Finite Group Databasebeta

← #13322370

Subgroups — #13322370

Order 1792.

1230 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#532C211yesmaximal, characteristic
2#11739494C212yesmaximal, complemented
3#11729564C214yesmaximal, complemented
4#11729559C214yesmaximal, complemented
5#11729531C212yesmaximal, complemented
6#11729514C212yesmaximal, complemented
7C22×C7×#41C412yes—
8C7×#532—22no—
9C7×#532—22no—
10C7×#532C412yes—
11C7×#532C412yes—
12C7×#532C2212yes—
13C7×#532C2212yes—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C7×#127C2211yescharacteristic
16C2×C7×#124C412yes—
17C2×C7×#121—22no—
18C2×C4×C7×D4—22no—
19C22×C42×C7C2211yescharacteristic
20#89979—22no—
21#89698—22no—
22#89698C2214yes—
23#89697—22no—
24#89697C2214yescomplemented
25#89696C2214yescomplemented
26C4×#1136—22no—
27#89341C2218yescomplemented
28#89339C2218yescomplemented
29#17738—71nomaximal, Sylow
30C2×C7×#41—22no—
31C2×C7×#41—22no—
32C2×C7×#41—48no—
33C2×C7×#41C2×C414yes—
34C2×C7×#41C2×C414yes—
35C22×C7×Q8C2×C412yes—
36C22×C7×D4—22no—
37C22×C7×D4—22no—
38C22×C7×D4C2×C412yes—
39C23×C4×C7—22no—
40C23×C4×C7C2×C411yescharacteristic
41C23×C4×C7D412yes—
42C7×C4⋊Q8—22no—
43C7×C4⋊Q8C2×C412yes—
44C7×C4⋊Q8C2312yes—
45C7×#127—22no—
46C7×#127C2×C412yes—
47C7×#127C2312yes—
48C7×#124—24no—
49C7×#124C2×C414yes—
50C7×#124C2×C414yes—
51C7×#121—24no—
52C7×#121—24no—
53C7×#121—24no—
54C7×#121—24no—
55C4×C7×D4—24no—
56C4×C7×D4—24no—
57C4×C7×D4—24no—
58C4×C7×D4—24no—
59C2×C7×C4⋊C4—22no—
60C2×C7×C22⋊C4—24no—
61C2×C42×C7C2×C411yescharacteristic
62C2×C42×C7C2×C411yescharacteristic
63C2×C42×C7C2×C411yescharacteristic
64C2×C42×C7D412yes—
65C2×C42×C7D412yes—
66C2×C42×C7D412yes—
67C2×C42×C7C2311yescharacteristic
68C2×C42×C7C2311yescharacteristic
69C2×C42×C7C2311yescharacteristic
70C2×#1136—24no—
71C22⋊(C7⋊C8)—24no—
72C22⋊(C7⋊C8)—24no—
73C4⋊(C7⋊C8)—24no—
74C4⋊(C7⋊C8)C2318yes—
75#6377—24no—
76C4×C7⋊C8—24no—
77C2×#532D711yescharacteristic
78#2920—72no—
79#1560—74no—
80#1558—72no—
81#1555—72no—
82#1543—74no—
83C24×C7—22no—
84C24×C7C22⋊C411yescharacteristic
85C7×#41—48no—
86C7×#41—48no—
87C7×#41—48no—
88C7×#41—48no—
89C2×C7×Q8—22no—
90C2×C7×Q8—44no—
91C2×C7×Q8C22×C414yes—
92C2×C7×D4—24no—
93C2×C7×D4—24no—
94C2×C7×D4—24no—
95C2×C7×D4—22no—
96C2×C7×D4—24no—
97C2×C7×D4—48no—
98C2×C7×D4—44no—
99C2×C7×D4—48no—
100C2×C7×D4C22×C414yes—
101C22×C4×C7—24no—
102C22×C4×C7—22no—
103C22×C4×C7—24no—
104C22×C4×C7—24no—
105C22×C4×C7—44no—
106C22×C4×C7—48no—
107C22×C4×C7C22⋊C411yescharacteristic
108C22×C4×C7C22⋊C411yescharacteristic
109C22×C4×C7C22⋊C412yes—
110C22×C4×C7C22⋊C412yes—
111C22×C4×C7C22⋊C412yes—
112C22×C4×C7C22⋊C411yescharacteristic
113C22×C4×C7C22×C411yescharacteristic
114C22×C4×C7C22×C411yescharacteristic
115C22×C4×C7C22×C411yescharacteristic
116C22×C4×C7C2×D412yes—
117C22×C4×C7C2×D412yes—
118C22×C4×C7C2×D412yes—
119C7×C4⋊C4—24no—
120C7×C4⋊C4—24no—
121C7×C22⋊C4—28no—
122C7×C22⋊C4—28no—
123C42×C7C22⋊C412yes—
