Finite Group Databasebeta

← #33086508

Subgroups — #33086508

Order 18688.

862 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988643C211yesmaximal, characteristic
2C2×#17988639C211yesmaximal, characteristic
3C4×#14556548C211yesmaximal, characteristic
4#22610083C211yesmaximal, characteristic, complemented
5#22610047C211yesmaximal, characteristic, complemented
6#22610047C211yesmaximal, characteristic, complemented
7#22609912C214yesmaximal
8#22609790C214yesmaximal, complemented
9C73×#1842C211yesmaximal, characteristic, complemented
10C2×#14556548C2212yes—
11C2×C42×D73C2211yescharacteristic
12#17988643—24no—
13#17988639—24no—
14C2×C4⋊#10596831C2214yes—
15C2×C4⋊#10596831C2211yescharacteristic
16C2×C4⋊#10596831C2211yescharacteristic
17C2×#14556503C2212yes—
18C2×#14556503C2212yes—
19C2×#14556501C2212yes—
20C2×C8×Dic73C2212yes—
21C4×#11924007C411yescharacteristic
22C4×#11924007C411yescharacteristic
23C4×#11924007C412yes—
24C4×#11924005C411yescharacteristic
25C4×#11924005C411yescharacteristic
26C4×#11924005C412yes—
27#17988433C2212yes—
28C42×Dic73C2211yescharacteristic
29#17988341C2214yes—
30#17988341C2214yes—
31C2×C4⋊C8×C73C2214yes—
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×C4⋊C8×C73C2211yescharacteristic
34C43×C73C2211yescharacteristic
35C22×C4×D73C2×C411yescharacteristic
36C22×C4×D73C2×C411yescharacteristic
37C22×C4×D73C2311yescharacteristic
38C22×#10596831C2312yes—
39C22×#10596831C2312yes—
40#14556548—24no—
41#14556548—24no—
42C2×#11924007C2×C412yes—
43C2×#11924007C2×C412yes—
44C2×#11924005C2×C412yes—
45C2×#11924005C2×C412yes—
46C2×C4×Dic73C2×C411yescharacteristic
47C2×C4×Dic73C2×C411yescharacteristic
48C2×C4×Dic73C2×C412yes—
49C2×C4×Dic73C2×C411yescharacteristic
50C2×C4×Dic73C2×C411yescharacteristic
51C2×C4×Dic73C2312yes—
52C2×C4×Dic73C2311yescharacteristic
53C42×D73D414yes—
54C42×D73Q814yes—
55C4⋊#10596831—22no—
56C4⋊#10596831—22no—
57C4⋊#10596831—28no—
58#14556503—24no—
59#14556503—24no—
60#14556501—24no—
61C8×Dic73—24no—
62#14556498C2×C412yes—
63#14556498C2×C412yes—
64#14556498C2×C412yes—
65#14556498C2×C412yes—
66C22×C8×C73C2312yes—
67C22×C8×C73C2312yes—
68C2×C42×C73C2×C411yescharacteristic
69C2×C42×C73C2×C411yescharacteristic
70C2×C42×C73C2×C412yes—
71C2×C42×C73C2311yescharacteristic
72C2×C42×C73C2312yes—
73C4⋊C8×C73—22no—
74C4⋊C8×C73—22no—
75C4⋊C8×C73—28no—
76C23×D73C22×C411yescharacteristic
77C22×Dic73C22×C412yes—
78C22×Dic73C22×C412yes—
79C22×Dic73C22×C411yescharacteristic
80C22×Dic73C22×C411yescharacteristic
81C22×Dic73C22×C411yescharacteristic
82C2×C4×D73—22no—
83C2×C4×D73—22no—
84C2×C4×D73—22no—
85C2×C4×D73—22no—
86C2×C4×D73—42no—
87C2×C4×D73C4⋊C414yes—
88C2×C4×D73C4⋊C414yes—
89C2×C4×D73C2×D412yes—
90C2×C4×D73C2×Q812yes—
91C2×#10596831—22no—
92C2×#10596831—22no—
93C2×#10596831—24no—
94C2×#10596831—24no—
95#11924007—24no—
96#11924007—24no—
97#11924005—24no—
98#11924005—24no—
99C4×Dic73—22no—
100C4×Dic73—22no—
101C4×Dic73—22no—
102C4×Dic73—22no—
103C4×Dic73—42no—
104C4×Dic73C4⋊C414yes—
105C4×Dic73C4⋊C414yes—
106C4×Dic73C2×D412yes—
107C4×Dic73C2×Q812yes—
108C22×C4×C73C22×C411yescharacteristic
109C22×C4×C73C22×C412yes—
110C22×C4×C73C22×C412yes—
