Finite Group Databasebeta

← #32985353

Subgroups — #32985353

Order 18688.

416 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620253C211yesmaximal, characteristic
2#22609800C211yesmaximal, characteristic, complemented
3#22608677C211yesmaximal, characteristic, complemented
4#22608429C211yesmaximal, characteristic, complemented
5#22608335C211yesmaximal, characteristic, complemented
6#22608330C211yesmaximal, characteristic
7C73×#1502C211yesmaximal, characteristic
8#17989144C2211yescharacteristic
9#17988941—21no—
10#17988941—21no—
11#17988937C411yescharacteristic, complemented
12#17988937C411yescharacteristic, complemented
13#17988933C411yescharacteristic, complemented
14#17988933C411yescharacteristic, complemented
15#17988640C2211yescharacteristic
16C2×C4⋊#10596831C2211yescharacteristic
17#17988583—21no—
18#17988583—21no—
19C2×#14556502—21no—
20C2×C4×#10596831C2211yescharacteristic
21#17988342—21no—
22#17988339—21no—
23#17988337—21no—
24#17988323—22no—
25#17988319—22no—
26D4⋊#10596831—22no—
27#532×C73C2211yescharacteristic
28#431×C73C2211yescharacteristic
29C4×C4⋊C4×C73C2211yescharacteristic
30#327×C73—22no—
31C22×#10596831—21no—
32C22×#10596831D411yescharacteristic
33C22×#10596831D411yescharacteristic
34#14556591C2×C411yescharacteristic
35#14556591C2×C411yescharacteristic
36#14556583—21no—
37#14556570—21no—
38#14556570—21no—
39C4×Dic146—21no—
40C4×Dic146—21no—
41#14556550—21no—
42C4⋊#10596831—21no—
43C4⋊#10596831—21no—
44C4⋊#10596831D412yes—
45#14556515—21no—
46#14556515—21no—
47#14556515—21no—
48#14556515—21no—
49#14556512—21no—
50#14556512—21no—
51#14556512—21no—
52#14556512—21no—
53C22⋊#10596831—21no—
54#14556502—42no—
55C4×#10596831—21no—
56C4×#10596831C2×C411yescharacteristic
57C4×#10596831C2×C411yescharacteristic
58C4×#10596831D411yescharacteristic
59C4×#10596831D411yescharacteristic
60C2×#41×C73—21no—
61C4⋊Q8×C73C2×C411yescharacteristic
62#127×C73C2×C411yescharacteristic
63#124×C73—21no—
64#121×C73—21no—
65#121×C73—21no—
66C4×D4×C73—21no—
67C4×D4×C73—21no—
68C2×C4⋊C4×C73—21no—
69C2×C42×C73—21no—
70C2×C42×C73C2311yescharacteristic
71C4⋊C8×C73—21no—
72C22⋊C8×C73—21no—
73C4×C8×C73—21no—
74#95×C73D412yes—
75C2×Dic146—21no—
76C2×Dic146—21no—
77C2×#10596831—21no—
78C2×#10596831—21no—
79C2×#10596831—21no—
80C2×#10596831—21no—
81C2×#10596831—22no—
82C2×#10596831—41no—
83C2×#10596831—41no—
84C2×#10596831—41no—
85C2×#10596831C22⋊C411yescharacteristic
86C2×#10596831C22⋊C411yescharacteristic
87C2×#10596831C22⋊C411yescharacteristic
88C2×#10596831C22⋊C411yescharacteristic
89C4⋊Dic73—21no—
90C4⋊Dic73—21no—
91C4⋊Dic73—21no—
92C4⋊Dic73—21no—
93#11924007—41no—
94#11924007—41no—
95C22⋊Dic73—41no—
96C4×Dic73—41no—
97#41×C73—41no—
98#41×C73—41no—
99#41×C73—41no—
100#41×C73—41no—
101C2×Q8×C73—21no—
102C2×D4×C73—21no—
103C2×D4×C73—21no—
104C2×D4×C73—21no—
105C2×D4×C73—41no—
106C22×C4×C73—22no—
107C22×C4×C73—41no—
108C22×C4×C73C2×D411yescharacteristic
109C22×C4×C73C2×D411yescharacteristic
110C22×C4×C73#4111yescharacteristic
