Finite Group Databasebeta

← #33003056

Subgroups — #33003056

Order 18688.

554 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
1C22×#14556536C211yesmaximal, characteristic
2C2×#17988669C211yesmaximal, characteristic
3C2×#17988390C211yesmaximal, characteristic, complemented
4C2×#17988387C211yesmaximal, characteristic
5#22610790C211yesmaximal, characteristic, complemented
6#22608008C211yesmaximal, characteristic, complemented
7C73×#1380C211yesmaximal, characteristic, complemented
8C22×Dic292C2211yescharacteristic
9C22×D584C2211yescharacteristic
10C2×#14556553—21no—
11C2×#14556536—22no—
12C2×#14556536—22no—
13C2×#14556536C414yescomplemented
14C22×#11924003C2211yescharacteristic
15#17988669—22no—
16#17988669—22no—
17C2×#14556514—21no—
18C2×#14556511—21no—
19C2×C8×Dic73C2211yescharacteristic
20#17988492—21no—
21#17988390—22no—
22#17988387—22no—
23C22×C16×C73C2211yescharacteristic
24C2×#107×C73C2211yescharacteristic
25C2×#107×C73C2211yescharacteristic
26C22×Dic146—21no—
27C22×D292—21no—
28C22×C4×D73—41no—
29C2×Dic292—21no—
30C2×Dic292—21no—
31C2×Dic292—21no—
32C2×Dic292—21no—
33C2×Dic292—21no—
34C2×Dic292C2×C412yescomplemented
35C2×D584—21no—
36C2×D584—21no—
37C2×D584—21no—
38C2×D584C2×C412yes—
39C2×D584D412yes—
40C2×D584D412yes—
41C22×#10596831D411yescharacteristic
42#14556553—24no—
43#14556553—42no—
44C2×#11924005—41no—
45C2×C4×Dic73D411yescharacteristic
46#14556536—28no—
47C2×#11924003—21no—
48C2×#11924003—21no—
49C2×#11924003—21no—
50#14556514—42no—
51#14556511—24no—
52C8×Dic73—21no—
53C8×Dic73—21no—
54#14556498—41no—
55#14556498—41no—
56C22×C8×C73C2311yescharacteristic
57C2×C4⋊C4×C73—21no—
58C2×C4⋊C4×C73—21no—
59C2×C16×C73—21no—
60C2×C16×C73—21no—
61C2×C16×C73C2×C412yescomplemented
62#107×C73—21no—
63#107×C73—21no—
64#107×C73—21no—
65#107×C73D412yes—
66C23×D73—41no—
67C2×Dic146—22no—
68C2×Dic146—41no—
69C2×Dic146—41no—
70C2×Dic146—41no—
71C2×Dic146—41no—
72C2×Dic146—41no—
73C2×D292—22no—
74C2×D292—22no—
75C2×D292—22no—
76C2×D292—41no—
77C2×D292—41no—
78C2×D292—41no—
79C22×Dic73—41no—
80C22×Dic73D811yescharacteristic
81C22×Dic73D811yescharacteristic
82C2×C4×D73—44no—
83C2×C4×D73—82no—
84C2×C4×D73—82no—
85Dic292—22no—
86Dic292—22no—
87Dic292—41no—
88Dic292—41no—
89D584—22no—
90D584—22no—
91D584—22no—
92D584C22⋊C414yes—
93C2×#10596831—21no—
94C2×#10596831—21no—
95C2×#10596831—21no—
96#11924005—44no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99#11924003—41no—
100C22×C4×C73—41no—
101C22×C4×C73—41no—
102C22×C4×C73C2×D411yescharacteristic
103C2×C8×C73C22×C411yescharacteristic
104C2×C8×C73C2×D411yescharacteristic
105C2×C8×C73C2×D411yescharacteristic
106C2×C8×C73C2×D411yescharacteristic
107C2×C8×C73#4111yescharacteristic
108C2×C8×C73#4111yescharacteristic
109C4⋊C4×C73—22no—
110C4⋊C4×C73—41no—
111C4⋊C4×C73—41no—
112C4⋊C4×C73—41no—
113C16×C73—22no—
114C23×C73C2×D811yescharacteristic
115C22×D73—42no—
116C22×D73—42no—
117C22×D73—42no—
118C22×D73—81no—
119C22×D73—81no—
120C22×D73—81no—
121C22×D73—81no—
122C2×C4×C73—42no—
123C2×C4×C73—81no—
124C2×C4×C73—81no—
