Finite Group Databasebeta

← #13272477

Subgroups — #13272477

Order 1792.

404 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 93 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#11733989C211yesmaximal, characteristic
2#11727851C211yesmaximal, characteristic
3Dic7×#101C211yesmaximal, characteristic
4C7×#1394C211yesmaximal, characteristic
5#11725505C211yesmaximal, characteristic
6#11725505C211yesmaximal, characteristic
7#11725450C211yesmaximal, characteristic
8C2×Q8×Dic7C2211yescharacteristic
9C2×#6451C411yescharacteristic
10C2×C7×#101C2211yescharacteristic
11C2×C7×#101C2211yescharacteristic
12C7×#391C2211yescharacteristic
13#90002C2211yescharacteristic
14C2×#6410C2211yescharacteristic
15C2×#6410C2211yescharacteristic
16#89890—21no—
17M16×Dic7—21no—
18#89749C411yescharacteristic
19#89708C411yescharacteristic
20C4×Dic7⋊C4C411yescharacteristic
21#89432—21no—
22#89432—21no—
23#89418—21no—
24#89418—21no—
25#89349—21no—
26#89349—21no—
27#13301—71nomaximal, Sylow
28C22×C7×Q8C2311yescharacteristic
29C22×Dic14—21no—
30C2×C7×M16—21no—
31C2×C7×M16—21no—
32C2×C7×C4⋊C4C2×C411yescharacteristic
33C2×C42×C7C2×C411yescharacteristic
34Q8×Dic7—41no—
35Q8×Dic7—41no—
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×C4⋊Dic7C2×C411yescharacteristic
38C2×C4⋊Dic7D411yescharacteristic
39C2×C4⋊Dic7D411yescharacteristic
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×C4×Dic7C2×C411yescharacteristic
43C2×C4×Dic7C2×C411yescharacteristic
44C2×C4×Dic7D411yescharacteristic
45C2×C4×Dic7D411yescharacteristic
46C2×#1136—21no—
47C2×#1136—21no—
48#6451—41no—
49#6451—41no—
50C7×#101—21no—
51C7×#101—21no—
52C7×#101—21no—
53C7×#101Q812yescomplemented
54C7×#95—21no—
55C7×#95—21no—
56#6410—21no—
57#6410—21no—
58#6410—21no—
59#6410Q812yescomplemented
60C7⋊#95—21no—
61C7⋊#95—21no—
62C7⋊#95—21no—
63C7⋊#95—21no—
64C7⋊#95—21no—
65C7⋊#95—21no—
66C7⋊#95—21no—
67#6389—41no—
68Dic7⋊C8—41no—
69Dic7⋊C8—41no—
70C8×Dic7—41no—
71#2568—71no—
72#1801—71no—
73C4×#101—71no—
74#1394—71no—
75#1394—71no—
76#1394—71no—
77#1394D711yescharacteristic
78C2×C7×Q8—41no—
79C2×C7×Q8—41no—
80C2×C7×Q8C2×Q811yescharacteristic
81C2×C7×Q8C2×Q811yescharacteristic
82C2×C7×Q8#4111yescharacteristic
83C2×C7×Q8#4111yescharacteristic
84C22×C4×C7—21no—
85C22×C4×C7—21no—
86C22×C4×C7C22×C411yescharacteristic
87C22×C4×C7C2×D411yescharacteristic
88C22×C4×C7C2×D411yescharacteristic
89C22×Dic7—21no—
90C22×Dic7—21no—
91C22×Dic7C22⋊C411yescharacteristic
92C22×Dic7C22⋊C411yescharacteristic
93C22×Dic7C22⋊C411yescharacteristic
94C22×Dic7C22⋊C411yescharacteristic
95C2×Dic14—44no—
96C2×Dic14—41no—
97C2×Dic14—41no—
98C7×M16—22no—
99C7×M16—41no—
