Finite Group Databasebeta

← #13272005

Subgroups — #13272005

Order 1792.

420 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11741201C211yesmaximal, characteristic
2C2×C7×#349C211yesmaximal, characteristic, complemented
3C2×#89348C211yesmaximal, characteristic, complemented
4#11729192C211yesmaximal, characteristic, complemented
5#11729191C211yesmaximal, characteristic, complemented
6#11729179C211yesmaximal, characteristic, complemented
7#11729177C211yesmaximal, characteristic, complemented
8C22×C7×M16C2211yescharacteristic
9#90482C411yescharacteristic
10C2×#6464C2211yescharacteristic
11C2×C7×M32C2211yescharacteristic
12C2×C7×M32C2211yescharacteristic
13#89979C411yescharacteristic
14#89900—22no—
15#89899—22no—
16#89882C411yescharacteristic
17#89874C411yescharacteristic
18#89873C2211yescharacteristic
19C2×#6386C2211yescharacteristic
20C2×#6386C2211yescharacteristic
21C7×#349—22no—
22#89348—22no—
23#89310—22no—
24#89307—22no—
25#89306—22no—
26#89303—22no—
27#13201—71nomaximal, Sylow
28C23×C4×C7C2×C411yescharacteristic
29C2×#1157C2×C411yescharacteristic
30C2×C7×M16—21no—
31C2×C7×M16—21no—
32C2×C7×M16—21no—
33C2×C7×M16—21no—
34C2×C7×M16—21no—
35C2×C7×M16—21no—
36C22×C7×C8C2×C411yescharacteristic
37C22×C7×C8C2311yescharacteristic
38#6516—21no—
39#6493—21no—
40#6492—21no—
41C4×C22⋊D7—22no—
42#6489C2×C411yescharacteristic
43#6487—21no—
44C2×#1136C2×C411yescharacteristic
45C2×#1136C2×C411yescharacteristic
46#6464—21no—
47#6464—21no—
48#6464—21no—
49#6464—21no—
50C2×#1131—21no—
51C2×C8×D7—21no—
52C7×M32—21no—
53C7×M32—21no—
54C7×M32—21no—
55C7×M32D412yescomplemented
56C2×C7×C16—21no—
57C2×C7×C16—21no—
58C22⋊(C7⋊C8)—22no—
59(C2×D7)⋊C8—22no—
60#6389D412yes—
61Dic7⋊C8—22no—
62C8×Dic7D412yes—
63#6386—21no—
64#6386—21no—
65#6386—21no—
66#6386D412yescomplemented
67C2×C7⋊C16—21no—
68C2×C7⋊C16—21no—
69#2930—71no—
70#2153—71no—
71#2117—71no—
72#2117—71no—
73C2×#349—71no—
74C2×#349D711yescharacteristic, complemented
75#2110—71no—
76C24×C7M1611yescharacteristic
77C22×C4×C7—21no—
78C22×C4×C7—21no—
79C22×C4×C7—21no—
80C22×C4×C7—21no—
81C22×C4×C7—21no—
82C22×C4×C7—21no—
83C22×C4×C7M1611yescharacteristic
84C22×C4×C7C22×C411yescharacteristic
85C2×C22⋊D7—21no—
86C2×C22⋊D7—22no—
87#1157—21no—
88#1157—21no—
89#1157—21no—
90#1157—21no—
91C2×D28M1611yescharacteristic
92C2×C4×D7—21no—
93C2×Dic14M1611yescharacteristic
94C7×M16—41no—
95C7×M16—41no—
96C7×M16—41no—
97C7×M16—41no—
98C2×C7×C8—21no—
99C2×C7×C8—21no—
100C2×C7×C8—21no—
101C2×C7×C8C2×D411yescharacteristic
102C2×C7×C8C2×D411yescharacteristic
103C2×C7×C8C2×D411yescharacteristic
104C2×C7×C8C2×D411yescharacteristic
105C2×C7×C8#4111yescharacteristic
106C2×C7×C8#4111yescharacteristic
107C22⋊Dic7—22no—
