Finite Group Databasebeta

← #33002046

Subgroups — #33002046

Order 18688.

422 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556613C211yesmaximal, characteristic
2C2×#17988395C212yesmaximal
3#22610103C211yesmaximal, characteristic, complemented
4#22608027C212yesmaximal, complemented
5C2×C4⋊C16×C73C211yesmaximal, characteristic, complemented
6C2×#14556613C2211yescharacteristic
7C4×#11924028—21no—
8C4×Dic292C411yescharacteristic
9C4×Dic292C411yescharacteristic
10C4×#11924017—21no—
11C4×#11924017—21no—
12C4×D584C411yescharacteristic
13C4×D584C411yescharacteristic
14C2×#14556527—21no—
15C2×#14556527C2212yes—
16#17988625C2211yescharacteristic
17#17988611—21no—
18#17988584—21no—
19#17988395—24no—
20C22×C16×C73C2212yes—
21C2×C4×C8×C73C2211yescharacteristic
22C4⋊C16×C73—21no—
23C4⋊C16×C73—21no—
24C2×#11924028—21no—
25#14556613—21no—
26#14556613—21no—
27#14556613D412yes—
28#14556613Q812yes—
29C2×Dic292C2×C411yescharacteristic
30C2×#11924017—21no—
31C2×D584C2×C411yescharacteristic
32C2×#11924012—22no—
33C4×Dic146—21no—
34C4×Dic146—21no—
35C4×D292—21no—
36C4×D292—21no—
37C4×C22⋊D73—41no—
38C4×C22⋊D73—41no—
39#14556550—21no—
40#14556548—41no—
41C42×D73—41no—
42#14556527—22no—
43#14556527—22no—
44#14556527—42no—
45#14556525C2×C411yescharacteristic
46#14556525C2×C411yescharacteristic
47#14556523—21no—
48C4⋊#10596831—41no—
49C4⋊#10596831—41no—
50#14556516—21no—
51#14556516—21no—
52#14556513—21no—
53#14556513—21no—
54C22×C8×C73D411yescharacteristic
55C22×C8×C73C2311yescharacteristic
56C2×C42×C73D411yescharacteristic
57C2×C16×C73—22no—
58C2×C16×C73—22no—
59C2×C16×C73—22no—
60C4×C8×C73C2×C411yescharacteristic
61C4×C8×C73C2×C411yescharacteristic
62C4×C8×C73D411yescharacteristic
63C4×C8×C73D411yescharacteristic
64#11924028—22no—
65#11924028—22no—
66#11924028—41no—
67#11924028—41no—
68C2×Dic146—21no—
69C2×D292—21no—
70C2×C22⋊D73—41no—
71C2×C4×D73—41no—
72C2×C4×D73—41no—
73C2×C4×D73—41no—
74Dic292—21no—
75Dic292C4⋊C412yes—
76#11924017—22no—
77#11924017—22no—
78D584—21no—
79D584C4⋊C412yes—
80#11924012—42no—
81#11924012—42no—
82C2×#10596831—42no—
83C4⋊Dic73—21no—
84C4⋊Dic73—21no—
85#11924007—41no—
86#11924007—41no—
87C22⋊Dic73—41no—
88#11924005—41no—
89#11924005—41no—
90C4×Dic73—41no—
91C4×Dic73—41no—
92C4×Dic73—41no—
93C22×C4×C73SD1611yescharacteristic
94C22×C4×C73SD1611yescharacteristic
95C22×C4×C73C2×D411yescharacteristic
96C2×C8×C73—21no—
97C2×C8×C73—21no—
98C2×C8×C73C22⋊C411yescharacteristic
99C2×C8×C73C22⋊C411yescharacteristic
100C2×C8×C73C22×C411yescharacteristic
101C2×C8×C73C2×D411yescharacteristic
102C2×C8×C73C2×D411yescharacteristic
103C2×C8×C73C2×Q811yescharacteristic
104C2×C8×C73#4111yescharacteristic
105C2×C8×C73#4111yescharacteristic
106C42×C73C22⋊C411yescharacteristic
107C42×C73C22⋊C411yescharacteristic
108C42×C73D811yescharacteristic
109C42×C73D811yescharacteristic
110C16×C73—42no—
111C23×C73C2×SD1611yescharacteristic
112C22×D73—41no—
113C2×C4×C73—22no—