100C7×M16—41no—
101C7×M16—41no—
102C2×C7×C8—41no—
103C2×C7×C8—41no—
104C7×C4⋊C4—41no—
105C42×C7—41no—
106C4⋊Dic7—41no—
107C4⋊Dic7—41no—
108C4⋊Dic7—41no—
109C4⋊Dic7—41no—
110Dic7⋊C4—42no—
111Dic7⋊C4—42no—
112C4×Dic7—21no—
113C4×Dic7—21no—
114C4×Dic7—21no—
115C4×Dic7—21no—
116C4×Dic7—21no—
117C4×Dic7—21no—
118C4×Dic7—41no—
119#1136—22no—
120#1136—41no—
121#1136—41no—
122#1136—41no—
123C2×C7⋊C8—41no—
124C2×C7⋊C8—41no—
125C2×C4⋊Q8—71no—
126C2×C4×Q8—71no—
127#423—141no—
128C2×#101—71no—
129C2×#101—71no—
130C2×#101C2×D711yescharacteristic
131C2×#101C2×D711yescharacteristic
132C4×M16—141no—
133#400—141no—
134#400—141no—
135#391—71no—
136#391—141no—
137#391—141no—
138#391C2×D711yescharacteristic
139#382—71no—
140#382—71no—
141C4×C4⋊C4—71no—
142#343—141no—
143#343—141no—
144C23×C7C2×C22⋊C411yescharacteristic
145C7×Q8—41no—
146C7×Q8—41no—
147C7×Q8—41no—
148C7×Q8—41no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—41no—
156C2×C4×C7—42no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7C4×Q811yescharacteristic
161C2×C4×C7C4×Q811yescharacteristic
162C2×C4×C7C22⋊Q811yescharacteristic
163C2×C4×C7C22⋊Q811yescharacteristic
164C2×C4×C7#12411yescharacteristic
165C2×C4×C7C4⋊Q811yescharacteristic
166C2×Dic7—22no—
167C2×Dic7—21no—
168C2×Dic7—21no—
169C2×Dic7—21no—
170C2×Dic7—41no—
171C2×Dic7—41no—
172C2×Dic7—41no—
173C2×Dic7—41no—
174C2×Dic7—42no—
175C2×Dic7—41no—
176C2×Dic7—41no—
177C2×Dic7—41no—
178C2×Dic7#9911yescharacteristic
179C2×Dic7#9911yescharacteristic
180Dic14—82no—
181Dic14—82no—
182C7×C8—42no—
183C7×C8—81no—
184C7⋊C8—42no—
185C7⋊C8—81no—
186C22×Q8—141no—
187C22×Q8C22×D711yescharacteristic
188C2×M16—21no—
189C2×M16—21no—
190C2×M16—141no—
191C2×M16—141no—
192C4⋊Q8—281no—
193C4⋊Q8—281no—
194C4×Q8—281no—
195C4×Q8—281no—
196C2×C4⋊C4—71no—
197C2×C4⋊C4—71no—
198C2×C4⋊C4—71no—
199C2×C4⋊C4—71no—
200C2×C4⋊C4—141no—
201C2×C4⋊C4—141no—
202C2×C4⋊C4C4×D711yescharacteristic
203C2×C42—71no—
204C2×C42—71no—
205C2×C42—71no—
206C2×C42—71no—
207C2×C42C4×D711yescharacteristic
208C4⋊C8—281no—
209C4⋊C8—281no—
210#101—21no—
211#101—21no—
212#101—21no—
213#101—72no—
214#101—141no—
215#101—141no—
216#101—141no—
217#101Dic1412yescomplemented
218#97—281no—
219C4×C8—281no—
220#95—21no—
221#95—21no—
222#95—141no—
223#95—141no—
224#95—141no—
225#95—141no—
226#95—141no—
227#95—141no—
228#95—141no—
229C22×C7—21no—
230C22×C7—21no—
231C22×C7#39111yescharacteristic
232C22×C7C2×#9911yescharacteristic
233C22×C7#41011yescharacteristic
234C4×C7—21no—
235C4×C7—21no—
236C4×C7—21no—
237C4×C7—21no—
238C4×C7—21no—
239C4×C7—21no—
240C4×C7—81no—
241C4×C7—81no—
242Dic7—21no—
243Dic7—41no—
244Dic7—41no—
245Dic7—41no—