125C2×C4×C73—81no—
126C2×C4×C73—81no—
127C2×C4×C73—81no—
128C2×C4×C73C4×D411yescharacteristic
129C2×C4×C73#12011yescharacteristic
130C2×C4×C73#12111yescharacteristic
131C2×C4×C73#13511yescharacteristic
132C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—42no—
140C2×Dic73—81no—
141C2×Dic73—81no—
142C2×Dic73SD3212yescomplemented
143D292—24no—
144D292—42no—
145D292—42no—
146D292—42no—
147C4×D73—88no—
148Dic146—42no—
149Dic146—42no—
150Dic146—81no—
151Dic146—81no—
152C8×C73C2×C22⋊C411yescharacteristic
153C8×C73C4×D411yescharacteristic
154C8×C73#12111yescharacteristic
155C8×C73#12311yescharacteristic
156#10596831—41no—
157C22×C73C4×D811yescharacteristic
158C22×C73#44711yescharacteristic
159C22×C73#45911yescharacteristic
160C22×C73C2×SD3211yescharacteristic
161C22×C73#50811yescharacteristic
162C22×C73#50911yescharacteristic
163C22×C73#51011yescharacteristic
164C2×D73—44no—
165C2×D73—82no—
166C2×D73—82no—
167C2×D73—82no—
168C2×D73—82no—
169C2×D73—82no—
170C2×D73—82no—
171C4×C73—82no—
172C4×C73—161no—
173C4×C73#38611yescharacteristic
174C4×C73#44211yescharacteristic
175C4×C73#44911yescharacteristic
176C4×C73#46311yescharacteristic
177Dic73—22no—
178Dic73—41no—
179Dic73—82no—
180#13014—731nomaximal, Sylow
181C2×C73#187911yescharacteristic
182C2×C73C4×SD3211yescharacteristic
183C2×C73#217511yescharacteristic
184C2×C73#218711yescharacteristic
185C2×C73#218911yescharacteristic
186C2×C73#220811yescharacteristic
187C2×C73#221011yescharacteristic
188D73—84no—
189C22×SD32—731no—
190C2×C4×D8—731no—
191C2×#358—731no—
192C2×#357—731no—
193#1969—731no—
194#1380D7311yescharacteristic, complemented
195#1374—731no—
196C73#1301411yescharacteristic, complemented, Sylow
197C22×Q16—731no—
198C22×D8—731no—
199C2×C4×D4—1461no—
200C2×SD32—734no—
201C2×SD32—1462no—
202C2×SD32—1462no—
203C22×C16—731no—
204C22×C16C2×D7311yescharacteristic
205C4×D8—1462no—
206C4×D8—1462no—
207C2×#107C2×D7311yescharacteristic
208C2×#107C2×D7311yescharacteristic
209C2×#103—1461no—
210C2×#102—1461no—
211C2×C4×C8—731no—
212#391—1461no—
213#358—1462no—
214#357—1462no—
215C22×Q8—1461no—
216C22×D4—1461no—
217C23×C4—2921no—
218C2×Q16—732no—
219C2×Q16—1461no—
220C2×Q16—1461no—
221C2×Q16—1461no—
222C2×Q16—1461no—
223C2×Q16—1461no—
224C2×D8—732no—
225C2×D8—732no—
226C2×D8—732no—
227C2×D8—1461no—
228C2×D8—1461no—
229C2×D8—1461no—
230C22×C8—731no—
231C22×C8C22×D7311yescharacteristic
232C4×D4—2922no—
233C4×D4—1464no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C22⋊C4—2921no—
237C2×C42—731no—
238SD32—1468no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—1461no—
242C2×C16—1461no—
243C2×C16—1461no—
244C2×C16C4×D7312yescomplemented
245#107—21no—
246#107—21no—
247#107—21no—
248#107D29212yes—
249#103—2922no—
250#102—1464no—
251C4×C8—1461no—
252C4×C8—1461no—
253#95—2921no—
254#95—2921no—
255C24—2921no—
256C2×Q8—2921no—
257C2×Q8—2921no—
258C2×Q8—2921no—
259C2×Q8—2921no—
260C2×Q8—2921no—
261C2×Q8—1462no—
262C2×D4—2921no—
263C2×D4—2921no—
264C2×D4—2921no—
265C2×D4—1462no—
266C2×D4—1462no—
