Finite Group Databasebeta

← #32979938

Subgroups — #32979938

Order 18688.

516 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988664C211yesmaximal, characteristic
2#22610650C211yesmaximal, characteristic, complemented
3C4×#14556511C211yesmaximal, characteristic
4C2×#17988337C211yesmaximal, characteristic, complemented
5C2×#17988316C211yesmaximal, characteristic
6#22607758C211yesmaximal, characteristic, complemented
7C73×#1279C211yesmaximal, characteristic, complemented
8C22×#11924011—21no—
9C2×C4×D292C2211yescharacteristic
10#17988664—22no—
11#17988664—22no—
12C2×C4⋊#10596831—21no—
13C2×C4⋊#10596831C2211yescharacteristic
14C2×#14556511C411yescharacteristic
15C2×#14556511C411yescharacteristic
16C2×#14556503—21no—
17C2×C4×#10596831C2211yescharacteristic
18C2×C4×#10596831C2211yescharacteristic
19#17988349C411yescharacteristic
20#17988349C411yescharacteristic
21#17988342—21no—
22#17988337—22no—
23#17988316—22no—
24C2×C4⋊C8×C73C2211yescharacteristic
25C2×C4×C8×C73C2211yescharacteristic
26C4×C4⋊C4×C73C2211yescharacteristic
27C22×D292C2×C411yescharacteristic
28C22×C4×D73—21no—
29C2×#11924011—24no—
30C2×#11924011—42no—
31C2×#11924011—42no—
32C22×#10596831—21no—
33C22×#10596831C2×C411yescharacteristic
34C22×#10596831C2×C411yescharacteristic
35C22×#10596831D411yescharacteristic
36C22×#10596831D411yescharacteristic
37C4×D292—21no—
38C4×D292—21no—
39C4×D292D412yes—
40C4×D292Q812yes—
41C2×C4⋊Dic73C2×C411yescharacteristic
42C2×#11924005—21no—
43C4⋊#10596831—21no—
44C4⋊#10596831—21no—
45C4⋊#10596831—42no—
46#14556511—22no—
47#14556511—22no—
48#14556503—24no—
49C4×#10596831—21no—
50C4×#10596831—21no—
51C4×#10596831—21no—
52C4×#10596831—21no—
53C22×C8×C73—21no—
54C22×C8×C73—21no—
55C2×C4⋊C4×C73C2×C411yescharacteristic
56C2×C4⋊C4×C73C2×C411yescharacteristic
57C2×C42×C73—21no—
58C2×C42×C73C2311yescharacteristic
59C4⋊C8×C73—21no—
60C4⋊C8×C73D412yes—
61C4×C8×C73—21no—
62C4×C8×C73—21no—
63#95×C73—21no—
64C23×D73—21no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292—21no—
69C2×D292—21no—
70C2×D292C4⋊C412yes—
71C22×Dic73—21no—
72C2×C4×D73—22no—
73C2×C4×D73—22no—
74C2×C4×D73—41no—
75C2×C4×D73—41no—
76C2×C4×D73—41no—
77C2×C4×D73—41no—
78#11924011—48no—
79C2×#10596831—21no—
80C2×#10596831—21no—
81C2×#10596831—21no—
82C2×#10596831—21no—
83C2×#10596831—21no—
84C2×#10596831—21no—
85C2×#10596831—21no—
86C2×#10596831—21no—
87C2×#10596831—21no—
88C2×#10596831—21no—
89C2×#10596831—41no—
90C2×#10596831—41no—
91C2×#10596831—41no—
92C2×#10596831M1612yescomplemented
93C2×#10596831SD1612yes—
94C4⋊Dic73—21no—
95C4⋊Dic73C4⋊C412yes—
96#11924005—22no—
97#11924005—22no—
98C22×C4×C73—21no—
99C22×C4×C73—21no—
100C22×C4×C73C22×C411yescharacteristic
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73#4111yescharacteristic
103C2×C8×C73—22no—
104C2×C8×C73—22no—
105C2×C8×C73—41no—
106C2×C8×C73—41no—
107C2×C8×C73—41no—
108C2×C8×C73—41no—
109C4⋊C4×C73—21no—
110C4⋊C4×C73—21no—
111C4⋊C4×C73—21no—
112C4⋊C4×C73M1612yescomplemented
113C42×C73—41no—
114C42×C73—41no—
115C42×C73C2×D411yescharacteristic
116C42×C73C2×D411yescharacteristic
117C42×C73C2×Q811yescharacteristic
118C42×C73#4111yescharacteristic
119C23×C73C4×D411yescharacteristic
120C22×D73—22no—
121C22×D73—41no—
122C22×D73—41no—
123C22×D73—41no—
124C22×D73—41no—
125C22×D73—41no—
126C22×D73—41no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—22no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73C2×C4⋊C411yescharacteristic
