Finite Group Databasebeta

← #32980295

Subgroups — #32980295

Order 18688.

438 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618500C211yesmaximal, characteristic
2#22609948C211yesmaximal, characteristic
3#22608703C211yesmaximal, characteristic, complemented
4#22608314C211yesmaximal, characteristic
5#22607832C211yesmaximal, characteristic, complemented
6#22607771C211yesmaximal, characteristic, complemented
7C73×#1566C211yesmaximal, characteristic, complemented
8C2×#14556599—21no—
9C4×#11924028C2211yescharacteristic
10#17988640C2211yescharacteristic
11#17988615—21no—
12#17988612—22no—
13#17988609—21no—
14C2×C4⋊#10596831C2211yescharacteristic
15C4⋊C8×D73—21no—
16C2×#14556517—21no—
17C4×C4⋊Dic73C2211yescharacteristic
18#17988348—21no—
19#17988337—21no—
20#17988337—21no—
21#17988319C411yescharacteristic, complemented
22#17988319C411yescharacteristic, complemented
23#17988316C411yescharacteristic, complemented
24#17988316C411yescharacteristic, complemented
25#423×C73C2211yescharacteristic
26#423×C73C2211yescharacteristic
27C2×C4×C8×C73C2211yescharacteristic
28#334×C73—22no—
29C2×#11924028D411yescharacteristic
30#14556599—42no—
31#14556599—42no—
32C2×#11924011—22no—
33C22×#10596831—21no—
34C2×C8×D73—22no—
35C4×Dic146C2×C411yescharacteristic
36C4×Dic146Q811yescharacteristic
37C4×D292C2×C411yescharacteristic
38C4×D292Q811yescharacteristic
39C4×C22⋊D73—21no—
40C4×C22⋊D73—21no—
41#14556550D411yescharacteristic
42#14556548—21no—
43C2×C4⋊Dic73—21no—
44C2×C4×Dic73—21no—
45C42×D73—21no—
46C4⋊#10596831—21no—
47C4⋊#10596831C2×C411yescharacteristic
48C4⋊#10596831C2×C411yescharacteristic
49C4⋊#10596831D411yescharacteristic
50C4⋊#10596831D411yescharacteristic
51#14556520—22no—
52#14556520—22no—
53#14556517—42no—
54C22⋊#10596831—21no—
55C4×#10596831—21no—
56#14556498—21no—
57C2×M16×C73—21no—
58C2×M16×C73—21no—
59C22×C8×C73—21no—
60C2×C42×C73C2311yescharacteristic
61C4⋊C8×C73—21no—
62C4⋊C8×C73—21no—
63C4⋊C8×C73—21no—
64C4⋊C8×C73D412yes—
65C4×C8×C73—21no—
66C4×C8×C73C2×C411yescharacteristic
67C4×C8×C73C2×C411yescharacteristic
68#11924028—21no—
69#11924028—21no—
70#11924028SD1612yes—
71#11924028SD1612yes—
72C2×Dic146C4⋊C411yescharacteristic
73C2×D292C4⋊C411yescharacteristic
74C2×C22⋊D73—21no—
75C22×Dic73—41no—
76C2×C4×D73—21no—
77C2×C4×D73—21no—
78C2×C4×D73—21no—
79#11924011—44no—
80C2×#10596831—21no—
81C2×#10596831—21no—
82C2×#10596831—21no—
83C2×#10596831—21no—
84C2×#10596831—41no—
85C2×#10596831—41no—
86C8×D73—44no—
87C4⋊Dic73—22no—
88C4⋊Dic73—41no—
89C4⋊Dic73C4⋊C411yescharacteristic
90C4⋊Dic73C4⋊C411yescharacteristic
91#11924007—21no—
92#11924007—21no—
93C22⋊Dic73—21no—
94#11924005—21no—
95#11924005—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99C4×Dic73—41no—
100C4×Dic73—41no—
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73#4111yescharacteristic
103C22×C4×C73#4111yescharacteristic
104M16×C73—41no—
105M16×C73—41no—
106M16×C73—41no—
107M16×C73—41no—
108C2×C8×C73—21no—
109C2×C8×C73—21no—
110C2×C8×C73—22no—
111C2×C8×C73—42no—
112C2×C8×C73—41no—