111C22×C4×C73C22×C411yescharacteristic
112C22×C4×C73C2411yescharacteristic
113C2×C8×C73—22no—
114C2×C8×C73—22no—
115C2×C8×C73—24no—
116C2×C8×C73—24no—
117C42×C73—22no—
118C42×C73—22no—
119C42×C73—42no—
120C42×C73C2×D412yes—
121C42×C73C2×Q812yes—
122C42×C73#4114yes—
123C42×C73#4114yes—
124C23×C73C23×C411yescharacteristic
125C22×D73—22no—
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—22no—
129C22×D73C2×C4⋊C412yes—
130C2×C4×C73—22no—
131C2×C4×C73—22no—
132C2×C4×C73—22no—
133C2×C4×C73—22no—
134C2×C4×C73—22no—
135C2×C4×C73C2×C4⋊C412yes—
136C2×C4×C73C2×C4⋊C412yes—
137C2×C4×C73#11714yes—
138C2×C4×C73#11714yes—
139C2×C4×C73#13112yes—
140C2×C4×C73#13112yes—
141C2×C4×C73C22×D411yescharacteristic
142C2×C4×C73C22×Q811yescharacteristic
143C2×C4×C73C2×#4112yes—
144C2×C4×C73C2×#4112yes—
145C2×Dic73—22no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—22no—
149C2×Dic73—22no—
150C2×Dic73—22no—
151C2×Dic73—22no—
152C2×Dic73—22no—
153C2×Dic73—22no—
154C2×Dic73—22no—
155C2×Dic73C2×C4⋊C412yes—
156C2×Dic73C2×C4⋊C412yes—
157C2×Dic73C2×C4⋊C412yes—
158C4×D73—22no—
159C4×D73—22no—
160C4×D73—24no—
161C4×D73—28no—
162C4×D73—44no—
163C8×C73—42no—
164C8×C73—42no—
165#10596831—42no—
166#10596831—42no—
167C22×C73C22×C4⋊C411yescharacteristic
168C22×C73C2×#11712yes—
169C22×C73C2×#13111yescharacteristic
170C22×C73C2×#13111yescharacteristic
171C22×C73#56812yes—
172C2×D73—22no—
173C2×D73—22no—
174C2×D73—22no—
175C2×D73—42no—
176C2×D73—42no—
177C4×C73—22no—
178C4×C73—24no—
179C4×C73—24no—
180C4×C73#42414yes—
181C4×C73#53211yescharacteristic
182C4×C73#53211yescharacteristic
183C4×C73#53312yes—
184Dic73—22no—
185Dic73—22no—
186Dic73—22no—
187Dic73—42no—
188Dic73—42no—
189#20815—731nomaximal, Sylow
190C2×C73#228511yescharacteristic
191C2×C73C2×#42411yescharacteristic
192C2×C73#290511yescharacteristic
193C2×C73#292512yes—
194C2×C73#292512yes—
195D73—42no—
196C2×#432—731no—
197C2×#431—731no—
198C4×#117—731no—
199#1842—731no—
200#1842D7311yescharacteristic, complemented
201#1831—731no—
202#1831—731no—
203#1798—734no—
204#1768—734no—
205C73#2081511yescharacteristic, complemented, Sylow
206C2×#117—732no—
207C22×C42—731no—
208#432—1464no—
209#431—1464no—
210C2×C4⋊C8—734no—
211C2×C4⋊C8—731no—
212C2×C4⋊C8—731no—
213C2×C4⋊C8C2×D7314yes—
214C2×C4⋊C8C2×D7311yescharacteristic
215C2×C4⋊C8C2×D7311yescharacteristic
216C2×C22⋊C8—732no—
217C2×C22⋊C8—732no—
218C2×#97—732no—
219C2×C4×C8—732no—
220C4×C4⋊C4—732no—
221C4×C4⋊C4—731no—
222C4×C4⋊C4—731no—
223C4×C22⋊C4—732no—
224C4×C22⋊C4—731no—
225C4×C22⋊C4—731no—
226#376—732no—
227C43—731no—
228C43C2×D7311yescharacteristic
229#336—734no—
230#336—734no—
231C23×C4—731no—
232C23×C4—731no—
233C23×C4—731no—
234C22×C8—732no—
235C22×C8—732no—
236C22×C8C22×D7312yes—
237C22×C8C22×D7312yes—
238#117—1464no—
239#117—1464no—
240C2×C4⋊C4—732no—
241C2×C4⋊C4—732no—
242C2×C22⋊C4—732no—
243C2×C22⋊C4—732no—
244C2×C42—732no—
245C2×C42—731no—
246C2×C42—731no—
247C2×C42—731no—
248C2×C42—734no—
249C2×C42—734no—
250C2×C42—731no—
251C2×C42—731no—
252C2×C42—732no—
253C2×C42C4×D7311yescharacteristic
254C2×C42C4×D7311yescharacteristic
255C2×C42C4×D7312yes—
256C2×C42C22×D7311yescharacteristic
257C2×C42C22×D7312yes—
258C4⋊C8—22no—
