Finite Group Databasebeta

← #32984262

Subgroups — #32984262

Order 18688.

450 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610725C211yesmaximal, characteristic
2#22610649C211yesmaximal, characteristic, complemented
3C4×#14556513C211yesmaximal, characteristic
4C2×#17988316C211yesmaximal, characteristic
5#22607771C211yesmaximal, characteristic, complemented
6#22607766C211yesmaximal, characteristic, complemented
7C2×#322×C73C211yesmaximal, characteristic, complemented
8C2×C4×D292C2211yescharacteristic
9C2×C4⋊#10596831C2211yescharacteristic
10C2×C4⋊#10596831C2211yescharacteristic
11C2×#14556520—21no—
12C2×#14556513C411yescharacteristic
13C2×#14556513C411yescharacteristic
14C2×#14556503—21no—
15C2×#14556503—21no—
16C4×C4⋊Dic73C2211yescharacteristic
17#17988350C411yescharacteristic
18#17988350C411yescharacteristic
19#17988341—21no—
20#17988316—22no—
21C2×C4×C8×C73C2211yescharacteristic
22C2×C4×C8×C73C2211yescharacteristic
23C2×C4×C8×C73C2211yescharacteristic
24#322×C73—22no—
25C22×D292C2×C411yescharacteristic
26C22×C4×D73—21no—
27C22×#10596831—21no—
28C22×#10596831—21no—
29C4×D292—21no—
30C4×D292—21no—
31C4×D292—21no—
32C4×D292—21no—
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×#11924005—21no—
37C2×C4×Dic73—21no—
38C4⋊#10596831—21no—
39C4⋊#10596831—21no—
40C4⋊#10596831—21no—
41C4⋊#10596831—21no—
42#14556520—42no—
43#14556513—22no—
44#14556513C814yescomplemented
45#14556503—42no—
46#14556503—42no—
47#14556498—21no—
48C22×C8×C73—21no—
49C22×C8×C73C2×C411yescharacteristic
50C22×C8×C73C2×C411yescharacteristic
51C22×C8×C73D411yescharacteristic
52C22×C8×C73D411yescharacteristic
53C2×C42×C73C2311yescharacteristic
54C4×C8×C73—21no—
55C4×C8×C73—21no—
56C4×C8×C73—21no—
57C4×C8×C73—21no—
58C4×C8×C73—21no—
59C4×C8×C73D412yes—
60C23×D73—21no—
61C2×D292—21no—
62C2×D292—21no—
63C2×D292—21no—
64C2×D292—21no—
65C2×D292—21no—
66C2×D292C2×C812yes—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C2×C4×D73—41no—
71C2×C4×D73—41no—
72C2×C4×D73—41no—
73C2×C4×D73—41no—
74C2×C4×D73—41no—
75C2×C4×D73—41no—
76C2×#10596831—41no—
77C2×#10596831—41no—
78C2×#10596831—41no—
79C2×#10596831—41no—
80C2×#10596831—41no—
81C2×#10596831—41no—
82C4⋊Dic73—21no—
83C4⋊Dic73—21no—
84C4⋊Dic73—21no—
85C4⋊Dic73—21no—
86C4⋊Dic73—21no—
87C4⋊Dic73C2×C812yes—
88#11924005—41no—
89#11924005—41no—
90C4×Dic73—41no—
91C4×Dic73—41no—
92C22×C4×C73C22×C411yescharacteristic
93C22×C4×C73C2×D411yescharacteristic
94C22×C4×C73#4111yescharacteristic
95C2×C8×C73—21no—
96C2×C8×C73—21no—
97C2×C8×C73—21no—
98C2×C8×C73—21no—
99C2×C8×C73—21no—
100C2×C8×C73—21no—
101C2×C8×C73—22no—
102C2×C8×C73—21no—
103C2×C8×C73—21no—
104C2×C8×C73—21no—
105C2×C8×C73—21no—
106C2×C8×C73—41no—
107C2×C8×C73—41no—
108C2×C8×C73C2×C812yes—
109C2×C8×C73M1612yes—
110C42×C73C2×D411yescharacteristic
111C42×C73#4111yescharacteristic
112C42×C73#4111yescharacteristic
113C42×C73#4111yescharacteristic
114C23×C73C4×D411yescharacteristic
115C22×D73—22no—
116C22×D73—41no—
117C22×D73—41no—
118C22×D73—41no—
119C22×D73—41no—
120C22×D73—41no—
121C22×D73—41no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73#11711yescharacteristic
125C2×C4×C73C4×D411yescharacteristic
126C2×C4×C73#12111yescharacteristic