111C2×C8×C73—41no—
112C4⋊C4×C73—21no—
113C4⋊C4×C73—21no—
114C4⋊C4×C73—42no—
115C22⋊C4×C73—41no—
116C22⋊C4×C73—41no—
117C42×C73—41no—
118C42×C73—41no—
119C42×C73C22×C411yescharacteristic
120C42×C73C2×D411yescharacteristic
121C42×C73C2×D411yescharacteristic
122C42×C73#4111yescharacteristic
123C23×C73—41no—
124C23×C73#12111yescharacteristic
125Q8×C73—41no—
126Q8×C73—41no—
127D4×C73—41no—
128D4×C73—41no—
129D4×C73—42no—
130D4×C73—81no—
131D4×C73—81no—
132D4×C73—81no—
133C2×C4×C73—22no—
134C2×C4×C73—41no—
135C2×C4×C73—42no—
136C2×C4×C73—42no—
137C2×C4×C73—41no—
138C2×C4×C73—42no—
139C2×C4×C73—81no—
140C2×C4×C73—81no—
141C2×C4×C73C2×C22⋊C411yescharacteristic
142C2×C4×C73C4×D411yescharacteristic
143C2×C4×C73C4×D411yescharacteristic
144C2×C4×C73#12111yescharacteristic
145C2×C4×C73#12411yescharacteristic
146C2×C4×C73#12711yescharacteristic
147C2×C4×C73#13511yescharacteristic
148C2×C4×C73#13511yescharacteristic
149C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C73#13711yescharacteristic
151C2×Dic73—41no—
152C2×Dic73—41no—
153Dic146—42no—
154Dic146—81no—
155C8×C73—81no—
156#10596831—21no—
157#10596831—21no—
158#10596831—21no—
159#10596831—21no—
160#10596831—42no—
161#10596831—81no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—81no—
165C22×C73—81no—
166C22×C73—81no—
167C22×C73#39011yescharacteristic
168C22×C73#46311yescharacteristic
169C22×C73#46411yescharacteristic
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—82no—
174C4×C73—81no—
175C4×C73#41611yescharacteristic
176C4×C73#41711yescharacteristic
177C4×C73#44412yes—
178C4×C73#46311yescharacteristic
179C4×C73#46411yescharacteristic
180Dic73—81no—
181Dic73—81no—
182#9754—731nomaximal, Sylow
183C2×C73—21no—
184C2×C73—21no—
185C2×C73—161no—
186C2×C73#197511yescharacteristic
187C2×C73#197611yescharacteristic
188C2×C73#198311yescharacteristic
189#3131—731no—
190#1770—731no—
191#1564—731no—
192#1503—731no—
193#1502D7311yescharacteristic
194#1481—731no—
195#1480—731no—
196C73#975411yescharacteristic, complemented, Sylow
197#533—731no—
198#532C2×D7311yescharacteristic
199#488—1461no—
200#488—1461no—
201#487—731no—
202#487—731no—
203#486—731no—
204#486—731no—
205#431—731no—
206#431C2×D7311yescharacteristic
207C2×C4⋊C8—731no—
208#416—1461no—
209#416—1461no—
210C2×#97—1461no—
211C2×C4×C8—731no—
212C4×C4⋊C4C2×D7311yescharacteristic
213#336—1461no—
214#335—1461no—
215#334—1461no—
216#328—1462no—
217#327—22no—
218Q8⋊C8—1462no—
219D4⋊C8—1462no—
220C2×#41—21no—
221C22×C8—731no—
222C22×C8—731no—
223C22×C8—1461no—
224C4⋊Q8—731no—
225C4⋊Q8—731no—
226C4⋊Q8C4×D7311yescharacteristic
227#127C4×D7311yescharacteristic
228#125—1461no—
229#124—21no—
230C22⋊Q8—1461no—
231C22⋊Q8—1461no—
232#121—21no—
233#121—21no—
234C4×Q8—1461no—
235C4×Q8—1461no—
236C4×D4—21no—
237C4×D4—21no—
238#117—1461no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C22×D7311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—732no—
244C4⋊C8—1461no—
245C4⋊C8—1461no—
246#103—1461no—
247#103—1461no—