108C22⋊Dic7—21no—
109(C2×D7)⋊C4—22no—
110C4⋊Dic7—21no—
111Dic7⋊C4—22no—
112C4×Dic7C22⋊C412yes—
113#1136—21no—
114#1136—21no—
115#1136—21no—
116#1136—21no—
117C2×C7⋊C8—21no—
118C2×C7⋊C8C22⋊C412yes—
119#1131—41no—
120#1131—41no—
121C8×D7—41no—
122C8×D7—41no—
123C7×C16—22no—
124C7×C16—41no—
125C7⋊C16—22no—
126C7⋊C16—41no—
127C2×#131—71no—
128C22×M16C2×D711yescharacteristic
129#525—71no—
130C2×M32—71no—
131C2×M32—71no—
132C2×M32C2×D711yescharacteristic
133C2×M32C2×D711yescharacteristic
134#436—142no—
135#435—142no—
136#424—71no—
137#408—71no—
138#407—71no—
139#405—71no—
140#364—142no—
141#350—142no—
142#350—142no—
143#349—22no—
144#349—142no—
145#347—142no—
146C23×C7—21no—
147C23×C7—21no—
148C23×C7—21no—
149C23×C7—81no—
150C23×C7C2×M1611yescharacteristic
151C22×D7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—41no—
156C2×C4×C7—41no—
157C2×C4×C7—41no—
158C2×C4×C7—41no—
159C2×C4×C7C2×C22⋊C411yescharacteristic
160C2×C4×C7C4×D411yescharacteristic
161C2×C4×C7C4×D411yescharacteristic
162C2×C4×C7C2×M1611yescharacteristic
163C2×C4×C7#13111yescharacteristic
164C2×C4×C7#13111yescharacteristic
165C22⋊D7—41no—
166C22⋊D7—41no—
167C22⋊D7—82no—
168C2×Dic7—22no—
169C2×Dic7—21no—
170D28—21no—
171D28—21no—
172C4×D7—41no—
173C4×D7—41no—
174Dic14—21no—
175Dic14—21no—
176C7×C8—41no—
177C7×C8#12111yescharacteristic
178C7×C8#12111yescharacteristic
179C7×C8#12411yescharacteristic
180C7×C8#12711yescharacteristic
181C7⋊C8—22no—
182C7⋊C8—41no—
183C2×#41—71no—
184C23×C4C4×D711yescharacteristic
185#131—141no—
186#131—141no—
187#131—141no—
188#131—141no—
189C2×M16—21no—
190C2×M16—21no—
191C2×M16—21no—
192C2×M16—21no—
193C2×M16—21no—
194C2×M16—21no—
195C2×M16—71no—
196C2×M16—71no—
197C2×M16—141no—
198C22×C8—141no—
199C22×C8C4×D711yescharacteristic
200C22×C8C22×D711yescharacteristic
201#123—141no—
202C22⋊Q8—141no—
203#121—141no—
204#120—141no—
205C4×D4—142no—
206#117—71no—
207M32—21no—
208M32—21no—
209M32—21no—
210M32—72no—
211M32—141no—
212M32—141no—
213M32—141no—
214M32C22⋊D712yescomplemented
215C2×C16—21no—
216C2×C16—21no—
217C2×C16—141no—
218C2×C16—141no—
219C4⋊C8—142no—
220C22⋊C8—142no—
221C22⋊C8—142no—
222#97—72no—
223C4×C8—72no—
224C22×C7—41no—
225C22×C7—41no—
226C22×C7—41no—
227C22×C7—41no—
228C22×C7—81no—
229C22×C7—81no—
230C22×C7#40711yescharacteristic
231C22×C7#43511yescharacteristic
232C22×C7#43511yescharacteristic
233C2×D7—42no—
234C2×D7—41no—
235C4×C7—41no—
236C4×C7#39011yescharacteristic
237C4×C7#40811yescharacteristic
238C4×C7#43511yescharacteristic
239C4×C7#43511yescharacteristic
240Dic7—42no—
241Dic7—41no—
242C24#113111yescharacteristic
243#41—141no—
244#41—141no—
245#41—141no—
246#41—141no—
247C2×Q8—71no—
248C2×D4—71no—
249C2×D4—141no—
