Finite Group Databasebeta

← #13271961

Subgroups — #13271961

Order 1792.

442 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11741231C211yesmaximal, characteristic
2C2×C7×#350C211yesmaximal, characteristic, complemented
3C2×#89356C211yesmaximal, characteristic, complemented
4C2×#89310C211yesmaximal, characteristic, complemented
5#11729174C211yesmaximal, characteristic, complemented
6C2×#89303C211yesmaximal, characteristic, complemented
7C2×#89297C211yesmaximal, characteristic, complemented
8C2×C7×#131C2211yescharacteristic
9#90523C411yescharacteristic
10C2×#6464C2211yescharacteristic
11C2×C7×M32C2211yescharacteristic
12C22×C7×C16C2211yescharacteristic
13#90006C411yescharacteristic
14#89901C411yescharacteristic
15#89900—22no—
16#89890C411yescharacteristic
17C8×C22⋊D7—22no—
18C2×C8×Dic7C2211yescharacteristic
19C2×#6386C2211yescharacteristic
20C22×C7⋊C16C2211yescharacteristic
21C7×#350—22no—
22#89356—22no—
23#89310—22no—
24#89303—22no—
25#89297—22no—
26Dic7⋊C16—22no—
27#13192—71nomaximal, Sylow
28C2×C7×#41C2×C411yescharacteristic
29C2×#1157C2×C411yescharacteristic
30C7×#131—21no—
31C7×#131—21no—
32C7×#131—21no—
33C7×#131—21no—
34C2×C7×M16—21no—
35C2×C7×M16C2×C411yescharacteristic
36C22×C7×C8—21no—
37C22×C7×C8C2311yescharacteristic
38#6510C811yescharacteristic
39#6507C811yescharacteristic
40#6503C811yescharacteristic
41#6502—22no—
42#6499C811yescharacteristic
43C4×C22⋊D7—22no—
44C2×C4×Dic7C2×C411yescharacteristic
45C2×#1136C2×C411yescharacteristic
46C22×C7⋊C8C2×C411yescharacteristic
47#6464—21no—
48#6464—21no—
49#6464—21no—
50#6464—21no—
51C2×#1131—21no—
52C2×C8×D7—21no—
53C7×M32—21no—
54C7×M32—21no—
55C2×C7×C16—21no—
56C2×C7×C16—21no—
57C2×C7×C16—21no—
58C2×C7×C16D412yescomplemented
59C22⋊(C7⋊C8)—22no—
60(C2×D7)⋊C8—22no—
61Dic7⋊C8—22no—
62C8×Dic7D412yes—
63C8×Dic7D412yes—
64#6386—21no—
65#6386—21no—
66C2×C7⋊C16—21no—
67C2×C7⋊C16—21no—
68C2×C7⋊C16—21no—
69C2×C7⋊C16D412yescomplemented
70#2931—71no—
71#2150—71no—
72C2×#350—71no—
73C2×#350—71no—
74C2×#350—71no—
75C2×#350D711yescharacteristic, complemented
76C2×#346—71no—
77C7×#41—21no—
78C7×#41—21no—
79C7×#41—21no—
80C7×#41—21no—
81C2×C7×Q8C2×C811yescharacteristic
82C2×C7×D4—21no—
83C2×C7×D4C2×C811yescharacteristic
84C22×C4×C7—21no—
85C22×C4×C7C22×C411yescharacteristic
86C2×C22⋊D7—21no—
87C2×C22⋊D7—22no—
88C22×Dic7M1612yes—
89#1157—21no—
90#1157—21no—
91#1157—21no—
92#1157—21no—
93C2×D28C2×C811yescharacteristic
94C2×C4×D7—21no—
95C2×Dic14C2×C811yescharacteristic
96C7×M16—21no—
97C7×M16—21no—
98C7×M16—41no—
99C7×M16—41no—
100C2×C7×C8—21no—
101C2×C7×C8—41no—
102C2×C7×C8—41no—
103C2×C7×C8C2×D411yescharacteristic
104C2×C7×C8C2×D411yescharacteristic
105C2×C7×C8C2×D411yescharacteristic
106C2×C7×C8C2×D411yescharacteristic
107C2×C7×C8#4111yescharacteristic
108C2×C7×C8#4111yescharacteristic
109C22⋊Dic7—22no—
110(C2×D7)⋊C4—22no—