267C2×D4—1462no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—2924no—
271C22×C4—2921no—
272C22×C4—5842no—
273C22×C4—5842no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4D4×D7311yescharacteristic
277Q16—2921no—
278Q16—2921no—
279Q16—1462no—
280Q16—1462no—
281D8—734no—
282D8—1462no—
283D8—1462no—
284D8—1462no—
285C2×C8—1461no—
286C2×C8—1461no—
287C2×C8—1461no—
288C2×C8C2×C4×D7311yescharacteristic
289C2×C8D4×D7311yescharacteristic
290C2×C8D4×D7311yescharacteristic
291C2×C8C2×D29211yescharacteristic
292C2×C8#1192402811yescharacteristic
293C2×C8#1192402911yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—2924no—
299C42—1461no—
300C42—1461no—
301C16—22no—
302C16—2921no—
303C23—2922no—
304C23—2922no—
305C23—2922no—
306C23—5841no—
307C23—5841no—
308C23—5841no—
309C23—5841no—
310C23D8×D7311yescharacteristic
311Q8—2922no—
312Q8—2922no—
313Q8—5841no—
314Q8—5841no—
315D4—2922no—
316D4—2922no—
317D4—2922no—
318D4—1464no—
319C2×C4—42no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—2922no—
326C2×C4—5848no—
327C2×C4—5841no—
328C2×C4—5841no—
329C2×C4—732no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4#1455655311yescharacteristic
336C2×C4#1455656111yescharacteristic
337C2×C4#1455656411yescharacteristic
338C2×C4#1455661411yescharacteristic
339C2×C4#1455661811yescharacteristic
340C2×C4#1455661811yescharacteristic
341C8—2921no—
342C8C22⋊C4×D7311yescharacteristic
343C8C4×D29211yescharacteristic
344C8#1455656611yescharacteristic
345C8#1455657611yescharacteristic
346C22—2924no—
347C22—5842no—
348C22—5842no—
349C22—5842no—
350C22—5842no—
351C22—5842no—
352C22—5842no—
353C22#1798866911yescharacteristic
354C22#1798872211yescharacteristic
355C22#1798878111yescharacteristic
356C22SD32×D7311yescharacteristic
357C22#1798901811yescharacteristic
358C22#1798902111yescharacteristic
359C22#1798902911yescharacteristic
360C4—82no—
361C4—161no—
362C4—2921no—
363C4—5842no—
364C4—1462no—
365C4#1798846511yescharacteristic
366C4#1798869811yescharacteristic
367C4#1798873511yescharacteristic
368C4#1798880511yescharacteristic
369C2—5844no—
370C2#2261028011yescharacteristic
371C2#2261178211yescharacteristic
372C2#2261179411yescharacteristic
373C2#2261186111yescharacteristic
374C2#2261187411yescharacteristic
375C2#2261197511yescharacteristic
376C2#2261198511yescharacteristic
subgroupG/H
centerC23D8×D73
commutatorC2×C8×C73C22×C4
FrattiniC22×C8C22×D73
FittingC73×#1380C2
socleC23×C73C2×D8
prime radicalC22×D584C22
cosocleC22×C8×C73C23
hypercenter#1380D73
hypocenterC73#13014
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. C2×#17988390C2semidirect
5. #22610790C2semidirect
6. #22608008C2semidirect
7. C73×#1380C2semidirect
13. C2×#14556536C4semidirect
34. C2×Dic292C2×C4semidirect
61. C2×C16×C73C2×C4semidirect
142. C2×Dic73SD32semidirect
194. #1380D73semidirect
196. C73#13014semidirect
244. C2×C16C4×D73semidirect

Maximal subgroups

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

subgroupindex
C22×#145565362
C2×#179886692
C2×#179883902
C2×#179883872
#226107902
#226080082
C73×#13802
#1301473