Finite Group Databasebeta

← #13270855

Subgroups — #13270855

Order 1792.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×D16C211yesmaximal, characteristic
2C2×D8×Dic7C211yesmaximal, characteristic, complemented
3#11729792C211yesmaximal, characteristic, complemented
4C2×#89357C211yesmaximal, characteristic, complemented
5C2×#89357C211yesmaximal, characteristic, complemented
6#11725612C211yesmaximal, characteristic, complemented
7#11725610C211yesmaximal, characteristic, complemented
8C22×C7×D8C2211yescharacteristic
9C22×C7×D8C2211yescharacteristic
10C2×D4×Dic7—21no—
11C2×C7×D16—22no—
12C2×C7×D16—22no—
13C2×C7×D16C414yescomplemented
14C22×C7×C16C2211yescharacteristic
15#89993—21no—
16C2×#6406—21no—
17C2×#6406—21no—
18D8×Dic7—22no—
19D8×Dic7—22no—
20C2×#6392C2211yescharacteristic
21C2×#6392C2211yescharacteristic
22C2×C8×Dic7C2211yescharacteristic
23C22×C7⋊C16C2211yescharacteristic
24#89357—22no—
25#89357—22no—
26#13012—71nomaximal, Sylow
27C22×C7×D4—21no—
28C22×C7×D4—21no—
29C23×Dic7—41no—
30C2×C7×D8—21no—
31C2×C7×D8—21no—
32C2×C7×D8—21no—
33C2×C7×D8—21no—
34C2×C7×D8—21no—
35C2×C7×D8—21no—
36C2×C7×D8—21no—
37C2×C7×D8—21no—
38C2×C7×D8C2×C412yes—
39C2×C7×D8C2×C412yescomplemented
40C2×C7×D8D412yes—
41C2×C7×D8D412yes—
42C22×C7×C8C2311yescharacteristic
43C2×C22⋊Dic7—41no—
44C2×C22⋊Dic7—41no—
45C2×C22⋊Dic7—41no—
46D4×Dic7—24no—
47D4×Dic7—42no—
48C2×C4⋊Dic7—21no—
49C2×C4⋊Dic7—21no—
50C2×C4×Dic7D411yescharacteristic
51C22×C7⋊C8D411yescharacteristic
52C7×D16—28no—
53C2×C7×C16—21no—
54C2×C7×C16—21no—
55C2×C7×C16C2×C412yescomplemented
56#6406—24no—
57#6406—42no—
58#6392—21no—
59#6392—21no—
60#6392—21no—
61#6392D412yes—
62C8×Dic7—21no—
63C8×Dic7—21no—
64C2×C7⋊C16—21no—
65C2×C7⋊C16—21no—
66C2×C7⋊C16—21no—
67C22×D16D711yescharacteristic
68C2×C4×D8—71no—
69C2×#357—71no—
70C2×#357—71no—
71#1970—71no—
72#1380—71no—
73#1374—71no—
74C24×C7—41no—
75C24×C7—41no—
76C2×C7×D4—22no—
77C2×C7×D4—22no—
78C2×C7×D4—22no—
79C2×C7×D4—22no—
80C2×C7×D4—41no—
81C2×C7×D4—41no—
82C2×C7×D4—41no—
83C2×C7×D4—41no—
84C2×C7×D4—41no—
85C2×C7×D4—41no—
86C2×C7×D4—41no—
87C2×C7×D4—41no—
88C22×C4×C7C2×D411yescharacteristic
89C22×Dic7—44no—
90C22×Dic7—41no—
91C22×Dic7—41no—
92C22×Dic7—82no—
93C22×Dic7—82no—
94C22×Dic7D811yescharacteristic
95C22×Dic7D811yescharacteristic
96C7×D8—22no—
97C7×D8—22no—
98C7×D8—22no—
99C7×D8—22no—
100C7×D8—22no—
101C7×D8—41no—
102C7×D8—41no—
103C7×D8C22⋊C414yescomplemented
104C2×C7×C8C22×C411yescharacteristic
105C2×C7×C8C2×D411yescharacteristic
106C2×C7×C8C2×D411yescharacteristic
107C2×C7×C8C2×D411yescharacteristic
108C2×C7×C8#4111yescharacteristic
109C2×C7×C8#4111yescharacteristic
110C22⋊Dic7—44no—
111C22⋊Dic7—82no—
112C22⋊Dic7—82no—
113C4⋊Dic7—22no—
114C4⋊Dic7—41no—
115C4⋊Dic7—41no—
116C4⋊Dic7—41no—
117C4×Dic7—21no—
118C4×Dic7—21no—
119C2×C7⋊C8—21no—
120C2×C7⋊C8—21no—
121C2×C7⋊C8—21no—
122C7×C16—22no—
123C7⋊C16—41no—
124C22×D8C2×D711yescharacteristic
125C22×D8C2×D711yescharacteristic
126C2×C4×D4—141no—
127C2×D16—22no—
128C2×D16—22no—
129C2×D16Dic714yescomplemented
