Finite Group Databasebeta

← #32981217

Subgroups — #32981217

Order 18688.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620486C211yesmaximal, characteristic
2#22618675C211yesmaximal, characteristic
3#22610874C211yesmaximal, characteristic, complemented
4#22608335C211yesmaximal, characteristic, complemented
5#22607772C211yesmaximal, characteristic, complemented
6#22607767C211yesmaximal, characteristic, complemented
7C73×#1502C211yesmaximal, characteristic
8C2×#14556598—21no—
9#17989144C2211yescharacteristic
10#17988983C411yescharacteristic, complemented
11#17988959C411yescharacteristic, complemented
12#17988939C411yescharacteristic, complemented
13#17988933C411yescharacteristic, complemented
14#17988814—22no—
15C4×#11924016—22no—
16#17988665—21no—
17#17988659—22no—
18D4×#10596831—21no—
19C2×C4⋊#10596831C2211yescharacteristic
20#17988554—21no—
21C4×#11924012C2211yescharacteristic
22C2×C4×#10596831C2211yescharacteristic
23#17988347—21no—
24#17988347—21no—
25#17988319—21no—
26#17988319—21no—
27#532×C73C2211yescharacteristic
28#431×C73C2211yescharacteristic
29C4×C4⋊C4×C73C2211yescharacteristic
30#327×C73—22no—
31C2×#11924016—22no—
32#14556598—42no—
33#14556598—42no—
34C2×#11924012—22no—
35C2×#11924012D411yescharacteristic
36C2×#11924012D411yescharacteristic
37C22×#10596831—22no—
38C22×#10596831—21no—
39C22×#10596831—21no—
40#14556591C2×C411yescharacteristic
41#14556591C2×C411yescharacteristic
42#14556583—21no—
43#14556570—21no—
44#14556570—21no—
45C4×Dic146—21no—
46C4×Dic146—21no—
47#14556550—21no—
48#14556522—22no—
49C4⋊#10596831—21no—
50C4⋊#10596831D411yescharacteristic
51C4⋊#10596831D411yescharacteristic
52#14556514—22no—
53#14556512—22no—
54C22⋊#10596831—22no—
55C22⋊#10596831—22no—
56#14556502—21no—
57C4×#10596831—21no—
58C4×#10596831—21no—
59C4×#10596831C2×C411yescharacteristic
60C4×#10596831C2×C411yescharacteristic
61C2×#41×C73—21no—
62C4⋊Q8×C73C2×C411yescharacteristic
63#127×C73C2×C411yescharacteristic
64#124×C73—21no—
65#121×C73—21no—
66#121×C73D412yes—
67C4×D4×C73—21no—
68C4×D4×C73D412yes—
69C2×C4⋊C4×C73—21no—
70C2×C42×C73—21no—
71C2×C42×C73C2311yescharacteristic
72C4⋊C8×C73—21no—
73C22⋊C8×C73—21no—
74C4×C8×C73—21no—
75#95×C73—21no—
76C2×Dic146—21no—
77C2×Dic146—21no—
78#11924016—44no—
79#11924012—21no—
80#11924012—21no—
81#11924012—21no—
82#11924012—44no—
83#11924012SD1612yescomplemented
84C2×#10596831—21no—
85C2×#10596831—21no—
86C2×#10596831—21no—
87C2×#10596831—21no—
88C2×#10596831—21no—
89C2×#10596831—21no—
90C2×#10596831—42no—
91C2×#10596831—44no—
92C2×#10596831—41no—
93C2×#10596831—41no—
94C4⋊Dic73—21no—
95C4⋊Dic73—21no—
96C4⋊Dic73—21no—
97C4⋊Dic73—21no—
98#11924007—41no—
99#11924007—41no—
100C22⋊Dic73—41no—
101C4×Dic73—41no—
102#41×C73—41no—
103#41×C73—41no—
104#41×C73—41no—
105#41×C73—41no—
106C2×Q8×C73—21no—
107C2×D4×C73—22no—
108C2×D4×C73—21no—
109C2×D4×C73—21no—
110C2×D4×C73C22⋊C412yes—
111C22×C4×C73—22no—
112C22×C4×C73—41no—
113C22×C4×C73C2×D411yescharacteristic
114C22×C4×C73C2×D411yescharacteristic
115C22×C4×C73#4111yescharacteristic
116C2×C8×C73—41no—
117C4⋊C4×C73—21no—
118C4⋊C4×C73—22no—
119C4⋊C4×C73—41no—
120C4⋊C4×C73C22⋊C412yes—
121C22⋊C4×C73—22no—
