Finite Group Databasebeta

← #32974241

Subgroups — #32974241

Order 18688.

556 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556570C211yesmaximal, characteristic
2#22609693C211yesmaximal, characteristic
3#22607756C212yesmaximal, complemented
4#22607755C212yesmaximal, complemented
5C73×#1728C211yesmaximal, characteristic
6C2×#14556570C411yescharacteristic
7C2×C4×Dic146C411yescharacteristic
8C2×C22⋊#10596831—21no—
9C2×#14556502—21no—
10#17988493C2211yescharacteristic
11#17988485C2211yescharacteristic
12#17988471—21no—
13#17988460—21no—
14#17988447C411yescharacteristic
15C4×#11924007—21no—
16C4×C4⋊Dic73C411yescharacteristic
17C4×C22⋊Dic73—21no—
18#17988342C2212yes—
19C22×M16×C73—21no—
20C22×C42×C73C2211yescharacteristic
21#336×C73—21no—
22#336×C73C2212yes—
23C22×Dic146C2×C411yescharacteristic
24C22×#10596831—22no—
25#14556570—22no—
26#14556570—22no—
27C4×Dic146—42no—
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—21no—
36C2×C4×Dic73—21no—
37C2×C4×Dic73—21no—
38C22⋊#10596831—24no—
39#14556502—42no—
40#14556498—21no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45C23×C4×C73C2×C411yescharacteristic
46C23×C4×C73D411yescharacteristic
47C23×C4×C73D411yescharacteristic
48C2×M16×C73—24no—
49C2×M16×C73—42no—
50C2×M16×C73—42no—
51C22×C8×C73—22no—
52C2×C42×C73—42no—
53C2×C42×C73C2×C411yescharacteristic
54C2×C42×C73D411yescharacteristic
55C2×C42×C73D411yescharacteristic
56C2×C42×C73C2311yescharacteristic
57C2×Dic146—21no—
58C2×Dic146—41no—
59C2×Dic146—41no—
60C2×Dic146M1612yescomplemented
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C2×#10596831—24no—
66C2×#10596831—42no—
67C2×#10596831—42no—
68C4⋊Dic73—21no—
69C4⋊Dic73—41no—
70C4⋊Dic73—41no—
71C4⋊Dic73M1612yescomplemented
72#11924007—24no—
73#11924007—42no—
74#11924007—41no—
75#11924007—41no—
76C22⋊Dic73—24no—
77C22⋊Dic73—42no—
78C4×Dic73—42no—
79C4×Dic73—42no—
80C24×C73C22⋊C411yescharacteristic
81C22×C4×C73—22no—
82C22×C4×C73—22no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—22no—
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73—22no—
89C22×C4×C73—41no—
90C22×C4×C73—41no—
91C22×C4×C73—41no—
92C22×C4×C73C22⋊C411yescharacteristic
93C22×C4×C73C22⋊C411yescharacteristic
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22×C411yescharacteristic
96C22×C4×C73C2×D411yescharacteristic
97C22×C4×C73C2×D411yescharacteristic
98M16×C73—48no—
99C2×C8×C73—24no—
100C2×C8×C73—42no—
101C2×C8×C73—42no—
102C42×C73—22no—
103C42×C73—22no—
104C42×C73—41no—
105C42×C73—41no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73#10412yes—
113C23×C73C2×C22⋊C411yescharacteristic
114C2×C4×C73—24no—
115C2×C4×C73—24no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—44no—
130C2×C4×C73—42no—
131C2×C4×C73—42no—
132C2×C4×C73#9912yes—
133C2×C4×C73#10412yes—
134C2×C4×C73C2×M1611yescharacteristic
135C2×C4×C73C2×M1611yescharacteristic
136C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C73#13711yescharacteristic
138C2×C4×C73#13712yes—
139C2×Dic73—22no—
140C2×Dic73—22no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151Dic146—42no—
152Dic146—42no—
153C8×C73—44no—
154#10596831—44no—
155C22×C73—22no—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73#40711yescharacteristic
163C22×C73C2×#9911yescharacteristic
164C22×C73#41311yescharacteristic
165C22×C73#41711yescharacteristic
166C22×C73#41911yescharacteristic
167C22×C73C2×#10411yescharacteristic
168C22×C73C2×#10411yescharacteristic
169C4×C73—21no—
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—22no—
173C4×C73—21no—
174C4×C73—22no—
175C4×C73—22no—
176C4×C73—41no—
177Dic73—42no—
178Dic73—42no—
179Dic73—81no—
180Dic73—81no—
181#7634—731nomaximal, Sylow
182C2×C73—42no—
183C2×C73#146511yescharacteristic
184C2×C73#148911yescharacteristic
185C2×C73#149111yescharacteristic
186C2×C73#150411yescharacteristic
187C2×C73#150811yescharacteristic
188C2×C73#152411yescharacteristic
