Finite Group Databasebeta

← #32984374

Subgroups — #32984374

Order 18688.

454 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610858C211yesmaximal, characteristic
2#22610737C211yesmaximal, characteristic
3#22610694C211yesmaximal, characteristic, complemented
4C2×#17988330C211yesmaximal, characteristic
5#22607815C211yesmaximal, characteristic, complemented
6#22607766C211yesmaximal, characteristic, complemented
7C73×#1770C211yesmaximal, characteristic, complemented
8C2×#14556588C2211yescharacteristic
9C2×#14556522—21no—
10C2×C4⋊#10596831C2211yescharacteristic
11C2×C4⋊#10596831C2211yescharacteristic
12C2×#14556513—21no—
13C2×#14556513—21no—
14C2×#14556511—21no—
15C2×#14556511—21no—
16#17988457C2211yescharacteristic
17#17988349—21no—
18#17988330C414yescomplemented
19C2×C4⋊C8×C73C2211yescharacteristic
20C2×#97×C73—21no—
21C2×C4×C8×C73C2211yescharacteristic
22C4×C4⋊C4×C73C2211yescharacteristic
23#336×C73—21no—
24C22×D292—21no—
25C22×D292—21no—
26C22×D292—21no—
27C22×#10596831—21no—
28C22×#10596831—21no—
29#14556588—21no—
30#14556588—21no—
31#14556588—21no—
32#14556588C2×C412yes—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73—21no—
36#14556522—42no—
37C4⋊#10596831—21no—
38C4⋊#10596831—21no—
39C4⋊#10596831—21no—
40C4⋊#10596831C2×C412yes—
41#14556513—42no—
42#14556513—42no—
43#14556511—42no—
44#14556511—42no—
45C22×C8×C73—21no—
46C22×C8×C73D411yescharacteristic
47C22×C8×C73D411yescharacteristic
48C2×C4⋊C4×C73D411yescharacteristic
49C2×C4⋊C4×C73D411yescharacteristic
50C2×C42×C73—21no—
51C2×C42×C73C2311yescharacteristic
52C4⋊C8×C73—21no—
53C4⋊C8×C73C2×C412yes—
54#97×C73—42no—
55C4×C8×C73—21no—
56C4×C8×C73—21no—
57#95×C73—21no—
58C23×D73—41no—
59C2×D292—22no—
60C2×D292—22no—
61C2×D292—22no—
62C2×D292—41no—
63C2×D292—41no—
64C2×D292—41no—
65C2×D292—41no—
66C2×D292—41no—
67C2×D292—41no—
68C2×D292—41no—
69C2×D292—41no—
70C2×D292—41no—
71C2×D292—41no—
72C2×D292—41no—
73C2×D292—81no—
74C2×D292—81no—
75C22×Dic73—41no—
76C2×#10596831—22no—
77C2×#10596831—41no—
78C2×#10596831—41no—
79C2×#10596831—41no—
80C2×#10596831—41no—
81C2×#10596831—41no—
82C4⋊Dic73—41no—
83C4⋊Dic73—41no—
84C4⋊Dic73—41no—
85C4⋊Dic73—41no—
86C4⋊Dic73—81no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73C2×D411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73#4111yescharacteristic
92C2×C8×C73—21no—
93C2×C8×C73—21no—
94C2×C8×C73—22no—
95C2×C8×C73—21no—
96C2×C8×C73—21no—
97C2×C8×C73—21no—
98C2×C8×C73—41no—
99C2×C8×C73—41no—
100C2×C8×C73SD1612yes—
101C4⋊C4×C73—21no—
102C4⋊C4×C73—21no—
103C4⋊C4×C73—21no—
104C4⋊C4×C73—21no—
105C42×C73—41no—
106C42×C73—41no—
107C42×C73C22×C411yescharacteristic
108C42×C73#4111yescharacteristic
109C42×C73#4111yescharacteristic
110C42×C73#4111yescharacteristic
111C23×C73#12111yescharacteristic
112C22×D73—42no—
113C22×D73—81no—
114C22×D73—81no—
115C22×D73—81no—
116C22×D73—81no—
117C22×D73—81no—
118C22×D73—81no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73#11711yescharacteristic
128C2×C4×C73C4×D411yescharacteristic
129C2×C4×C73C4×D411yescharacteristic
130C2×C4×C73#12311yescharacteristic
131C2×C4×C73#12411yescharacteristic