259C4⋊C8—22no—
260C4⋊C8—28no—
261C4⋊C8—1462no—
262C4⋊C8—1462no—
263C4⋊C8—1468no—
264C22⋊C8—1464no—
265C22⋊C8—1464no—
266#97—1464no—
267C4×C8—1464no—
268#95—732no—
269#95—732no—
270#95—732no—
271#95—732no—
272C24—731no—
273C22×C4—2922no—
274C22×C4—734no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—734no—
279C22×C4—732no—
280C22×C4—732no—
281C22×C4—732no—
282C22×C4—732no—
283C22×C4—1462no—
284C22×C4—1462no—
285C22×C4—1462no—
286C22×C4—1462no—
287C22×C4C2×C4×D7311yescharacteristic
288C22×C4C2×C4×D7312yes—
289C22×C4C2×C4×D7312yes—
290C22×C4C2×C4×D7311yescharacteristic
291C22×C4C23×D7311yescharacteristic
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—24no—
295C2×C8—24no—
296C2×C8—1462no—
297C2×C8—1462no—
298C2×C8—1464no—
299C2×C8—1464no—
300C4⋊C4—1464no—
301C4⋊C4—1464no—
302C22⋊C4—1464no—
303C22⋊C4—1464no—
304C42—22no—
305C42—22no—
306C42—42no—
307C42—2922no—
308C42—734no—
309C42—734no—
310C42—732no—
311C42—732no—
312C42—1462no—
313C42—1462no—
314C42—1462no—
315C42—1462no—
316C42D4×D7312yes—
317C42Q8×D7312yes—
318C42#1192402714yes—
319C42#1192402914yes—
320C23—732no—
321C23—1462no—
322C23—1461no—
323C23—1461no—
324C23—1462no—
325C23C22×C4×D7311yescharacteristic
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—2924no—
332C2×C4—732no—
333C2×C4—732no—
334C2×C4—732no—
335C2×C4—1462no—
336C2×C4—1462no—
337C2×C4—1462no—
338C2×C4—1462no—
339C2×C4—1462no—
340C2×C4—1462no—
341C2×C4—1462no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1462no—
345C2×C4—1468no—
346C2×C4—1462no—
347C2×C4—1462no—
348C2×C4—1464no—
349C2×C4C4⋊C4×D7312yes—
350C2×C4C4⋊C4×D7312yes—
351C2×C4#1455654914yes—
352C2×C4#1455654914yes—
353C2×C4#1455659712yes—
354C2×C4#1455659912yes—
355C2×C4C2×D4×D7311yescharacteristic
356C2×C4C2×Q8×D7311yescharacteristic
357C2×C4C2×#1192402712yes—
358C2×C4C2×#1192402912yes—
359C8—42no—
360C8—42no—
361C8—2922no—
362C8—2922no—
363C22—2922no—
364C22—2922no—
365C22—1462no—
366C22—1462no—
367C22—1462no—
368C22C2×C4⋊C4×D7311yescharacteristic
369C22C2×#1455654912yes—
370C22C2×#1455659711yescharacteristic
371C22C2×#1455659911yescharacteristic
372C22#1798935312yes—
373C4—22no—
374C4—24no—
375C4—24no—
376C4—2922no—
377C4—2922no—
378C4—1462no—
379C4—1462no—
380C4—1462no—
381C4#1798861214yes—
382C4#1798913511yescharacteristic
383C4#1798913811yescharacteristic
384C4#1798914212yes—
385C2—2922no—
386C2#2261233611yescharacteristic
387C2C2×#1798861211yescharacteristic
388C2#2261849311yescharacteristic
389C2#2261859612yes—
390C2#2261859912yes—
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1842C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1842D73
hypocenterC73#20815
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1842

Complements

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

NH ≅ G/Ntype
4. #22610083C2semidirect
5. #22610047C2semidirect
6. #22610047C2semidirect
8. #22609790C2semidirect
9. C73×#1842C2semidirect
200. #1842D73semidirect
205. C73#20815semidirect

Maximal subgroups

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

subgroupindex
C2×#179886432
C2×#179886392
C4×#145565482
#226100832
#226100472
#226099122
#226097902
C73×#18422
#2081573