Finite Group Databasebeta

← #33013242

Subgroups — #33013242

Order 18688.

2070 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988446C213yesmaximal
2C2×#17988444C213yesmaximal
3C2×#95×D73C211yesmaximal, characteristic
4#22608196C211yesmaximal, characteristic, complemented
5#22608195C213yesmaximal, complemented
6#22608194C213yesmaximal, complemented
7C73×#1444C211yesmaximal, characteristic, complemented
8C23×C4×D73C2213yes—
9C22×C4⋊Dic73C2213yes—
10C22×#11924007C2213yes—
11C22×#11924007C2213yes—
12C22×#11924005C2213yes—
13C22×#11924005C2211yescharacteristic
14#17988446—212no—
15#17988444—212no—
16C2×#14556498C2216yes—
17C2×#14556498C2213yes—
18C2×#14556498C2213yes—
19#95×D73C418yescomplemented
20C22×C4⋊C4×C73C2213yes—
21C2×#95×C73C2213yes—
22C2×#95×C73C2211yescharacteristic
23C24×D73C2311yescharacteristic
24C23×Dic73C2311yescharacteristic
25C23×Dic73C2313yes—
26C23×Dic73C2313yes—
27C22×C4×D73—46no—
28C22×C4×D73—46no—
29C22×C4×D73C2×C4112yes—
30C22×C4×D73D4112yes—
31C22×C4×D73Q8112yes—
32C2×C4⋊Dic73—26no—
33C2×C4⋊Dic73—46no—
34C2×#11924007—26no—
35C2×#11924007—26no—
36C2×#11924007—46no—
37C2×#11924007—46no—
38C2×#11924005—212no—
39C2×#11924005—26no—
40C2×#11924005—26no—
41#14556498—212no—
42#14556498—26no—
43#14556498C2×C4112yes—
44C23×C4×C73C2313yes—
45C23×C4×C73C2311yescharacteristic
46C23×C4×C73C2313yes—
47C2×C4⋊C4×C73—26no—
48C2×C4⋊C4×C73—46no—
49#95×C73—26no—
50#95×C73C2×C414yes—
51C23×D73—23no—
52C23×D73—23no—
53C23×D73—21no—
54C23×D73—21no—
55C23×D73C22×C412yes—
56C23×D73C2×D416yes—
57C23×D73C2×Q816yes—
58C22×Dic73—26no—
59C22×Dic73—26no—
60C22×Dic73—23no—
61C22×Dic73—23no—
62C22×Dic73—26no—
63C22×Dic73—23no—
64C22×Dic73—26no—
65C22×Dic73—23no—
66C22×Dic73—21no—
67C22×Dic73—23no—
68C22×Dic73C22×C416yes—
69C22×Dic73C2×D416yes—
70C22×Dic73C2×Q816yes—
71C2×C4×D73—424no—
72C2×C4×D73—412no—
73C2×C4×D73—412no—
74C2×C4×D73—424no—
75C2×C4×D73C4⋊C4148yescomplemented
76C4⋊Dic73—412no—
77#11924007—412no—
78#11924007—412no—
79#11924005—412no—
80#11924005—44no—
81C24×C73C2411yescharacteristic
82C22×C4×C73—26no—
83C22×C4×C73—26no—
84C22×C4×C73—23no—
85C22×C4×C73—23no—
86C22×C4×C73—26no—
87C22×C4×C73—23no—
88C22×C4×C73—26no—
89C22×C4×C73—23no—
90C22×C4×C73—23no—
91C22×C4×C73—21no—
92C22×C4×C73C22×C416yes—
93C22×C4×C73C2×D416yes—
94C22×C4×C73C2×Q816yes—
95C4⋊C4×C73—412no—
96C23×C73C23×C411yescharacteristic
97C23×C73C22×D413yes—
98C23×C73C22×Q813yes—
99C23×C73H(5,𝔽2)13yes—
100C23×C73H(5,𝔽2)13yes—
101C23×C732−1+411yescharacteristic
102C23×C732−1+411yescharacteristic
103C22×D73—26no—
104C22×D73—22no—
105C22×D73—26no—
106C22×D73—26no—
107C22×D73—26no—
108C22×D73—26no—
109C22×D73—212no—