248#103—1461no—
249#103—1461no—
250#102—1461no—
251#102—1461no—
252#102—1461no—
253#102—1461no—
254C22⋊C8—21no—
255C22⋊C8—1461no—
256#97—2922no—
257C4×C8—21no—
258C4×C8—731no—
259C4×C8—731no—
260C4×C8—731no—
261C4×C8—731no—
262C4×C8—1461no—
263#95C22⋊D7312yes—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—1461no—
270C2×Q8—1461no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—22no—
276C22×C4—41no—
277C22×C4D4×D7311yescharacteristic
278C22×C4C2×C22⋊D7311yescharacteristic
279C22×C4#1192402711yescharacteristic
280C2×C8—41no—
281C2×C8—2921no—
282C2×C8—2921no—
283C2×C8—2921no—
284C2×C8—731no—
285C2×C8—731no—
286C2×C8—731no—
287C2×C8—731no—
288C2×C8—1462no—
289C2×C8—1461no—
290C2×C8—1461no—
291C2×C8—1461no—
292C2×C8—1461no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—42no—
296C4⋊C4—2921no—
297C4⋊C4—2921no—
298C4⋊C4—1461no—
299C4⋊C4—1461no—
300C4⋊C4—1461no—
301C4⋊C4—1461no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—2921no—
305C42—41no—
306C42—41no—
307C42—2921no—
308C42C2×C4×D7311yescharacteristic
309C42D4×D7311yescharacteristic
310C42D4×D7311yescharacteristic
311C42#1192402811yescharacteristic
312C23—41no—
313C23#1455656311yescharacteristic
314Q8—41no—
315Q8—41no—
316Q8—2922no—
317Q8—5841no—
318D4—42no—
319D4—41no—
320D4—41no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—2921no—
333C2×C4—2921no—
334C2×C4C22⋊C4×D7311yescharacteristic
335C2×C4#1455655111yescharacteristic
336C2×C4C4×C22⋊D7311yescharacteristic
337C2×C4#1455656411yescharacteristic
338C2×C4#1455657711yescharacteristic
339C2×C4#1455658711yescharacteristic
340C2×C4#1455661011yescharacteristic
341C2×C4#1455661211yescharacteristic
342C2×C4#1455661511yescharacteristic
343C2×C4#1455662011yescharacteristic
344C8—81no—
345C8—2922no—
346C8—5841no—
347C8—1461no—
348C8—1461no—
349C8—1461no—
350C8—1461no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1798848711yescharacteristic
357C22#1798880011yescharacteristic
358C22#1798880711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—81no—
364C4—5841no—
365C4—5841no—
366C4#1798858011yescharacteristic
367C4#1798858511yescharacteristic
368C4#1798870612yes—
369C4#1798880111yescharacteristic
370C4#1798880811yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2#2261082111yescharacteristic
375C2#2261082611yescharacteristic
376C2#2261086211yescharacteristic
subgroupG/H
centerC2×C4#14556564
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1502C2
socleC22×C73#390
prime radical#532×C73C22
cosocleC2×C42×C73C23
hypercenter#1502D73
hypocenterC73#9754
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #22609800C2semidirect
3. #22608677C2semidirect
4. #22608429C2semidirect
5. #22608335C2semidirect
11. #17988937C4semidirect
12. #17988937C4semidirect
13. #17988933C4semidirect
14. #17988933C4semidirect
196. C73#9754semidirect

Maximal subgroups

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

subgroupindex
#226202532
#226098002
#226086772
#226084292
#226083352
#226083302
C73×#15022
#975473