Finite Group Databasebeta

← #13250079

Subgroups — #13250079

Order 1792.

474 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 111 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#11740813C211yesmaximal, characteristic
2#11731063C211yesmaximal, characteristic
3C7×#1503C211yesmaximal, characteristic
4#11729593C211yesmaximal, characteristic
5#11728524C211yesmaximal, characteristic
6#11725542C211yesmaximal, characteristic
7#11725426C211yesmaximal, characteristic
8C7×#533C2211yescharacteristic
9C2×C4×Dic14C2211yescharacteristic
10C7×#431C2211yescharacteristic
11C4×C7×C4⋊C4C2211yescharacteristic
12#89863C412yescomplemented
13#89862C412yescomplemented
14#89822—21no—
15#89816—21no—
16C4×#1144—22no—
17#89746—21no—
18#89745—21no—
19#89704—21no—
20C4×Dic7⋊C4—21no—
21C42×Dic7C2211yescharacteristic
22#89697C2211yescharacteristic
23#89696C2211yescharacteristic
24#89424—22no—
25C7×#328—22no—
26#89327—21no—
27#89327—21no—
28#89251—22no—
29#9236—71nomaximal, Sylow
30C22×Dic14D411yescharacteristic
31C7×C4⋊Q8C2×C411yescharacteristic
32C7×C4⋊Q8C2×C411yescharacteristic
33C7×#125—21no—
34C7×C22⋊Q8—21no—
35C7×C22⋊Q8—21no—
36C4×C7×Q8—21no—
37C4×C7×Q8—21no—
38C7×#117—21no—
39C2×C7×C4⋊C4—21no—
40C2×C42×C7—21no—
41C2×C42×C7C2311yescharacteristic
42C2×#1144—22no—
43C2×C4⋊Dic7D411yescharacteristic
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—22no—
46C2×C4×Dic7—21no—
47C2×C4×Dic7—21no—
48C2×C4×Dic7—21no—
49C2×C4×Dic7D411yescharacteristic
50C2×C4×Dic7D411yescharacteristic
51C2×#1136—21no—
52C4×Dic14—21no—
53C4×Dic14—21no—
54C4×Dic14C2×C412yes—
55C4×Dic14D412yes—
56C7×C4⋊C8—21no—
57C7×C22⋊C8—21no—
58C4×C7×C8—21no—
59C7×#95D412yes—
60#6409—22no—
61C7⋊#95—22no—
62C7⋊#95—22no—
63C7⋊#95—22no—
64C22⋊(C7⋊C8)—21no—
65#6384—22no—
66#6381—22no—
67C4⋊(C7⋊C8)—21no—
68C4⋊(C7⋊C8)—21no—
69C4⋊(C7⋊C8)C2×C412yes—
70C4×C7⋊C8—21no—
71#3104—71no—
72#2295—71no—
73#1994—71no—
74#1503D711yescharacteristic
75#1487—71no—
76#1303—71no—
77#1276—71no—
78C2×C7×Q8—21no—
79C2×C7×Q8—21no—
80C22×C4×C7—22no—
81C22×C4×C7C2×D411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C22×C4×C7C2×D411yescharacteristic
84C22×Dic7—21no—
85C22×Dic7—21no—
86C22×Dic7—21no—
87C22×Dic7—21no—
88C2×Dic14—21no—
89C2×Dic14—42no—
90C2×Dic14C22⋊C412yes—
91C2×C7×C8—41no—
92C7×C4⋊C4—21no—
93C7×C4⋊C4—21no—
94C7×C4⋊C4—21no—
95C7×C4⋊C4—21no—
96C7×C4⋊C4—42no—
97C7×C4⋊C4—41no—
98C7×C4⋊C4—41no—
99C7×C22⋊C4—41no—
100C42×C7—41no—
101C42×C7—41no—
102C42×C7—41no—
103C42×C7C22×C411yescharacteristic
104C42×C7C2×D411yescharacteristic
105C42×C7#4111yescharacteristic
106C42×C7#4111yescharacteristic
107#1144—44no—
108C4⋊Dic7—21no—
109C4⋊Dic7C22⋊C412yes—
110Dic7⋊C4—22no—