111Dic7⋊C4—22no—
112C4×Dic7C22⋊C412yes—
113C4×Dic7C2×C811yescharacteristic
114C4×Dic7C2×C811yescharacteristic
115#1136—21no—
116#1136—21no—
117C2×C7⋊C8—21no—
118C2×C7⋊C8—21no—
119C2×C7⋊C8—21no—
120C2×C7⋊C8C22⋊C412yes—
121#1131—41no—
122#1131—41no—
123C8×D7—41no—
124C8×D7—41no—
125C7×C16—22no—
126C7×C16—41no—
127C7⋊C16—22no—
128C7⋊C16—41no—
129C2×#131—71no—
130C2×#131C2×D711yescharacteristic
131#532—71no—
132C2×M32—71no—
133C2×M32C2×D711yescharacteristic
134C22×C16—71no—
135C22×C16C2×D711yescharacteristic
136#436—142no—
137C8×D4—142no—
138#423—71no—
139#408—71no—
140#408—71no—
141C2×C4×C8—71no—
142C4⋊C16—142no—
143#350—22no—
144#350—142no—
145#350—142no—
146#350—142no—
147#346—142no—
148C23×C7—21no—
149C23×C7C2×M1611yescharacteristic
150C22×D7—21no—
151C7×Q8—21no—
152C7×Q8—21no—
153C7×D4—21no—
154C7×D4—21no—
155C7×D4—41no—
156C7×D4—41no—
157C2×C4×C7—21no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7C2×C22⋊C411yescharacteristic
161C2×C4×C7C4×D411yescharacteristic
162C2×C4×C7C4×D411yescharacteristic
163C2×C4×C7C22×C811yescharacteristic
164C2×C4×C7#13111yescharacteristic
165C2×C4×C7#13111yescharacteristic
166C22⋊D7—44no—
167C22⋊D7—41no—
168C22⋊D7—41no—
169C2×Dic7—21no—
170C2×Dic7—42no—
171C2×Dic7C22⋊C812yes—
172C2×Dic7C22⋊C812yes—
173D28—21no—
174D28—21no—
175C4×D7—41no—
176C4×D7—41no—
177Dic14—21no—
178Dic14—21no—
179C7×C8—41no—
180C7×C8#12111yescharacteristic
181C7×C8#12111yescharacteristic
182C7×C8#12411yescharacteristic
183C7×C8#12711yescharacteristic
184C7⋊C8—22no—
185C7⋊C8—41no—
186C2×#41—71no—
187C2×#41C4×D711yescharacteristic
188#131—21no—
189#131—21no—
190#131—21no—
191#131—21no—
192#131—141no—
193#131—141no—
194#131—141no—
195#131—141no—
196C2×M16—21no—
197C2×M16—71no—
198C2×M16—141no—
199C2×M16C4×D711yescharacteristic
200C22×C8—21no—
201C22×C8—71no—
202C22×C8—141no—
203C22×C8C22×D711yescharacteristic
204C4⋊Q8—71no—
205#127—71no—
206#124—71no—
207#124—71no—
208#121—142no—
209C4×D4—142no—
210C2×C42—71no—
211M32—21no—
212M32—21no—
213M32—141no—
214M32—141no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16—21no—
218C2×C16—72no—
219C2×C16—141no—
220C2×C16—141no—
221C2×C16—141no—
222C2×C16C22⋊D712yescomplemented
223C4⋊C8—142no—
224C22⋊C8—142no—
225C22⋊C8—142no—
226C4×C8—72no—
227C4×C8—72no—
228C22×C7—22no—
229C22×C7—42no—
230C22×C7—41no—
231C22×C7C2×C22⋊C811yescharacteristic
232C22×C7#43611yescharacteristic
233C22×C7#43611yescharacteristic
234C2×D7—42no—
235C2×D7—41no—
236C4×C7—41no—
237C4×C7#39011yescharacteristic
238C4×C7#40811yescharacteristic
239C4×C7C8×D411yescharacteristic
240C4×C7C8×D411yescharacteristic
241Dic7—22no—
242Dic7—22no—
243Dic7—41no—
244#41—21no—
245#41—21no—
246#41—21no—
247#41—21no—
248#41—141no—
249#41—141no—
250#41—141no—
251#41—141no—
252C2×Q8—71no—
253C2×Q8C8×D711yescharacteristic
254C2×D4—21no—
255C2×D4—71no—
