Finite Group Databasebeta

← #13272949

Subgroups — #13272949

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×#89929C211yesmaximal, characteristic
2C2×C7×#357C211yesmaximal, characteristic, complemented
3C2×#89357C211yesmaximal, characteristic, complemented
4C2×(C2×D7)⋊C16C211yesmaximal, characteristic, complemented
5#11728384C211yesmaximal, characteristic, complemented
6C2×#89284C211yesmaximal, characteristic, complemented
7#11725612C211yesmaximal, characteristic, complemented
8C22×C7×D8C2211yescharacteristic
9C2×#6501—21no—
10C22×C8×D7C2211yescharacteristic
11C22×C7×C16C2211yescharacteristic
12C2×C7×#107C2211yescharacteristic
13C2×#6406—21no—
14#89929—22no—
15#89929—22no—
16C2×#6392C2211yescharacteristic
17C2×#6392C2211yescharacteristic
18C22×C7⋊C16C2211yescharacteristic
19#89759—21no—
20C7×#357—22no—
21#89357—22no—
22#89324—21no—
23(C2×D7)⋊C16—22no—
24#89284—22no—
25#13380—71nomaximal, Sylow
26C22×C7×D4—21no—
27C22×C22⋊D7—41no—
28C22×C4×D7D411yescharacteristic
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×C8C2311yescharacteristic
36C2×C7×C4⋊C4—21no—
37C2×C22⋊Dic7—41no—
38#6501—24no—
39#6501—42no—
40C2×(C2×D7)⋊C4—41no—
41C2×C4⋊Dic7—21no—
42C2×C4⋊Dic7—21no—
43C22×C7⋊C8D411yescharacteristic
44C2×C8×D7—21no—
45C2×C8×D7—21no—
46C2×C8×D7—21no—
47C2×C8×D7—21no—
48C2×C8×D7—21no—
49C2×C8×D7—21no—
50C2×C7×C16—21no—
51C2×C7×C16—21no—
52C2×C7×C16—21no—
53C7×#107—21no—
54C7×#107—21no—
55#6406—24no—
56C7⋊#95—41no—
57#6392—21no—
58#6392—21no—
59#6392—21no—
60#6392D412yes—
61C2×C7⋊C16—21no—
62C2×C7⋊C16—21no—
63C2×C7⋊C16D412yescomplemented
64C2×#466—71no—
65C2×#366—71no—
66C2×#357—71no—
67C2×#357D711yescharacteristic, complemented
68C2×C22⋊C16—71no—
69#1808—71no—
70#1380—71no—
71C24×C7—41no—
72C23×D7D811yescharacteristic
73C2×C7×D4—22no—
74C2×C7×D4—41no—
75C2×C7×D4—41no—
76C2×C7×D4—41no—
77C2×C7×D4—41no—
78C2×C7×D4—41no—
79C22×C4×C7—41no—
80C22×C4×C7C2×D411yescharacteristic
81C2×C22⋊D7—44no—
82C2×C22⋊D7—82no—
83C2×C22⋊D7—82no—
84C22×Dic7—41no—
85C22×Dic7—41no—
86C22×Dic7D811yescharacteristic
87C2×C4×D7—21no—
88C2×C4×D7—21no—
89C2×C4×D7—21no—
90C2×C4×D7—21no—
91C2×C4×D7—21no—
92C2×C4×D7—21no—
93C7×D8—22no—
94C7×D8—22no—
95C7×D8—41no—
96C7×D8—41no—
97C2×C7×C8C2×D411yescharacteristic
98C2×C7×C8C2×D411yescharacteristic
99C2×C7×C8C2×D411yescharacteristic
100C2×C7×C8#4111yescharacteristic
101C2×C7×C8#4111yescharacteristic
102C2×C7×C8#4111yescharacteristic
103C7×C4⋊C4—41no—
104C7×C4⋊C4—41no—
105C22⋊Dic7—44no—
106(C2×D7)⋊C4—82no—
107C4⋊Dic7—22no—
108C4⋊Dic7—41no—
109C4⋊Dic7—41no—
110C4⋊Dic7—41no—
111C2×C7⋊C8—21no—
112C2×C7⋊C8—21no—
113C2×C7⋊C8—21no—
114C8×D7—41no—
115C8×D7—41no—
116C8×D7—41no—
117C8×D7—41no—
118C7×C16—41no—
119C7⋊C16—22no—
120C22×D8C2×D711yescharacteristic
121C23×C8—71no—
122C2×#121—141no—
123C22×C16—71no—
124C22×C16C2×D711yescharacteristic
125#466—142no—
126#466—142no—
127C2×#107—71no—
128C2×#107—71no—
129C2×#107C2×D711yescharacteristic
130C2×#102—141no—
131#380—141no—
