Finite Group Databasebeta

← #32991650

Subgroups — #32991650

Order 18688.

850 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
1C2×#17988346C212yesmaximal
2C2×#17988346C212yesmaximal
3#22609625C211yesmaximal, characteristic
4C4×#14556498C211yesmaximal, characteristic
5C4×#117×C73C211yesmaximal, characteristic
6C22×#11924012C2212yes—
7C22×C4×Dic73C2212yes—
8C2×#14556498—22no—
9#17988346—24no—
10#17988346C418yescomplemented
11#17988342—21no—
12#17988342—21no—
13C2×#117×C73C2211yescharacteristic
14C2×#117×C73C2211yescharacteristic
15C22×C42×C73C2211yescharacteristic
16C4×C4⋊C4×C73C412yescomplemented
17C4×C4⋊C4×C73C412yescomplemented
18C4×C22⋊C4×C73—22no—
19#376×C73—21no—
20C43×C73—21no—
21C23×Dic73—22no—
22C2×#11924012—22no—
23C2×#11924012—22no—
24C2×#11924012—22no—
25C2×#11924012—22no—
26C2×#11924012—22no—
27C2×#11924012C2×C414yes—
28C22×#10596831—22no—
29C2×C4×Dic73—22no—
30C2×C4×Dic73—22no—
31C2×C4×Dic73—22no—
32C2×C4×Dic73—22no—
33C2×C4×Dic73—22no—
34C2×C4×Dic73C2×C414yes—
35#14556498—28no—
36C23×C4×C73D412yes—
37C23×C4×C73C2311yescharacteristic
38#117×C73—22no—
39#117×C73—21no—
40#117×C73—21no—
41#117×C73C2×C414yes—
42#117×C73D412yes—
43#117×C73Q812yes—
44C2×C4⋊C4×C73C2×C411yescharacteristic
45C2×C4⋊C4×C73C2×C411yescharacteristic
46C2×C4⋊C4×C73C2×C412yes—
47C2×C22⋊C4×C73—21no—
48C2×C22⋊C4×C73—21no—
49C2×C42×C73—21no—
50C2×C42×C73—21no—
51C2×C42×C73—22no—
52C2×C42×C73—22no—
53C2×C42×C73—22no—
54C2×C42×C73—22no—
55C2×C42×C73C2×C412yes—
56C2×C42×C73D411yescharacteristic
57C2×C42×C73D411yescharacteristic
58#95×C73—22no—
59#95×C73—22no—
60C22×Dic73—28no—
61C22×Dic73—24no—
62C22×Dic73—44no—
63C22×Dic73—42no—
64C22×Dic73—42no—
65#11924012—24no—
66#11924012—24no—
67#11924012—42no—
68#11924012—42no—
69C2×#10596831—24no—
70C2×#10596831—42no—
71C2×#10596831—42no—
72C4×Dic73—24no—
73C4×Dic73—24no—
74C4×Dic73—42no—
75C4×Dic73—42no—
76C24×C73C2×D411yescharacteristic
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—22no—
80C22×C4×C73—24no—
81C22×C4×C73—24no—
82C22×C4×C73—42no—
83C22×C4×C73C22⋊C412yes—
84C22×C4×C73C22⋊C412yes—
85C22×C4×C73C22×C412yes—
86C22×C4×C73C22×C411yescharacteristic
87C22×C4×C73C2×D411yescharacteristic
88C22×C4×C73C2×D411yescharacteristic
89C22×C4×C73C2×Q811yescharacteristic
90C22×C4×C73#4111yescharacteristic
91C22×C4×C73#4111yescharacteristic
92C22×C4×C73#4112yes—
93C22×C4×C73#4112yes—
94C22×C4×C73#4112yes—
95C4⋊C4×C73—21no—
96C4⋊C4×C73—21no—
97C4⋊C4×C73—22no—
98C4⋊C4×C73C4212yes—
99C4⋊C4×C73C4212yes—
100C4⋊C4×C73C4⋊C414yes—
101C22⋊C4×C73—24no—
102C22⋊C4×C73—22no—
103C22⋊C4×C73—22no—
104C42×C73—22no—
105C42×C73—22no—
106C42×C73—24no—
107C42×C73—22no—
108C42×C73—22no—
109C42×C73—22no—
110C42×C73—22no—
111C42×C73—44no—
112C42×C73—44no—
113C23×C73—22no—
114C23×C73—22no—
115C23×C73C2×C22⋊C411yescharacteristic
116C23×C73C4×D412yes—
117C23×C73#12111yescharacteristic
118C23×C73C22⋊Q811yescharacteristic
119C23×C73#12312yes—
120C2×C4×C73—22no—
121C2×C4×C73—22no—
122C2×C4×C73—22no—
123C2×C4×C73—22no—
124C2×C4×C73—24no—
