Finite Group Databasebeta

← #13272948

Subgroups — #13272948

Order 1792.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#466C211yesmaximal, characteristic
2C2×#89357C211yesmaximal, characteristic, complemented
3C2×#89357C211yesmaximal, characteristic, complemented
4#11729725C211yesmaximal, characteristic, complemented
5C2×C22⋊(C7⋊C16)C211yesmaximal, characteristic, complemented
6C2×#89284C211yesmaximal, characteristic, complemented
7#11725528C211yesmaximal, characteristic, complemented
8C22×C7×D8C2211yescharacteristic
9C23×C7×C8C2211yescharacteristic
10C2×C7×#121—21no—
11C7×#466—22no—
12C7×#466—22no—
13C2×C7×#107C2211yescharacteristic
14C2×C7×#102—21no—
15#89984—21no—
16C2×#6392C2211yescharacteristic
17C2×#6392C2211yescharacteristic
18C22×C7⋊C16C2211yescharacteristic
19C22×C7⋊C16C2211yescharacteristic
20#89357—22no—
21#89357—22no—
22#89346—21no—
23C22⋊(C7⋊C16)—22no—
24#89284—22no—
25#13380—71nomaximal, Sylow
26C22×C7×D4—21no—
27C22×C7×D4—41no—
28C23×C4×C7D411yescharacteristic
29C2×C7×D8—21no—
30C2×C7×D8—21no—
31C2×C7×D8—21no—
32C2×C7×D8—21no—
33C2×C7×D8—21no—
34C2×C7×D8D412yes—
35C22×C7×C8—21no—
36C22×C7×C8—21no—
37C22×C7×C8—21no—
38C22×C7×C8—21no—
39C22×C7×C8—21no—
40C22×C7×C8—21no—
41C22×C7×C8D411yescharacteristic
42C22×C7×C8C2311yescharacteristic
43C7×#121—24no—
44C7×#121—42no—
45C2×C7×C4⋊C4—21no—
46C2×C7×C22⋊C4—41no—
47C2×C22⋊Dic7—41no—
48C2×C4⋊Dic7—21no—
49C2×C4⋊Dic7—21no—
50C7×#107—21no—
51C7×#107D412yes—
52C7×#102—24no—
53C7⋊#95—41no—
54#6392—21no—
55#6392—21no—
56#6392—21no—
57#6392—21no—
58C2×C7⋊C16—21no—
59C2×C7⋊C16—21no—
60C2×C7⋊C16—21no—
61C2×C7⋊C16—21no—
62C2×C7⋊C16—21no—
63C2×C7⋊C16D412yescomplemented
64C2×#466D711yescharacteristic
65C2×#366—71no—
66C2×#357—71no—
67C2×#357—71no—
68C2×C22⋊C16—71no—
69#1808—71no—
70#1380—71no—
71C24×C7—41no—
72C24×C7D811yescharacteristic
73C2×C7×D4—22no—
74C2×C7×D4—44no—
75C2×C7×D4—41no—
76C2×C7×D4—41no—
77C2×C7×D4—41no—
78C2×C7×D4—41no—
79C2×C7×D4—41no—
80C2×C7×D4—82no—
81C2×C7×D4—82no—
82C22×C4×C7—21no—
83C22×C4×C7—21no—
84C22×C4×C7—21no—
85C22×C4×C7—21no—
86C22×C4×C7—21no—
87C22×C4×C7—21no—
88C22×C4×C7—41no—
89C22×C4×C7D811yescharacteristic
90C22×C4×C7C2×D411yescharacteristic
91C22×Dic7—41no—
92C22×Dic7—41no—
93C7×D8—22no—
94C7×D8—22no—
95C7×D8—41no—
96C7×D8—41no—
97C2×C7×C8—21no—
98C2×C7×C8—21no—
99C2×C7×C8—21no—
100C2×C7×C8—41no—
101C2×C7×C8—41no—
102C2×C7×C8—41no—
103C2×C7×C8—41no—
104C2×C7×C8C2×D411yescharacteristic
105C2×C7×C8C2×D411yescharacteristic
106C2×C7×C8C2×D411yescharacteristic
107C2×C7×C8#4111yescharacteristic
108C2×C7×C8#4111yescharacteristic
109C2×C7×C8#4111yescharacteristic
110C7×C4⋊C4—22no—
111C7×C4⋊C4—41no—
112C7×C22⋊C4—44no—
113C22⋊Dic7—82no—
114C4⋊Dic7—41no—
115C4⋊Dic7—41no—
116C4⋊Dic7—41no—
117C4⋊Dic7—41no—
118C7⋊C16—22no—
119C7⋊C16—41no—
120C22×D8C2×D711yescharacteristic
121C23×C8C2×D711yescharacteristic