110C22×D73—26no—
111C22×D73—26no—
112C22×D73C2×C4⋊C4112yes—
113C22×D73#12714yes—
114C22×D73C4⋊Q8112yes—
115C2×C4×C73—212no—
116C2×C4×C73—26no—
117C2×C4×C73—26no—
118C2×C4×C73—212no—
119C2×C4×C73—41no—
120C2×C4×C73—43no—
121C2×C4×C73—46no—
122C2×C4×C73—43no—
123C2×C4×C73—43no—
124C2×C4×C73—43no—
125C2×C4×C73—46no—
126C2×C4×C73—43no—
127C2×C4×C73C2×C4⋊C4112yes—
128C2×Dic73—212no—
129C2×Dic73—26no—
130C2×Dic73—26no—
131C2×Dic73—212no—
132C2×Dic73—41no—
133C2×Dic73—43no—
134C2×Dic73—43no—
135C2×Dic73—43no—
136C2×Dic73—46no—
137C2×Dic73—43no—
138C2×Dic73—43no—
139C2×Dic73—46no—
140C2×Dic73C2×C4⋊C4112yes—
141C4×D73—448no—
142C22×C73C22×C4⋊C413yes—
143C22×C73#51813yes—
144C22×C73#51911yescharacteristic
145C22×C73C2×#12711yescharacteristic
146C22×C73C2×C4⋊Q813yes—
147C22×C73#53413yes—
148C22×C73#53413yes—
149C22×C73#53713yes—
150C22×C73#53713yes—
151C22×C73#54316yes—
152C22×C73#54413yes—
153C22×C73#54413yes—
154C2×D73—212no—
155C2×D73—212no—
156C2×D73—24no—
157C2×D73—24no—
158C2×D73—212no—
159C2×D73—212no—
160C2×D73#38418yes—
161C4×C73—212no—
162C4×C73—83no—
163C4×C73—81no—
164Dic73—212no—
165Dic73—81no—
166Dic73—83no—
167#14353—731nomaximal, Sylow
168C2×C73C2×#38411yescharacteristic
169C2×C73#231513yes—
170C2×C73#231613yes—
171C2×C73#265611yescharacteristic
172C2×C73#265611yescharacteristic
173C2×C73#265913yes—
174C2×C73#265913yes—
175D73—28no—
176C2×#380—733no—
177C2×#380—733no—
178C22×#95—731no—
179#1444—733no—
180#1444—731no—
181#1444—733no—
182#1444D7311yescharacteristic, complemented
183C73#1435311yescharacteristic, complemented, Sylow
184C24×C4—733no—
185C22×C4⋊C4—733no—
186C22×C4⋊C4—733no—
187C22×C4⋊C4—733no—
188C22×C4⋊C4C2×D7313yes—
189C22×C22⋊C4—731no—
190C22×C22⋊C4—733no—
191#380—14612no—
192#380—14612no—
193C2×#95—733no—
194C2×#95—738no—
195C2×#95—736no—
196C2×#95—733no—
197C2×#95C2×D7313yes—
198C2×#95C2×D7311yescharacteristic
199C25—731no—
200C23×C4—2926no—
201C23×C4—2926no—
202C23×C4—7312no—
203C23×C4—7312no—
204C23×C4—7312no—
205C23×C4—733no—
206C23×C4—731no—
207C23×C4—733no—
208C23×C4C22×D7311yescharacteristic
209C23×C4C22×D7313yes—
210C23×C4C22×D7313yes—
211C2×C4⋊C4—26no—
212C2×C4⋊C4—46no—
213C2×C4⋊C4—2926no—
214C2×C4⋊C4—2926no—
215C2×C4⋊C4—2926no—
216C2×C4⋊C4—1466no—
217C2×C4⋊C4—1466no—
218C2×C4⋊C4—1466no—
219C2×C22⋊C4—1466no—
220C2×C22⋊C4—1466no—
221C2×C22⋊C4—14612no—
222#95—26no—
223#95—7312no—
224#95—14612no—
225#95—1466no—
226#95C4×D7314yes—
227C24—732no—
228C24—736no—
229C24—736no—
230C24—1463no—
231C24—1463no—
232C24—1461no—
233C24—1461no—
234C24C23×D7311yescharacteristic
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—23no—
238C22×C4—23no—