127C2×C4×C73#12311yescharacteristic
128C2×C4×C73#12411yescharacteristic
129C2×C4×C73#12611yescharacteristic
130C2×C4×C73C22×C811yescharacteristic
131C2×C4×C73C2×M1611yescharacteristic
132C2×C4×C73#13111yescharacteristic
133C2×C4×C73#13111yescharacteristic
134C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C73#13711yescharacteristic
138C2×Dic73—22no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146C2×Dic73—41no—
147D292—22no—
148D292—22no—
149D292—41no—
150D292—41no—
151C4×D73—81no—
152C4×D73—81no—
153C4×D73—81no—
154C4×D73—81no—
155C8×C73—22no—
156C8×C73—22no—
157C8×C73—42no—
158C8×C73—41no—
159C8×C73—41no—
160#10596831—81no—
161#10596831—81no—
162C22×C73#38811yescharacteristic
163C22×C73C8×D411yescharacteristic
164C22×C73#43611yescharacteristic
165C22×C73#44011yescharacteristic
166C22×C73#44211yescharacteristic
167C22×C73#44411yescharacteristic
168C22×C73#44411yescharacteristic
169C2×D73—42no—
170C2×D73—42no—
171C2×D73—42no—
172C2×D73—81no—
173C2×D73—81no—
174C2×D73—81no—
175C2×D73—81no—
176C4×C73—21no—
177C4×C73—21no—
178C4×C73#43111yescharacteristic
179C4×C73#43311yescharacteristic
180C4×C73C8×D411yescharacteristic
181C4×C73#43511yescharacteristic
182C4×C73#46811yescharacteristic
183C4×C73#46911yescharacteristic
184C4×C73#48911yescharacteristic
185C4×C73#49011yescharacteristic
186Dic73—42no—
187Dic73—81no—
188Dic73—81no—
189#9556—731nomaximal, Sylow
190C2×C73SD16⋊C811yescharacteristic
191C2×C73#158011yescharacteristic
192C2×C73#159211yescharacteristic
193C2×C73#159411yescharacteristic
194C2×C73#192311yescharacteristic
195C2×C73#193611yescharacteristic
196C2×C73#193811yescharacteristic
197D73—82no—
198#1954—731no—
199#1939—731no—
200C4×#102—731no—
201C2×D4⋊C8—731no—
202C2×#322D7311yescharacteristic, complemented
203#1279—731no—
204#1277—731no—
205C73#955611yescharacteristic, complemented, Sylow
206C2×C4×D4—731no—
207C2×C4⋊C8—731no—
208C2×C4⋊C8—731no—
209C2×C4⋊C8—1461no—
210C2×#102—731no—
211C2×#102—731no—
212C2×C22⋊C8—1461no—
213C2×C22⋊C8—1461no—
214C2×C4×C8C2×D7311yescharacteristic
215C2×C4×C8C2×D7311yescharacteristic
216C2×C4×C8C2×D7311yescharacteristic
217C4×C4⋊C4—731no—
218#340—731no—
219#340—731no—
220#336—1461no—
221D4⋊C8—1462no—
222#322—22no—
223C22×D4—731no—
224C23×C4—1461no—
225C22×C8—21no—
226C22×C8—1461no—
227C22×C8—1461no—
228C22×C8C4×D7311yescharacteristic
229C22×C8C4×D7311yescharacteristic
230C22×C8D29211yescharacteristic
231C22×C8D29211yescharacteristic
232C4×D4—1461no—
233C4×D4—1461no—
234C4×D4—1461no—
235C4×D4—1461no—
236C2×C4⋊C4—731no—
237C2×C4⋊C4—731no—
238C2×C4⋊C4—731no—
239C2×C22⋊C4—1461no—
240C2×C42—1461no—
241C2×C42C22×D7311yescharacteristic
242C4⋊C8—2922no—
243C4⋊C8—1461no—
244C4⋊C8—1461no—
245C4⋊C8—1461no—
246C4⋊C8—1461no—
247#102—734no—
248#102—1462no—
249C22⋊C8—2922no—
250C22⋊C8—2922no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8C22⋊D7312yes—
257#95—1461no—
258C24—1461no—
259C2×D4—732no—
260C2×D4—1461no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1461no—
265C22×C4—2921no—
266C22×C4—2921no—
267C22×C4—2921no—
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—2921no—
271C22×C4—1461no—
272C22×C4—1461no—
273C22×C4—1461no—
274C22×C4C2×C4×D7311yescharacteristic