122C22⋊C4×C73—22no—
123C42×C73—41no—
124C42×C73—41no—
125C42×C73C22×C411yescharacteristic
126C42×C73C2×D411yescharacteristic
127C42×C73C2×D411yescharacteristic
128C42×C73#4111yescharacteristic
129C23×C73—22no—
130C23×C73#12111yescharacteristic
131Q8×C73—41no—
132Q8×C73—41no—
133D4×C73—42no—
134D4×C73—42no—
135D4×C73—42no—
136D4×C73—41no—
137D4×C73—41no—
138D4×C73—41no—
139D4×C73—41no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—22no—
143C2×C4×C73—41no—
144C2×C4×C73—42no—
145C2×C4×C73—42no—
146C2×C4×C73—42no—
147C2×C4×C73—81no—
148C2×C4×C73—81no—
149C2×C4×C73C2×C22⋊C411yescharacteristic
150C2×C4×C73C4×D411yescharacteristic
151C2×C4×C73C4×D411yescharacteristic
152C2×C4×C73#12011yescharacteristic
153C2×C4×C73#12111yescharacteristic
154C2×C4×C73#12311yescharacteristic
155C2×C4×C73C2×SD1611yescharacteristic
156C2×C4×C73#13511yescharacteristic
157C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C73#13711yescharacteristic
159C2×Dic73—41no—
160C2×Dic73—41no—
161Dic146—42no—
162Dic146—41no—
163Dic146—41no—
164C8×C73—81no—
165#10596831—22no—
166#10596831—22no—
167#10596831—41no—
168#10596831—41no—
169#10596831—41no—
170#10596831—41no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—42no—
174C22×C73—42no—
175C22×C73—42no—
176C22×C73#38611yescharacteristic
177C22×C73#46111yescharacteristic
178C22×C73#46311yescharacteristic
179C4×C73—21no—
180C4×C73—21no—
181C4×C73—21no—
182C4×C73—42no—
183C4×C73—82no—
184C4×C73C4×SD1611yescharacteristic
185C4×C73#44011yescharacteristic
186C4×C73#44311yescharacteristic
187C4×C73#44411yescharacteristic
188C4×C73#45011yescharacteristic
189C4×C73#45211yescharacteristic
190Dic73—81no—
191Dic73—81no—
192#9055—731nomaximal, Sylow
193C2×C73—21no—
194C2×C73—21no—
195C2×C73—82no—
196C2×C73#187611yescharacteristic
197C2×C73#187711yescharacteristic
198C2×C73#188411yescharacteristic
199#3167—731no—
200#2935—731no—
201#1986—731no—
202#1502D7311yescharacteristic
203#1481—731no—
204#1279—731no—
205#1278—731no—
206C73#905511yescharacteristic, complemented, Sylow
207C2×#131—1461no—
208#533—731no—
209#532C2×D7311yescharacteristic
210#498—731no—
211#492—731no—
212#487—731no—
213#486—731no—
214#465—1462no—
215C4×SD16—1462no—
216#436—1461no—
217#435—1462no—
218C8×D4—1461no—
219#431C2×D7311yescharacteristic
220C2×C4⋊C8—731no—
221#408—1461no—
222C4×M16—731no—
223C2×C4×C8—731no—
224C4×C4⋊C4C2×D7311yescharacteristic
225#339—1461no—
226#339—1461no—
227#327—22no—
228Q8⋊C8—1461no—
229Q8⋊C8—1461no—
230C2×#41—21no—
231C2×SD16—1462no—
232#131—2922no—
233#131—2922no—
234C2×M16—731no—
235C2×M16—731no—
236C2×M16—1462no—
237C22×C8—1462no—
238C22×C8—1461no—
239C22×C8—1461no—
240C4⋊Q8—731no—
241C4⋊Q8—731no—
242C4⋊Q8C4×D7311yescharacteristic
243#127C4×D7311yescharacteristic
244#125—1461no—
245#124—21no—
246C22⋊Q8—1461no—
247C22⋊Q8—1461no—
248#121—21no—
249#121C22⋊D7312yes—
250C4×Q8—1461no—
251C4×Q8—1461no—
252C4×D4—21no—
253C4×D4D29212yes—
254#117—1461no—
255C2×C4⋊C4—21no—
256C2×C42—21no—
257C2×C42C22×D7311yescharacteristic
258#106—1462no—
259C4⋊C8—21no—
260C4⋊C8—731no—
261C4⋊C8—731no—
262C4⋊C8—1461no—
263#103—1462no—
264#102—1462no—
265C22⋊C8—21no—
266C22⋊C8—1462no—
267C22⋊C8—1462no—