246Dic7—81no—
247Dic7—81no—
248Dic7#35512yes—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—281no—
252C2×Q8—281no—
253C2×Q8—284no—
254C2×Q8C2×Dic1411yescharacteristic
255C2×Q8#115711yescharacteristic
256C2×Q8#115911yescharacteristic
257C2×Q8Q8×D711yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—71no—
261C22×C4—71no—
262C22×C4—71no—
263C22×C4—71no—
264C22×C4—141no—
265C22×C4—141no—
266C22×C4C2×C4×D711yescharacteristic
267C22×C4D4×D711yescharacteristic
268C22×C4D4×D711yescharacteristic
269M16—22no—
270M16—41no—
271M16—41no—
272M16—41no—
273M16—142no—
274M16—281no—
275M16—281no—
276M16—281no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—281no—
280C2×C8—281no—
281C4⋊C4—41no—
282C4⋊C4—281no—
283C4⋊C4—281no—
284C4⋊C4—281no—
285C4⋊C4—281no—
286C4⋊C4—282no—
287C4⋊C4—282no—
288C42—41no—
289C42—141no—
290C42—141no—
291C42—141no—
292C42—141no—
293C42—141no—
294C42—141no—
295C42—281no—
296C2×C7—21no—
297C2×C7—21no—
298C2×C7#199611yescharacteristic
299C2×C7C2×#35511yescharacteristic
300C2×C7#213511yescharacteristic
301C23D7×C22⋊C411yescharacteristic
302Q8—41no—
303Q8—41no—
304Q8—41no—
305Q8—41no—
306Q8—562no—
307Q8—562no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—71no—
320C2×C4—71no—
321C2×C4—142no—
322C2×C4—141no—
323C2×C4—141no—
324C2×C4—141no—
325C2×C4—281no—
326C2×C4—281no—
327C2×C4—281no—
328C2×C4—281no—
329C2×C4—281no—
330C2×C4—282no—
331C2×C4—281no—
332C2×C4—281no—
333C2×C4C4×Dic1411yescharacteristic
334C2×C4#644111yescharacteristic
335C2×C4#644811yescharacteristic
336C2×C4#645011yescharacteristic
337C2×C4#645111yescharacteristic
338C2×C4#645911yescharacteristic
339C8—42no—
340C8—81no—
341C8—282no—
342C8—561no—
343C7#1330111yescharacteristic, complemented, Sylow
344C22—21no—
345C22—21no—
346C22#8941811yescharacteristic
347C22#8951211yescharacteristic
348C22D7×#9911yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—72no—
356C4—81no—
357C4—81no—
358C4—141no—
359C4—281no—
360C4—281no—
361C4—281no—
362C4—561no—
363C4—561no—
364C2—21no—
365C2—21no—
366C2#1172670911yescharacteristic
367C2D7×#35511yescharacteristic
368C2#1172692711yescharacteristic
subgroupG/H
centerC22D7×#99
commutatorC22×C4×C7C22×C4
FrattiniC22×Q8C22×D7
FittingC7×#1394C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC22×C7×Q8C23
hypercenter#1394D7
hypocenterC7#13301
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
53. C7×#101Q8semidirect
59. #6410Q8semidirect
217. #101Dic14semidirect
343. C7#13301semidirect

Maximal subgroups

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

subgroupindex
#117339892
#117278512
Dic7×#1012
C7×#13942
#117255052
#117254502
#133017