Finite Group Databasebeta

← #33086494

Subgroups — #33086494

Order 18688.

854 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988649C211yesmaximal, characteristic
2C2×#17988646C211yesmaximal, characteristic
3#22612270C211yesmaximal, characteristic
4#22610084C212yesmaximal, complemented
5#22610046C212yesmaximal, complemented
6#22609914C212yesmaximal
7#22609908C212yesmaximal
8#22609788C211yesmaximal, characteristic, complemented
9#22609785C211yesmaximal, characteristic, complemented
10C4×#14556520C211yesmaximal, characteristic, complemented
11C73×#1768C211yesmaximal, characteristic, complemented
12C2×#14556548C2211yescharacteristic
13C2×#14556548C2211yescharacteristic
14C2×C42×D73C2211yescharacteristic
15#17988649—24no—
16#17988646—24no—
17C2×C4⋊#10596831C2212yes—
18C2×#14556520C2212yes—
19C2×#14556520C2212yes—
20C2×#14556520C2212yes—
21C2×#14556520C2212yes—
22C2×#14556503C2212yes—
23C2×#14556503C2212yes—
24C2×#14556502C2211yescharacteristic
25C2×C4×#10596831C2211yescharacteristic
26#17988438C412yes—
27#17988438C412yes—
28#17988434C412yes—
29#17988434C412yes—
30#17988433C2211yescharacteristic
31C42×Dic73C2211yescharacteristic
32C42×Dic73C2211yescharacteristic
33#17988342C2212yes—
34#17988341C2212yes—
35#17988341C2212yes—
36C2×C4⋊C8×C73C2212yes—
37C2×#97×C73C2211yescharacteristic
38C2×C4×C8×C73C2211yescharacteristic
39#376×C73C2211yescharacteristic
40#336×C73C2212yes—
41C22×C4×D73C2×C412yes—
42C22×C4×D73C2311yescharacteristic
43C22×#10596831C2312yes—
44C22×#10596831C2312yes—
45#14556548—24no—
46#14556548D414yes—
47#14556548Q814yes—
48C2×#11924007C2×C411yescharacteristic
49C2×#11924007C2×C411yescharacteristic
50C2×#11924007C2×C412yes—
51C2×#11924005C2×C411yescharacteristic
52C2×#11924005C2×C411yescharacteristic
53C2×#11924005C2×C412yes—
54C2×C4×Dic73C2×C412yes—
55C2×C4×Dic73C2×C412yes—
56C2×C4×Dic73C2×C412yes—
57C2×C4×Dic73C2×C412yes—
58C2×C4×Dic73C2×C412yes—
59C2×C4×Dic73C2311yescharacteristic
60C2×C4×Dic73C2311yescharacteristic
61C2×C4×Dic73C2311yescharacteristic
62C42×D73—24no—
63C4⋊#10596831—24no—
64#14556520—24no—
65#14556520—24no—
66#14556520—24no—
67#14556520—24no—
68#14556503—24no—
69#14556503—24no—
70#14556502—22no—
71C4×#10596831—22no—
72#14556498C2×C412yes—
73#14556498C2×C412yes—
74C22×C8×C73C2312yes—
75C22×C8×C73C2312yes—
76C2×C42×C73C2311yescharacteristic
77C2×C42×C73C2311yescharacteristic
78C2×C42×C73C2311yescharacteristic
79C4⋊C8×C73—24no—
80#97×C73—22no—
81C4×C8×C73—22no—
82#95×C73C2×C412yes—
83#95×C73C2×C412yes—
84C23×D73C22×C411yescharacteristic
85C22×Dic73C22×C412yes—
86C22×Dic73C22×C411yescharacteristic
87C22×Dic73C22×C411yescharacteristic
88C22×Dic73C22×C411yescharacteristic
89C22×Dic73C22×C412yes—
90C2×C4×D73—22no—
91C2×C4×D73—22no—
92C2×C4×D73—24no—
93C2×C4×D73—24no—
94C2×C4×D73—42no—
95C2×C4×D73C2×D412yes—
96C2×C4×D73C2×Q812yes—
97C2×#10596831—22no—
98C2×#10596831—22no—
99C2×#10596831—22no—
100C2×#10596831—22no—
101C2×#10596831—22no—
102C2×#10596831—22no—
103#11924007—22no—
104#11924007—22no—
105#11924007C4⋊C418yes—
106#11924005—22no—
107#11924005—22no—
108#11924005C4⋊C418yes—
109C4×Dic73—24no—
110C4×Dic73—22no—
111C4×Dic73—24no—
112C4×Dic73—24no—
113C4×Dic73—42no—