111Dic7⋊C4—22no—
112Dic7⋊C4—44no—
113C4×Dic7—22no—
114C4×Dic7—22no—
115C4×Dic7—21no—
116C4×Dic7—21no—
117C4×Dic7—21no—
118C4×Dic7—42no—
119C4×Dic7—42no—
120C4×Dic7Q1612yescomplemented
121#1136—41no—
122#1136—41no—
123C2×C7⋊C8—22no—
124C2×C7⋊C8—41no—
125#533C2×D711yescharacteristic
126C2×C4×Q8—71no—
127#484—141no—
128#477—72no—
129#462—72no—
130#451—141no—
131C4×Q16—142no—
132#431—71no—
133#431C2×D711yescharacteristic
134#423—71no—
135#391—141no—
136#389—141no—
137#387—142no—
138C4×C4⋊C4—141no—
139C4×C4⋊C4C2×D711yescharacteristic
140#376—141no—
141C43—71no—
142#339—141no—
143#339—141no—
144#328—22no—
145Q8⋊C8—142no—
146C23×C7#12011yescharacteristic
147C7×Q8—42no—
148C7×Q8—81no—
149C2×C4×C7—22no—
150C2×C4×C7—41no—
151C2×C4×C7—42no—
152C2×C4×C7—42no—
153C2×C4×C7—41no—
154C2×C4×C7—41no—
155C2×C4×C7—42no—
156C2×C4×C7C2×C22⋊C411yescharacteristic
157C2×C4×C7C4×D411yescharacteristic
158C2×C4×C7C4×D411yescharacteristic
159C2×C4×C7#12111yescharacteristic
160C2×C4×C7#12111yescharacteristic
161C2×C4×C7#12311yescharacteristic
162C2×C4×C7C2×Q1611yescharacteristic
163C2×C4×C7#13511yescharacteristic
164C2×C4×C7#13711yescharacteristic
165C2×C4×C7#13711yescharacteristic
166C2×Dic7—22no—
167C2×Dic7—22no—
168C2×Dic7—22no—
169C2×Dic7—22no—
170C2×Dic7—41no—
171C2×Dic7—41no—
172C2×Dic7—41no—
173C2×Dic7—42no—
174C2×Dic7—42no—
175C2×Dic7—41no—
176Dic14—22no—
177Dic14—22no—
178Dic14—42no—
179C7×C8—81no—
180C7⋊C8—42no—
181C7⋊C8—81no—
182C22×Q8—71no—
183C2×Q16—142no—
184C2×M16—141no—
185C4⋊Q8C4×D711yescharacteristic
186C4⋊Q8C4×D711yescharacteristic
187#125—21no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190C4×Q8—21no—
191C4×Q8—21no—
192C4×Q8—72no—
193C4×Q8—72no—
194C4×Q8—141no—
195C4×Q8—141no—
196#117—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—71no—
199C2×C4⋊C4—141no—
200C2×C4⋊C4—142no—
201C2×C42—21no—
202C2×C42—71no—
203C2×C42—71no—
204C2×C42—141no—
205C2×C42—141no—
206C2×C42—141no—
207C2×C42C22×D711yescharacteristic
208#107—142no—
209C4⋊C8—21no—
210C4⋊C8—72no—
211C4⋊C8—141no—
212C4⋊C8—141no—
213#103—142no—
214#103—142no—
215C22⋊C8—21no—
216C22⋊C8—141no—
217C4×C8—21no—
218C4×C8—141no—
219#95—142no—
220#95—142no—
221#95—142no—
222#95C22⋊D712yes—
223C22×C7—21no—
224C22×C7—21no—
225C22×C7#38611yescharacteristic
226C22×C7#45111yescharacteristic
227C22×C7#45211yescharacteristic
228C4×C7—21no—
229C4×C7—21no—
230C4×C7—21no—
231C4×C7—82no—
232C4×C7—81no—
233C4×C7—81no—
234C4×C7#42112yes—
235C4×C7C4×Q1611yescharacteristic
236C4×C7#44111yescharacteristic
237C4×C7#46211yescharacteristic
238C4×C7#46411yescharacteristic
239Dic7—42no—
240Dic7—42no—
241Dic7—42no—
242Dic7—42no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—72no—