125C2×C4×C73—22no—
126C2×C4×C73—22no—
127C2×C4×C73—22no—
128C2×C4×C73—48no—
129C2×C4×C73—42no—
130C2×C4×C73—42no—
131C2×C4×C73—42no—
132C2×C4×C73—42no—
133C2×C4×C73#10414yes—
134C2×C4×C73C2×C4211yescharacteristic
135C2×C4×C73C2×C4⋊C411yescharacteristic
136C2×C4×C73#11712yes—
137C2×C4×C73#11712yes—
138C2×C4×C73#11711yescharacteristic
139C2×C4×C73#11711yescharacteristic
140C2×C4×C73#11711yescharacteristic
141C2×C4×C73#11711yescharacteristic
142C2×C4×C73C4×D412yes—
143C2×C4×C73C4×D412yes—
144C2×C4×C73C4×Q812yes—
145C2×C4×C73#12111yescharacteristic
146C2×C4×C73C22⋊Q811yescharacteristic
147C2×C4×C73#12312yes—
148C2×C4×C73#12412yes—
149C2×C4×C73#12512yes—
150C2×C4×C73#12612yes—
151C2×C4×C73#12612yes—
152C2×Dic73—28no—
153C2×Dic73—48no—
154C2×Dic73—48no—
155C2×Dic73—44no—
156C2×Dic73—44no—
157#10596831—44no—
158C22×C73—22no—
159C22×C73—22no—
160C22×C73—24no—
161C22×C73—22no—
162C22×C73—22no—
163C22×C73C4×C22⋊C411yescharacteristic
164C22×C73#38011yescharacteristic
165C22×C73#38111yescharacteristic
166C22×C73#38712yes—
167C22×C73#38812yes—
168C22×C73C2×#10412yes—
169C22×C73#42112yes—
170C4×C73—24no—
171C4×C73—44no—
172C4×C73—42no—
173C4×C73—42no—
174C4×C73—42no—
175C4×C73#37611yescharacteristic
176C4×C73C4×C4⋊C411yescharacteristic
177C4×C73#38211yescharacteristic
178C4×C73#38311yescharacteristic
179C4×C73#38712yes—
180C4×C73#38812yes—
181Dic73—48no—
182#10808—731nomaximal, Sylow
183C2×C73—22no—
184C2×C73—22no—
185C2×C73#143411yescharacteristic
186C2×C73C4×#10411yescharacteristic
187C2×C73#175911yescharacteristic
188C2×C73#180612yes—
189C2×C73#182612yes—
190C4×#117D7311yescharacteristic
191C2×#339—732no—
192C2×#339—732no—
193#1728—731no—
194C4×#95—731no—
195C73#1080811yescharacteristic, complemented, Sylow
196C22×M16—732no—
197C2×#117C2×D7311yescharacteristic
198C2×#117C2×D7311yescharacteristic
199C22×C42—732no—
200C22×C42C2×D7311yescharacteristic
201C4×C4⋊C4Dic7312yescomplemented
202C4×C4⋊C4Dic7312yescomplemented
203C4×C22⋊C4—22no—
204#376—21no—
205C2×#95—1462no—
206C43—21no—
207#339—738no—
208#339—1464no—
209#336—1461no—
210#336—1461no—
211C23×C4—1462no—
212C23×C4C22⋊D7312yes—
213C23×C4C22×D7311yescharacteristic
214C2×M16—734no—
215C2×M16—1462no—
216C2×M16—1462no—
217C2×M16—1462no—
218C2×M16—1462no—
219C2×M16—1462no—
220C22×C8—1462no—
221#117—22no—
222#117—21no—
223#117—21no—
224#117Dic14612yes—
225#117C4×D7314yes—
226#117D29212yes—
227C2×C4⋊C4C2×Dic7311yescharacteristic
228C2×C4⋊C4C2×Dic7311yescharacteristic
229C2×C4⋊C4C2×Dic7312yes—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42—22no—
235C2×C42—22no—
236C2×C42—22no—
237C2×C42—22no—
238C2×C42—734no—
239C2×C42—1462no—
240C2×C42—1462no—
241C2×C42—1462no—
242C2×C42—1462no—
243C2×C42—1462no—
244C2×C42C2×Dic7312yes—
245C2×C42C22⋊D7311yescharacteristic
246C2×C42C22⋊D7311yescharacteristic
247#95—22no—
248#95—22no—
249#95—1468no—
250C24C2×C22⋊D7311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—42no—
257C22×C4—2924no—
258C22×C4—2922no—
259C22×C4—2922no—
260C22×C4—1468no—
261C22×C4—1464no—