132C2×C4×C73#12611yescharacteristic
133C2×C4×C73C2×SD1611yescharacteristic
134C2×C4×C73#13511yescharacteristic
135C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C73#13711yescharacteristic
141C2×Dic73—81no—
142C2×Dic73—81no—
143C2×Dic73—81no—
144D292—42no—
145D292—42no—
146D292—42no—
147D292—42no—
148D292—82no—
149D292—82no—
150D292—81no—
151D292—81no—
152D292—81no—
153D292—81no—
154C8×C73—22no—
155C8×C73—42no—
156C8×C73—41no—
157#10596831—42no—
158#10596831—81no—
159C22×C73#38811yescharacteristic
160C22×C73#46011yescharacteristic
161C22×C73#46311yescharacteristic
162C22×C73#46811yescharacteristic
163C22×C73#46911yescharacteristic
164C22×C73#47111yescharacteristic
165C22×C73#47211yescharacteristic
166C2×D73—82no—
167C2×D73—82no—
168C2×D73—82no—
169C2×D73—161no—
170C2×D73—161no—
171C2×D73—161no—
172C2×D73—161no—
173C4×C73—21no—
174C4×C73—21no—
175C4×C73—81no—
176C4×C73—81no—
177C4×C73C4×SD1611yescharacteristic
178C4×C73#44011yescharacteristic
179C4×C73#44211yescharacteristic
180C4×C73#44211yescharacteristic
181C4×C73#48111yescharacteristic
182C4×C73#48211yescharacteristic
183C4×C73#48911yescharacteristic
184C4×C73#49011yescharacteristic
185Dic73—161no—
186#9572—731nomaximal, Sylow
187C2×C73#168611yescharacteristic
188C2×C73#168811yescharacteristic
189C2×C73#169711yescharacteristic
190C2×C73#170111yescharacteristic
191C2×C73#192611yescharacteristic
192C2×C73#193111yescharacteristic
193C2×C73#193611yescharacteristic
194D73—162no—
195#1982—731no—
196#1957—731no—
197#1948—731no—
198#1770D7311yescharacteristic, complemented
199C2×#331—731no—
200#1296—731no—
201#1277—731no—
202C73#957211yescharacteristic, complemented, Sylow
203C2×#127—731no—
204C2×#106—1461no—
205C2×C4⋊C8—731no—
206C2×C4⋊C8—731no—
207C2×C4⋊C8C2×D7311yescharacteristic
208C2×#102—1461no—
209C2×#102—1461no—
210C2×#102—1461no—
211C2×#102—1461no—
212C2×#97—21no—
213C2×C4×C8C2×D7311yescharacteristic
214#384—731no—
215C4×C4⋊C4C2×D7311yescharacteristic
216#340—1461no—
217#336—21no—
218#331—734no—
219C22×D4—1461no—
220C22×D4—1461no—
221C22×D4—1461no—
222C22×C8—21no—
223C22×C8—1461no—
224C22×C8—1461no—
225C22×C8C22⋊D7311yescharacteristic
226C22×C8C22⋊D7311yescharacteristic
227#127—732no—
228#127—1461no—
229#127—1461no—
230#127—1461no—
231C2×C4⋊C4—1461no—
232C2×C4⋊C4—1461no—
233C2×C4⋊C4—1461no—
234C2×C4⋊C4D29211yescharacteristic
235C2×C4⋊C4D29211yescharacteristic
236C2×C42—21no—
237C2×C42C22×D7311yescharacteristic
238#106—2922no—
239C4⋊C8—21no—
240C4⋊C8—732no—
241C4⋊C8—1461no—
242C4⋊C8—1461no—
243C4⋊C8—1461no—
244C4⋊C8C4×D7312yes—
245#102—2922no—
246#102—2922no—
247#102—2922no—
248#102—2922no—
249#97—42no—
250C4×C8—21no—
251C4×C8—21no—
252#95—21no—
253C24—2921no—
254C2×D4—2921no—
255C2×D4—2921no—
256C2×D4—2921no—
257C2×D4—2921no—
258C2×D4—2921no—
259C2×D4—2921no—
260C2×D4—2921no—
261C2×D4—2921no—
262C2×D4—2921no—
263C2×D4—2921no—
264C2×D4—2921no—
265C2×D4—5841no—
266C2×D4—5841no—
267C2×D4—1462no—
268C2×D4—1462no—
269C2×D4—1462no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—2921no—
273C22×C4C2×C22⋊D7311yescharacteristic
274C22×C4C2×D29211yescharacteristic
