Finite Group Databasebeta

← #13264953

Subgroups — #13264953

Order 1792.

440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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#11739830C211yesmaximal, characteristic
2C7×#1800C211yesmaximal, characteristic
3#11729354C211yesmaximal, characteristic
4#11725302C212yesmaximal, complemented
5#11725300C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6487C411yescharacteristic
8C7×#423—21no—
9C2×C7×#100—21no—
10#89992—21no—
11#89982—21no—
12C2×C7⋊#95C411yescharacteristic
13C2×C22⋊(C7⋊C8)—21no—
14#89758C2211yescharacteristic
15#89751C2211yescharacteristic
16#89721C411yescharacteristic
17#89719C411yescharacteristic
18#89714—21no—
19#89705—21no—
20C7×#343C2212yes—
21#89323C2212yes—
22#89320—21no—
23#11906—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C23×Dic7—21no—
28C22×Dic14C2×C411yescharacteristic
29C2×C7×M16—22no—
30C4×C7×D4—41no—
31C4×C7×D4—41no—
32C2×C7×C4⋊C4C2311yescharacteristic
33C2×C7×C22⋊C4C2×C411yescharacteristic
34C2×C7×C22⋊C4D411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C4⋊Dic7C2×C411yescharacteristic
40#6487—41no—
41#6487—41no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—21no—
45C22×C7⋊C8—41no—
46C7×C4⋊C8—41no—
47C7×C4⋊C8—41no—
48C7×#100—42no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95C2×C411yescharacteristic
55C7⋊#95C2×C411yescharacteristic
56C22⋊(C7⋊C8)—22no—
57C22⋊(C7⋊C8)—41no—
58#2564—71no—
59#1800D711yescharacteristic
60#1459—71no—
61#1354—72no—
62#1353—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C22⋊C411yescharacteristic
65C2×C7×D4—41no—
66C2×C7×D4—41no—
67C2×C7×D4SD1612yes—
68C2×C7×D4Q1612yes—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—81no—
74C22×C4×C7—81no—
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22×C411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—21no—
84C22×Dic7—42no—
85C22×Dic7—42no—
86C22×Dic7—81no—
87C2×Dic14—41no—
88C2×Dic14—81no—
89C7×M16—42no—
90C7×M16—42no—
91C2×C7×C8—42no—
92C7×C4⋊C4—41no—
93C7×C22⋊C4—41no—
94C7×C22⋊C4—41no—
95C42×C7—21no—
96C42×C7—21no—
97C22⋊Dic7—42no—
98C22⋊Dic7—42no—
99C22⋊Dic7—81no—
100C4⋊Dic7—41no—
101Dic7⋊C4—42no—
102Dic7⋊C4—41no—
103Dic7⋊C4—41no—
104Dic7⋊C4—81no—
105C2×C7⋊C8—42no—
106C2×C7⋊C8—82no—
107C2×C22⋊Q8—71no—
108C2×C4×D4C2×D711yescharacteristic
109#423—21no—
110C2×#100—21no—
111C2×C22⋊C8—141no—
112#400—71no—
113#399—71no—
114#395—71no—
115#393—71no—
116#387—141no—
117#386—141no—
118#385—141no—
119#380—141no—
120C2×#95—71no—
121#343C2×D712yes—
122#324—72no—
123#323—141no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—41no—
129C23×C7—41no—
130C23×C7—41no—
131C23×C7—41no—
132C23×C7#10312yes—
133C23×C7#10312yes—
134C23×C7C2×C22⋊C411yescharacteristic
135C7×D4—42no—
136C7×D4—42no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—21no—
141C2×C4×C7—21no—
142C2×C4×C7—41no—
143C2×C4×C7—42no—
144C2×C4×C7—41no—
145C2×C4×C7—41no—
146C2×C4×C7—41no—
147C2×C4×C7—81no—
148C2×C4×C7—81no—
149C2×C4×C7—81no—
150C2×C4×C7#9911yescharacteristic
151C2×C4×C7#9911yescharacteristic
152C2×C4×C7C2×SD1611yescharacteristic
153C2×C4×C7C2×Q1611yescharacteristic
154C2×Dic7—22no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—84no—
167Dic14—82no—
168C7×C8—82no—
169C7⋊C8—82no—
170C22×Q8—71no—
171C22×D4C22⋊D711yescharacteristic
172C23×C4—141no—
173C23×C4C4×D711yescharacteristic
174C23×C4D2811yescharacteristic
175C2×M16—22no—
176C22×C8—281no—
177C22⋊Q8—281no—
178C22⋊Q8—281no—
179C4×D4—41no—