122C2×#121—21no—
123C22×C16—71no—
124C22×C16—71no—
125#466—22no—
126#466—22no—
127C2×#107—71no—
128C2×#107—71no—
129C2×#107C2×D711yescharacteristic
130C2×#102—21no—
131#380—141no—
132#366—142no—
133#357—142no—
134#357—142no—
135C22⋊C16—142no—
136#340—141no—
137C23×C7—21no—
138C23×C7—21no—
139C23×C7—21no—
140C23×C7—21no—
141C23×C7—21no—
142C23×C7—21no—
143C23×C7—42no—
144C23×C7—81no—
145C23×C7—81no—
146C23×C7—81no—
147C23×C7—81no—
148C23×C7—81no—
149C23×C7—81no—
150C23×C7D1612yes—
151C23×C7C2×D811yescharacteristic
152C7×D4—42no—
153C7×D4—42no—
154C7×D4—88no—
155C7×D4—81no—
156C7×D4—81no—
157C2×C4×C7—21no—
158C2×C4×C7—21no—
159C2×C4×C7—21no—
160C2×C4×C7—41no—
161C2×C4×C7—41no—
162C2×C4×C7—41no—
163C2×C4×C7—41no—
164C2×C4×C7—42no—
165C2×C4×C7—81no—
166C2×C4×C7—81no—
167C2×C4×C7#12011yescharacteristic
168C2×C4×C7#12111yescharacteristic
169C2×C4×C7#12311yescharacteristic
170C2×C4×C7#13511yescharacteristic
171C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C7#13711yescharacteristic
173C2×Dic7—81no—
174C2×Dic7—81no—
175C2×Dic7—81no—
176C2×Dic7—81no—
177C2×Dic7—81no—
178C2×Dic7—81no—
179C7×C8—41no—
180C7×C8#12111yescharacteristic
181C7×C8#12111yescharacteristic
182C7×C8#12311yescharacteristic
183C7×C8#12411yescharacteristic
184C22×D4—21no—
185C22×D4—41no—
186C23×C4C22⋊D711yescharacteristic
187C2×D8—21no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8—21no—
191C2×D8—21no—
192C2×D8C22⋊D712yes—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8C22⋊D711yescharacteristic
200C22×C8C22×D711yescharacteristic
201#121—24no—
202#121—42no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—141no—
205C2×C4⋊C4—141no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4—281no—
208C2×C16—72no—
209C2×C16—141no—
210C2×C16—141no—
211C2×C16—141no—
212C2×C16—141no—
213C2×C16—141no—
214#107—21no—
215#107—141no—
216#107—141no—
217#107—141no—
218#107—141no—
219#107C22⋊D712yes—
220#102—24no—
221#95—281no—
222C22×C7—22no—
223C22×C7—22no—
224C22×C7—22no—
225C22×C7—41no—
226C22×C7—41no—
227C22×C7—41no—
228C22×C7—41no—
229C22×C7—82no—
230C22×C7—82no—
231C22×C7—82no—
232C22×C7—161no—
233C22×C7—161no—
234C22×C7—161no—
235C22×C7—161no—
236C22×C7#44711yescharacteristic
237C22×C7#46611yescharacteristic
238C22×C7#48011yescharacteristic
239C22×C7C2×D1611yescharacteristic
240C22×C7#50811yescharacteristic
241C22×C7#50911yescharacteristic
242C22×C7#51011yescharacteristic
243C4×C7—41no—
244C4×C7—82no—
245C4×C7#39411yescharacteristic
246C4×C7#45211yescharacteristic
247C4×C7#46811yescharacteristic
248C4×C7#48211yescharacteristic
249Dic7—161no—
250Dic7—161no—
251C24—41no—
252C24#114111yescharacteristic
253C2×D4—22no—
254C2×D4—44no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—82no—
261C2×D4—82no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—281no—
270C22×C4—281no—
271C22×C4#114111yescharacteristic
