Finite Group Databasebeta

← #13264580

Subgroups — #13264580

Order 1792.

476 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 79 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#11739866C211yesmaximal, characteristic
2C7×#1799C211yesmaximal, characteristic, complemented
3#11729356C211yesmaximal, characteristic, complemented
4#11725296C212yesmaximal, complemented
5#11725295C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6438C411yescharacteristic, complemented
8C2×C7×#99—21no—
9C7×#380—21no—
10#89995—21no—
11#89985—21no—
12#89985—21no—
13#89979—21no—
14#89765—21no—
15#89732C411yescharacteristic, complemented
16#89732C2211yescharacteristic
17#89719C411yescharacteristic, complemented
18#89719C2211yescharacteristic
19#89709C411yescharacteristic, complemented
20C7×#342C2212yes—
21#89323—21no—
22#89320C2212yes—
23#11825—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×C22⋊D7—21no—
28C22×C22⋊D7—21no—
29C22×D28C2×C411yescharacteristic
30C22×Dic14C2×C411yescharacteristic
31C4×C7×D4—41no—
32C4×C7×D4—41no—
33C2×C7×C4⋊C4—41no—
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C7×C22⋊C4—22no—
36C2×C7×C22⋊C4C2×C411yescharacteristic
37C2×C7×C22⋊C4C2311yescharacteristic
38C2×C42×C7C2×C411yescharacteristic
39C2×C22⋊Dic7—21no—
40C2×C22⋊Dic7—21no—
41C2×(C2×D7)⋊C4—21no—
42C2×(C2×D7)⋊C4—21no—
43C2×(C2×D7)⋊C4—21no—
44C2×(C2×D7)⋊C4—21no—
45C2×#1136—41no—
46#6438—41no—
47#6438—41no—
48C7×#99—42no—
49C7×#95—41no—
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#2631—71no—
59#1799D711yescharacteristic, complemented
60#1465—71no—
61#1351—72no—
62#1343—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C2×D411yescharacteristic
65C23×D7—21no—
66C2×C7×D4—21no—
67C2×C7×D4—21no—
68C2×C7×D4—41no—
69C2×C7×D4—41no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—21no—
74C22×C4×C7—42no—
75C22×C4×C7—81no—
76C22×C4×C7—81no—
77C22×C4×C7C22⋊C411yescharacteristic
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22×C411yescharacteristic
81C22×C4×C7C2×D411yescharacteristic
82C2×C22⋊D7—42no—
83C2×C22⋊D7—41no—
84C2×C22⋊D7—41no—
85C2×C22⋊D7—81no—
86C2×C22⋊D7—81no—
87C2×C22⋊D7—81no—
88C2×C22⋊D7—81no—
89C22×Dic7—21no—
90C22×Dic7—21no—
91C22×Dic7—21no—
92C2×D28—41no—
93C2×D28—81no—
94C2×Dic14—41no—
95C2×Dic14—81no—
96C7×C4⋊C4—41no—
97C7×C4⋊C4—82no—
98C7×C22⋊C4—41no—
99C7×C22⋊C4—41no—
100C7×C22⋊C4—42no—
101C7×C22⋊C4—42no—
102C42×C7—21no—
103C42×C7—21no—
104C22⋊Dic7—81no—
105C22⋊Dic7—81no—
106(C2×D7)⋊C4—42no—
107(C2×D7)⋊C4—41no—
108(C2×D7)⋊C4—41no—
109(C2×D7)⋊C4—81no—
110(C2×D7)⋊C4—81no—
111#1136—82no—
112C2×C7⋊C8—42no—
113C2×#124—71no—
114C2×C4×D4C2×D711yescharacteristic
115C2×#99—21no—
116#407—141no—
117#397—141no—
118#393—71no—
119#393—71no—
120#392—71no—
121#392—71no—
122#392—141no—
123#386—141no—
124#386—141no—
125#383—71no—
126#380—21no—
127#342C2×D712yes—
128#324—141no—
129#323—72no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7—21no—
134C23×C7—21no—
135C23×C7—41no—
136C23×C7—41no—
137C23×C7—41no—
138C23×C7—41no—
139C23×C7C2×C22⋊C411yescharacteristic
140C23×C7AGL(1,ℤ/8)11yescharacteristic
141C23×C7#13711yescharacteristic
142C22×D7—41no—
143C22×D7—41no—
144C22×D7—41no—
145C22×D7—41no—
146C22×D7—41no—
147C22×D7—41no—
148C22×D7—41no—
149C7×D4—42no—
150C7×D4—42no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—21no—
156C2×C4×C7—21no—
157C2×C4×C7—41no—
158C2×C4×C7—42no—
159C2×C4×C7—42no—
160C2×C4×C7—41no—
161C2×C4×C7—41no—
162C2×C4×C7—41no—
163C2×C4×C7—81no—
164C2×C4×C7—81no—
165C2×C4×C7—82no—
166C2×C4×C7—82no—
167C2×C4×C7—82no—
168C2×C4×C7#9911yescharacteristic
169C2×C4×C7#9911yescharacteristic
170C22⋊D7—82no—
171C22⋊D7—82no—
172C22⋊D7—84no—
173C2×Dic7—41no—
174C2×Dic7—41no—
175C2×Dic7—41no—
176C2×Dic7—41no—
177C2×Dic7—41no—
178C2×Dic7—41no—
179C2×Dic7—41no—
180C2×Dic7—41no—
181C2×Dic7—41no—
182D28—82no—
183Dic14—82no—
184C7⋊C8—82no—
185C22×Q8—71no—
186C22×D4—71no—
187C22×D4—141no—
188C22×D4—141no—
189C22×D4C22⋊D711yescharacteristic
190C23×C4D2811yescharacteristic