124C42×C7C22⋊C412yes—
125C42×C7C22⋊C412yes—
126C42×C7C22×C411yescharacteristic
127C42×C7C22×C411yescharacteristic
128C42×C7C22×C411yescharacteristic
129C42×C7C2×D412yes—
130C42×C7C2×D412yes—
131C42×C7C2×D412yes—
132C42×C7C2411yescharacteristic
133#1136—48no—
134C2×C7⋊C8—28no—
135C22×#41Dic712yes—
136#532—22no—
137#532—22no—
138#532Dic712yes—
139#532Dic712yes—
140#532C2×D712yes—
141#532C2×D712yes—
142C2×C4⋊Q8C2×D711yescharacteristic
143C2×#127C2×D711yescharacteristic
144C2×#124Dic712yes—
145C2×#121—22no—
146C2×C4×D4—22no—
147C22×C42C2×D711yescharacteristic
148#432—74no—
149#432—142no—
150#431—74no—
151#431—142no—
152#423—74no—
153#407—142no—
154C4×M16—142no—
155#333—78no—
156#331—78no—
157C23×C7—22no—
158C23×C7—24no—
159C23×C7—42no—
160C23×C7—48no—
161C23×C7—44no—
162C23×C7C2×C22⋊C411yescharacteristic
163C23×C7C2×C22⋊C411yescharacteristic
164C23×C7C2×C22⋊C411yescharacteristic
165C7×Q8—44no—
166C7×Q8—44no—
167C7×D4—44no—
168C7×D4—48no—
169C7×D4—44no—
170C7×D4—48no—
171C7×D4—48no—
172C7×D4—48no—
173C2×C4×C7—22no—
174C2×C4×C7—24no—
175C2×C4×C7—24no—
176C2×C4×C7—24no—
177C2×C4×C7—22no—
178C2×C4×C7—22no—
179C2×C4×C7—22no—
180C2×C4×C7—22no—
181C2×C4×C7—24no—
182C2×C4×C7—42no—
183C2×C4×C7—42no—
184C2×C4×C7—42no—
185C2×C4×C7—44no—
186C2×C4×C7—48no—
187C2×C4×C7—48no—
188C2×C4×C7#10014yes—
189C2×C4×C7C2×C22⋊C412yes—
190C2×C4×C7C2×C22⋊C412yes—
191C2×C4×C7C2×C22⋊C412yes—
192C2×C4×C7C2×C22⋊C411yescharacteristic
193C2×C4×C7C2×C22⋊C411yescharacteristic
194C2×C4×C7C2×C22⋊C411yescharacteristic
195C2×C4×C7C23×C411yescharacteristic
196C2×C4×C7C22×D412yes—
197C7⋊C8—48no—
198C2×#41—22no—
199C2×#41—22no—
200C2×#41—48no—
201C2×#41C2×Dic714yes—
202C2×#41C2×Dic714yes—
203C22×Q8C2×Dic712yes—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4C2×Dic712yes—
207C23×C4—22no—
208C23×C4C2×Dic711yescharacteristic
209C23×C4C22⋊D712yes—
210C2×M16—144no—
211C4⋊Q8—22no—
212C4⋊Q8C2×Dic712yes—
213C4⋊Q8C22×D712yes—
214#127—22no—
215#127C2×Dic712yes—
216#127C22×D712yes—
217#124—24no—
218#124C2×Dic714yes—
219#124C2×Dic714yes—
220#121—24no—
221#121—24no—
222#121—24no—
223#121—24no—
224C4×D4—24no—
225C4×D4—24no—
226C4×D4—24no—
227C4×D4—24no—
228C2×C4⋊C4—22no—
229C2×C22⋊C4—24no—
230C2×C42C2×Dic711yescharacteristic
231C2×C42C2×Dic711yescharacteristic
232C2×C42C2×Dic711yescharacteristic
233C2×C42C22⋊D712yes—
234C2×C42C22⋊D712yes—
235C2×C42C22⋊D712yes—
236C2×C42C22×D711yescharacteristic
237C2×C42C22×D711yescharacteristic
238C2×C42C22×D711yescharacteristic
239C4⋊C8—78no—
240C4⋊C8—144no—
241C22⋊C8—144no—
242C22⋊C8—144no—
243#97—144no—
244C4×C8—144no—
245C22×C7—22no—
246C22×C7—21no—
247C22×C7—21no—
248C22×C7—22no—
249C22×C7—22no—
250C22×C7—44no—
251C22×C7—44no—
252C22×C7—48no—
253C22×C7—88no—
254C22×C7C2×#10012yes—
255C22×C7C22×C22⋊C411yescharacteristic
256C4×C7—21no—
257C4×C7—21no—
258C4×C7—22no—
259C4×C7—22no—
260C4×C7—22no—
261C4×C7—44no—
262C4×C7C2×#10012yes—
263C4×C7C2×#10012yes—
264C4×C7#57514yes—
265C24—22no—