272C22×C4C2×C22⋊D711yescharacteristic
273D8—22no—
274D8—22no—
275D8—41no—
276D8—41no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8D4×D711yescharacteristic
285C2×C8#115911yescharacteristic
286C2×C8#115911yescharacteristic
287C2×C8#115911yescharacteristic
288C2×C8C2×C22⋊D711yescharacteristic
289C2×C8C2×C22⋊D711yescharacteristic
290C4⋊C4—22no—
291C4⋊C4—41no—
292C4⋊C4—281no—
293C4⋊C4—281no—
294C4⋊C4—281no—
295C4⋊C4—281no—
296C22⋊C4—44no—
297C22⋊C4—562no—
298C16—142no—
299C16—281no—
300C2×C7—42no—
301C2×C7—162no—
302C2×C7#203311yescharacteristic
303C2×C7#218411yescharacteristic
304C2×C7#218911yescharacteristic
305C2×C7#221511yescharacteristic
306C2×C7#222011yescharacteristic
307C2×C7#223211yescharacteristic
308C2×C7#223411yescharacteristic
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—42no—
316C23—81no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23#640012yes—
323C23C2×#114111yescharacteristic
324D4—42no—
325D4—42no—
326D4—88no—
327D4—81no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—561no—
340C2×C4—561no—
341C2×C4—561no—
342C2×C4—561no—
343C2×C4—561no—
344C2×C4—561no—
345C2×C4#649511yescharacteristic
346C2×C4#649811yescharacteristic
347C2×C4#650211yescharacteristic
348C2×C4#651311yescharacteristic
349C2×C4#651411yescharacteristic
350C2×C4#651611yescharacteristic
351C8—41no—
352C8#649811yescharacteristic
353C8#649911yescharacteristic
354C8#650111yescharacteristic
355C8#650211yescharacteristic
356C7#1338011yescharacteristic, complemented, Sylow
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—161no—
368C22—161no—
369C22—161no—
370C22—161no—
371C22#8980511yescharacteristic
372C22#8981011yescharacteristic
373C22C2×#640011yescharacteristic
374C22#8991911yescharacteristic
375C22#8996611yescharacteristic
376C22#8996711yescharacteristic
377C22#8998911yescharacteristic
378C4—41no—
379C4—82no—
380C4—1121no—
381C4—1121no—
382C4#8980711yescharacteristic
383C4#8981411yescharacteristic
384C4#8999411yescharacteristic
385C4#9001111yescharacteristic
386C2—42no—
387C2—162no—
388C2#1172882211yescharacteristic
389C2#1172882411yescharacteristic
390C2#1172882511yescharacteristic
391C2#1172882811yescharacteristic
392C2#1172943311yescharacteristic
393C2#1172978911yescharacteristic
394C2#1172983711yescharacteristic
subgroupG/H
centerC23C2×#1141
commutator, cosocleC22×C7×C8C23
FrattiniC22×C8C22×D7
Fitting, prime radicalC2×C7×#466C2
socleC23×C7C2×D8
hypercenterC2×#466D7
hypocenterC7#13380
LCSG ▷ C22×C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
2. C2×#89357C2semidirect
3. C2×#89357C2semidirect
4. #11729725C2semidirect
5. C2×C22⋊(C7⋊C16)C2semidirect
6. C2×#89284C2semidirect
7. #11725528C2semidirect
63. C2×C7⋊C16D4semidirect
356. C7#13380semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4662
C2×#893572
#117297252
C2×C22⋊(C7⋊C16)2
C2×#892842
#117255282
#133807