114C2×C4×C73—41no—
115C2×C4×C73#10211yescharacteristic
116C2×C4×C73#10211yescharacteristic
117C2×C4×C73#10211yescharacteristic
118C2×C4×C73#10211yescharacteristic
119C2×C4×C73C2×C22⋊C411yescharacteristic
120C2×C4×C73#12111yescharacteristic
121C2×C4×C73C22⋊Q811yescharacteristic
122C2×C4×C73C2×D811yescharacteristic
123C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C73#13711yescharacteristic
125C22⋊D73—42no—
126C22⋊D73—42no—
127C2×Dic73—41no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130D292—22no—
131D292—41no—
132C4×D73—42no—
133C4×D73—42no—
134C4×D73—82no—
135C4×D73—82no—
136Dic146—22no—
137Dic146—41no—
138C8×C73—21no—
139C8×C73—21no—
140C8×C73C2×C4⋊C411yescharacteristic
141C8×C73#11711yescharacteristic
142C8×C73#12111yescharacteristic
143C8×C73C22⋊Q811yescharacteristic
144#10596831—82no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73C2×#10211yescharacteristic
148C22×C73#46111yescharacteristic
149C22×C73#47611yescharacteristic
150C2×D73—42no—
151C2×D73—81no—
152C2×D73—81no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73#35912yescomplemented
157C4×C73#38011yescharacteristic
158C4×C73#41711yescharacteristic
159C4×C73#45911yescharacteristic
160C4×C73#47411yescharacteristic
161Dic73—42no—
162Dic73—81no—
163Dic73—81no—
164#12815—731nomaximal, Sylow
165C2×C73—21no—
166C2×C73—21no—
167C2×C73#180211yescharacteristic
168C2×C73C2×#35911yescharacteristic
169C2×C73#214311yescharacteristic
170D73—82no—
171C4×#135—731no—
172C2×C4⋊C16D7311yescharacteristic, complemented
173C2×#359—732no—
174#1848—731no—
175#1382—732no—
176C73#1281511yescharacteristic, complemented, Sylow
177C2×#135—731no—
178C4×#41—1461no—
179C22×C16C2×D7312yes—
180C4×Q16—731no—
181C4×Q16—731no—
182C4×SD16—1461no—
183C4×SD16—1461no—
184C4×D8—731no—
185C4×D8—731no—
186C2×#108—732no—
187C2×#108—1461no—
188#427—731no—
189#423—1461no—
190#416—1461no—
191C2×C4×C8C2×D7311yescharacteristic
192C4⋊C16—21no—
193C4⋊C16—21no—
194#359—1464no—
195C2×#41—1461no—
196#135—732no—
197#135—732no—
198#135—1461no—
199#135—1461no—
200C2×Q16—731no—
201C2×SD16—1461no—
202C2×D8—731no—
203C2×M16—1462no—
204C22×C8D29211yescharacteristic
205C22×C8C22×D7311yescharacteristic
206C4×Q8—1461no—
207C4×Q8—1461no—
208C4×D4—2921no—
209C4×D4—2921no—
210C4×D4—1461no—
211C4×D4—1461no—
212#117—2921no—
213#117—1461no—
214C2×C42—2921no—
215C2×C42D29211yescharacteristic
216C2×C16—22no—
217C2×C16—22no—
218C2×C16—22no—
219#108—2922no—
220#108—1462no—
221#108—1462no—
222#107—731no—
223#107—731no—
224#106—1461no—
225C4⋊C8—2921no—
226C4⋊C8—2921no—
227#103—1461no—
228#103—1461no—
229#102—1461no—
230#102—1461no—
231C4×C8C4×D7311yescharacteristic
232C4×C8C4×D7311yescharacteristic
233C4×C8C22⋊D7311yescharacteristic
234C4×C8C22⋊D7311yescharacteristic
235#41—2921no—
236#41—2921no—
237#41—1462no—
238#41—1462no—
239C2×Q8—1461no—
240C2×D4—2921no—
241C2×D4—1461no—
242C22×C4—2921no—
243C22×C4—2921no—
244C22×C4—2921no—
245C22×C4#1192401711yescharacteristic