266C24C22⋊Dic711yescharacteristic
267#41—48no—
268#41—48no—
269#41—48no—
270#41—48no—
271C2×Q8—22no—
272C2×Q8—44no—
273C2×Q8C22×Dic714yes—
274C2×D4—24no—
275C2×D4—24no—
276C2×D4—24no—
277C2×D4—22no—
278C2×D4—24no—
279C2×D4—44no—
280C2×D4—48no—
281C2×D4—48no—
282C2×D4C22×Dic714yes—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—44no—
288C22×C4—48no—
289C22×C4C22⋊Dic711yescharacteristic
290C22×C4C22⋊Dic711yescharacteristic
291C22×C4C22⋊Dic712yes—
292C22×C4C22⋊Dic712yes—
293C22×C4C22⋊Dic712yes—
294C22×C4C22⋊Dic711yescharacteristic
295C22×C4C22×Dic711yescharacteristic
296C22×C4C22×Dic711yescharacteristic
297C22×C4C22×Dic711yescharacteristic
298C22×C4C2×C22⋊D712yes—
299C22×C4C2×C22⋊D712yes—
300C22×C4C2×C22⋊D712yes—
301M16—288no—
302C2×C8—148no—
303C4⋊C4—24no—
304C4⋊C4—24no—
305C22⋊C4—28no—
306C22⋊C4—28no—
307C42C22⋊Dic712yes—
308C42C22⋊Dic712yes—
309C42C22⋊Dic712yes—
310C42C22×Dic711yescharacteristic
311C42C22×Dic711yescharacteristic
312C42C22×Dic711yescharacteristic
313C42C2×C22⋊D712yes—
314C42C2×C22⋊D712yes—
315C42C2×C22⋊D712yes—
316C42C23×D711yescharacteristic
317C2×C7—22no—
318C2×C7—41no—
319C2×C7—41no—
320C2×C7—84no—
321C2×C7C22×#10011yescharacteristic
322C2×C7#289612yes—
323C23—22no—
324C23—24no—
325C23—42no—
326C23—48no—
327C23—44no—
328C23C2×C22⋊Dic711yescharacteristic
329C23C2×C22⋊Dic711yescharacteristic
330C23C2×C22⋊Dic711yescharacteristic
331Q8—44no—
332Q8—44no—
333D4—44no—
334D4—48no—
335D4—44no—
336D4—48no—
337D4—48no—
338D4—48no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—48no—
353C2×C4—48no—
354C2×C4#640714yes—
355C2×C4C2×C22⋊Dic712yes—
356C2×C4C2×C22⋊Dic712yes—
357C2×C4C2×C22⋊Dic712yes—
358C2×C4C2×C22⋊Dic711yescharacteristic
359C2×C4C2×C22⋊Dic711yescharacteristic
360C2×C4C2×C22⋊Dic711yescharacteristic
361C2×C4C23×Dic711yescharacteristic
362C2×C4C22×C22⋊D712yes—
363C8—288no—
364C7#1773811yescharacteristic, complemented, Sylow
365C22—22no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—22no—
370C22—44no—
371C22—44no—
372C22—48no—
373C22—88no—
374C22C2×#640712yes—
375C22C22×C22⋊Dic711yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—22no—
380C4—22no—
381C4—44no—
382C4C2×#640712yes—
383C4C2×#640712yes—
384C4#9051314yes—
385C2—22no—
386C2—41no—
387C2—41no—
388C2—84no—
389C2C22×#640711yescharacteristic
390C2#1174151712yes—
subgroupG/H
centerC2×C4C2×C22⋊Dic7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
Fitting, prime radicalC2×C7×#532C2
socleC22×C7C22×C22⋊C4
cosocleC42×C7C24
hypercenterC2×#532D7
hypocenterC7#17738
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
2. #11739494C2semidirect
3. #11729564C2semidirect
4. #11729559C2semidirect
5. #11729531C2semidirect
6. #11729514C2semidirect
24. #89697C22semidirect
25. #89696C22semidirect
27. #89341C22semidirect
28. #89339C22semidirect
364. C7#17738semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5322
#117394942
#117295642
#117295592
#117295312
#117295142
#177387