Finite Group Databasebeta

← #13264262

Subgroups — #13264262

Order 1792.

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

normal subgroups only

This group has 586 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
1C7×#2482C211yesmaximal, characteristic
2C2×#89321C211yesmaximal, characteristic
3#11729293C211yesmaximal, characteristic
4#11725457C212yesmaximal, complemented
5#11725455C212yesmaximal, complemented
6C2×C7×#117C411yescharacteristic, complemented
7C22×C7×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic7—21no—
9C7×#399C411yescharacteristic, complemented
10C7×#399C2211yescharacteristic
11C7×#397C411yescharacteristic, complemented
12C7×#397C2211yescharacteristic
13C7×#388—21no—
14C7×#388—21no—
15C7×#385—21no—
16C7×#381C411yescharacteristic, complemented
17C7×#379—21no—
18#89979—21no—
19#89321—21no—
20#89321C2212yes—
21#89320—21no—
22#89320C2212yes—
23#11755—71nomaximal, Sylow
24C25×C7D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C23×Dic7—41no—
28C7×#117—41no—
29C7×#117—41no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
33C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
34C2×C7×C22⋊C4—21no—
35C2×C7×C22⋊C4—21no—
36C2×C7×C22⋊C4—21no—
37C2×C7×C22⋊C4—21no—
38C2×C7×C22⋊C4—21no—
39C2×C7×C22⋊C4—21no—
40C2×C7×C22⋊C4—41no—
41C2×C7×C22⋊C4—41no—
42C2×C7×C22⋊C4C2×C411yescharacteristic
43C2×C7×C22⋊C4D411yescharacteristic
44C2×C7×C22⋊C4D411yescharacteristic
45C2×C7×C22⋊C4C2311yescharacteristic
46C2×C42×C7—21no—
47C2×C22⋊Dic7—24no—
48C2×C22⋊Dic7—22no—
49C2×C22⋊Dic7—41no—
50C2×C22⋊Dic7—42no—
51C2×#1136—41no—
52C7×#95—21no—
53C7×#95—21no—
54C7×#95—21no—
55C7×#95C2×C411yescharacteristic, complemented
56C7×#95C2×C411yescharacteristic, complemented
57C22⋊(C7⋊C8)—22no—
58C22⋊(C7⋊C8)—41no—
59#2482D711yescharacteristic
60C2×#342—71no—
61#1462—71no—
62#1352—72no—
63#1344—72no—
64C24×C7—21no—
65C24×C7—21no—
66C24×C7—22no—
67C24×C7—21no—
68C24×C7—21no—
69C24×C7—42no—
70C24×C7—81no—
71C24×C7C22⋊C411yescharacteristic
72C24×C7C22⋊C411yescharacteristic
73C24×C7C2×D411yescharacteristic
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—21no—
78C22×C4×C7—21no—
79C22×C4×C7—21no—
80C22×C4×C7—21no—
81C22×C4×C7—21no—
82C22×C4×C7—42no—
83C22×C4×C7—81no—
84C22×C4×C7C22⋊C411yescharacteristic
85C22×C4×C7C22⋊C411yescharacteristic
86C22×C4×C7C22×C411yescharacteristic
87C22×C4×C7C2×D411yescharacteristic
88C22×Dic7—44no—
89C22×Dic7—42no—
90C22×Dic7—82no—
91C22×Dic7—82no—
92C7×C4⋊C4—41no—
93C7×C4⋊C4—41no—
94C7×C4⋊C4—81no—
95C7×C4⋊C4—81no—
96C7×C22⋊C4—41no—
97C7×C22⋊C4—41no—
98C7×C22⋊C4—41no—
99C7×C22⋊C4—41no—
100C7×C22⋊C4—42no—
101C7×C22⋊C4—41no—
102C7×C22⋊C4—41no—
103C7×C22⋊C4—42no—
104C7×C22⋊C4—41no—
105C7×C22⋊C4—41no—
106C7×C22⋊C4—81no—
107C7×C22⋊C4—81no—
108C42×C7—42no—
109C22⋊Dic7—24no—
110C22⋊Dic7—44no—
111C22⋊Dic7—42no—
112#1136—82no—
113C2×C7⋊C8—42no—
114C2×#117Dic711yescharacteristic, complemented
115C22×C22⋊C4—141no—
