Finite Group Databasebeta

← #33096476

Subgroups — #33096476

Order 18688.

770 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988642C211yesmaximal, characteristic
2C2×#17988609C211yesmaximal, characteristic
3#22612327C211yesmaximal, characteristic
4#22610655C211yesmaximal, characteristic, complemented
5#22610654C211yesmaximal, characteristic, complemented
6#22610652C211yesmaximal, characteristic, complemented
7#22610115C212yesmaximal
8#22610112C212yesmaximal
9#22610084C212yesmaximal, complemented
10#22610049C212yesmaximal, complemented
11C73×#1940C211yesmaximal, characteristic, complemented
12C22×#11924011C2212yes—
13C2×C42×D73C2211yescharacteristic
14#17988642—24no—
15#17988609—24no—
16C2×C4⋊#10596831C2211yescharacteristic
17C2×C4⋊#10596831C2212yes—
18C2×#14556520C2212yes—
19C2×#14556520C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2212yes—
22C2×#14556520C2212yes—
23C2×#14556503C2211yescharacteristic
24C2×#14556503C2211yescharacteristic
25C2×#14556502C2211yescharacteristic
26#17988454C412yes—
27#17988452C412yes—
28#17988449C412yes—
29#17988444C412yes—
30C4×C4⋊Dic73C2211yescharacteristic
31C4×#11924005C2212yes—
32#17988433C2212yes—
33#17988342C2212yes—
34#17988341C2212yes—
35#17988341C2212yes—
36C2×C4⋊C8×C73C2211yescharacteristic
37C2×C4⋊C8×C73C2212yes—
38C2×#97×C73C2211yescharacteristic
39C4×C4⋊C4×C73C2211yescharacteristic
40#336×C73C2212yes—
41C22×C4×D73C2×C411yescharacteristic
42C22×C4×D73C2×C411yescharacteristic
43C22×C4×D73C2311yescharacteristic
44C2×#11924011—24no—
45C2×#11924011—42no—
46C2×#11924011—42no—
47C22×#10596831C2311yescharacteristic
48C22×#10596831C2312yes—
49C22×#10596831C2311yescharacteristic
50C2×C4⋊Dic73C2×C412yes—
51C2×#11924005C2×C414yes—
52C2×C4×Dic73C2×C411yescharacteristic
53C2×C4×Dic73C2×C411yescharacteristic
54C2×C4×Dic73C2312yes—
55C2×C4×Dic73C2311yescharacteristic
56C42×D73D414yes—
57C42×D73Q814yes—
58C4⋊#10596831—22no—
59C4⋊#10596831—42no—
60#14556520—24no—
61#14556520—22no—
62#14556520—22no—
63#14556520—42no—
64#14556520—42no—
65#14556503—22no—
66#14556503—22no—
67#14556502—22no—
68#14556498C2×C414yes—
69#14556498C2×C414yes—
70#14556498C2×C414yes—
71#14556498C2×C412yes—
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2312yes—
75C2×C4⋊C4×C73C2×C412yes—
76C2×C42×C73C2312yes—
77C2×C42×C73C2311yescharacteristic
78C4⋊C8×C73—22no—
79C4⋊C8×C73—42no—
80#97×C73—22no—
81#95×C73C2×C412yes—
82C23×D73C22×C411yescharacteristic
83C22×Dic73C22×C414yes—
84C22×Dic73C22×C411yescharacteristic
85C22×Dic73C22×C411yescharacteristic
86C22×Dic73C22×C411yescharacteristic
87C2×C4×D73—21no—
88C2×C4×D73—21no—
89C2×C4×D73—21no—
90C2×C4×D73—21no—
91C2×C4×D73—42no—
92C2×C4×D73—42no—
93C2×C4×D73C4⋊C414yes—
94C2×C4×D73C4⋊C414yes—
95C2×C4×D73C2×D412yes—
96C2×C4×D73C2×Q812yes—
97#11924011—48no—
98C2×#10596831—21no—
99C2×#10596831—21no—
100C2×#10596831—22no—
101C2×#10596831—21no—
102C2×#10596831—22no—
103C2×#10596831—21no—
104C2×#10596831—22no—
105C2×#10596831—21no—
106C2×#10596831—21no—
107C4⋊Dic73—42no—
108#11924005—44no—
109C4×Dic73—22no—
110C4×Dic73—22no—
111C4×Dic73C4⋊C414yes—
112C4×Dic73C4⋊C414yes—
113C4×Dic73C2×D412yes—
114C4×Dic73C2×Q812yes—
