Finite Group Databasebeta

← #32983356

Subgroups — #32983356

Order 18688.

594 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618954C211yesmaximal, characteristic
2#22614885C211yesmaximal, characteristic
3#22609920C211yesmaximal, characteristic
4#22608616C211yesmaximal, characteristic, complemented
5#22607833C211yesmaximal, characteristic, complemented
6#22607832C211yesmaximal, characteristic, complemented
7C73×#1549C211yesmaximal, characteristic, complemented
8C2×#14556567—22no—
9C2×C4×D292C2211yescharacteristic
10C8×D292—22no—
11#17988652—22no—
12#17988640C2211yescharacteristic
13#17988611C2211yescharacteristic
14C2×#14556507—21no—
15C22⋊C8×D73—22no—
16#17988522C414yes—
17#17988488—21no—
18#17988456—21no—
19C4×C4⋊Dic73C2211yescharacteristic
20#17988355—21no—
21#17988333—22no—
22C2×C4⋊Q8×C73C2211yescharacteristic
23#431×C73C2211yescharacteristic
24#423×C73C2211yescharacteristic
25#332×C73—22no—
26C22×D292D411yescharacteristic
27C22×C4×D73D412yes—
28C2×#11924012—21no—
29C2×C8×D73—24no—
30#14556567—48no—
31C4×D292—21no—
32C4×D292—21no—
33C4×D292—21no—
34C4×D292—21no—
35C2×C4⋊Dic73—21no—
36C2×C4⋊Dic73D411yescharacteristic
37C2×#11924007—24no—
38C2×#11924005—24no—
39C2×#11924005C2×C412yes—
40C2×C4×Dic73—21no—
41C4⋊#10596831—21no—
42C4⋊#10596831—21no—
43C4⋊#10596831D412yes—
44#14556507—42no—
45C22⋊#10596831—21no—
46#14556503—24no—
47C4×#10596831—21no—
48#14556498C2×C412yes—
49C22×Q8×C73—21no—
50C2×M16×C73—21no—
51C4⋊Q8×C73—21no—
52C4⋊Q8×C73—21no—
53C4⋊Q8×C73—21no—
54C4⋊Q8×C73—21no—
55C2×C4⋊C4×C73—21no—
56C2×C4⋊C4×C73C2×C412yes—
57C2×C42×C73C2311yescharacteristic
58C4⋊C8×C73—21no—
59C4⋊C8×C73—21no—
60C4⋊C8×C73D412yes—
61C22⋊C8×C73—21no—
62C4×C8×C73—21no—
63C23×D73C22⋊C412yes—
64C2×D292—21no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292SD1612yes—
69C2×D292Q1612yes—
70C22×Dic73—22no—
71C22×Dic73C22⋊C412yes—
72C2×C4×D73—22no—
73C2×C4×D73—22no—
74C2×C4×D73—44no—
75#11924012—41no—
76#11924012—41no—
77C2×#10596831—22no—
78C2×#10596831—41no—
79C8×D73—84no—
80C4⋊Dic73—24no—
81C4⋊Dic73—21no—
82C4⋊Dic73—21no—
83#11924007—48no—
84#11924005—22no—
85#11924005—22no—
86#11924005—48no—
87C4×Dic73—41no—
88C4×Dic73—41no—
89C2×Q8×C73—44no—
90C2×Q8×C73—41no—
91C2×Q8×C73—41no—
92C22×C4×C73—22no—
93C22×C4×C73C22×C411yescharacteristic
94C22×C4×C73C2×D411yescharacteristic
95C22×C4×C73C2×D411yescharacteristic
96M16×C73—41no—
97M16×C73—41no—
98C2×C8×C73—22no—
99C2×C8×C73—41no—
100C4⋊C4×C73—22no—
101C4⋊C4×C73—22no—
102C4⋊C4×C73—41no—
103C4⋊C4×C73—41no—
104C42×C73C2×D411yescharacteristic
105C42×C73C2×D411yescharacteristic
106C42×C73#4111yescharacteristic
107C42×C73#4111yescharacteristic
108C23×C73C2×C22⋊C411yescharacteristic
109C22×D73—22no—
110C22×D73—22no—
111C22×D73—42no—
112C22×D73—42no—
113C22×D73#10314yes—
114Q8×C73—82no—
115Q8×C73—82no—
116C2×C4×C73—22no—
117C2×C4×C73—41no—
118C2×C4×C73—44no—
119C2×C4×C73—42no—
120C2×C4×C73C4×D411yescharacteristic
121C2×C4×C73C4×D411yescharacteristic
122C2×C4×C73#12011yescharacteristic
123C2×C4×C73#12111yescharacteristic
124C2×C4×C73#12111yescharacteristic
125C2×C4×C73#12311yescharacteristic
126C2×C4×C73C2×SD1611yescharacteristic
127C2×C4×C73C2×Q1611yescharacteristic
128C2×C4×C73#13511yescharacteristic
129C2×C4×C73#13511yescharacteristic
130C2×Dic73—24no—
131C2×Dic73—22no—
132C2×Dic73—42no—
133C2×Dic73—42no—
134C2×Dic73—42no—
135D292—22no—
136D292—22no—
137D292—22no—
138D292—22no—
139C4×D73—44no—
140C4×D73—82no—
141C8×C73—42no—
142C8×C73—81no—
143#10596831—42no—
144#10596831—81no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73#38611yescharacteristic
148C22×C73C2×#10311yescharacteristic
149C22×C73#41611yescharacteristic
150C2×D73—24no—
151C2×D73—42no—
152C2×D73—42no—
153C2×D73—44no—
154C2×D73—82no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—82no—
159C4×C73#45312yes—
160C4×C73#46511yescharacteristic
161C4×C73#46511yescharacteristic
162C4×C73#46711yescharacteristic
163C4×C73#46711yescharacteristic
164Dic73—44no—
165Dic73—42no—
166#9395—731nomaximal, Sylow
167C2×C73—21no—
168C2×C73—21no—
169C2×C73#188711yescharacteristic
170C2×C73#189211yescharacteristic