132#366—142no—
133#357—22no—
134#357—142no—
135C22⋊C16—142no—
136#340—141no—
137C23×C7—42no—
138C23×C7—81no—
139C23×C7—81no—
140C23×C7—81no—
141C23×C7—81no—
142C23×C7—81no—
143C23×C7—81no—
144C23×C7C2×D811yescharacteristic
145C22×D7—21no—
146C22×D7—21no—
147C22×D7—21no—
148C22×D7—21no—
149C22×D7—21no—
150C22×D7—21no—
151C22×D7D1612yes—
152C7×D4—42no—
153C7×D4—42no—
154C7×D4—81no—
155C7×D4—81no—
156C2×C4×C7—81no—
157C2×C4×C7—81no—
158C2×C4×C7—81no—
159C2×C4×C7#12011yescharacteristic
160C2×C4×C7#12111yescharacteristic
161C2×C4×C7#12311yescharacteristic
162C2×C4×C7#13511yescharacteristic
163C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C7#13711yescharacteristic
165C22⋊D7—88no—
166C2×Dic7—21no—
167C2×Dic7—21no—
168C2×Dic7—21no—
169C2×Dic7—42no—
170C2×Dic7—81no—
171C2×Dic7—81no—
172C2×Dic7—81no—
173C2×Dic7—81no—
174C2×Dic7—81no—
175C4×D7—41no—
176C4×D7—41no—
177C4×D7—41no—
178C4×D7—41no—
179C7×C8#12111yescharacteristic
180C7×C8#12111yescharacteristic
181C7×C8#12311yescharacteristic
182C7×C8#12411yescharacteristic
183C7⋊C8—41no—
184C22×D4—21no—
185C22×D4—281no—
186C23×C4—71no—
187C2×D8—21no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8—21no—
191C2×D8—21no—
192C2×D8C22⋊D712yes—
193C22×C8—71no—
194C22×C8—141no—
195C22×C8—141no—
196C22×C8—141no—
197C22×C8—141no—
198C22×C8—141no—
199C22×C8—141no—
200C22×C8C22×D711yescharacteristic
201#121—144no—
202#121—282no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—141no—
205C2×C4⋊C4—141no—
206C2×C22⋊C4—281no—
207C2×C22⋊C4—281no—
208C2×C16—21no—
209C2×C16—21no—
210C2×C16—21no—
211C2×C16—72no—
212C2×C16—141no—
213C2×C16—141no—
214#107—21no—
215#107—21no—
216#107—72no—
217#107—141no—
218#107—141no—
219#107—141no—
220#102—144no—
221#95—281no—
222C22×C7—82no—
223C22×C7—82no—
224C22×C7—82no—
225C22×C7—161no—
226C22×C7—161no—
227C22×C7—161no—
228C22×C7—161no—
229C22×C7#44711yescharacteristic
230C22×C7#46611yescharacteristic
231C22×C7#48011yescharacteristic
232C22×C7C2×D1611yescharacteristic
233C22×C7#50811yescharacteristic
234C22×C7#50911yescharacteristic
235C22×C7#51011yescharacteristic
236C2×D7—22no—
237C2×D7—22no—
238C2×D7—22no—
239C2×D7—41no—
240C2×D7—41no—
241C2×D7—41no—
242C2×D7—41no—
243C4×C7—161no—
244C4×C7#39411yescharacteristic
245C4×C7#45211yescharacteristic
246C4×C7#46811yescharacteristic
247C4×C7#48211yescharacteristic
248Dic7—41no—
249Dic7—82no—
250Dic7—161no—
251C24—41no—
252C24—71no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—284no—
260C2×D4—562no—
261C2×D4—562no—
262C22×C4—41no—
263C22×C4—71no—
264C22×C4—141no—
265C22×C4—141no—
266C22×C4—141no—
267C22×C4—141no—
268C22×C4—141no—
269C22×C4—141no—
270C22×C4—281no—
271C22×C4—281no—
272C22×C4D4×D711yescharacteristic
273D8—22no—
274D8—22no—
275D8—41no—
276D8—41no—
277C2×C8—141no—
278C2×C8—141no—
279C2×C8—141no—
280C2×C8—281no—
281C2×C8—281no—
282C2×C8—281no—
283C2×C8—281no—
284C2×C8#115711yescharacteristic
285C2×C8#115711yescharacteristic