262C22×C4C22⋊Dic7312yes—
263C22×C4C22⋊Dic7312yes—
264C22×C4C2×C4×D7312yes—
265C22×C4C22×Dic7311yescharacteristic
266C22×C4C2×C22⋊D7311yescharacteristic
267C22×C4C2×D29211yescharacteristic
268C22×C4C2×Dic14611yescharacteristic
269C22×C4#1192402811yescharacteristic
270C22×C4#1192402811yescharacteristic
271C22×C4#1192402812yes—
272C22×C4#1192402812yes—
273C22×C4#1192402812yes—
274M16—2922no—
275M16—2922no—
276M16—1464no—
277M16—1464no—
278C2×C8—2922no—
279C2×C8—2922no—
280C2×C8—1464no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4C4×Dic7312yes—
285C4⋊C4C4×Dic7312yes—
286C4⋊C4C4⋊Dic7314yes—
287C22⋊C4—24no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C42—22no—
291C42—22no—
292C42—24no—
293C42—22no—
294C42—22no—
295C42—22no—
296C42—22no—
297C42—44no—
298C42—44no—
299C42—2922no—
300C42—2922no—
301C42—1464no—
302C42—1464no—
303C23—22no—
304C23—22no—
305C23C2×C22⋊Dic7311yescharacteristic
306C23C4×C22⋊D7312yes—
307C23#1455656511yescharacteristic
308C23#1455657011yescharacteristic
309C23#1455657412yes—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—48no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—2928no—
324C2×C4—2924no—
325C2×C4—2928no—
326C2×C4—2924no—
327C2×C4—1468no—
328C2×C4#1455651814yes—
329C2×C4C2×C4×Dic7311yescharacteristic
330C2×C4C2×C4⋊Dic7311yescharacteristic
331C2×C4#1455654812yes—
332C2×C4#1455654812yes—
333C2×C4#1455655011yescharacteristic
334C2×C4#1455655011yescharacteristic
335C2×C4#1455655011yescharacteristic
336C2×C4#1455655011yescharacteristic
337C2×C4C4×C22⋊D7312yes—
338C2×C4C4×D29212yes—
339C2×C4C4×Dic14612yes—
340C2×C4#1455656511yescharacteristic
341C2×C4#1455657011yescharacteristic
342C2×C4#1455657412yes—
343C2×C4#1455657912yes—
344C2×C4#1455658312yes—
345C2×C4#1455658512yes—
346C2×C4#1455658512yes—
347C8—2924no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—24no—
353C22C4×C22⋊Dic7311yescharacteristic
354C22#1798844711yescharacteristic
355C22#1798845011yescharacteristic
356C22#1798847112yes—
357C22#1798847812yes—
358C22C2×#1455651812yes—
359C22#1798860412yes—
360C4—24no—
361C4—44no—
362C4—42no—
363C4—42no—
364C4—42no—
365C4—2928no—
366C4#1798843311yescharacteristic
367C4C4×C4⋊Dic7311yescharacteristic
368C4#1798845311yescharacteristic
369C4#1798845511yescharacteristic
370C4#1798847112yes—
371C4#1798847812yes—
372C2—22no—
373C2—22no—
374C2#2260815811yescharacteristic
375C2C4×#1455651811yescharacteristic
376C2#2260974111yescharacteristic
377C2#2260995112yes—
378C2#2261003012yes—
subgroupG/H
centerC22×C4C2×C22⋊D73
commutatorC2×C4×C73C2×C42
FrattiniC23×C4C22×D73
FittingC4×#117×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C2×D4
cosocleC23×C4×C73C23
hypercenterC4×#117D73
hypocenterC73#10808
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
10. #17988346C4semidirect
16. C4×C4⋊C4×C73C4semidirect
17. C4×C4⋊C4×C73C4semidirect
195. C73#10808semidirect
201. C4×C4⋊C4Dic73semidirect
202. C4×C4⋊C4Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179883462
#226096252
C4×#145564982
C4×#117×C732
#1080873