Finite Group Databasebeta

← #13264685

Subgroups — #13264685

Order 1792.

506 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 83 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#11739561C211yesmaximal, characteristic
2C2×C7×#323C211yesmaximal, characteristic
3#11729296C211yesmaximal, characteristic
4#11725256C212yesmaximal, complemented
5#11725255C212yesmaximal, complemented
6C22×C7×C22⋊C4C2211yescharacteristic
7C2×#6487C411yescharacteristic, complemented
8C2×C7×C22⋊C8—21no—
9#90019—21no—
10#90019—21no—
11#89983—21no—
12C4×C22⋊Dic7C411yescharacteristic, complemented
13#89725C411yescharacteristic, complemented
14#89725C2211yescharacteristic
15#89719C411yescharacteristic, complemented
16#89719C2211yescharacteristic
17#89717—21no—
18#89717—21no—
19C7×#323—21no—
20C7×#323C2212yes—
21#89321—21no—
22#89321C2212yes—
23#11845—71nomaximal, Sylow
24C25×C7D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×Dic14C2×C411yescharacteristic
28C22×C7×C8—41no—
29C2×C7×C22⋊C4—41no—
30C2×C7×C22⋊C4—41no—
31C2×C7×C22⋊C4C2×C411yescharacteristic
32C2×C7×C22⋊C4D411yescharacteristic
33C2×C7×C22⋊C4D411yescharacteristic
34C2×C7×C22⋊C4C2311yescharacteristic
35C2×C22⋊Dic7—21no—
36C2×C22⋊Dic7—21no—
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C22⋊Dic7—22no—
40C2×C22⋊Dic7—21no—
41C2×C22⋊Dic7—21no—
42C2×C22⋊Dic7—41no—
43C2×C22⋊Dic7—41no—
44C2×C4⋊Dic7C2×C411yescharacteristic
45#6487—41no—
46#6487—41no—
47C2×Dic7⋊C4—21no—
48C2×C4×Dic7—21no—
49C7×C22⋊C8—22no—
50C7×C22⋊C8—41no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95C2×C411yescharacteristic
56C7⋊#95C2×C411yescharacteristic
57#2561—71no—
58#1819—71no—
59C2×#323D711yescharacteristic
60#1351—72no—
61#1344—72no—
62C24×C7—21no—
63C24×C7—21no—
64C24×C7—22no—
65C24×C7—41no—
66C24×C7—42no—
67C24×C7—81no—
68C24×C7C22⋊C411yescharacteristic
69C24×C7C22⋊C411yescharacteristic
70C24×C7C2×D411yescharacteristic
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—42no—
76C22×C4×C7—81no—
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22×C411yescharacteristic
80C22×C4×C7C2×D411yescharacteristic
81C22×Dic7—21no—
82C22×Dic7—21no—
83C22×Dic7—21no—
84C22×Dic7—21no—
85C22×Dic7—42no—
86C2×Dic14—41no—
87C2×Dic14—81no—
88C2×C7×C8—42no—
89C2×C7×C8—82no—
90C7×C22⋊C4—41no—
91C7×C22⋊C4—41no—
92C7×C22⋊C4—41no—
93C7×C22⋊C4—41no—
94C22⋊Dic7—42no—
95C22⋊Dic7—42no—
96C22⋊Dic7—41no—
97C22⋊Dic7—41no—
98C22⋊Dic7—42no—
99C22⋊Dic7—42no—
100C22⋊Dic7—42no—
101C22⋊Dic7—81no—
102C22⋊Dic7—81no—
103C22⋊Dic7—82no—
104C22⋊Dic7—82no—
105C4⋊Dic7—41no—
106Dic7⋊C4—42no—
107C4×Dic7—81no—
108C2×C22⋊Q8—71no—
109C22×C22⋊C4C2×D711yescharacteristic
110C2×C22⋊C8—21no—
111#397—71no—
112#397—71no—
113#393—71no—
114#393—71no—
115#388—141no—
116#388—141no—
117#381—141no—
118#379—141no—
119#379—141no—
120C4×C22⋊C4—71no—
121#342—72no—
122#342—141no—
123#323—21no—
124#323C2×D712yes—
125C23×C7—22no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7—41no—
134C23×C7—42no—
135C23×C7—42no—
136C23×C7—41no—
137C23×C7—41no—
138C23×C7—41no—
139C23×C7—41no—
140C23×C7—42no—
141C23×C7—42no—
142C23×C7—81no—
143C23×C7—81no—
144C23×C7—84no—
145C23×C7—84no—
146C23×C7#9911yescharacteristic
147C23×C7#9911yescharacteristic
148C23×C7C2×C22⋊C411yescharacteristic
149C23×C7#13512yes—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—42no—
155C2×C4×C7—41no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7—81no—
160C2×C4×C7—81no—
161C2×C4×C7—81no—
162C2×Dic7—41no—
163C2×Dic7—41no—
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—41no—
167C2×Dic7—41no—
168C2×Dic7—41no—
169C2×Dic7—41no—
170C2×Dic7—41no—
171C2×Dic7—41no—
172C2×Dic7—41no—
173C2×Dic7—41no—
174C2×Dic7—82no—
175C2×Dic7—82no—
176C2×Dic7—82no—
177Dic14—82no—
178C7×C8—82no—
179C25D2811yescharacteristic
180C22×Q8—71no—
181C23×C4C4×D711yescharacteristic
182C23×C4C22⋊D711yescharacteristic
183C22×C8—41no—
184C22⋊Q8—281no—
