Finite Group Databasebeta

← #13264183

Subgroups — #13264183

Order 1792.

400 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 83 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
1#11739948C211yesmaximal, characteristic
2C4×C7×#101C211yesmaximal, characteristic, complemented
3#11729378C211yesmaximal, characteristic, complemented
4#11725300C212yesmaximal, complemented
5#11725299C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6438C411yescharacteristic
8C2×C7×#101—21no—
9C4×C7×M16—21no—
10#90003—21no—
11#89764—21no—
12#89763C411yescharacteristic
13#89763C2211yescharacteristic
14#89751C411yescharacteristic
15#89751C2211yescharacteristic
16#89712—21no—
17#89712—21no—
18#89709C411yescharacteristic
19#89697—21no—
20C7×#343C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11738—71nomaximal, Sylow
24C22×C7×Q8D411yescharacteristic
25C22×D28C2×C411yescharacteristic
26C22×Dic14C2×C411yescharacteristic
27C2×C7×M16—22no—
28C4×C7×Q8—41no—
29C4×C7×Q8—41no—
30C2×C7×C4⋊C4C2×C411yescharacteristic
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C4⋊C4C2311yescharacteristic
33C2×C42×C7C2×C411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×(C2×D7)⋊C4—21no—
37C2×(C2×D7)⋊C4—21no—
38C2×(C2×D7)⋊C4—21no—
39C2×(C2×D7)⋊C4—21no—
40C2×(C2×D7)⋊C4—21no—
41C2×(C2×D7)⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44#6438—41no—
45#6438—41no—
46C7×#101—24no—
47C7×#97—41no—
48C4×C7×C8—41no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95C2×C411yescharacteristic
54C7⋊#95C2×C411yescharacteristic
55C22⋊(C7⋊C8)—22no—
56C4⋊(C7⋊C8)—41no—
57C4×C7⋊C8—41no—
58#2632—71no—
59C4×#101D711yescharacteristic, complemented
60#1461—71no—
61#1354—72no—
62#1345—72no—
63C23×D7—21no—
64C2×C7×Q8—22no—
65C2×C7×Q8—22no—
66C2×C7×Q8—41no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22×C411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×Dic7—21no—
75C22×Dic7—21no—
76C22×Dic7—21no—
77C2×D28—41no—
78C2×D28—81no—
79C2×Dic14—41no—
80C2×Dic14—81no—
81C7×M16—24no—
82C7×M16—42no—
83C2×C7×C8—42no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—41no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C42×C7—21no—
93(C2×D7)⋊C4—42no—
94(C2×D7)⋊C4—41no—
95(C2×D7)⋊C4—41no—
96(C2×D7)⋊C4—42no—
97(C2×D7)⋊C4—42no—
98(C2×D7)⋊C4—81no—
99(C2×D7)⋊C4—81no—
100Dic7⋊C4—81no—
101Dic7⋊C4—81no—
102C2×C7⋊C8—42no—
103C2×#124—71no—
104C2×C4×Q8C2×D711yescharacteristic
105#431—141no—
106C2×#101—21no—
107C4×M16—21no—
108#399—141no—
109#395—71no—
110#395—71no—
111#394—71no—
112#394—71no—
113#393—141no—
114#388—141no—
115#388—141no—
116#383—71no—
117#343C2×D712yes—
118#324—72no—
119#324—141no—
120C23×C7C2×C22⋊C411yescharacteristic
121C22×D7—41no—
122C22×D7—41no—
123C22×D7—41no—
124C22×D7—41no—
125C22×D7—41no—
126C22×D7—41no—
127C22×D7—41no—
128C7×Q8—44no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7—41no—
142C2×C4×C7—41no—
143C2×C4×C7#9911yescharacteristic
144C2×C4×C7#9911yescharacteristic
145C2×C4×C7#10412yes—
146C2×C4×C7#13512yes—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156D28—82no—
157Dic14—82no—
158C7×C8—44no—
159C7⋊C8—82no—
160C22×Q8—71no—
161C22×Q8C22⋊D711yescharacteristic
162C22×D4—71no—
163C2×M16—22no—
164#124—281no—
165#124—281no—
166C4×Q8—41no—
167C4×Q8—41no—
168C2×C4⋊C4—141no—
169C2×C4⋊C4—141no—
