Finite Group Databasebeta

← #13264620

Subgroups — #13264620

Order 1792.

382 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 79 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
2C7×#1801C211yesmaximal, characteristic, complemented
3#11729379C211yesmaximal, characteristic, complemented
4#11725300C212yesmaximal, complemented
5#11725299C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6438C411yescharacteristic
8C7×#423—21no—
9C2×C7×#101—21no—
10#90003—21no—
11#89764—21no—
12#89763C411yescharacteristic
13#89763C2211yescharacteristic
14#89751C411yescharacteristic
15#89751C2211yescharacteristic
16#89712—21no—
17#89712—21no—
18#89709C411yescharacteristic
19#89698—21no—
20C7×#343C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11833—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×C4⋊C8—41no—
47C7×C4⋊C8—41no—
48C7×#101—42no—
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—
57#6377—41no—
58#2632—71no—
59#1801D711yescharacteristic, complemented
60#1467—71no—
61#1354—72no—
62#1345—72no—
63C23×D7—21no—
64C2×C7×Q8—21no—
65C2×C7×Q8—21no—
66C2×C7×Q8—41no—
67C2×C7×Q8—41no—
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22×C411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×Dic7—21no—
76C22×Dic7—21no—
77C22×Dic7—21no—
78C2×D28—41no—
79C2×D28—81no—
80C2×Dic14—41no—
81C2×Dic14—81no—
82C7×M16—42no—
83C7×M16—42no—
84C2×C7×C8—42no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—41no—
87C7×C4⋊C4—41no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C42×C7—21no—
93C42×C7—21no—
94(C2×D7)⋊C4—42no—
95(C2×D7)⋊C4—42no—
96(C2×D7)⋊C4—41no—
97(C2×D7)⋊C4—41no—
98(C2×D7)⋊C4—41no—
99(C2×D7)⋊C4—41no—
100(C2×D7)⋊C4—81no—
101(C2×D7)⋊C4—81no—
102Dic7⋊C4—81no—
103Dic7⋊C4—81no—
104C2×C7⋊C8—42no—
105C2×#124—71no—
106C2×C4×Q8C2×D711yescharacteristic
107#432—141no—
108#423—21no—
109C2×#101—21no—
110#399—141no—
111#395—71no—
112#395—71no—
113#394—71no—
114#394—71no—
115#393—141no—
116#388—141no—
117#388—141no—
118#383—71no—
119#343C2×D712yes—
120#324—72no—
121#324—141no—
122C23×C7C2×C22⋊C411yescharacteristic
123C22×D7—41no—
124C22×D7—41no—
125C22×D7—41no—
126C22×D7—41no—
127C22×D7—41no—
128C22×D7—41no—
129C22×D7—41no—
130C7×Q8—42no—
131C7×Q8—42no—
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—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—41no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7#9911yescharacteristic
148C2×C4×C7#9911yescharacteristic
149C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C7#13711yescharacteristic
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160D28—82no—
161Dic14—82no—
162C7×C8—82no—
163C7⋊C8—82no—
164C22×Q8—71no—
165C22×Q8C22⋊D711yescharacteristic
166C22×D4—71no—
167C2×M16—22no—
168#124—281no—
169#124—281no—
170C4×Q8—41no—
171C4×Q8—41no—
172C2×C4⋊C4—141no—
173C2×C4⋊C4—141no—
174C2×C4⋊C4C4×D711yescharacteristic
175C2×C4⋊C4D2811yescharacteristic
176C2×C4⋊C4C22×D711yescharacteristic
177C2×C22⋊C4—141no—
178C2×C22⋊C4—141no—
179C2×C22⋊C4—141no—
180C2×C22⋊C4—141no—
181C2×C22⋊C4—141no—
182C2×C22⋊C4—141no—
183C2×C42C4×D711yescharacteristic
184C2×C42D2811yescharacteristic
185C2×C42C22⋊D711yescharacteristic
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—281no—
189#101—42no—
190C22⋊C8—142no—
191#97—281no—
192#95—71no—
193#95—71no—
194#95—141no—
195#95—141no—
196#95—141no—
197#95—141no—
198C22×C7—21no—
199C22×C7—21no—
200C22×C7C2×#9911yescharacteristic
201C22×C7#41711yescharacteristic
202C22×C7#42111yescharacteristic
203C2×D7—81no—
204C2×D7—81no—
205C2×D7—81no—
206C2×D7—81no—
207C2×D7—81no—
208C2×D7—81no—
209C2×D7—81no—
210C4×C7—21no—
211C4×C7—21no—
212C4×C7—21no—
213C4×C7—21no—
214C4×C7—41no—
215C4×C7—41no—
216C4×C7—41no—
217C4×C7—41no—
218C4×C7—41no—
219Dic7—81no—
220Dic7—81no—
221Dic7—81no—
222C24—141no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—281no—
228C2×Q8—561no—
229C2×D4—281no—
230C2×D4—561no—
231C22×C4—141no—
232C22×C4—141no—
233C22×C4—141no—
234C22×C4(C2×D7)⋊C411yescharacteristic
235C22×C4(C2×D7)⋊C411yescharacteristic
236C22×C4(C2×D7)⋊C411yescharacteristic
237C22×C4(C2×D7)⋊C411yescharacteristic
238C22×C4C2×C4×D711yescharacteristic
239C22×C4C2×D2811yescharacteristic
240C22×C4C2×C22⋊D711yescharacteristic
241M16—42no—
242M16—42no—
243C2×C8—42no—
244C2×C8—282no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—561no—
249C4⋊C4—561no—
250C22⋊C4—282no—
251C22⋊C4—282no—
252C22⋊C4—281no—
253C22⋊C4—281no—
254C22⋊C4—281no—
255C22⋊C4—281no—
256C22⋊C4—561no—
257C22⋊C4—561no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C2×C7—21no—
265C2×C7—21no—
266C2×C7#151311yescharacteristic
267C2×C7#212211yescharacteristic
268C2×C7#213311yescharacteristic
269D7—161no—
270C23—281no—
271C23—281no—
272C23—281no—
273C23—281no—
274C23—281no—
275C23—281no—
276C23—281no—
277C23C2×(C2×D7)⋊C411yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—562no—
281D4—562no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—281no—
298C2×C4—281no—
299C2×C4—281no—
300C2×C4—281no—
301C2×C4—281no—
302C2×C4—281no—
303C2×C4—281no—
304C2×C4—281no—
305C2×C4—281no—
306C2×C4#638011yescharacteristic
307C2×C4#638011yescharacteristic
308C2×C4#649511yescharacteristic
309C2×C4#650511yescharacteristic
310C8—82no—
311C8—562no—
312C7#1183311yescharacteristic, complemented, Sylow
313C22—21no—
314C22—21no—
315C22—561no—
316C22—561no—
317C22—561no—
318C22—561no—
319C22—561no—
320C22—561no—
321C22—561no—
322C22C2×#638011yescharacteristic
323C22#8973811yescharacteristic
324C22#8977711yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—561no—
335C4—561no—
336C4—561no—
337C2—21no—
338C2—21no—
339C2—1121no—
340C2#1172726211yescharacteristic
341C2#1172788211yescharacteristic
342C2#1172790011yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1801C2
socleC22×C7C2×#99
prime radicalC22×D28C2×C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1801D7
hypocenterC7#11833
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. C7×#1801C2semidirect
3. #11729379C2semidirect
4. #11725300C2semidirect
59. #1801D7semidirect
312. C7#11833semidirect

Maximal subgroups

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

subgroupindex
#117399482
C7×#18012
#117293792
#117253002
#117252992
#118337