246C2×Q8—141no—
247C2×Q8—282no—
248C22×C4—22no—
249C22×C4—141no—
250C22×C4—141no—
251C22×C4—141no—
252C22×C4—141no—
253C22×C4D4×D711yescharacteristic
254C22×C4D4×D711yescharacteristic
255C22×C4C2×C22⋊D711yescharacteristic
256Q16—284no—
257M16—281no—
258M16—281no—
259C2×C8—41no—
260C2×C8—142no—
261C2×C8—281no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—72no—
270C4⋊C4—141no—
271C4⋊C4—142no—
272C4⋊C4—142no—
273C4⋊C4—284no—
274C22⋊C4—41no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42—72no—
279C42—142no—
280C42—142no—
281C42—141no—
282C42—141no—
283C42—141no—
284C42—282no—
285C42—282no—
286C42C2×C4×D711yescharacteristic
287C42#115711yescharacteristic
288C42D4×D711yescharacteristic
289C42#115911yescharacteristic
290C2×C7—21no—
291C2×C7—21no—
292C2×C7#187811yescharacteristic
293C2×C7#189711yescharacteristic
294C2×C7#190611yescharacteristic
295C23#650011yescharacteristic
296Q8—42no—
297Q8—81no—
298Q8—142no—
299Q8—142no—
300Q8—282no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—142no—
309C2×C4—142no—
310C2×C4—142no—
311C2×C4—142no—
312C2×C4—281no—
313C2×C4—281no—
314C2×C4—281no—
315C2×C4—282no—
316C2×C4—282no—
317C2×C4—281no—
318C2×C4D7×C22⋊C411yescharacteristic
319C2×C4(C22⋊D7)⋊C411yescharacteristic
320C2×C4#644611yescharacteristic
321C2×C4#644711yescharacteristic
322C2×C4#647811yescharacteristic
323C2×C4#647911yescharacteristic
324C2×C4D7×Q1611yescharacteristic
325C2×C4#648111yescharacteristic
326C2×C4C4×C22⋊D711yescharacteristic
327C2×C4#650111yescharacteristic
328C8—81no—
329C8—282no—
330C8—561no—
331C7#923611yescharacteristic, complemented, Sylow
332C22—21no—
333C22—21no—
334C22#8972811yescharacteristic
335C22#8994511yescharacteristic
336C22#8995811yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—81no—
342C4—81no—
343C4—282no—
344C4—282no—
345C4—282no—
346C4—282no—
347C4#8956111yescharacteristic
348C4#8956211yescharacteristic
349C4#8956511yescharacteristic
350C4#8957011yescharacteristic
351C4#8959312yes—
352C2—21no—
353C2—21no—
354C2#1172780911yescharacteristic
355C2#1172803511yescharacteristic
356C2#1172813711yescharacteristic
subgroupG/H
centerC2×C4#6447
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1503C2
socleC22×C7#386
prime radicalC23×C7#120
cosocleC2×C42×C7C23
hypercenter#1503D7
hypocenterC7#9236
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
12. #89863C4semidirect
13. #89862C4semidirect
120. C4×Dic7Q16semidirect
331. C7#9236semidirect

Maximal subgroups

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

subgroupindex
#117408132
#117310632
C7×#15032
#117295932
#117285242
#117255422
#117254262
#92367