Finite Group Databasebeta

← #33090352

Subgroups — #33090352

Order 18688.

862 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988698C211yesmaximal, characteristic
2#22612570C212yesmaximal, complemented
3#22610807C211yesmaximal, characteristic
4#22610795C211yesmaximal, characteristic
5#22610660C211yesmaximal, characteristic, complemented
6#22610629C212yesmaximal, complemented
7#22610613C212yesmaximal, complemented
8#22609830C211yesmaximal, characteristic, complemented
9#22609745C212yesmaximal, complemented
10#22609619C211yesmaximal, characteristic, complemented
11C73×#1944C211yesmaximal, characteristic, complemented
12C22×D584C2211yescharacteristic
13C2×#14556553C2212yes—
14#17988698C418yescomplemented
15C2×#14556523C2211yescharacteristic
16C2×#14556513C2212yes—
17C2×#14556511C2212yes—
18C2×#14556511C2212yes—
19C2×#14556501C2211yescharacteristic
20C2×#14556501C2211yescharacteristic
21C2×C4×#10596831C2211yescharacteristic
22C2×C8×Dic73C2211yescharacteristic
23C2×C8×Dic73C2211yescharacteristic
24#17988489C2212yes—
25#17988488C2212yes—
26#17988486C2212yes—
27#17988479—22no—
28#17988477—22no—
29#17988449—22no—
30#17988444—22no—
31C4⋊C4×Dic73C2212yes—
32#17988433C2211yescharacteristic
33#17988349C2212yes—
34#17988349C2212yes—
35C2×#107×C73C2211yescharacteristic
36C2×#106×C73C2211yescharacteristic
37C2×#97×C73C2211yescharacteristic
38#389×C73C2212yes—
39#340×C73C2212yes—
40C22×D292C2312yes—
41C22×C4×D73—22no—
42C2×D584—22no—
43C2×D584—22no—
44C2×D584C2×C414yes—
45C22×#10596831C2311yescharacteristic
46C22×#10596831C2311yescharacteristic
47#14556553—24no—
48#14556553C2×C418yes—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73C2312yes—
51C2×#11924005—22no—
52C2×#11924005—22no—
53C2×#11924005—22no—
54C2×#11924005—22no—
55C2×#11924005—22no—
56C2×C4×Dic73—22no—
57C2×C4×Dic73C2311yescharacteristic
58C2×C4×Dic73C2311yescharacteristic
59#14556523—22no—
60#14556513—24no—
61#14556511—24no—
62#14556511C2×C418yes—
63#14556501—22no—
64#14556501C2×C414yes—
65C4×#10596831—22no—
66C8×Dic73—22no—
67C8×Dic73—22no—
68#14556498—22no—
69#14556498—22no—
70#14556498D412yes—
71#14556498D412yes—
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C2×C4⋊C4×C73—22no—
75C2×C4⋊C4×C73C2312yes—
76C2×C4⋊C4×C73C2312yes—
77C2×C42×C73C2311yescharacteristic
78#107×C73—22no—
79#106×C73C2×C414yes—
80#97×C73—22no—
81#95×C73—22no—
82C23×D73—22no—
83C2×D292—22no—
84C2×D292—22no—
85C2×D292—22no—
86C2×D292—22no—
87C2×D292—22no—
88C2×D292C22×C414yes—
89C22×Dic73—22no—
90C22×Dic73C2×D412yes—
91C22×Dic73C2×D412yes—
92C2×C4×D73—28no—
93C2×C4×D73—82no—
94C2×C4×D73—82no—
95D584—28no—
96C2×#10596831—21no—
97C2×#10596831—21no—
98C2×#10596831—21no—