114C4×Dic73—42no—
115C4×Dic73C2×D412yes—
116C4×Dic73C2×Q812yes—
117C4×Dic73#4114yes—
118C22×C4×C73C22×C411yescharacteristic
119C22×C4×C73C22×C411yescharacteristic
120C22×C4×C73C22×C412yes—
121C22×C4×C73C22×C412yes—
122C22×C4×C73C2411yescharacteristic
123C2×C8×C73—22no—
124C2×C8×C73—22no—
125C2×C8×C73—22no—
126C2×C8×C73—22no—
127C2×C8×C73—22no—
128C2×C8×C73—22no—
129C42×C73—22no—
130C42×C73C2×D412yes—
131C42×C73C2×Q812yes—
132C42×C73#4114yes—
133C23×C73C23×C411yescharacteristic
134C22×D73—21no—
135C22×D73—21no—
136C22×D73—22no—
137C22×D73—22no—
138C22×D73C2×C4⋊C412yes—
139C2×C4×C73—22no—
140C2×C4×C73—22no—
141C2×C4×C73—22no—
142C2×C4×C73—22no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—22no—
146C2×C4×C73—22no—
147C2×C4×C73C2×C4⋊C414yes—
148C2×C4×C73#11714yes—
149C2×C4×C73C22×D411yescharacteristic
150C2×C4×C73C22×Q811yescharacteristic
151C2×C4×C73C2×#4112yes—
152C2×C4×C73C2×#4112yes—
153C2×Dic73—22no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73—22no—
157C2×Dic73—22no—
158C2×Dic73—22no—
159C2×Dic73—22no—
160C2×Dic73—22no—
161C2×Dic73C2×C4⋊C414yes—
162C2×Dic73C2×C4⋊C412yes—
163C2×Dic73#11712yes—
164C2×Dic73#11712yes—
165C2×Dic73#13114yes—
166C4×D73—24no—
167C4×D73—24no—
168C4×D73—48no—
169C8×C73—42no—
170C8×C73—42no—
171#10596831—42no—
172#10596831—42no—
173C22×C73C22×C4⋊C411yescharacteristic
174C22×C73C2×#11711yescharacteristic
175C22×C73C2×#11711yescharacteristic
176C22×C73C2×#13112yes—
177C22×C73#56812yes—
178C2×D73—24no—
179C2×D73—22no—
180C2×D73—41no—
181C2×D73—41no—
182C2×D73—42no—
183C4×C73—24no—
184C4×C73—24no—
185C4×C73—41no—
186C4×C73—41no—
187C4×C73#53212yes—
188C4×C73#53312yes—
189Dic73—24no—
190Dic73—22no—
191Dic73—22no—
192Dic73—24no—
193Dic73—22no—
194#20813—731nomaximal, Sylow
195C2×C73#228511yescharacteristic
196C2×C73#290612yes—
197C2×C73#292211yescharacteristic
198C2×C73#292311yescharacteristic
199C2×C73#292412yes—
200D73—42no—
201C2×#433—731no—
202C2×#433—731no—
203C4×#117—731no—
204#1843—732no—
205#1831—732no—
206#1798—732no—
207#1797—732no—
208#1768—731no—
209#1768D7311yescharacteristic, complemented
210#1767—731no—
211C4×C4⋊C8—731no—
212C73#2081311yescharacteristic, complemented, Sylow
213C2×#117—731no—
214C2×#117—731no—
215C22×C42—731no—
216#433—1464no—
217#433—1464no—
218C2×C4⋊C8—732no—
219C2×C4⋊C8—732no—
220C2×C4⋊C8—732no—
221C2×C4⋊C8—732no—
222C2×C4⋊C8—732no—
223C2×C4⋊C8C2×D7312yes—
224C2×C22⋊C8—732no—
225C2×C22⋊C8—732no—
226C2×#97—731no—
227C2×#97C2×D7311yescharacteristic
228C2×C4×C8—731no—
229C2×C4×C8C2×D7311yescharacteristic
230C4×C4⋊C4—732no—
231C4×C4⋊C4—732no—
232C4×C22⋊C4—732no—
233C4×C22⋊C4—732no—
234#376—731no—
235#376C2×D7311yescharacteristic
236C43—731no—
237C43—731no—
238#336—732no—
239#336—732no—
240#336—732no—
241#336C2×D7312yes—
242C23×C4—732no—
243C23×C4—731no—
244C22×C8—732no—
245C22×C8—732no—
246C22×C8C22×D7312yes—
247C22×C8C22×D7312yes—
248#117—734no—
249#117—734no—
250#117—1464no—
251C2×C4⋊C4—732no—
252C2×C4⋊C4—731no—
253C2×C4⋊C4—731no—
254C2×C22⋊C4—732no—
255C2×C22⋊C4—731no—
256C2×C22⋊C4—731no—
257C2×C42—732no—
258C2×C42—732no—
259C2×C42—731no—
260C2×C42—731no—
261C2×C42—732no—
262C2×C42—732no—
263C2×C42—732no—
264C2×C42—731no—