136C2×C4×C73C4×D411yescharacteristic
137C2×C4×C73#12011yescharacteristic
138C2×C4×C73C22⋊Q811yescharacteristic
139C2×C4×C73C22⋊Q811yescharacteristic
140C2×C4×C73#12311yescharacteristic
141C2×C4×C73C2×M1611yescharacteristic
142C2×C4×C73C2×M1611yescharacteristic
143C2×C4×C73#13111yescharacteristic
144C2×C4×C73#13111yescharacteristic
145C2×C4×C73C2×SD1611yescharacteristic
146C2×C4×C73#13511yescharacteristic
147C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
149C2×Dic73—22no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152D292—22no—
153D292—22no—
154D292—41no—
155D292—41no—
156C4×D73—42no—
157C4×D73—42no—
158C4×D73—42no—
159C4×D73—42no—
160C8×C73—42no—
161C8×C73—42no—
162#10596831—22no—
163#10596831—22no—
164#10596831—41no—
165#10596831—41no—
166#10596831—81no—
167C22×C73#38511yescharacteristic
168C22×C73#43511yescharacteristic
169C22×C73#43611yescharacteristic
170C22×C73C4×SD1611yescharacteristic
171C22×C73#44211yescharacteristic
172C22×C73#44311yescharacteristic
173C22×C73#44411yescharacteristic
174C2×D73—42no—
175C2×D73—42no—
176C2×D73—42no—
177C2×D73—81no—
178C2×D73—81no—
179C2×D73—81no—
180C2×D73—81no—
181C4×C73—21no—
182C4×C73—21no—
183C4×C73—42no—
184C4×C73—81no—
185C4×C73#42311yescharacteristic
186C4×C73#42411yescharacteristic
187C4×C73#43511yescharacteristic
188C4×C73#43611yescharacteristic
189C4×C73#44911yescharacteristic
190C4×C73#45011yescharacteristic
191C4×C73#47611yescharacteristic
192C4×C73#47811yescharacteristic
193Dic73—42no—
194#8849—731nomaximal, Sylow
195C2×C73#158311yescharacteristic
196C2×C73#158611yescharacteristic
197C2×C73#159011yescharacteristic
198C2×C73#159411yescharacteristic
199C2×C73#185111yescharacteristic
200C2×C73#186411yescharacteristic
201C2×C73#186611yescharacteristic
202D73—82no—
203C2×#436—731no—
204#1939—731no—
205C4×#102—731no—
206C2×#334—731no—
207C2×D4⋊C8—731no—
208#1279D7311yescharacteristic, complemented
209#1273—731no—
210C73#884911yescharacteristic, complemented, Sylow
211C22×M16—1461no—
212C2×C4×D4—731no—
213#436—1462no—
214#436—1462no—
215C2×C4⋊C8—731no—
216C2×C4⋊C8—1461no—
217C2×C4⋊C8C2×D7311yescharacteristic
218C2×#102—731no—
219C2×#102—731no—
220C2×C22⋊C8—1461no—
221C2×C4×C8—731no—
222C2×C4×C8—731no—
223C2×C4×C8C2×D7311yescharacteristic
224C4×C4⋊C4C2×D7311yescharacteristic
225#340—731no—
226#340—731no—
227#336—1461no—
228#334—1462no—
229D4⋊C8—1462no—
230C22×D4—731no—
231C23×C4—1461no—
232C2×M16—2922no—
233C2×M16—2922no—
234C2×M16—1464no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—731no—
238C22×C8—731no—
239C22×C8—731no—
240C22×C8—731no—
241C22×C8—1461no—
242C4×D4—732no—
243C4×D4—732no—
244C4×D4—1461no—
245C4×D4—1461no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4C4×D7311yescharacteristic
248C2×C4⋊C4C4×D7311yescharacteristic
249C2×C22⋊C4—1461no—
250C2×C42—21no—
251C2×C42C22×D7311yescharacteristic
252C4⋊C8—21no—
253C4⋊C8—2922no—
254C4⋊C8—1461no—
255C4⋊C8—1461no—
256C4⋊C8D29212yes—
257#102—1462no—
258#102—1462no—
259C22⋊C8—1464no—
260C4×C8—21no—
261C4×C8—21no—
262C4×C8—1461no—
263C4×C8—1461no—
264C4×C8—1461no—
265C4×C8—1461no—
266#95—21no—
267C24—1461no—
268C2×D4—732no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4—1461no—
272C2×D4—1461no—
273C2×D4—1461no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—2921no—
277C22×C4—2921no—