246C22×C4#1192401711yescharacteristic
247C22×C4C2×D29211yescharacteristic
248Q16—732no—
249Q16—1461no—
250SD16—1462no—
251SD16—1462no—
252D8—732no—
253D8—1461no—
254M16—2922no—
255M16—2922no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—2922no—
259C2×C8#1192400511yescharacteristic
260C2×C8#1192400511yescharacteristic
261C2×C8C2×C4×D7311yescharacteristic
262C2×C8D4×D7311yescharacteristic
263C2×C8C2×C22⋊D7311yescharacteristic
264C2×C8Q8×D7311yescharacteristic
265C2×C8#1192402711yescharacteristic
266C2×C8#1192402911yescharacteristic
267C4⋊C4—2921no—
268C4⋊C4—2921no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C22⋊C4—2921no—
272C22⋊C4—2921no—
273C22⋊C4—2921no—
274C42—2921no—
275C42—2921no—
276C42—2921no—
277C42#1192400511yescharacteristic
278C42#1192400511yescharacteristic
279C42D58411yescharacteristic
280C42D58411yescharacteristic
281C16—42no—
282C23—2921no—
283C23C2×#1192401711yescharacteristic
284Q8—2921no—
285Q8—1462no—
286D4—2922no—
287D4—2922no—
288D4—2921no—
289D4—1462no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—2921no—
293C2×C4—2922no—
294C2×C4—2922no—
295C2×C4—2921no—
296C2×C4—2921no—
297C2×C4—5842no—
298C2×C4—5842no—
299C2×C4#1455651311yescharacteristic
300C2×C4#1455651311yescharacteristic
301C2×C4#1455651311yescharacteristic
302C2×C4#1455651311yescharacteristic
303C2×C4C2×#1192400511yescharacteristic
304C2×C4#1455656611yescharacteristic
305C2×C4#1455657111yescharacteristic
306C2×C4C2×D58411yescharacteristic
307C2×C4#1455661911yescharacteristic
308C2×C4#1455662411yescharacteristic
309C8—21no—
310C8—21no—
311C8—5842no—
312C8C4⋊C4×D7311yescharacteristic
313C8#1455654911yescharacteristic
314C8#1455656211yescharacteristic
315C8#1455656711yescharacteristic
316C22—21no—
317C22—21no—
318C22—2922no—
319C22—5841no—
320C22—5841no—
321C22C2×#1455651311yescharacteristic
322C22#1798879311yescharacteristic
323C22#1798887811yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—2922no—
328C4—5841no—
329C4—5841no—
330C4#1798839512yescomplemented
331C4#1798844411yescharacteristic
332C4#1798858911yescharacteristic
333C4#1798878311yescharacteristic
334C4#1798886811yescharacteristic
335C2—21no—
336C2—21no—
337C2—5842no—
338C2#2260993211yescharacteristic
339C2C2×#1798839511yescharacteristic
340C2#2261166011yescharacteristic
subgroupG/H
centerC2×C4C2×D584
commutatorC2×C8×C73C22×C4
FrattiniC22×C8C22×D73
FittingC2×C4⋊C16×C73C2
socleC22×C73C2×#102
prime radicalC2×#14556613C22
cosocleC22×C8×C73C23
hypercenterC2×C4⋊C16D73
hypocenterC73#12815
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
3. #22610103C2semidirect
4. #22608027C2semidirect
5. C2×C4⋊C16×C73C2semidirect
156. C4×C73#359semidirect
172. C2×C4⋊C16D73semidirect
176. C73#12815semidirect
330. C4#17988395semidirect

Maximal subgroups

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

subgroupindex
C4×#145566132
C2×#179883952
#226101032
#226080272
C2×C4⋊C16×C732
#1281573