180C4×D4—41no—
181C2×C4⋊C4—71no—
182C2×C4⋊C4—141no—
183C2×C4⋊C4—141no—
184C2×C4⋊C4—141no—
185C2×C4⋊C4C22×D711yescharacteristic
186C2×C22⋊C4—141no—
187C2×C22⋊C4—141no—
188C2×C22⋊C4—141no—
189C2×C22⋊C4C4×D711yescharacteristic
190C2×C22⋊C4D2811yescharacteristic
191C2×C42C22⋊D711yescharacteristic
192C4⋊C8—41no—
193C4⋊C8—41no—
194#100—42no—
195C22⋊C8—142no—
196C22⋊C8—281no—
197#95—71no—
198#95—71no—
199#95—141no—
200#95—141no—
201#95—141no—
202#95—141no—
203#95—141no—
204C22×C7—21no—
205C22×C7—21no—
206C22×C7—22no—
207C22×C7—22no—
208C22×C7—42no—
209C22×C7—42no—
210C22×C7—42no—
211C22×C7—41no—
212C22×C7—41no—
213C22×C7—41no—
214C22×C7—41no—
215C22×C7—81no—
216C22×C7C2×#9911yescharacteristic
217C22×C7C2×#10311yescharacteristic
218C22×C7#42111yescharacteristic
219C4×C7—21no—
220C4×C7—21no—
221C4×C7—21no—
222C4×C7—21no—
223C4×C7—41no—
224C4×C7—41no—
225C4×C7—41no—
226Dic7—42no—
227Dic7—81no—
228Dic7—81no—
229Dic7—81no—
230C24(C2×D7)⋊C411yescharacteristic
231C24(C2×D7)⋊C411yescharacteristic
232C2×Q8—281no—
233C2×Q8—561no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4#114212yes—
237C2×D4#114412yes—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4—141no—
245C22×C4—141no—
246C22×C4—141no—
247C22×C4—141no—
248C22×C4—282no—
249C22×C4—282no—
250C22×C4—561no—
251C22×C4(C2×D7)⋊C411yescharacteristic
252C22×C4(C2×D7)⋊C411yescharacteristic
253C22×C4C2×C4×D711yescharacteristic
254C22×C4C2×D2811yescharacteristic
255C22×C4C2×C22⋊D711yescharacteristic
256M16—42no—
257M16—42no—
258C2×C8—42no—
259C2×C8—282no—
260C2×C8—562no—
261C4⋊C4—41no—
262C4⋊C4—281no—
263C4⋊C4—282no—
264C4⋊C4—281no—
265C4⋊C4—281no—
266C4⋊C4—561no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—282no—
270C22⋊C4—282no—
271C22⋊C4—561no—
272C42—21no—
273C42—21no—
274C2×C7—21no—
275C2×C7—21no—
276C2×C7—42no—
277C2×C7—42no—
278C2×C7#152011yescharacteristic
279C2×C7#212111yescharacteristic
280C2×C7#213211yescharacteristic
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23#638412yes—
290C23#638412yes—
291C23C2×(C2×D7)⋊C411yescharacteristic
292Q8—562no—
293D4—42no—
294D4—42no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—142no—
309C2×C4—281no—
310C2×C4—281no—
311C2×C4—281no—
312C2×C4—281no—
313C2×C4—281no—
314C2×C4—281no—
315C2×C4—281no—
316C2×C4—281no—
317C2×C4—281no—
318C2×C4—281no—
319C2×C4—281no—
320C2×C4—564no—
321C2×C4#638011yescharacteristic
322C2×C4#638011yescharacteristic
323C2×C4C2×#114211yescharacteristic
324C2×C4C2×#114411yescharacteristic
325C8—82no—
326C8—562no—
327C7#1190611yescharacteristic, complemented, Sylow
328C22—21no—
329C22—21no—
330C22—22no—
331C22—22no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—81no—
340C22C2×#638011yescharacteristic
341C22C2×#638411yescharacteristic
342C22#8977711yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—282no—
351C4—561no—
352C4—561no—
353C4—561no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—42no—
358C2#1172726411yescharacteristic
359C2#1172784811yescharacteristic
360C2#1172790211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1800C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C4⋊C4C23
hypercenter#1800D7
hypocenterC7#11906
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
4. #11725302C2semidirect
5. #11725300C2semidirect
327. C7#11906semidirect

Maximal subgroups

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

subgroupindex
#117398302
C7×#18002
#117293542
#117253022
#117253002
#119067