256C2×D4—142no—
257C2×D4—141no—
258C2×D4C8×D711yescharacteristic
259C22×C4—21no—
260C22×C4—72no—
261C22×C4—141no—
262C22×C4C2×C4×D711yescharacteristic
263M16—21no—
264M16—21no—
265M16—41no—
266M16—41no—
267M16—141no—
268M16—141no—
269M16—281no—
270M16—281no—
271C2×C8—21no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—72no—
275C2×C8—141no—
276C2×C8—141no—
277C2×C8—141no—
278C2×C8—281no—
279C2×C8—281no—
280C2×C8#115711yescharacteristic
281C2×C8D4×D711yescharacteristic
282C2×C8D4×D711yescharacteristic
283C2×C8D4×D711yescharacteristic
284C2×C8#115911yescharacteristic
285C2×C8C2×C22⋊D711yescharacteristic
286C4⋊C4—142no—
287C22⋊C4—142no—
288C22⋊C4—142no—
289C42—72no—
290C42—71no—
291C42—71no—
292C16—22no—
293C16—41no—
294C16—142no—
295C16—281no—
296C2×C7—21no—
297C2×C7—21no—
298C2×C7—81no—
299C2×C7#195411yescharacteristic
300C2×C7#211712yes—
301D7—81no—
302C23—21no—
303C23—141no—
304C23D7×M1611yescharacteristic
305Q8—21no—
306Q8—21no—
307Q8—141no—
308Q8—141no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—41no—
313D4—141no—
314D4—141no—
315D4—284no—
316D4—281no—
317D4—281no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—72no—
322C2×C4—72no—
323C2×C4—141no—
324C2×C4—282no—
325C2×C4—281no—
326C2×C4—281no—
327C2×C4D7×C22⋊C411yescharacteristic
328C2×C4(C22⋊D7)⋊C411yescharacteristic
329C2×C4C2×C8×D711yescharacteristic
330C2×C4#646411yescharacteristic
331C2×C4#647011yescharacteristic
332C2×C4C4×C22⋊D711yescharacteristic
333C8—41no—
334C8—142no—
335C8—281no—
336C8#644711yescharacteristic
337C8#644811yescharacteristic
338C8#650211yescharacteristic
339C8#650311yescharacteristic
340C7#1319211yescharacteristic, complemented, Sylow
341C22—22no—
342C22—42no—
343C22—41no—
344C22—282no—
345C22—281no—
346C22D7×C22⋊C811yescharacteristic
347C22#8950111yescharacteristic
348C22#8990011yescharacteristic
349C4—41no—
350C4—142no—
351C4—142no—
352C4—281no—
353C4(C22⋊D7)⋊C811yescharacteristic
354C4#8949911yescharacteristic
355C4#8972911yescharacteristic
356C4C8×C22⋊D711yescharacteristic
357C2—21no—
358C2—21no—
359C2—81no—
360C2—561no—
361C2#1172687912yes—
362C2#1172767011yescharacteristic
subgroupG/H
centerC2×C8D4×D7
commutatorC2×C4×C7C22×C8
FrattiniC22×C8C22×D7
FittingC2×C7×#350C2
socleC22×C7C2×C22⋊C8
prime radical#90523C4
cosocleC22×C7×C8C23
hypercenterC2×#350D7
hypocenterC7#13192
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. C2×C7×#350C2semidirect
3. C2×#89356C2semidirect
4. C2×#89310C2semidirect
5. #11729174C2semidirect
6. C2×#89303C2semidirect
7. C2×#89297C2semidirect
58. C2×C7×C16D4semidirect
69. C2×C7⋊C16D4semidirect
75. C2×#350D7semidirect
222. C2×C16C22⋊D7semidirect
340. C7#13192semidirect

Maximal subgroups

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

subgroupindex
#117412312
C2×C7×#3502
C2×#893562
C2×#893102
#117291742
C2×#893032
C2×#892972
#131927