Finite Group Databasebeta

← #13249762

Subgroups — #13249762

Order 1792.

530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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#11739837C211yesmaximal, characteristic
2#11739749C211yesmaximal, characteristic
3C4×C7×#99C211yesmaximal, characteristic
4#11727199C212yesmaximal, complemented
5#11725422C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6487C2211yescharacteristic
8C2×C7×#99—21no—
9C4×C7×C22⋊C4C2212yes—
10#89994—21no—
11#89983C2211yescharacteristic
12#89982—21no—
13#89979—21no—
14#89979C2212yes—
15#89784—24no—
16#89755C411yescharacteristic, complemented
17#89751C411yescharacteristic, complemented
18#89725C411yescharacteristic, complemented
19#89724—21no—
20#89719C411yescharacteristic, complemented
21#89705—21no—
22#89697—21no—
23C7×#342—21no—
24#89247—24no—
25#9184—71nomaximal, Sylow
26C22×C7×D4D411yescharacteristic
27C23×C4×C7D411yescharacteristic
28C23×C4×C7C2311yescharacteristic
29C22×Dic14C2×C411yescharacteristic
30C4×C7×D4—22no—
31C4×C7×D4—22no—
32C2×C7×C4⋊C4C2×C411yescharacteristic
33C2×C7×C22⋊C4—22no—
34C2×C7×C22⋊C4C2×C411yescharacteristic
35C2×C7×C22⋊C4D411yescharacteristic
36C2×C42×C7—22no—
37C2×C42×C7D411yescharacteristic
38C2×C22⋊Dic7—21no—
39C2×C22⋊Dic7—21no—
40C2×C22⋊Dic7—21no—
41C2×C22⋊Dic7—21no—
42C2×C4⋊Dic7C2×C411yescharacteristic
43#6487—22no—
44#6487—22no—
45C2×Dic7⋊C4—21no—
46C2×Dic7⋊C4—21no—
47C2×Dic7⋊C4—21no—
48C2×#1136—22no—
49C2×#1136—22no—
50C7×#99—24no—
51C7×#95—22no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95C2×C411yescharacteristic
58C7⋊#95C2×C411yescharacteristic
59C22⋊(C7⋊C8)—22no—
60C22⋊(C7⋊C8)—22no—
61C22⋊(C7⋊C8)D414yes—
62C4⋊(C7⋊C8)—22no—
63C4×C7⋊C8—22no—
64#2975—71no—
65#2638—71no—
66C4×#99D711yescharacteristic
67#1508—72no—
68#1284—72no—
69C24×C7C22⋊C411yescharacteristic
70C24×C7C2×D411yescharacteristic
71C2×C7×D4—22no—
72C2×C7×D4—22no—
73C2×C7×D4—41no—
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—42no—
77C22×C4×C7—81no—
78C22×C4×C7—81no—
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C22×C411yescharacteristic
83C22×C4×C7C2×D412yes—
84C22×C4×C7C2×D411yescharacteristic
85C22×C4×C7#4112yes—
86C22×Dic7—21no—
87C22×Dic7—21no—
88C22×Dic7—21no—
89C22×Dic7—21no—
90C2×Dic14—22no—
91C2×Dic14—81no—
92C7×C4⋊C4—22no—
93C7×C22⋊C4—22no—
94C7×C22⋊C4—22no—
95C7×C22⋊C4—24no—
96C7×C22⋊C4—42no—
97C42×C7—21no—
98C42×C7—21no—
99C42×C7—82no—
100C22⋊Dic7—42no—
101C22⋊Dic7—42no—
102C22⋊Dic7—81no—
103C22⋊Dic7—81no—
104C4⋊Dic7—22no—
105Dic7⋊C4—42no—
106Dic7⋊C4—41no—
107Dic7⋊C4—41no—
108Dic7⋊C4—81no—
109#1136—82no—
110#1136—82no—
111C2×C7⋊C8—24no—
112C2×C22⋊Q8—71no—
113C2×C4×D4C2×D711yescharacteristic
114#436—144no—
115#431—141no—
116C2×#99—21no—
117#407—72no—
118#407—141no—
119#398—71no—
120#397—71no—
121#397—141no—
122#395—71no—
123#394—141no—
124#393—71no—
125#387—141no—
126#385—141no—
127#381—71no—
128C4×C22⋊C4C2×D712yes—
129#342—21no—
130#328—144no—
131C23×C7—21no—
132C23×C7—21no—
133C23×C7—21no—
134C23×C7—21no—
135C23×C7—21no—
136C23×C7—41no—
137C23×C7—41no—
138C23×C7—41no—
139C23×C7—41no—
140C23×C7C2×C22⋊C411yescharacteristic
141C23×C7#12112yes—
142C7×D4—44no—
143C2×C4×C7—21no—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—42no—
148C2×C4×C7—42no—
149C2×C4×C7—41no—
150C2×C4×C7—41no—
151C2×C4×C7—42no—
152C2×C4×C7—41no—
153C2×C4×C7—41no—
154C2×C4×C7—44no—
155C2×C4×C7—81no—
156C2×C4×C7—82no—
157C2×C4×C7—82no—
158C2×C4×C7#10412yes—
159C2×C4×C7C4×D412yes—
160C2×C4×C7#12011yescharacteristic
161C2×C4×C7#12311yescharacteristic
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—
174Dic14—82no—
175C7⋊C8—44no—
176C22×Q8—71no—
177C22×D4C22⋊D711yescharacteristic
178C23×C4D2811yescharacteristic