189C2×C73#155911yescharacteristic
190C4×C22⋊Q8—731no—
191#1749—731no—
192#1728D7311yescharacteristic
193#1272—732no—
194#1271—732no—
195C73#763411yescharacteristic, complemented, Sylow
196C22×M16—21no—
197C2×C22⋊Q8—731no—
198C2×C4×Q8—731no—
199C22×C42C2×D7311yescharacteristic
200C2×C22⋊C8—1461no—
201C2×#97—1461no—
202#391—731no—
203#389—731no—
204#387—1461no—
205#385—1461no—
206#380—731no—
207C4×C4⋊C4—731no—
208C4×C4⋊C4—1461no—
209C4×C22⋊C4—1461no—
210#336—21no—
211#336—732no—
212#336C2×D7312yes—
213C22×Q8—731no—
214C23×C4C4×D7311yescharacteristic
215C23×C4D29211yescharacteristic
216C23×C4C22⋊D7311yescharacteristic
217C2×M16—24no—
218C2×M16—42no—
219C2×M16—42no—
220C22×C8—22no—
221C22×C8—1462no—
222C22⋊Q8—1462no—
223C22⋊Q8—1462no—
224C4×Q8—2922no—
225C2×C4⋊C4—731no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4—731no—
228C2×C4⋊C4—1461no—
229C2×C4⋊C4—1461no—
230C2×C4⋊C4—1461no—
231C2×C22⋊C4—1461no—
232C2×C22⋊C4—1461no—
233C2×C42—42no—
234C2×C42—1461no—
235C2×C42—1461no—
236C2×C42C4×D7311yescharacteristic
237C2×C42D29211yescharacteristic
238C2×C42C22⋊D7311yescharacteristic
239C2×C42C22×D7311yescharacteristic
240C22⋊C8—1464no—
241#97—2922no—
242#95—1461no—
243#95—1461no—
244#95—1461no—
245#95—1461no—
246#95—1461no—
247C24#1192400511yescharacteristic
248C2×Q8—2921no—
249C2×Q8—2921no—
250C2×Q8—732no—
251C2×Q8—1461no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266C22×C4—1461no—
267C22×C4#1192400511yescharacteristic
268C22×C4#1192400511yescharacteristic
269C22×C4#1192400511yescharacteristic
270C22×C4C2×C4×D7311yescharacteristic
271C22×C4C2×C22⋊D7311yescharacteristic
272C22×C4C2×D29211yescharacteristic
273M16—48no—
274C2×C8—24no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—2922no—
278C2×C8—2922no—
279C2×C8—1464no—
280C4⋊C4—2921no—
281C4⋊C4—2921no—
282C4⋊C4—2922no—
283C4⋊C4—2921no—
284C4⋊C4—2921no—
285C4⋊C4—732no—
286C4⋊C4—1464no—
287C4⋊C4—1461no—
288C22⋊C4—2922no—
289C22⋊C4—1464no—
290C42—22no—
291C42—22no—
292C42—41no—
293C42—41no—
294C42—2922no—
295C42—2922no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23#1455651912yes—
303C23C2×#1192400511yescharacteristic
304Q8—2922no—
305Q8—2922no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—44no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—2921no—
325C2×C4—2921no—
326C2×C4—2921no—
327C2×C4—2921no—
328C2×C4—2921no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—2921no—
332C2×C4—2921no—
333C2×C4—2921no—
334C2×C4—1462no—
335C2×C4—1462no—
336C2×C4#1455650512yes—
337C2×C4#1455651712yes—
338C2×C4M16×D7311yescharacteristic
339C2×C4M16×D7311yescharacteristic
340C2×C4#1455661711yescharacteristic
341C2×C4#1455662211yescharacteristic
342C2×C4#1455662412yes—
343C8—44no—
344C8—2924no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22#1798855011yescharacteristic
353C22C2×#1455650511yescharacteristic
354C22#1798856911yescharacteristic
355C22#1798858611yescharacteristic
356C22#1798859711yescharacteristic
357C22C2×#1455651711yescharacteristic
358C22C2×#1455651911yescharacteristic
359C4—21no—
360C4—22no—
361C4—21no—
362C4—22no—
363C4—22no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—2922no—
368C4—2922no—
369C4—5841no—
370C4—5841no—
371C2—42no—
372C2#2260826711yescharacteristic
373C2#2260836811yescharacteristic
374C2#2260837911yescharacteristic
375C2#2260843311yescharacteristic
376C2#2260845211yescharacteristic
377C2#2260852011yescharacteristic
378C2#2260865911yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1728C2
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1728D73
hypocenterC73#7634
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
3. #22607756C2semidirect
4. #22607755C2semidirect
60. C2×Dic146M16semidirect
71. C4⋊Dic73M16semidirect
195. C73#7634semidirect

Maximal subgroups

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

subgroupindex
C4×#145565702
#226096932
#226077562
#226077552
C73×#17282
#763473