115C22×C4×C73C22×C414yes—
116C22×C4×C73C22×C411yescharacteristic
117C22×C4×C73C22×C411yescharacteristic
118C22×C4×C73C2411yescharacteristic
119C2×C8×C73—21no—
120C2×C8×C73—21no—
121C2×C8×C73—22no—
122C2×C8×C73—21no—
123C2×C8×C73—22no—
124C2×C8×C73—21no—
125C2×C8×C73—22no—
126C2×C8×C73—21no—
127C2×C8×C73—21no—
128C4⋊C4×C73—42no—
129C42×C73—22no—
130C42×C73—22no—
131C42×C73C2×D412yes—
132C42×C73C2×Q812yes—
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—24no—
142C2×C4×C73—24no—
143C2×C4×C73—24no—
144C2×C4×C73C2×C4⋊C412yes—
145C2×C4×C73C2×C4⋊C412yes—
146C2×C4×C73C22×D411yescharacteristic
147C2×C4×C73C22×Q811yescharacteristic
148C2×C4×C73H(5,𝔽2)11yescharacteristic
149C2×C4×C73H(5,𝔽2)11yescharacteristic
150C2×C4×C732−1+411yescharacteristic
151C2×C4×C732−1+411yescharacteristic
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—22no—
155C2×Dic73—22no—
156C2×Dic73—24no—
157C2×Dic73—24no—
158C2×Dic73—24no—
159C2×Dic73C2×C4⋊C412yes—
160C2×Dic73C2×C4⋊C412yes—
161C2×Dic73C2×C4⋊C412yes—
162C4×D73—22no—
163C4×D73—22no—
164C4×D73—22no—
165C4×D73—22no—
166C4×D73—44no—
167C4×D73—44no—
168C8×C73—41no—
169C8×C73—42no—
170C8×C73—41no—
171#10596831—41no—
172#10596831—42no—
173#10596831—41no—
174C22×C73C22×C4⋊C411yescharacteristic
175C22×C73#52011yescharacteristic
176C22×C73#52011yescharacteristic
177C22×C73#56812yes—
178C22×C73#56812yes—
179C2×D73—22no—
180C2×D73—22no—
181C2×D73—22no—
182C2×D73—42no—
183C2×D73—42no—
184C4×C73—22no—
185C4×C73—22no—
186C4×C73—44no—
187C4×C73#53511yescharacteristic
188C4×C73#53611yescharacteristic
189C4×C73#54411yescharacteristic
190C4×C73#54411yescharacteristic
191Dic73—22no—
192Dic73—22no—
193Dic73—22no—
194Dic73—44no—
195#21979—731nomaximal, Sylow
196C2×C73#231711yescharacteristic
197C2×C73#290511yescharacteristic
198C2×C73#290511yescharacteristic
199C2×C73#299512yes—
200C2×C73#299512yes—
201D73—42no—
202C2×#432—731no—
203C2×#423—731no—
204#2283—731no—
205#1940—731no—
206#1940—731no—
207#1940—731no—
208#1940D7311yescharacteristic, complemented
209#1851—732no—
210#1851—732no—
211#1843—732no—
212#1832—732no—
213C73#2197911yescharacteristic, complemented, Sylow
214C22×M16—732no—
215C22×C42—731no—
216#432—1464no—
217#423—1464no—
218C2×C4⋊C8—732no—
219C2×C4⋊C8—732no—
220C2×C4⋊C8—732no—
221C2×C4⋊C8—731no—
222C2×C4⋊C8—732no—
223C2×C4⋊C8—731no—
224C2×C4⋊C8—731no—
225C2×C4⋊C8C2×D7311yescharacteristic
226C2×C4⋊C8C2×D7312yes—
227C2×C22⋊C8—731no—
228C2×C22⋊C8—731no—
229C2×#97—731no—
230C2×#97C2×D7311yescharacteristic
231#383—732no—
232#382—732no—
233#381—732no—
234#380—732no—
235C4×C4⋊C4—731no—
236C4×C4⋊C4C2×D7311yescharacteristic
237C4×C22⋊C4—732no—
238#376—732no—
239#336—732no—
240#336—732no—
241#336—732no—
242#336C2×D7312yes—
243C23×C4—731no—
244C23×C4—731no—
245C23×C4—731no—
246C2×M16—2922no—
247C2×M16—2922no—
248C2×M16—1464no—
249C22×C8—732no—
250C22×C8—731no—
251C22×C8—731no—
252C22×C8C22×D7312yes—
253C22×C8C22×D7311yescharacteristic
254C22×C8C22×D7311yescharacteristic
255C2×C4⋊C4—732no—
256C2×C4⋊C4C4×D7312yes—
257C2×C22⋊C4—734no—
258C2×C42—731no—
259C2×C42—731no—
260C2×C42—731no—
261C2×C42—734no—
262C2×C42—734no—
263C2×C42—732no—
264C2×C42C22×D7312yes—