130C22×C16—71no—
131C22×C16C2×D711yescharacteristic
132C4×D8—142no—
133C4×D8—142no—
134C2×#107—71no—
135C2×#107—71no—
136C2×#102—141no—
137C2×#102—141no—
138C2×C4×C8—71no—
139#390—141no—
140#357—142no—
141#357—142no—
142C23×C7—42no—
143C23×C7—42no—
144C23×C7—42no—
145C23×C7—42no—
146C23×C7—81no—
147C23×C7—81no—
148C23×C7—81no—
149C23×C7—81no—
150C23×C7—81no—
151C23×C7—81no—
152C23×C7—81no—
153C23×C7—81no—
154C23×C7—81no—
155C23×C7—81no—
156C23×C7C2×D811yescharacteristic
157C7×D4—24no—
158C7×D4—42no—
159C7×D4—42no—
160C7×D4—42no—
161C7×D4—42no—
162C7×D4—42no—
163C7×D4—81no—
164C7×D4—81no—
165C2×C4×C7C4×D411yescharacteristic
166C2×C4×C7#12011yescharacteristic
167C2×C4×C7#12111yescharacteristic
168C2×C4×C7#13511yescharacteristic
169C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
171C2×Dic7—21no—
172C2×Dic7—21no—
173C2×Dic7—21no—
174C2×Dic7—21no—
175C2×Dic7—21no—
176C2×Dic7—42no—
177C2×Dic7—88no—
178C2×Dic7—81no—
179C2×Dic7—81no—
180C2×Dic7—81no—
181C2×Dic7—81no—
182C2×Dic7—81no—
183C2×Dic7D1612yescomplemented
184C7×C8C2×C22⋊C411yescharacteristic
185C7×C8C4×D411yescharacteristic
186C7×C8#12111yescharacteristic
187C7×C8#12311yescharacteristic
188C7⋊C8—41no—
189C22×D4—21no—
190C22×D4—21no—
191C23×C4—281no—
192C2×D8—21no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8—21no—
200C2×D8C2×Dic712yes—
201C2×D8C2×Dic712yescomplemented
202C2×D8C22⋊D712yes—
203C2×D8C22⋊D712yes—
204C22×C8—71no—
205C22×C8C22×D711yescharacteristic
206C4×D4—144no—
207C4×D4—282no—
208C2×C4⋊C4—141no—
209C2×C4⋊C4—141no—
210C2×C22⋊C4—281no—
211C2×C22⋊C4—281no—
212C2×C22⋊C4—281no—
213C2×C42—71no—
214D16—28no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16—141no—
218C2×C16—141no—
219C2×C16—141no—
220C2×C16C2×Dic712yescomplemented
221#107—72no—
222#107—141no—
223#107—141no—
224#107—141no—
225#102—144no—
226#102—282no—
227C4×C8—141no—
228C4×C8—141no—
229C22×C7—44no—
230C22×C7—82no—
231C22×C7—82no—
232C22×C7—82no—
233C22×C7—82no—
234C22×C7—82no—
235C22×C7—82no—
236C22×C7—82no—
237C22×C7—82no—
238C22×C7—82no—
239C22×C7—161no—
240C22×C7—161no—
241C22×C7—161no—
242C22×C7—161no—
243C22×C7C4×D811yescharacteristic
244C22×C7#44711yescharacteristic
245C22×C7#45911yescharacteristic
246C22×C7C2×D1611yescharacteristic
247C22×C7#50811yescharacteristic
248C22×C7#50911yescharacteristic
249C22×C7#50911yescharacteristic
250C4×C7#38611yescharacteristic
251C4×C7#44211yescharacteristic
252C4×C7#44911yescharacteristic
253C4×C7#46311yescharacteristic
254Dic7—22no—
255Dic7—41no—
256Dic7—82no—
257Dic7—161no—
258C24—41no—
259C24—41no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C22×C4—71no—
273C22×C4—71no—
274C22×C4—284no—
275C22×C4—281no—
276C22×C4—281no—
277C22×C4—562no—
278C22×C4—562no—
279C22×C4D4×D711yescharacteristic
280D8—22no—
281D8—22no—
282D8—22no—
283D8—22no—
284D8—22no—
285D8—41no—
286D8—41no—
287D8C22⋊Dic714yescomplemented
288C2×C8—141no—
289C2×C8—141no—
290C2×C8—141no—
291C2×C8D4×D711yescharacteristic
292C2×C8#115911yescharacteristic
293C2×C8#115911yescharacteristic