265C2×C42—1464no—
266C2×C42C22×D7311yescharacteristic
267C2×C42C22×D7311yescharacteristic
268C2×C42C22×D7311yescharacteristic
269C4⋊C8—24no—
270C4⋊C8—1464no—
271C4⋊C8—1464no—
272C4⋊C8—1464no—
273C4⋊C8—1464no—
274C4⋊C8—1464no—
275C22⋊C8—1464no—
276C22⋊C8—1464no—
277#97—22no—
278#97—1462no—
279C4×C8—22no—
280C4×C8—1462no—
281#95—732no—
282#95—732no—
283#95C4×D7312yes—
284#95C4×D7312yes—
285C24—731no—
286C22×C4—2922no—
287C22×C4—732no—
288C22×C4—731no—
289C22×C4—731no—
290C22×C4—732no—
291C22×C4—731no—
292C22×C4—732no—
293C22×C4—732no—
294C22×C4—1464no—
295C22×C4—1464no—
296C22×C4—1462no—
297C22×C4—1462no—
298C22×C4C2×C4×D7311yescharacteristic
299C22×C4C2×C4×D7311yescharacteristic
300C22×C4C2×C4×D7312yes—
301C22×C4C2×C4×D7312yes—
302C22×C4C23×D7311yescharacteristic
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—1462no—
310C2×C8—1462no—
311C2×C8—1462no—
312C2×C8—1462no—
313C2×C8—1462no—
314C2×C8—1462no—
315C4⋊C4—738no—
316C4⋊C4—1462no—
317C4⋊C4—1462no—
318C22⋊C4—738no—
319C22⋊C4—1462no—
320C22⋊C4—1462no—
321C42—22no—
322C42—2922no—
323C42—2922no—
324C42—732no—
325C42—732no—
326C42—734no—
327C42—1464no—
328C42—1464no—
329C42—1464no—
330C42—1462no—
331C42D4×D7312yes—
332C42Q8×D7312yes—
333C42#1192402814yes—
334C23—732no—
335C23—1461no—
336C23—1461no—
337C23—1462no—
338C23—1462no—
339C23C22×C4×D7311yescharacteristic
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—2928no—
349C2×C4—734no—
350C2×C4—732no—
351C2×C4—732no—
352C2×C4—732no—
353C2×C4—734no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1462no—
357C2×C4—1462no—
358C2×C4—1462no—
359C2×C4—1462no—
360C2×C4—1462no—
361C2×C4—1462no—
362C2×C4—1464no—
363C2×C4—1464no—
364C2×C4C4⋊C4×D7314yes—
365C2×C4#1455654814yes—
366C2×C4C2×D4×D7311yescharacteristic
367C2×C4C2×Q8×D7311yescharacteristic
368C2×C4#41×D7312yes—
369C2×C4C2×#1192402812yes—
370C8—42no—
371C8—42no—
372C8—2922no—
373C8—2922no—
374C22—2921no—
375C22—2921no—
376C22—2922no—
377C22—1462no—
378C22—1464no—
379C22C2×C4⋊C4×D7311yescharacteristic
380C22#117×D7311yescharacteristic
381C22C2×#1455654811yescharacteristic
382C22#131×D7312yes—
383C22#1798935212yes—
384C4—24no—
385C4—24no—
386C4—41no—
387C4—41no—
388C4—1462no—
389C4—1464no—
390C4—1462no—
391C4—1462no—
392C4—1464no—
393C4#1798913412yes—
394C4#1798914112yes—
395C2—2922no—
396C2#2261233511yescharacteristic
397C2#2261849812yes—
398C2#2261857211yescharacteristic
399C2#2261857911yescharacteristic
400C2#2261858612yes—
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1768C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1768D73
hypocenterC73#20813
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1768

Complements

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

NH ≅ G/Ntype
4. #22610084C2semidirect
5. #22610046C2semidirect
8. #22609788C2semidirect
9. #22609785C2semidirect
10. C4×#14556520C2semidirect
11. C73×#1768C2semidirect
209. #1768D73semidirect
212. C73#20813semidirect

Maximal subgroups

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

subgroupindex
C2×#179886492
C2×#179886462
#226122702
#226100842
#226100462
#226099142
#226099082
#226097882
#226097852
C4×#145565202
C73×#17682
#2081373