116C22×C22⋊C4C2×D711yescharacteristic
117#407—141no—
118#399Dic711yescharacteristic, complemented
119#399C2×D711yescharacteristic
120#397Dic711yescharacteristic, complemented
121#397C2×D711yescharacteristic
122#388—21no—
123#388—21no—
124#385—21no—
125#381Dic711yescharacteristic, complemented
126#379—21no—
127#342—72no—
128#342—141no—
129#323—72no—
130#323—141no—
131C23×C7—22no—
132C23×C7—22no—
133C23×C7—22no—
134C23×C7—22no—
135C23×C7—22no—
136C23×C7—21no—
137C23×C7—21no—
138C23×C7—21no—
139C23×C7—21no—
140C23×C7—21no—
141C23×C7—21no—
142C23×C7—41no—
143C23×C7—42no—
144C23×C7—41no—
145C23×C7—41no—
146C23×C7—41no—
147C23×C7—41no—
148C23×C7—42no—
149C23×C7—81no—
150C23×C7—81no—
151C23×C7—84no—
152C23×C7—82no—
153C23×C7—82no—
154C23×C7#9911yescharacteristic
155C23×C7#9911yescharacteristic
156C23×C7#10412yes—
157C23×C7C2×C22⋊C411yescharacteristic
158C23×C7AGL(1,ℤ/8)11yescharacteristic
159C23×C7#13711yescharacteristic
160C2×C4×C7—21no—
161C2×C4×C7—21no—
162C2×C4×C7—21no—
163C2×C4×C7—21no—
164C2×C4×C7—42no—
165C2×C4×C7—42no—
166C2×C4×C7—42no—
167C2×C4×C7—41no—
168C2×C4×C7—41no—
169C2×C4×C7—41no—
170C2×C4×C7—41no—
171C2×C4×C7—41no—
172C2×C4×C7—41no—
173C2×C4×C7—41no—
174C2×C4×C7—41no—
175C2×C4×C7—41no—
176C2×C4×C7—41no—
177C2×C4×C7—41no—
178C2×C4×C7—41no—
179C2×C4×C7—41no—
180C2×C4×C7—41no—
181C2×C4×C7—41no—
182C2×C4×C7—41no—
183C2×C4×C7—81no—
184C2×Dic7—44no—
185C2×Dic7—88no—
186C2×Dic7—82no—
187C2×Dic7—82no—
188C7⋊C8—82no—
189C25C22⋊D711yescharacteristic
190C23×C4—281no—
191C23×C4C2×Dic711yescharacteristic
192C23×C4C22⋊D711yescharacteristic
193C2×M16—281no—
194#117—41no—
195#117—41no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×Dic711yescharacteristic, complemented
199C2×C4⋊C4C2×Dic711yescharacteristic, complemented
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4—41no—
208C2×C22⋊C4—144no—
209C2×C22⋊C4—142no—
210C2×C22⋊C4—281no—
211C2×C22⋊C4—282no—
212C2×C22⋊C4C2×Dic711yescharacteristic
213C2×C22⋊C4C22⋊D711yescharacteristic
214C2×C22⋊C4C22⋊D711yescharacteristic
215C2×C22⋊C4C22×D711yescharacteristic
216C2×C42—21no—
217C22⋊C8—142no—
218C22⋊C8—281no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95C2×Dic711yescharacteristic, complemented
223#95C2×Dic711yescharacteristic, complemented
224C22×C7—21no—
225C22×C7—21no—
226C22×C7—21no—
227C22×C7—21no—
228C22×C7—21no—
229C22×C7—21no—
230C22×C7—21no—
231C22×C7—21no—
232C22×C7—22no—
233C22×C7—21no—
234C22×C7—42no—
235C22×C7—42no—
236C22×C7—42no—
237C22×C7—41no—
238C22×C7—41no—
239C22×C7—44no—
240C22×C7—44no—
241C22×C7—41no—
242C22×C7—41no—
243C22×C7—41no—
244C22×C7—41no—
245C22×C7—81no—
246C22×C7—81no—
247C22×C7—82no—
248C22×C7—82no—
249C22×C7#35212yes—
250C22×C7C2×#9911yescharacteristic
251C22×C7#41711yescharacteristic
252C22×C7C2×#10411yescharacteristic
253C4×C7—41no—
254C4×C7—41no—
255C4×C7—41no—
256C4×C7—41no—
257C4×C7—81no—
258C4×C7—81no—
259C4×C7—81no—
260C4×C7—81no—
261Dic7—84no—
262C24—21no—