250C2×D4—142no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—141no—
258C22×C4#113111yescharacteristic
259C22×C4C2×C4×D711yescharacteristic
260M16—41no—
261M16—41no—
262M16—41no—
263M16—41no—
264M16—141no—
265M16—141no—
266M16—141no—
267M16—141no—
268M16—281no—
269M16—281no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—72no—
274C2×C8—141no—
275C2×C8—281no—
276C2×C8—281no—
277C2×C8#115711yescharacteristic
278C2×C8D4×D711yescharacteristic
279C2×C8D4×D711yescharacteristic
280C2×C8D4×D711yescharacteristic
281C2×C8#115911yescharacteristic
282C2×C8C2×C22⋊D711yescharacteristic
283C4⋊C4—142no—
284C4⋊C4—141no—
285C22⋊C4—142no—
286C22⋊C4—142no—
287C22⋊C4—141no—
288C42—72no—
289C16—22no—
290C16—41no—
291C16—142no—
292C16—281no—
293C2×C7—21no—
294C2×C7—21no—
295C2×C7—21no—
296C2×C7—81no—
297C2×C7#195511yescharacteristic
298D7—81no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—81no—
303C23—141no—
304C23C2×#113111yescharacteristic
305Q8—141no—
306Q8—141no—
307D4—141no—
308D4—141no—
309D4—281no—
310D4—281no—
311D4—562no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—142no—
320C2×C4—141no—
321C2×C4—281no—
322C2×C4—281no—
323C2×C4D7×C22⋊C411yescharacteristic
324C2×C4(C22⋊D7)⋊C411yescharacteristic
325C2×C4#646411yescharacteristic
326C2×C4D7×M1611yescharacteristic
327C2×C4#647011yescharacteristic
328C2×C4C4×C22⋊D711yescharacteristic
329C8—41no—
330C8—142no—
331C8—281no—
332C8#644711yescharacteristic
333C8#644811yescharacteristic
334C8#650211yescharacteristic
335C8#650311yescharacteristic
336C7#1320111yescharacteristic, complemented, Sylow
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22—282no—
344C22—281no—
345C22#8949811yescharacteristic
346C22#8950211yescharacteristic
347C22#8988311yescharacteristic
348C4—41no—
349C4—282no—
350C4—281no—
351C4#8949911yescharacteristic
352C4#8950011yescharacteristic
353C4#8972911yescharacteristic
354C4#8989911yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—81no—
359C2—561no—
360C2#1172767111yescharacteristic
subgroupG/H
centerC4#89729
commutatorC22×C4×C7C22×C4
FrattiniC22×C8C22×D7
FittingC2×C7×#349C2
socleC2×C7#1955
prime radical#90482C4
cosocleC22×C7×C8C23
hypercenterC2×#349D7
hypocenterC7#13201
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. C2×C7×#349C2semidirect
3. C2×#89348C2semidirect
4. #11729192C2semidirect
5. #11729191C2semidirect
6. #11729179C2semidirect
7. #11729177C2semidirect
55. C7×M32D4semidirect
66. #6386D4semidirect
74. C2×#349D7semidirect
214. M32C22⋊D7semidirect
336. C7#13201semidirect

Maximal subgroups

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

subgroupindex
#117412012
C2×C7×#3492
C2×#893482
#117291922
#117291912
#117291792
#117291772
#132017