268#97—1461no—
269C4×C8—21no—
270C4×C8—731no—
271C4×C8—731no—
272C4×C8—1461no—
273C4×C8—1461no—
274#95—21no—
275#41—41no—
276#41—41no—
277#41—41no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—1461no—
281C2×Q8—1461no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4#1192400512yes—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4D4×D7311yescharacteristic
289C22×C4C2×C22⋊D7311yescharacteristic
290C22×C4#1192402711yescharacteristic
291SD16—2924no—
292M16—2924no—
293M16—732no—
294M16—1461no—
295M16—1461no—
296M16—1461no—
297C2×C8—41no—
298C2×C8—2921no—
299C2×C8—2921no—
300C2×C8—2922no—
301C2×C8—2924no—
302C2×C8—1461no—
303C2×C8—1461no—
304C2×C8—1461no—
305C2×C8—1461no—
306C2×C8—1461no—
307C2×C8—1461no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—2921no—
312C4⋊C4—2921no—
313C4⋊C4—1461no—
314C4⋊C4—1461no—
315C4⋊C4—1461no—
316C4⋊C4—1461no—
317C4⋊C4#1192400512yes—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—2921no—
321C42—41no—
322C42—41no—
323C42—2921no—
324C42C2×C4×D7311yescharacteristic
325C42D4×D7311yescharacteristic
326C42C2×D29211yescharacteristic
327C42#1192402711yescharacteristic
328C23—22no—
329C23#1455656311yescharacteristic
330Q8—41no—
331Q8—41no—
332Q8—2922no—
333Q8—2921no—
334Q8—2921no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—41no—
339D4—41no—
340D4—41no—
341D4—41no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—2921no—
352C2×C4—2921no—
353C2×C4C2×#1192400511yescharacteristic
354C2×C4#1455655111yescharacteristic
355C2×C4#1455655111yescharacteristic
356C2×C4#1455656111yescharacteristic
357C2×C4#1455656311yescharacteristic
358C2×C4#1455657511yescharacteristic
359C2×C4SD16×D7311yescharacteristic
360C2×C4#1455661011yescharacteristic
361C2×C4#1455661511yescharacteristic
362C2×C4#1455662011yescharacteristic
363C8—81no—
364C8—2921no—
365C8—2921no—
366C8—2921no—
367C8—2921no—
368C8—1462no—
369C8—1462no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22#1798846411yescharacteristic
376C22#1798879011yescharacteristic
377C22#1798880011yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—82no—
383C4—5841no—
384C4—5841no—
385C4#1798867811yescharacteristic
386C4#1798868411yescharacteristic
387C4#1798870111yescharacteristic
388C4#1798870611yescharacteristic
389C4#1798873911yescharacteristic
390C4#1798875011yescharacteristic
391C2—21no—
392C2—21no—
393C2—82no—
394C2#2261025611yescharacteristic
395C2#2261026311yescharacteristic
396C2#2261031211yescharacteristic
subgroupG/H
centerC2×C4#14556561
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1502C2
socleC22×C73#386
prime radical#532×C73C22
cosocleC2×C42×C73C23
hypercenter#1502D73
hypocenterC73#9055
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
3. #22610874C2semidirect
4. #22608335C2semidirect
5. #22607772C2semidirect
6. #22607767C2semidirect
10. #17988983C4semidirect
11. #17988959C4semidirect
12. #17988939C4semidirect
13. #17988933C4semidirect
83. #11924012SD16semidirect
206. C73#9055semidirect

Maximal subgroups

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

subgroupindex
#226204862
#226186752
#226108742
#226083352
#226077722
#226077672
C73×#15022
#905573