265C2×C42C22×D7311yescharacteristic
266C4⋊C8—22no—
267C4⋊C8—42no—
268C4⋊C8—2922no—
269C4⋊C8—2922no—
270C4⋊C8—2922no—
271C4⋊C8—1464no—
272C4⋊C8—1462no—
273C4⋊C8—1462no—
274C4⋊C8—1462no—
275C22⋊C8—1462no—
276C22⋊C8—1462no—
277#97—22no—
278#97—1462no—
279#95—734no—
280#95—734no—
281#95—734no—
282#95—732no—
283#95C4×D7312yes—
284C24—731no—
285C22×C4—2922no—
286C22×C4—2922no—
287C22×C4—734no—
288C22×C4—734no—
289C22×C4—731no—
290C22×C4—731no—
291C22×C4—731no—
292C22×C4—732no—
293C22×C4—732no—
294C22×C4—734no—
295C22×C4—1461no—
296C22×C4—1461no—
297C22×C4—1461no—
298C22×C4—1461no—
299C22×C4C2×C4×D7314yes—
300C22×C4C2×C4×D7311yescharacteristic
301C22×C4C2×C4×D7311yescharacteristic
302C22×C4C23×D7311yescharacteristic
303M16—2928no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—22no—
307C2×C8—21no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—1461no—
314C2×C8—1461no—
315C2×C8—1462no—
316C2×C8—1461no—
317C2×C8—1462no—
318C2×C8—1461no—
319C2×C8—1462no—
320C2×C8—1461no—
321C2×C8—1461no—
322C4⋊C4—42no—
323C4⋊C4—2922no—
324C22⋊C4—2924no—
325C42—22no—
326C42—22no—
327C42—734no—
328C42—734no—
329C42—732no—
330C42—732no—
331C42—1462no—
332C42—1462no—
333C42D4×D7312yes—
334C42Q8×D7312yes—
335C23—732no—
336C23—1461no—
337C23—1461no—
338C23—1462no—
339C23—1462no—
340C23C22×C4×D7311yescharacteristic
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—2924no—
347C2×C4—2924no—
348C2×C4—732no—
349C2×C4—732no—
350C2×C4—732no—
351C2×C4—1464no—
352C2×C4—1464no—
353C2×C4—1464no—
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×C4C4⋊C4×D7312yes—
363C2×C4C4⋊C4×D7312yes—
364C2×C4C2×D4×D7311yescharacteristic
365C2×C4C2×Q8×D7311yescharacteristic
366C2×C4#1455663611yescharacteristic
367C2×C4#1455663711yescharacteristic
368C2×C4#1455663811yescharacteristic
369C2×C4#1455663911yescharacteristic
370C8—42no—
371C8—41no—
372C8—41no—
373C8—2922no—
374C8—2921no—
375C8—2921no—
376C22—2922no—
377C22—2922no—
378C22—1462no—
379C22—1462no—
380C22—1462no—
381C22C2×C4⋊C4×D7311yescharacteristic
382C22#1798906611yescharacteristic
383C22#1798906911yescharacteristic
384C22#1798935212yes—
385C22#1798935312yes—
386C4—22no—
387C4—22no—
388C4—44no—
389C4—2924no—
390C4—1462no—
391C4—1462no—
392C4—1462no—
393C4#1798915311yescharacteristic
394C4#1798916011yescharacteristic
395C4#1798921411yescharacteristic
396C4#1798921711yescharacteristic
397C2—2922no—
398C2#2261255311yescharacteristic
399C2#2261849211yescharacteristic
400C2#2261849311yescharacteristic
401C2#2261909712yes—
402C2#2261910012yes—
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1940C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1940D73
hypocenterC73#21979
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
4. #22610655C2semidirect
5. #22610654C2semidirect
6. #22610652C2semidirect
9. #22610084C2semidirect
10. #22610049C2semidirect
11. C73×#1940C2semidirect
208. #1940D73semidirect
213. C73#21979semidirect

Maximal subgroups

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

subgroupindex
C2×#179886422
C2×#179886092
#226123272
#226106552
#226106542
#226106522
#226101152
#226101122
#226100842
#226100492
C73×#19402
#2197973