275C22×C4#1192402811yescharacteristic
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—2921no—
285C2×C8—2921no—
286C2×C8—2921no—
287C2×C8—2921no—
288C2×C8—2921no—
289C2×C8—1462no—
290C2×C8#1192401512yes—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—2921no—
296C4⋊C4—2921no—
297C4⋊C4—2921no—
298C4⋊C4—2921no—
299C4⋊C4—5841no—
300C42—41no—
301C42—41no—
302C42C2×C4×D7311yescharacteristic
303C42#1192402811yescharacteristic
304C42#1192402811yescharacteristic
305C42#1192402811yescharacteristic
306C23—2922no—
307C23—5841no—
308C23—5841no—
309C23—5841no—
310C23—5841no—
311C23—5841no—
312C23—5841no—
313C23#1455656511yescharacteristic
314D4—2922no—
315D4—2922no—
316D4—2922no—
317D4—2922no—
318D4—5842no—
319D4—5842no—
320D4—5841no—
321D4—5841no—
322D4—5841no—
323D4—5841no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—5841no—
333C2×C4—5841no—
334C2×C4—5841no—
335C2×C4#1455654811yescharacteristic
336C2×C4C4×C22⋊D7311yescharacteristic
337C2×C4C4×D29211yescharacteristic
338C2×C4#1455657411yescharacteristic
339C2×C4#1455657911yescharacteristic
340C2×C4#1455658511yescharacteristic
341C2×C4C2×#1192401511yescharacteristic
342C2×C4#1455661111yescharacteristic
343C2×C4#1455661611yescharacteristic
344C2×C4#1455661711yescharacteristic
345C2×C4#1455661911yescharacteristic
346C2×C4#1455661911yescharacteristic
347C2×C4#1455661911yescharacteristic
348C2×C4#1455662411yescharacteristic
349C8—22no—
350C8—41no—
351C8—42no—
352C8—2922no—
353C8—5841no—
354C22—5842no—
355C22—5842no—
356C22—5842no—
357C22—11681no—
358C22—11681no—
359C22—11681no—
360C22—11681no—
361C22#1798847811yescharacteristic
362C22#1798878711yescharacteristic
363C22#1798880211yescharacteristic
364C22#1798883311yescharacteristic
365C22#1798884011yescharacteristic
366C22#1798885011yescharacteristic
367C22#1798885711yescharacteristic
368C4—21no—
369C4—21no—
370C4—81no—
371C4—81no—
372C4—11681no—
373C4C4×#1192401511yescharacteristic
374C4#1798868911yescharacteristic
375C4#1798869711yescharacteristic
376C4#1798870011yescharacteristic
377C4#1798890511yescharacteristic
378C4#1798891111yescharacteristic
379C4#1798894711yescharacteristic
380C4#1798895211yescharacteristic
381C2—11682no—
382C2#2260940311yescharacteristic
383C2#2260941511yescharacteristic
384C2#2260946411yescharacteristic
385C2#2260949211yescharacteristic
386C2#2261055811yescharacteristic
387C2#2261059311yescharacteristic
388C2#2261062811yescharacteristic
subgroupG/H
centerC23#14556565
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1770C2
socleC23×C73#121
prime radicalC2×#14556588C22
cosocleC2×C42×C73C23
hypercenter#1770D73
hypocenterC73#9572
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1770

Complements

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

NH ≅ G/Ntype
3. #22610694C2semidirect
5. #22607815C2semidirect
6. #22607766C2semidirect
7. C73×#1770C2semidirect
18. #17988330C4semidirect
198. #1770D73semidirect
202. C73#9572semidirect

Maximal subgroups

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

subgroupindex
#226108582
#226107372
#226106942
C2×#179883302
#226078152
#226077662
C73×#17702
#957273