294C2×C8C22×Dic711yescharacteristic
295C2×C8C2×C22⋊D711yescharacteristic
296C2×C8C2×C22⋊D711yescharacteristic
297C4⋊C4—142no—
298C4⋊C4—281no—
299C4⋊C4—281no—
300C4⋊C4—281no—
301C22⋊C4—284no—
302C22⋊C4—562no—
303C22⋊C4—562no—
304C42—141no—
305C42—141no—
306C16—22no—
307C16—281no—
308C2×C7—84no—
309C2×C7—162no—
310C2×C7#187911yescharacteristic
311C2×C7C4×D1611yescharacteristic
312C2×C7#217711yescharacteristic
313C2×C7#218411yescharacteristic
314C2×C7#218611yescharacteristic
315C2×C7#220611yescharacteristic
316C2×C7#221011yescharacteristic
317C23—42no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23D7×D811yescharacteristic
332D4—24no—
333D4—42no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—81no—
339D4—81no—
340C2×C4—72no—
341C2×C4—141no—
342C2×C4—141no—
343C2×C4—141no—
344C2×C4—141no—
345C2×C4—141no—
346C2×C4—282no—
347C2×C4—568no—
348C2×C4—561no—
349C2×C4—561no—
350C2×C4—561no—
351C2×C4—561no—
352C2×C4—561no—
353C2×C4#647411yescharacteristic
354C2×C4#647411yescharacteristic
355C2×C4#647511yescharacteristic
356C2×C4D4×Dic711yescharacteristic
357C2×C4#650011yescharacteristic
358C2×C4#650211yescharacteristic
359C8—281no—
360C8D4×Dic711yescharacteristic
361C8#649811yescharacteristic
362C8#650211yescharacteristic
363C8C2×C22⋊Dic711yescharacteristic
364C7#1301211yescharacteristic, complemented, Sylow
365C22—44no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—82no—
373C22—82no—
374C22—82no—
375C22—161no—
376C22—161no—
377C22—161no—
378C22—161no—
379C22D7×D1611yescharacteristic
380C22#8968311yescharacteristic
381C22#8968311yescharacteristic
382C22#8968411yescharacteristic
383C22D8×Dic711yescharacteristic
384C22#8992211yescharacteristic
385C22#8992811yescharacteristic
386C4—142no—
387C4—281no—
388C4—562no—
389C4—1121no—
390C4#8992411yescharacteristic
391C4#8992511yescharacteristic
392C4#8993011yescharacteristic
393C4#8999211yescharacteristic
394C2—84no—
395C2—162no—
396C2Dic7×D1611yescharacteristic
397C2#1172921511yescharacteristic
398C2#1172921611yescharacteristic
399C2#1172921711yescharacteristic
400C2#1172922111yescharacteristic
401C2#1172922211yescharacteristic
402C2#1172979111yescharacteristic
subgroupG/H
centerC23D7×D8
commutatorC2×C7×C8C22×C4
FrattiniC22×C8C22×D7
Fitting, prime radicalC22×C7×D16C2
socleC23×C7C2×D8
cosocleC22×C7×C8C23
hypercenterC22×D16D7
hypocenterC7#13012
LCSG ▷ C2×C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
2. C2×D8×Dic7C2semidirect
3. #11729792C2semidirect
4. C2×#89357C2semidirect
5. C2×#89357C2semidirect
6. #11725612C2semidirect
7. #11725610C2semidirect
13. C2×C7×D16C4semidirect
39. C2×C7×D8C2×C4semidirect
55. C2×C7×C16C2×C4semidirect
103. C7×D8C22⋊C4semidirect
129. C2×D16Dic7semidirect
183. C2×Dic7D16semidirect
201. C2×D8C2×Dic7semidirect
220. C2×C16C2×Dic7semidirect
287. D8C22⋊Dic7semidirect
364. C7#13012semidirect

Maximal subgroups

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

subgroupindex
C22×C7×D162
C2×D8×Dic72
#117297922
C2×#893572
#117256122
#117256102
#130127