275C22×C4C2×D29211yescharacteristic
276C22×C4#1192402811yescharacteristic
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—2921no—
291C2×C8—2921no—
292C2×C8—2921no—
293C2×C8—2921no—
294C2×C8—2921no—
295C2×C8—2921no—
296C2×C8C8×D7312yes—
297C2×C8#1192401112yes—
298C4⋊C4—732no—
299C4⋊C4—1461no—
300C4⋊C4—1461no—
301C4⋊C4—1461no—
302C4⋊C4—1461no—
303C4⋊C4—1461no—
304C22⋊C4—2921no—
305C22⋊C4—2921no—
306C42—2921no—
307C42—2921no—
308C42C2×C22⋊D7311yescharacteristic
309C42#1192402811yescharacteristic
310C42#1192402811yescharacteristic
311C42#1192402811yescharacteristic
312C23—2921no—
313C23—2921no—
314C23—2921no—
315C23—2921no—
316C23—2921no—
317C23—2921no—
318C23—1462no—
319C23C4×D29211yescharacteristic
320D4—2921no—
321D4—2921no—
322D4—1462no—
323D4—1462no—
324C2×C4—21no—
325C2×C4—21no—
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—5841no—
335C2×C4—5841no—
336C2×C4—5841no—
337C2×C4—5841no—
338C2×C4—1462no—
339C2×C4#1455654811yescharacteristic
340C2×C4C4×C22⋊D7311yescharacteristic
341C2×C4#1455656511yescharacteristic
342C2×C4#1455657411yescharacteristic
343C2×C4#1455657911yescharacteristic
344C2×C4#1455658511yescharacteristic
345C2×C4C2×C8×D7311yescharacteristic
346C2×C4C2×#1192401111yescharacteristic
347C2×C4#1455659711yescharacteristic
348C2×C4#1455659711yescharacteristic
349C2×C4#1455661911yescharacteristic
350C2×C4#1455661911yescharacteristic
351C2×C4#1455661911yescharacteristic
352C2×C4#1455662411yescharacteristic
353C8—22no—
354C8—22no—
355C8—42no—
356C8—41no—
357C8—41no—
358C8—5841no—
359C8—5841no—
360C22—2922no—
361C22—2922no—
362C22—2922no—
363C22—5841no—
364C22—5841no—
365C22—5841no—
366C22—5841no—
367C22#1798847811yescharacteristic
368C22C8×D29211yescharacteristic
369C22#1798866611yescharacteristic
370C22#1798868911yescharacteristic
371C22#1798870011yescharacteristic
372C22#1798871011yescharacteristic
373C22#1798871011yescharacteristic
374C4—21no—
375C4—21no—
376C4—2922no—
377C4—5841no—
378C4—5841no—
379C4#1798863811yescharacteristic
380C4#1798864611yescharacteristic
381C4C8×C22⋊D7311yescharacteristic
382C4#1798865811yescharacteristic
383C4#1798883311yescharacteristic
384C4#1798884011yescharacteristic
385C4#1798894711yescharacteristic
386C4#1798895211yescharacteristic
387C2—5842no—
388C2#2260874511yescharacteristic
389C2#2260875611yescharacteristic
390C2#2260883511yescharacteristic
391C2#2260884611yescharacteristic
392C2#2261053711yescharacteristic
393C2#2261062811yescharacteristic
394C2#2261064211yescharacteristic
subgroupG/H
centerC22×C4C2×D292
commutatorC2×C4×C73C22×C8
FrattiniC2×C42C22×D73
FittingC2×#322×C73C2
socleC23×C73C4×D4
prime radicalC22×D292C2×C4
cosocleC2×C42×C73C23
hypercenterC2×#322D73
hypocenterC73#9556
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#322

Complements

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

NH ≅ G/Ntype
2. #22610649C2semidirect
5. #22607771C2semidirect
6. #22607766C2semidirect
7. C2×#322×C73C2semidirect
44. #14556513C8semidirect
202. C2×#322D73semidirect
205. C73#9556semidirect

Maximal subgroups

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

subgroupindex
#226107252
#226106492
C4×#145565132
C2×#179883162
#226077712
#226077662
C2×#322×C732
#955673