179C23×C4C22×D711yescharacteristic
180C2×M16—142no—
181C2×M16—142no—
182C22⋊Q8—142no—
183C22⋊Q8—142no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—71no—
187C2×C4⋊C4—141no—
188C2×C4⋊C4—141no—
189C2×C4⋊C4—141no—
190C2×C4⋊C4C4×D711yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—141no—
193C2×C22⋊C4—141no—
194C2×C22⋊C4—141no—
195C2×C22⋊C4—141no—
196C2×C22⋊C4C4×D711yescharacteristic
197C2×C22⋊C4C22⋊D711yescharacteristic
198C2×C42—22no—
199C2×C42D2811yescharacteristic
200C4⋊C8—142no—
201#99—24no—
202C22⋊C8—74no—
203C22⋊C8—142no—
204C22⋊C8—142no—
205C4×C8—142no—
206#95—22no—
207#95—71no—
208#95—71no—
209#95—141no—
210#95—141no—
211#95—141no—
212#95—141no—
213#95—141no—
214C22×C7—21no—
215C22×C7—21no—
216C22×C7—22no—
217C22×C7—22no—
218C22×C7—22no—
219C22×C7—42no—
220C22×C7—41no—
221C22×C7—41no—
222C22×C7—41no—
223C22×C7—81no—
224C22×C7—81no—
225C22×C7—81no—
226C22×C7#38611yescharacteristic
227C22×C7C2×#10411yescharacteristic
228C22×C7#42111yescharacteristic
229C4×C7—22no—
230C4×C7—21no—
231C4×C7—22no—
232C4×C7—21no—
233C4×C7—41no—
234C4×C7—41no—
235C4×C7—84no—
236Dic7—81no—
237Dic7—81no—
238Dic7—81no—
239Dic7—81no—
240C24(C2×D7)⋊C411yescharacteristic
241C24C2×C22⋊D711yescharacteristic
242C2×Q8—142no—
243C2×Q8—561no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—141no—
253C22×C4—141no—
254C22×C4—141no—
255C22×C4—141no—
256C22×C4(C2×D7)⋊C411yescharacteristic
257C22×C4(C2×D7)⋊C411yescharacteristic
258C22×C4(C2×D7)⋊C411yescharacteristic
259C22×C4C2×C4×D711yescharacteristic
260C22×C4C2×D2811yescharacteristic
261C22×C4D4×D712yes—
262C22×C4#115912yes—
263M16—562no—
264M16—562no—
265C2×C8—144no—
266C4⋊C4—22no—
267C4⋊C4—142no—
268C4⋊C4—281no—
269C4⋊C4—281no—
270C4⋊C4—282no—
271C4⋊C4—561no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—24no—
275C22⋊C4—42no—
276C22⋊C4—282no—
277C22⋊C4—282no—
278C22⋊C4—561no—
279C22⋊C4—561no—
280C42—21no—
281C42—21no—
282C42—82no—
283C2×C7—21no—
284C2×C7—21no—
285C2×C7—42no—
286C2×C7—81no—
287C2×C7#187111yescharacteristic
288C2×C7#190911yescharacteristic
289C2×C7#191311yescharacteristic
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C2×(C2×D7)⋊C411yescharacteristic
300C23#650212yes—
301Q8—562no—
302D4—44no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—44no—
315C2×C4—81no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—281no—
319C2×C4—281no—
320C2×C4—281no—
321C2×C4—281no—
322C2×C4—281no—
323C2×C4—281no—
324C2×C4—281no—
325C2×C4—281no—
326C2×C4—281no—
327C2×C4—281no—
328C2×C4—281no—
329C2×C4—281no—
330C2×C4#637912yes—
331C2×C4(C22⋊D7)⋊C412yes—
332C2×C4#644511yescharacteristic
333C2×C4#644911yescharacteristic
334C8—284no—
335C7#918411yescharacteristic, complemented, Sylow
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C2×#637911yescharacteristic
349C22#8973011yescharacteristic
350C22#8977711yescharacteristic
351C4—22no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—84no—
358C4—561no—
359C4—561no—
360C4—561no—
361C4—561no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—81no—
366C2#1172720711yescharacteristic
367C2#1172777811yescharacteristic
368C2#1172780011yescharacteristic
subgroupG/H
centerC22#89730
commutatorC22×C4×C7C22×C4
FrattiniC23×C4C22×D7
FittingC4×C7×#99C2
socleC22×C7#386
prime radicalC22×C7×D4D4
cosocleC23×C4×C7C23
hypercenterC4×#99D7
hypocenterC7#9184
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
4. #11727199C2semidirect
5. #11725422C2semidirect
16. #89755C4semidirect
17. #89751C4semidirect
18. #89725C4semidirect
20. #89719C4semidirect
335. C7#9184semidirect

Maximal subgroups

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

subgroupindex
#117398372
#117397492
C4×C7×#992
#117271992
#117254222
#91847