263C24—21no—
264C24—22no—
265C24—21no—
266C24—21no—
267C24—42no—
268C24—81no—
269C24C22⋊Dic711yescharacteristic
270C24C22⋊Dic711yescharacteristic
271C24C2×C22⋊D711yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—81no—
282C22×C4—284no—
283C22×C4—282no—
284C22×C4—562no—
285C22×C4—562no—
286C22×C4C22⋊Dic711yescharacteristic
287C22×C4C22⋊Dic711yescharacteristic
288C22×C4C22×Dic711yescharacteristic
289C22×C4C2×C22⋊D711yescharacteristic
290M16—562no—
291C2×C8—282no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—81no—
295C4⋊C4—81no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—144no—
309C22⋊C4—284no—
310C22⋊C4—282no—
311C42—42no—
312C2×C7—21no—
313C2×C7—21no—
314C2×C7—22no—
315C2×C7—41no—
316C2×C7—41no—
317C2×C7—42no—
318C2×C7—41no—
319C2×C7#150411yescharacteristic
320C2×C7C2×#35211yescharacteristic
321C2×C7#212711yescharacteristic
322C23—22no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—22no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—42no—
340C23—81no—
341C23—81no—
342C23—84no—
343C23—82no—
344C23—82no—
345C23#640811yescharacteristic
346C23#640811yescharacteristic
347C23#641112yes—
348C23#651211yescharacteristic
349C23#651411yescharacteristic
350C23C2×C22⋊Dic711yescharacteristic
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—284no—
376C2×C4—568no—
377C2×C4—562no—
378C2×C4—562no—
379C8—562no—
380C7#1175511yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—21no—
390C22—21no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—41no—
395C22—41no—
396C22—44no—
397C22—44no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22—81no—
404C22—82no—
405C22—82no—
406C22#8933412yes—
407C22C2×#640811yescharacteristic
408C22#9000411yescharacteristic
409C22C2×#641111yescharacteristic
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—81no—
415C4—81no—
416C4—81no—
417C4—81no—
418C4—564no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2—41no—
423C2—41no—
424C2—42no—
425C2—41no—
426C2C2×#8933411yescharacteristic
427C2#1172946211yescharacteristic
428C2#1172961411yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#2482C2
socleC22×C7C2×#99
prime radicalC25×C7D4
cosocleC2×C7×C22⋊C4C23
hypercenter#2482D7
hypocenterC7#11755
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
4. #11725457C2semidirect
5. #11725455C2semidirect
6. C2×C7×#117C4semidirect
9. C7×#399C4semidirect
11. C7×#397C4semidirect
16. C7×#381C4semidirect
32. C2×C7×C4⋊C4C2×C4semidirect
33. C2×C7×C4⋊C4C2×C4semidirect
55. C7×#95C2×C4semidirect
56. C7×#95C2×C4semidirect
114. C2×#117Dic7semidirect
118. #399Dic7semidirect
120. #397Dic7semidirect
125. #381Dic7semidirect
198. C2×C4⋊C4C2×Dic7semidirect
199. C2×C4⋊C4C2×Dic7semidirect
222. #95C2×Dic7semidirect
223. #95C2×Dic7semidirect
380. C7#11755semidirect

Maximal subgroups

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

subgroupindex
C7×#24822
C2×#893212
#117292932
#117254572
#117254552
#117557