C4—21no—
54C2×Dic7⋊C4—22no—
55C22×C7⋊C8—21no—
56C22×C7⋊C8—21no—
57#6433—21no—
58#6433—21no—
59#6433—21no—
60#6433—21no—
61C7×#107—24no—
62C7×#106—24no—
63C7×#97—21no—
64C7×#97D412yes—
65#6409—44no—
66C7⋊#95—22no—
67C7⋊#95—22no—
68C7⋊#95—22no—
69C7⋊#95—21no—
70C7⋊#95—21no—
71#6382—24no—
72#6381—24no—
73#6377—21no—
74#6377—21no—
75#6377—21no—
76#6377D412yes—
77C2×#501—71no—
78C2×#501D711yescharacteristic
79#2822—71no—
80#1960—71no—
81C2×#330—71no—
82C2×#330—71no—
83#1295—71no—
84C2×C7×Q8—22no—
85C2×C7×Q8—42no—
86C2×C7×Q8—42no—
87C2×C7×Q8—41no—
88C22×C4×C7—21no—
89C22×C4×C7—21no—
90C22×C4×C7—41no—
91C22×C4×C7C2×D411yescharacteristic
92C22×C4×C7C2×D411yescharacteristic
93C22×C4×C7C2×D411yescharacteristic
94C22×Dic7—22no—
95C22×Dic7—21no—
96C22×Dic7—21no—
97C2×C7×C8—24no—
98C2×C7×C8—22no—
99C7×C4⋊C4—21no—
100C7×C4⋊C4—22no—
101C7×C4⋊C4—21no—
102C7×C4⋊C4—22no—
103C7×C4⋊C4—21no—
104C7×C4⋊C4—21no—
105C7×C4⋊C4—41no—
106C7×C4⋊C4—41no—
107C7×C4⋊C4—41no—
108C7×C4⋊C4—41no—
109C7×C4⋊C4—41no—
110C7×C4⋊C4—41no—
111C42×C7C2×D411yescharacteristic
112C42×C7C2×D411yescharacteristic
113C42×C7C2×D411yescharacteristic
114C42×C7#4111yescharacteristic
115C4⋊Dic7—21no—
116C4⋊Dic7—21no—
117C4⋊Dic7—21no—
118C4⋊Dic7—21no—
119C4⋊Dic7—42no—
120Dic7⋊C4—41no—
121Dic7⋊C4—41no—
122Dic7⋊C4—41no—
123Dic7⋊C4—41no—
124Dic7⋊C4—82no—
125C2×C7⋊C8—24no—
126C2×C7⋊C8—22no—
127C2×C7⋊C8—22no—
128C2×C7⋊C8—41no—
129C2×C7⋊C8—41no—
130C2×C4⋊Q8C2×D711yescharacteristic
131C2×#125—71no—
132C2×#125C2×D711yescharacteristic
133#501—22no—
134#501—22no—
135#501—142no—
136#501—142no—
137C2×#107—21no—
138C2×#107—141no—
139C2×#106—21no—
140C2×#106—141no—
141C2×#103—142no—
142C2×#97—71no—
143C2×#97—71no—
144C2×#97C2×D711yescharacteristic
145#400—141no—
146#400—141no—
147#398—141no—
148#398—142no—
149#398—141no—
150#382—71no—
151#330—142no—
152#330—142no—
153C23×C7#12011yescharacteristic
154C7×Q8—44no—
155C7×Q8—82no—
156C2×C4×C7—21no—
157C2×C4×C7—21no—
158C2×C4×C7—22no—
159C2×C4×C7—22no—
160C2×C4×C7—41no—
161C2×C4×C7—41no—
162C2×C4×C7—42no—
163C2×C4×C7—41no—
164C2×C4×C7—41no—
165C2×C4×C7—42no—
166C2×C4×C7—81no—
167C2×C4×C7—81no—
168C2×C4×C7#12011yescharacteristic
169C2×C4×C7#12011yescharacteristic
170C2×C4×C7#12111yescharacteristic
171C2×C4×C7#12111yescharacteristic
172C2×C4×C7#12111yescharacteristic
173C2×C4×C7#12711yescharacteristic
174C2×Dic7—41no—
175C2×Dic7—41no—
176C2×Dic7—41no—
177C2×Dic7—42no—
178C2×Dic7—41no—
179C2×Dic7—42no—
180C2×Dic7—42no—
181C2×Dic7—42no—
182C7×C8—24no—
183C7⋊C8—24no—
184C7⋊C8—42no—
185C22×Q8—21no—
186C22×C8—21no—
187C22×C8—141no—
188C22×C8—141no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8C22⋊D712yes—
193#125—21no—
194#125—21no—
195#125—21no—
196#125—21no—
197#125—141no—
198#125—141no—
199#125—141no—
200#125—141no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—71no—