170C2×C4⋊C4C4×D711yescharacteristic
171C2×C4⋊C4D2811yescharacteristic
172C2×C4⋊C4C22×D711yescharacteristic
173C2×C22⋊C4—141no—
174C2×C22⋊C4—141no—
175C2×C22⋊C4—141no—
176C2×C22⋊C4—141no—
177C2×C22⋊C4—141no—
178C2×C22⋊C4—141no—
179C2×C42C4×D711yescharacteristic
180C2×C42D2811yescharacteristic
181C2×C42C22⋊D711yescharacteristic
182C4⋊C8—281no—
183#101—24no—
184C22⋊C8—142no—
185#97—41no—
186C4×C8—41no—
187C4×C8—281no—
188#95—71no—
189#95—71no—
190#95—141no—
191#95—141no—
192#95—141no—
193#95—141no—
194C22×C7—21no—
195C22×C7—21no—
196C22×C7C2×#9911yescharacteristic
197C22×C7#41611yescharacteristic
198C22×C7C2×#10411yescharacteristic
199C2×D7—81no—
200C2×D7—81no—
201C2×D7—81no—
202C2×D7—81no—
203C2×D7—81no—
204C2×D7—81no—
205C2×D7—81no—
206C4×C7—21no—
207C4×C7—21no—
208C4×C7—22no—
209C4×C7—22no—
210C4×C7—41no—
211C4×C7—41no—
212C4×C7—41no—
213C4×C7—41no—
214Dic7—81no—
215Dic7—81no—
216Dic7—81no—
217C24—141no—
218C2×Q8—22no—
219C2×Q8—22no—
220C2×Q8—41no—
221C2×Q8—281no—
222C2×Q8—561no—
223C2×D4—281no—
224C2×D4—561no—
225C22×C4—141no—
226C22×C4—141no—
227C22×C4—141no—
228C22×C4(C2×D7)⋊C411yescharacteristic
229C22×C4(C2×D7)⋊C411yescharacteristic
230C22×C4(C2×D7)⋊C411yescharacteristic
231C22×C4(C2×D7)⋊C411yescharacteristic
232C22×C4C2×C4×D711yescharacteristic
233C22×C4C2×D2811yescharacteristic
234C22×C4C2×C22⋊D711yescharacteristic
235M16—24no—
236M16—42no—
237C2×C8—42no—
238C2×C8—282no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—561no—
243C4⋊C4—561no—
244C22⋊C4—282no—
245C22⋊C4—282no—
246C22⋊C4—282no—
247C22⋊C4—281no—
248C22⋊C4—281no—
249C22⋊C4—561no—
250C22⋊C4—561no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C2×C7—21no—
258C2×C7—21no—
259C2×C7#150111yescharacteristic
260C2×C7#212211yescharacteristic
261C2×C7#213311yescharacteristic
262D7—161no—
263C23—281no—
264C23—281no—
265C23—281no—
266C23—281no—
267C23—281no—
268C23—281no—
269C23—281no—
270C23C2×(C2×D7)⋊C411yescharacteristic
271Q8—44no—
272Q8—562no—
273D4—562no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—281no—
289C2×C4—281no—
290C2×C4—281no—
291C2×C4—281no—
292C2×C4—281no—
293C2×C4—281no—
294C2×C4—281no—
295C2×C4—281no—
296C2×C4—281no—
297C2×C4#637912yes—
298C2×C4#638011yescharacteristic
299C2×C4#638011yescharacteristic
300C2×C4#651312yes—
301C8—44no—
302C8—562no—
303C7#1173811yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22—561no—
307C22—561no—
308C22—561no—
309C22—561no—
310C22—561no—
311C22—561no—
312C22—561no—
313C22C2×#637911yescharacteristic
314C22C2×#638011yescharacteristic
315C22#8977411yescharacteristic
316C4—21no—
317C4—21no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—561no—
325C4—561no—
326C4—561no—
327C2—21no—
328C2—21no—
329C2—1121no—
330C2#1172719711yescharacteristic
331C2#1172788211yescharacteristic
332C2#1172790011yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC4×C7×#101C2
socleC22×C7C2×#99
prime radicalC22×D28C2×C4
cosocleC2×C7×C4⋊C4C23
hypercenterC4×#101D7
hypocenterC7#11738
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. C4×C7×#101C2semidirect
3. #11729378C2semidirect
4. #11725300C2semidirect
59. C4×#101D7semidirect
303. C7#11738semidirect

Maximal subgroups

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

subgroupindex
#117399482
C4×C7×#1012
#117293782
#117253002
#117252992
#117387