239C22×C4—26no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—21no—
245C22×C4—29212no—
246C22×C4—29212no—
247C22×C4—29224no—
248C22×C4—29224no—
249C22×C4—7348no—
250C22×C4—736no—
251C22×C4—736no—
252C22×C4—736no—
253C22×C4—1463no—
254C22×C4—1463no—
255C22×C4—1466no—
256C22×C4—1463no—
257C22×C4—1466no—
258C22×C4—1463no—
259C22×C4—1461no—
260C22×C4—1463no—
261C22×C4—1466no—
262C22×C4—1466no—
263C22×C4C2×C4×D7316yes—
264C22×C4D4×D7316yes—
265C22×C4Q8×D7316yes—
266C4⋊C4—412no—
267C4⋊C4—29212no—
268C4⋊C4—29212no—
269C4⋊C4—29212no—
270C22⋊C4—29212no—
271C22⋊C4—2924no—
272C23—734no—
273C23—7312no—
274C23—7312no—
275C23—1466no—
276C23—1466no—
277C23—1466no—
278C23—1466no—
279C23—14612no—
280C23—1466no—
281C23—1466no—
282C23—1466no—
283C23—1462no—
284C23C22×C4×D7311yescharacteristic
285C23C2×D4×D7313yes—
286C23C2×Q8×D7313yes—
287C23#1455663613yes—
288C23#1455663713yes—
289C23#1455663811yescharacteristic
290C23#1455663911yescharacteristic
291C2×C4—26no—
292C2×C4—26no—
293C2×C4—212no—
294C2×C4—212no—
295C2×C4—43no—
296C2×C4—41no—
297C2×C4—46no—
298C2×C4—43no—
299C2×C4—43no—
300C2×C4—43no—
301C2×C4—46no—
302C2×C4—43no—
303C2×C4—29248no—
304C2×C4—2921no—
305C2×C4—2923no—
306C2×C4—2923no—
307C2×C4—2926no—
308C2×C4—2923no—
309C2×C4—2923no—
310C2×C4—2923no—
311C2×C4—2926no—
312C2×C4—7312no—
313C2×C4—1466no—
314C2×C4—1466no—
315C2×C4—14612no—
316C2×C4—14612no—
317C2×C4C4⋊C4×D73112yes—
318C22—738no—
319C22—14612no—
320C22—14612no—
321C22—1464no—
322C22—1464no—
323C22—14612no—
324C22—14612no—
325C22C2×C4⋊C4×D7313yes—
326C22#1798905913yes—
327C22#1798906311yescharacteristic
328C22#127×D7311yescharacteristic
329C22C4⋊Q8×D7313yes—
330C22#1798914713yes—
331C22#1798914813yes—
332C22#1798916613yes—
333C22#1798916713yes—
334C22#1798921216yes—
335C22#1798921413yes—
336C22#1798921713yes—
337C4—212no—
338C4—83no—
339C4—81no—
340C4—5841no—
341C4—5843no—
342C4—14612no—
343C2—1468no—
344C2#384×D7311yescharacteristic
345C2#2261254213yes—
346C2#2261254613yes—
347C2#2261603211yescharacteristic
348C2#2261603411yescharacteristic
349C2#2261604413yes—
350C2#2261604613yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×#1444C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenter#1444D73
hypocenterC73#14353
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. #22608196C2semidirect
5. #22608195C2semidirect
6. #22608194C2semidirect
7. C73×#1444C2semidirect
19. #95×D73C4semidirect
75. C2×C4×D73C4⋊C4semidirect
182. #1444D73semidirect
183. C73#14353semidirect

Maximal subgroups

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

subgroupindex
C2×#179884462
C2×#179884442
C2×#95×D732
#226081962
#226081952
#226081942
C73×#14442
#1435373