206C2×C4⋊C4—71no—
207C2×C4⋊C4—72no—
208C2×C4⋊C4—141no—
209C2×C4⋊C4—141no—
210C2×C4⋊C4—142no—
211C2×C4⋊C4C22⋊D711yescharacteristic
212C2×C4⋊C4C22⋊D711yescharacteristic
213C2×C42C22×D711yescharacteristic
214#107—24no—
215#107—144no—
216#106—24no—
217#106—144no—
218#103—284no—
219#97—21no—
220#97—72no—
221#97—141no—
222#97—141no—
223#97—141no—
224#97C22⋊D712yes—
225#95—142no—
226#95—142no—
227#95—142no—
228#95—141no—
229#95—141no—
230C22×C7#39211yescharacteristic
231C22×C7#45311yescharacteristic
232C22×C7#45411yescharacteristic
233C22×C7#45612yes—
234C22×C7#45612yes—
235C4×C7—21no—
236C4×C7—21no—
237C4×C7—21no—
238C4×C7—21no—
239C4×C7—21no—
240C4×C7—21no—
241C4×C7—81no—
242C4×C7—81no—
243C4×C7—82no—
244Dic7—82no—
245Dic7—81no—
246Dic7—81no—
247C2×Q8—22no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—142no—
255C22×C4—141no—
256C22×C4—141no—
257C22×C4D4×D711yescharacteristic
258C22×C4D4×D711yescharacteristic
259C22×C4C2×C22⋊D711yescharacteristic
260C2×C8—24no—
261C2×C8—22no—
262C2×C8—144no—
263C2×C8—142no—
264C2×C8—142no—
265C2×C8—281no—
266C2×C8—281no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—141no—
280C4⋊C4—141no—
281C4⋊C4—141no—
282C4⋊C4—141no—
283C4⋊C4—282no—
284C4⋊C4—281no—
285C4⋊C4—281no—
286C4⋊C4—281no—
287C4⋊C4—281no—
288C4⋊C4—562no—
289C42D4×D711yescharacteristic
290C42#115911yescharacteristic
291C42C2×C22⋊D711yescharacteristic
292C42C2×C22⋊D711yescharacteristic
293C2×C7#166012yes—
294C2×C7#166312yes—
295C2×C7#200511yescharacteristic
296C2×C7#200511yescharacteristic
297C2×C7#200611yescharacteristic
298C23#650011yescharacteristic
299Q8—44no—
300Q8—82no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—282no—
314C2×C4—282no—
315C2×C4—282no—
316C2×C4—281no—
317C2×C4—281no—
318C2×C4—282no—
319C2×C4—281no—
320C2×C4—281no—
321C2×C4#650011yescharacteristic
322C2×C4#650111yescharacteristic
323C2×C4#650211yescharacteristic
324C2×C4#650211yescharacteristic
325C2×C4#650311yescharacteristic
326C2×C4#651611yescharacteristic
327C8—24no—
328C8—144no—
329C8—282no—
330C7#1008711yescharacteristic, complemented, Sylow
331C22#8986712yes—
332C22#8997011yescharacteristic
333C22#8997311yescharacteristic
334C22#8997712yes—
335C22#8999511yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—81no—
343C4—82no—
344C4—81no—
345C4—561no—
346C4—561no—
347C4—562no—
348C2#1172914512yes—
349C2#1172914712yes—
350C2#1172954911yescharacteristic
351C2#1172985211yescharacteristic
352C2#1172986211yescharacteristic
subgroupG/H
centerC23#6500
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC2×C7×#501C2
socle, prime radicalC23×C7#120
hypercenterC2×#501D7
hypocenterC7#10087
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
330. C7#10087semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5012
C2×#898522
#117405002
#117295402
C2×#893382
C2×#892602
#117254652
#100877