185C22⋊Q8—281no—
186C2×C4⋊C4—71no—
187C2×C4⋊C4—141no—
188C2×C22⋊C4—41no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—141no—
191C2×C22⋊C4—141no—
192C2×C22⋊C4—141no—
193C2×C22⋊C4—141no—
194C2×C22⋊C4—142no—
195C2×C22⋊C4—141no—
196C2×C22⋊C4—141no—
197C2×C22⋊C4—281no—
198C2×C22⋊C4—281no—
199C2×C22⋊C4C4×D711yescharacteristic
200C2×C22⋊C4D2811yescharacteristic
201C2×C22⋊C4C22⋊D711yescharacteristic
202C2×C22⋊C4C22×D711yescharacteristic
203C2×C42—141no—
204C22⋊C8—22no—
205C22⋊C8—41no—
206#95—71no—
207#95—71no—
208#95—141no—
209#95—141no—
210#95—141no—
211#95—141no—
212C22×C7—21no—
213C22×C7—21no—
214C22×C7—21no—
215C22×C7—21no—
216C22×C7—21no—
217C22×C7—21no—
218C22×C7—22no—
219C22×C7—21no—
220C22×C7—42no—
221C22×C7—42no—
222C22×C7—42no—
223C22×C7—42no—
224C22×C7—41no—
225C22×C7—41no—
226C22×C7—41no—
227C22×C7—41no—
228C22×C7—41no—
229C22×C7—81no—
230C22×C7—84no—
231C22×C7—81no—
232C22×C7—84no—
233C22×C7#35412yes—
234C22×C7C2×#9911yescharacteristic
235C22×C7#41611yescharacteristic
236C22×C7#42111yescharacteristic
237C4×C7—41no—
238C4×C7—41no—
239C4×C7—41no—
240C4×C7—41no—
241Dic7—81no—
242Dic7—81no—
243Dic7—81no—
244Dic7—81no—
245Dic7—162no—
246C24—21no—
247C24—21no—
248C24—22no—
249C24—41no—
250C24—42no—
251C24—81no—
252C24(C2×D7)⋊C411yescharacteristic
253C24(C2×D7)⋊C411yescharacteristic
254C24C2×D2811yescharacteristic
255C2×Q8—281no—
256C2×Q8—561no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—42no—
262C22×C4—81no—
263C22×C4—141no—
264C22×C4—141no—
265C22×C4—141no—
266C22×C4—141no—
267C22×C4—282no—
268C22×C4(C2×D7)⋊C411yescharacteristic
269C22×C4(C2×D7)⋊C411yescharacteristic
270C22×C4C2×C4×D711yescharacteristic
271C22×C4C2×C22⋊D711yescharacteristic
272C2×C8—42no—
273C2×C8—82no—
274C4⋊C4—281no—
275C4⋊C4—282no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—282no—
281C22⋊C4—282no—
282C22⋊C4—282no—
283C22⋊C4—281no—
284C22⋊C4—281no—
285C22⋊C4—282no—
286C22⋊C4—282no—
287C22⋊C4—561no—
288C22⋊C4—561no—
289C22⋊C4—562no—
290C22⋊C4—562no—
291C42—561no—
292C2×C7—21no—
293C2×C7—21no—
294C2×C7—22no—
295C2×C7—42no—
296C2×C7—41no—
297C2×C7—81no—
298C2×C7#151611yescharacteristic
299C2×C7#212111yescharacteristic
300C2×C7C2×#35411yescharacteristic
301C23—21no—
302C23—21no—
303C23—21no—
304C23—22no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—81no—
320C23—84no—
321C23—84no—
322C23#638011yescharacteristic
323C23#638011yescharacteristic
324C23#646712yes—
325C23C2×(C2×D7)⋊C411yescharacteristic
326Q8—562no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—281no—
340C2×C4—281no—
341C2×C4—281no—
342C2×C4—281no—
343C2×C4—281no—
344C2×C4—281no—
345C2×C4—281no—
346C2×C4—281no—
347C2×C4—281no—
348C2×C4—281no—
349C2×C4—281no—
350C2×C4—281no—
351C2×C4—562no—
352C2×C4—562no—
353C2×C4—562no—
354C8—82no—
355C7#1184511yescharacteristic, complemented, Sylow
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—84no—
375C22—81no—
376C22—84no—
377C22#8926812yes—
378C22C2×#638011yescharacteristic
379C22#8988511yescharacteristic
380C22#8991111yescharacteristic
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—561no—
386C4—561no—
387C4—561no—
388C4—561no—
389C4—1122no—
390C2—21no—
391C2—21no—
392C2—22no—
393C2—42no—
394C2—41no—
395C2—81no—
396C2#1172769711yescharacteristic
397C2C2×#8926811yescharacteristic
398C2#1172784811yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC2×C7×#323C2
socleC22×C7C2×#99
prime radicalC25×C7D4
cosocleC2×C7×C22⋊C4C23
hypercenterC2×#323D7
hypocenterC7#11845
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
4. #11725256C2semidirect
5. #11725255C2semidirect
7. C2×#6487C4semidirect
12. C4×C22⋊Dic7C4semidirect
13. #89725C4semidirect
15. #89719C4semidirect
355. C7#11845semidirect

Maximal subgroups

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

subgroupindex
#117395612
C2×C7×#3232
#117292962
#117252562
#117252552
#118457