171C2×C73#191511yescharacteristic
172D73—44no—
173#2972—731no—
174#2542—731no—
175#1800—731no—
176#1549—731no—
177#1549D7311yescharacteristic, complemented
178#1303—731no—
179#1303—731no—
180C73#939511yescharacteristic, complemented, Sylow
181C2×C4⋊Q8C2×D7311yescharacteristic
182C2×C22⋊Q8—1462no—
183C2×C4×D4—731no—
184C8×D4—1462no—
185C8×D4—1462no—
186#431—731no—
187#431C2×D7311yescharacteristic
188#423—731no—
189#423C2×D7311yescharacteristic
190C2×#100—1461no—
191C2×C22⋊C8—1462no—
192#399—734no—
193#390—1461no—
194#384—1461no—
195C4×C4⋊C4—731no—
196#343—1461no—
197#332—22no—
198#332—1462no—
199C22×Q8—21no—
200C22×D4—731no—
201C23×C4—732no—
202C2×M16—21no—
203C2×M16—1461no—
204C22×C8—1464no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C22⋊Q8—2928no—
210C4×D4—1461no—
211C4×D4—1461no—
212C4×D4—1461no—
213C4×D4—1461no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—1464no—
217C2×C4⋊C4—1461no—
218C2×C4⋊C4C4×D7312yes—
219C2×C22⋊C4—732no—
220C2×C22⋊C4—1464no—
221C2×C42—1461no—
222C2×C42C22×D7311yescharacteristic
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—732no—
226C4⋊C8—1461no—
227C4⋊C8—1461no—
228C4⋊C8C22⋊D7312yes—
229#100—2922no—
230C22⋊C8—21no—
231C22⋊C8—1464no—
232C22⋊C8—1461no—
233C4×C8—21no—
234C4×C8—1461no—
235#95—732no—
236C24—732no—
237C2×Q8—44no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×D4—732no—
241C2×D4—732no—
242C2×D4—1461no—
243C2×D4—1461no—
244C2×D4—1461no—
245C2×D4—1461no—
246C22×C4—22no—
247C22×C4—2924no—
248C22×C4—732no—
249C22×C4—1462no—
250C22×C4—1462no—
251C22×C4—1462no—
252C22×C4C2×C4×D7311yescharacteristic
253C22×C4D4×D7311yescharacteristic
254C22×C4D4×D7311yescharacteristic
255M16—41no—
256M16—41no—
257M16—2921no—
258M16—2921no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—2921no—
262C2×C8—5844no—
263C2×C8—1462no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—2928no—
269C4⋊C4—1464no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C22⋊C4—2928no—
273C22⋊C4—1462no—
274C22⋊C4—1462no—
275C42—2921no—
276C42—2921no—
277C42D4×D7311yescharacteristic
278C42C2×C22⋊D7311yescharacteristic
279C42#1192402711yescharacteristic
280C42#1192402811yescharacteristic
281C23—2922no—
282C23—2922no—
283C23—734no—
284C23—1462no—
285C23—1462no—
286C23C22⋊C4×D7311yescharacteristic
287Q8—82no—
288Q8—82no—
289D4—1462no—
290D4—1462no—
291D4—1462no—
292D4—1462no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—2922no—
298C2×C4—2922no—
299C2×C4—2924no—
300C2×C4—2922no—
301C2×C4—5842no—
302C2×C4—1464no—
303C2×C4—1462no—
304C2×C4#1455655111yescharacteristic
305C2×C4C4×C22⋊D7311yescharacteristic
306C2×C4#1455655911yescharacteristic
307C2×C4#1455656211yescharacteristic
308C2×C4#1455656411yescharacteristic
309C2×C4#1455657311yescharacteristic
310C2×C4SD16×D7311yescharacteristic
311C2×C4Q16×D7311yescharacteristic
312C2×C4#1455661211yescharacteristic
313C2×C4#1455661411yescharacteristic
314C8—42no—
315C8—81no—
316C8—2922no—
317C8—5841no—
318C22—21no—
319C22—21no—
320C22—2924no—
321C22—2922no—
322C22—2922no—
323C22—5842no—
324C22—1464no—
325C22#1798846311yescharacteristic
326C22#103×D7311yescharacteristic
327C22#1798858211yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—82no—
332C4—2924no—
333C4—2922no—
334C4#1798875312yes—
335C4#1798881311yescharacteristic
336C4#1798881911yescharacteristic
337C4#1798882511yescharacteristic
338C4#1798882711yescharacteristic
339C2—21no—
340C2—21no—
341C2—2924no—
342C2#2261032611yescharacteristic
343C2#2261035111yescharacteristic
344C2#2261048011yescharacteristic
subgroupG/H
centerC22#17988463
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1549C2
socleC22×C73#386
prime radicalC22×D292D4
cosocleC2×C42×C73C23
hypercenter#1549D73
hypocenterC73#9395
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
4. #22608616C2semidirect
5. #22607833C2semidirect
6. #22607832C2semidirect
7. C73×#1549C2semidirect
177. #1549D73semidirect
180. C73#9395semidirect

Maximal subgroups

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

subgroupindex
#226189542
#226148852
#226099202
#226086162
#226078332
#226078322
C73×#15492
#939573