278C22×C4—2921no—
279C22×C4—2921no—
280C22×C4—1461no—
281C22×C4—1462no—
282C22×C4—1462no—
283C22×C4C2×C4×D7311yescharacteristic
284C22×C4D4×D7311yescharacteristic
285C22×C4#1192402711yescharacteristic
286M16—2928no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—2921no—
294C2×C8—2921no—
295C2×C8—2921no—
296C2×C8—732no—
297C2×C8—732no—
298C2×C8—1461no—
299C2×C8—1461no—
300C2×C8—1461no—
301C2×C8—1461no—
302C2×C8—1461no—
303C2×C8—1461no—
304C2×C8—1461no—
305C2×C8—1461no—
306C2×C8—1461no—
307C2×C8—1461no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—732no—
312C4⋊C4—1461no—
313C4⋊C4#1192401112yescomplemented
314C22⋊C4—1462no—
315C22⋊C4—1462no—
316C42—41no—
317C42—41no—
318C42D4×D7311yescharacteristic
319C42C2×D29211yescharacteristic
320C42Q8×D7311yescharacteristic
321C42#1192402811yescharacteristic
322C23—2921no—
323C23—2921no—
324C23—2921no—
325C23—2921no—
326C23—2921no—
327C23—2921no—
328C23—1462no—
329C23#1455655111yescharacteristic
330D4—2921no—
331D4—2921no—
332D4—1462no—
333D4—1462no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—2922no—
345C2×C4—2922no—
346C2×C4—2922no—
347C2×C4—2922no—
348C2×C4—1462no—
349C2×C4C4⋊C4×D7311yescharacteristic
350C2×C4C4×D29211yescharacteristic
351C2×C4#1455656111yescharacteristic
352C2×C4#1455656911yescharacteristic
353C2×C4#1455657111yescharacteristic
354C2×C4#1455657311yescharacteristic
355C2×C4M16×D7311yescharacteristic
356C2×C4C2×#1192401111yescharacteristic
357C2×C4#1455659711yescharacteristic
358C2×C4#1455659911yescharacteristic
359C2×C4SD16×D7311yescharacteristic
360C2×C4#1455661411yescharacteristic
361C2×C4#1455661511yescharacteristic
362C2×C4#1455661811yescharacteristic
363C8—42no—
364C8—42no—
365C8—2921no—
366C8—2921no—
367C8—5841no—
368C8—1462no—
369C8—1462no—
370C22—2922no—
371C22—2922no—
372C22—2922no—
373C22—5841no—
374C22—5841no—
375C22—5841no—
376C22—5841no—
377C22#1798846111yescharacteristic
378C22#1798865511yescharacteristic
379C22#1798866211yescharacteristic
380C22#1798867211yescharacteristic
381C22#1798869611yescharacteristic
382C22#1798870111yescharacteristic
383C22#1798870611yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—81no—
388C4—2922no—
389C4#1798860911yescharacteristic
390C4#1798861211yescharacteristic
391C4#1798866011yescharacteristic
392C4#1798866611yescharacteristic
393C4#1798873511yescharacteristic
394C4#1798873911yescharacteristic
395C4#1798887611yescharacteristic
396C4#1798889011yescharacteristic
397C2—5842no—
398C2#2260877111yescharacteristic
399C2#2260879211yescharacteristic
400C2#2260881811yescharacteristic
401C2#2260884211yescharacteristic
402C2#2261011511yescharacteristic
403C2#2261019311yescharacteristic
404C2#2261020711yescharacteristic
subgroupG/H
centerC22×C4D4×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1279C2
socleC23×C73C4×D4
prime radicalC22×D292C2×C4
cosocleC2×C42×C73C23
hypercenter#1279D73
hypocenterC73#8849
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #22610650C2semidirect
4. C2×#17988337C2semidirect
6. #22607758C2semidirect
7. C73×#1279C2semidirect
92. C2×#10596831M16semidirect
112. C4⋊C4×C73M16semidirect
208. #1279D73semidirect
210. C73#8849semidirect
313. C4⋊C4#11924011semidirect

Maximal subgroups

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

subgroupindex
C2×#179886642
#226106502
C4×#145565112
C2×#179883372
C2×#179883162
#226077582
C73×#12792
#884973