113C42×C73C22×C411yescharacteristic
114C42×C73C2×D411yescharacteristic
115C42×C73C2×D411yescharacteristic
116C42×C73C2×Q811yescharacteristic
117C23×C73#12311yescharacteristic
118C22×D73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—41no—
122C2×C4×C73C2×C4⋊C411yescharacteristic
123C2×C4×C73C4×D411yescharacteristic
124C2×C4×C73C4×D411yescharacteristic
125C2×C4×C73#12011yescharacteristic
126C2×C4×C73C22⋊Q811yescharacteristic
127C2×C4×C73C22⋊Q811yescharacteristic
128C2×C4×C73C2×SD1611yescharacteristic
129C2×C4×C73C2×SD1611yescharacteristic
130C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C73#13711yescharacteristic
132C22⋊D73—22no—
133C22⋊D73—22no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—42no—
138C2×Dic73—81no—
139C2×Dic73—81no—
140D292—21no—
141D292#10612yes—
142C4×D73—22no—
143C4×D73—22no—
144C4×D73—41no—
145C4×D73—41no—
146C4×D73—81no—
147Dic146—21no—
148Dic146#10612yes—
149C8×C73—22no—
150C8×C73—41no—
151C8×C73—42no—
152C8×C73—81no—
153#10596831—41no—
154#10596831—41no—
155#10596831—41no—
156#10596831—41no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73#38511yescharacteristic
160C22×C73#48111yescharacteristic
161C22×C73#48311yescharacteristic
162C2×D73—22no—
163C2×D73—41no—
164C2×D73—41no—
165C4×C73—21no—
166C4×C73—21no—
167C4×C73—21no—
168C4×C73C2×#10611yescharacteristic
169C4×C73#42811yescharacteristic
170C4×C73#44311yescharacteristic
171C4×C73#44411yescharacteristic
172C4×C73#44811yescharacteristic
173C4×C73#45011yescharacteristic
174Dic73—22no—
175Dic73—41no—
176Dic73—41no—
177Dic73—82no—
178#8904—731nomaximal, Sylow
179C2×C73—21no—
180C2×C73—21no—
181C2×C73#185311yescharacteristic
182C2×C73#186111yescharacteristic
183C2×C73#186611yescharacteristic
184D73—42no—
185#2906—731no—
186#1806—731no—
187#1570—731no—
188#1566D7311yescharacteristic, complemented
189#1476—731no—
190#1303—731no—
191#1279—731no—
192C73#890411yescharacteristic, complemented, Sylow
193C2×#131—1461no—
194C4×#41—731no—
195#431—731no—
196#424—1461no—
197#424—1462no—
198#423—1461no—
199#423C2×D7311yescharacteristic
200#423C2×D7311yescharacteristic
201C2×C4⋊C8—731no—
202C2×C4⋊C8—1461no—
203C2×#104—1461no—
204C2×C4×C8C2×D7311yescharacteristic
205C4×C4⋊C4—731no—
206#339—1461no—
207#334—22no—
208#334—1461no—
209#334—1461no—
210Q8⋊C8—731no—
211Q8⋊C8—731no—
212D4⋊C8—731no—
213D4⋊C8—731no—
214C2×#41—731no—
215#131—2922no—
216#131—2922no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—1462no—
220C22×C8—21no—
221C22×C8—1462no—
222C22×C8—1461no—
223C4×Q8—731no—
224C4×Q8—731no—
225C4×D4—731no—
226C4×D4—731no—
227C4×D4—1461no—
228C4×D4—1461no—
229#117—731no—
230#117—1461no—
231C2×C4⋊C4—1461no—
232C2×C42—1461no—
233C2×C42—1461no—
234C2×C42C22×D7311yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—731no—
239C4⋊C8—731no—
240C4⋊C8—731no—
241C4⋊C8—731no—
242C4⋊C8—1462no—
243C4⋊C8—1462no—
244C4⋊C8—1461no—
245C4⋊C8C22⋊D7312yes—
246#104—2922no—
247C22⋊C8—1461no—
248C4×C8—21no—
249C4×C8—1461no—
250C4×C8C4×D7311yescharacteristic
251C4×C8C4×D7311yescharacteristic
252#95—1461no—
253#41—732no—