286C2×C8D4×D711yescharacteristic
287C2×C8D4×D711yescharacteristic
288C2×C8#115911yescharacteristic
289C2×C8C2×C22⋊D711yescharacteristic
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—142no—
293C4⋊C4—281no—
294C4⋊C4—281no—
295C4⋊C4—281no—
296C22⋊C4—284no—
297C22⋊C4—562no—
298C16—41no—
299C16—142no—
300C2×C7—162no—
301C2×C7#203311yescharacteristic
302C2×C7#218411yescharacteristic
303C2×C7#218911yescharacteristic
304C2×C7#221511yescharacteristic
305C2×C7#222011yescharacteristic
306C2×C7#223211yescharacteristic
307C2×C7#223411yescharacteristic
308D7—42no—
309C23—42no—
310C23—72no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—81no—
315C23—81no—
316C23—81no—
317C23—141no—
318C23—141no—
319C23—141no—
320C23—141no—
321C23—141no—
322C23—141no—
323C23D7×D811yescharacteristic
324D4—42no—
325D4—42no—
326D4—81no—
327D4—81no—
328D4—568no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—141no—
333C2×C4—141no—
334C2×C4—141no—
335C2×C4—281no—
336C2×C4—281no—
337C2×C4—281no—
338C2×C4—281no—
339C2×C4—282no—
340C2×C4—561no—
341C2×C4—561no—
342C2×C4—561no—
343C2×C4—561no—
344C2×C4—561no—
345C2×C4#644611yescharacteristic
346C2×C4#644711yescharacteristic
347C2×C4#647411yescharacteristic
348C2×C4#647811yescharacteristic
349C2×C4#647911yescharacteristic
350C2×C4#650011yescharacteristic
351C8—281no—
352C8#644711yescharacteristic
353C8#644811yescharacteristic
354C8#649211yescharacteristic
355C8#650211yescharacteristic
356C7#1338011yescharacteristic, complemented, Sylow
357C22—82no—
358C22—82no—
359C22—82no—
360C22—142no—
361C22—142no—
362C22—142no—
363C22—161no—
364C22—161no—
365C22—161no—
366C22—161no—
367C22—281no—
368C22—281no—
369C22—281no—
370C22—281no—
371C22#8954611yescharacteristic
372C22#8954711yescharacteristic
373C22D7×D1611yescharacteristic
374C22#8968311yescharacteristic
375C22#8968711yescharacteristic
376C22#8968811yescharacteristic
377C22#8992811yescharacteristic
378C4—161no—
379C4—281no—
380C4—562no—
381C4—1121no—
382C4#8955111yescharacteristic
383C4#8955211yescharacteristic
384C4#8973111yescharacteristic
385C4#8994511yescharacteristic
386C2—162no—
387C2—282no—
388C2#1172693611yescharacteristic
389C2#1172694911yescharacteristic
390C2#1172695211yescharacteristic
391C2#1172695311yescharacteristic
392C2#1172796011yescharacteristic
393C2#1172922111yescharacteristic
394C2#1172924011yescharacteristic
subgroupG/H
centerC23D7×D8
commutator, cosocleC22×C7×C8C23
FrattiniC22×C8C22×D7
FittingC2×C7×#357C2
socleC23×C7C2×D8
prime radicalC2×#89929C2
hypercenterC2×#357D7
hypocenterC7#13380
LCSG ▷ C22×C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×C7×#357C2semidirect
3. C2×#89357C2semidirect
4. C2×(C2×D7)⋊C16C2semidirect
5. #11728384C2semidirect
6. C2×#89284C2semidirect
7. #11725612C2semidirect
63. C2×C7⋊C16D4semidirect
67. C2×#357D7semidirect
356. C7#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#899292
C2×C7×#3572
C2×#893572
C2×(C2×D7)⋊C162
#117283842
C2×#892842
#117256122
#133807