191C23×C4C22⋊D711yescharacteristic
192C2×M16—281no—
193#124—281no—
194#124—281no—
195C4×D4—41no—
196C4×D4—41no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4D2811yescharacteristic
199C2×C22⋊C4—22no—
200C2×C22⋊C4—141no—
201C2×C22⋊C4—141no—
202C2×C22⋊C4—141no—
203C2×C22⋊C4—141no—
204C2×C22⋊C4—141no—
205C2×C22⋊C4—141no—
206C2×C22⋊C4C4×D711yescharacteristic
207C2×C22⋊C4C22×D711yescharacteristic
208C2×C42C4×D711yescharacteristic
209#99—42no—
210C22⋊C8—142no—
211C22⋊C8—281no—
212#95—41no—
213#95—71no—
214#95—71no—
215#95—141no—
216#95—141no—
217#95—141no—
218#95—141no—
219C22×C7—21no—
220C22×C7—21no—
221C22×C7—21no—
222C22×C7—21no—
223C22×C7—41no—
224C22×C7—41no—
225C22×C7—42no—
226C22×C7—41no—
227C22×C7—41no—
228C22×C7—41no—
229C22×C7—41no—
230C22×C7—41no—
231C22×C7—81no—
232C22×C7—81no—
233C22×C7C2×#9911yescharacteristic
234C22×C7#41711yescharacteristic
235C22×C7#42111yescharacteristic
236C2×D7—81no—
237C2×D7—81no—
238C2×D7—81no—
239C2×D7—81no—
240C2×D7—81no—
241C2×D7—81no—
242C2×D7—81no—
243C4×C7—21no—
244C4×C7—21no—
245C4×C7—41no—
246C4×C7—41no—
247C4×C7—41no—
248C4×C7—41no—
249C4×C7—162no—
250Dic7—81no—
251Dic7—81no—
252Dic7—81no—
253C24—141no—
254C24(C2×D7)⋊C411yescharacteristic
255C24C2×C22⋊D711yescharacteristic
256C2×Q8—281no—
257C2×Q8—561no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—281no—
263C2×D4—282no—
264C2×D4—281no—
265C2×D4—281no—
266C2×D4—561no—
267C2×D4—561no—
268C2×D4—561no—
269C2×D4—561no—
270C2×D4—561no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4—141no—
279C22×C4—141no—
280C22×C4—141no—
281C22×C4(C2×D7)⋊C411yescharacteristic
282C22×C4(C2×D7)⋊C411yescharacteristic
283C22×C4(C2×D7)⋊C411yescharacteristic
284C22×C4C2×C4×D711yescharacteristic
285C22×C4C2×D2811yescharacteristic
286M16—562no—
287C2×C8—282no—
288C4⋊C4—41no—
289C4⋊C4—82no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—282no—
295C22⋊C4—281no—
296C22⋊C4—281no—
297C22⋊C4—561no—
298C22⋊C4—561no—
299C22⋊C4—561no—
300C22⋊C4—561no—
301C42—21no—
302C42—21no—
303C2×C7—21no—
304C2×C7—21no—
305C2×C7—41no—
306C2×C7—41no—
307C2×C7—81no—
308C2×C7#151311yescharacteristic
309C2×C7#212211yescharacteristic
310C2×C7#212711yescharacteristic
311D7—161no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—281no—
322C23—281no—
323C23—281no—
324C23—281no—
325C23—281no—
326C23—281no—
327C23—281no—
328C23C2×(C2×D7)⋊C411yescharacteristic
329C23#649511yescharacteristic
330C23#650511yescharacteristic
331Q8—562no—
332D4—42no—
333D4—42no—
334D4—562no—
335D4—562no—
336D4—562no—
337D4—564no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—281no—
356C2×C4—281no—
357C2×C4—281no—
358C2×C4—281no—
359C2×C4—281no—
360C2×C4—281no—
361C2×C4—281no—
362C2×C4—281no—
363C2×C4—281no—
364C2×C4#638011yescharacteristic
365C2×C4#638011yescharacteristic
366C8—562no—
367C7#1182511yescharacteristic, complemented, Sylow
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—561no—
383C22—561no—
384C22—561no—
385C22—561no—
386C22—561no—
387C22—561no—
388C22—561no—
389C22C2×#638011yescharacteristic
390C22#8973811yescharacteristic
391C22#8977711yescharacteristic
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—162no—
399C4—561no—
400C4—561no—
401C4—561no—
402C2—21no—
403C2—21no—
404C2—41no—
405C2—41no—
406C2—81no—
407C2—1121no—
408C2#1172726211yescharacteristic
409C2#1172777311yescharacteristic
410C2#1172781111yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1799C2
socleC22×C7C2×#99
prime radical#11739866C2
cosocleC2×C7×C22⋊C4C23
hypercenter#1799D7
hypocenterC7#11825
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. C7×#1799C2semidirect
3. #11729356C2semidirect
4. #11725296C2semidirect
5. #11725295C2semidirect
7. C2×#6438C4semidirect
15. #89732C4semidirect
17. #89719C4semidirect
19. #89709C4semidirect
59. #1799D7semidirect
367. C7#11825semidirect

Maximal subgroups

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

subgroupindex
#117398662
C7×#17992
#117293562
#117252962
#117252952
#118257