254#41—732no—
255#41—1461no—
256#41—1461no—
257C2×Q8—731no—
258C2×D4—731no—
259C2×D4—1461no—
260C22×C4—2921no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4D4×D7311yescharacteristic
265C22×C4#1192402811yescharacteristic
266C22×C4#1192402911yescharacteristic
267M16—41no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—2924no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—22no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—2924no—
278C2×C8—2921no—
279C2×C8—2921no—
280C2×C8—1461no—
281C2×C8—1461no—
282C2×C8—1461no—
283C2×C8—1461no—
284C4⋊C4—2921no—
285C4⋊C4—731no—
286C4⋊C4—731no—
287C4⋊C4—1462no—
288C4⋊C4—1461no—
289C4⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C42—2921no—
294C42—2921no—
295C42—1461no—
296C42—1461no—
297C42—1461no—
298C42C2×C4×D7311yescharacteristic
299C42D4×D7311yescharacteristic
300C42C2×C22⋊D7311yescharacteristic
301C42Q8×D7311yescharacteristic
302C23—1461no—
303C23#1455657611yescharacteristic
304Q8—732no—
305Q8—1461no—
306D4—732no—
307D4—1462no—
308D4—1462no—
309D4—1461no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—2921no—
314C2×C4—2921no—
315C2×C4—2922no—
316C2×C4—5841no—
317C2×C4—5841no—
318C2×C4—5841no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1462no—
323C2×C4—1462no—
324C2×C4C4⋊C4×D7311yescharacteristic
325C2×C4C4×C22⋊D7311yescharacteristic
326C2×C4#1455655311yescharacteristic
327C2×C4#1455655911yescharacteristic
328C2×C4#1455656711yescharacteristic
329C2×C4#1455656911yescharacteristic
330C2×C4SD16×D7311yescharacteristic
331C2×C4SD16×D7311yescharacteristic
332C2×C4#1455661811yescharacteristic
333C2×C4#1455662011yescharacteristic
334C8—22no—
335C8—41no—
336C8—42no—
337C8—81no—
338C8—2921no—
339C8—2921no—
340C8—2921no—
341C8—2921no—
342C22—21no—
343C22—21no—
344C22—2921no—
345C22—2921no—
346C22—1462no—
347C22#1798845811yescharacteristic
348C22#1798890711yescharacteristic
349C22#1798891911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—2921no—
354C4—2921no—
355C4—5842no—
356C4—1462no—
357C4#106×D7311yescharacteristic
358C4#1798862611yescharacteristic
359C4#1798870311yescharacteristic
360C4#1798870811yescharacteristic
361C4#1798872411yescharacteristic
362C4#1798873611yescharacteristic
363C2—21no—
364C2—21no—
365C2—2922no—
366C2#2261012211yescharacteristic
367C2#2261017011yescharacteristic
368C2#2261020311yescharacteristic
subgroupG/H
centerC2×C4#14556559
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1566C2
socleC22×C73#385
prime radicalC2×#11924028D4
cosocleC2×C42×C73C23
hypercenter#1566D73
hypocenterC73#8904
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
3. #22608703C2semidirect
5. #22607832C2semidirect
6. #22607771C2semidirect
7. C73×#1566C2semidirect
21. #17988319C4semidirect
22. #17988319C4semidirect
23. #17988316C4semidirect
24. #17988316C4semidirect
188. #1566D73semidirect
192. C73#8904semidirect

Maximal subgroups

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

subgroupindex
#226185002
#226099482
#226087032
#226083142
#226078322
#226077712
C73×#15662
#890473