99C2×#10596831—21no—
100C2×#10596831C22×C412yes—
101C2×#10596831#4112yes—
102C4⋊Dic73—22no—
103C4⋊Dic73—22no—
104C4⋊Dic73—82no—
105#11924005—28no—
106#11924005—82no—
107#11924005—82no—
108#11924005—82no—
109#11924005—82no—
110C4×Dic73—21no—
111C4×Dic73—21no—
112C4×Dic73—82no—
113C4×Dic73C22×C412yes—
114C4×Dic73#4112yes—
115C22×C4×C73—22no—
116C22×C4×C73—22no—
117C22×C4×C73C2×D411yescharacteristic
118C22×C4×C73C2×D411yescharacteristic
119C22×C4×C73C2411yescharacteristic
120C2×C8×C73—21no—
121C2×C8×C73—21no—
122C2×C8×C73C22×C412yes—
123C2×C8×C73#4112yes—
124C2×C8×C73#4112yes—
125C2×C8×C73#4112yes—
126C4⋊C4×C73—22no—
127C4⋊C4×C73—22no—
128C4⋊C4×C73—22no—
129C4⋊C4×C73—82no—
130C4⋊C4×C73C22×C414yes—
131C42×C73—21no—
132C42×C73—21no—
133C23×C73C22×D411yescharacteristic
134C22×D73—24no—
135C22×D73—42no—
136C22×D73—42no—
137C22×D73—42no—
138C22×D73—42no—
139C22×D73—42no—
140C22×D73—42no—
141C2×C4×C73—24no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—22no—
145C2×C4×C73—22no—
146C2×C4×C73—42no—
147C2×C4×C73—42no—
148C2×C4×C73—42no—
149C2×C4×C73—42no—
150C2×C4×C73—42no—
151C2×C4×C73C23×C411yescharacteristic
152C2×C4×C73C2×#4111yescharacteristic
153C2×C4×C73C2×#4111yescharacteristic
154C2×C4×C73C2×#4111yescharacteristic
155C2×C4×C73C2×#4111yescharacteristic
156C2×C4×C73C2×#4111yescharacteristic
157C2×Dic73—22no—
158C2×Dic73—22no—
159C2×Dic73—22no—
160C2×Dic73—22no—
161C2×Dic73—22no—
162C2×Dic73—42no—
163C2×Dic73—42no—
164C2×Dic73—42no—
165C2×Dic73C4×D414yes—
166D292—24no—
167D292—24no—
168D292—42no—
169D292—42no—
170C4×D73—88no—
171C8×C73—22no—
172C8×C73#11714yes—
173#10596831—22no—
174#10596831—22no—
175C22×C73C2×C4×D411yescharacteristic
176C22×C73#53211yescharacteristic
177C22×C73#53211yescharacteristic
178C22×C73#57612yes—
179C22×C73#57712yes—
180C2×D73—44no—
181C2×D73—44no—
182C2×D73—44no—
183C2×D73—82no—
184C2×D73—82no—
185C2×D73—82no—
186C2×D73—82no—
187C4×C73—41no—
188C4×C73—41no—
189C4×C73—44no—
190C4×C73—82no—
191C4×C73C2×#11711yescharacteristic
192C4×C73C4×#4111yescharacteristic
193C4×C73#52911yescharacteristic
194C4×C73#52911yescharacteristic
195Dic73—24no—
196Dic73—42no—
197Dic73—82no—
198#21290—731nomaximal, Sylow
199C2×C73#229311yescharacteristic
200C2×C73#294612yes—
201C2×C73#317311yescharacteristic
202C2×C73#317611yescharacteristic
203C2×C73#317912yes—
204D73—84no—
205C2×#442—731no—
206#2319—732no—
207#1972—731no—
208#1970—731no—
209#1944D7311yescharacteristic, complemented
210#1941—731no—
211#1936—732no—
212#1934—732no—
213#1776—731no—
214C4×#102—732no—
215#1726—731no—
216C73#2129011yescharacteristic, complemented, Sylow
217C22×D8—731no—
218C2×C4×D4—732no—
219#442—738no—
220C2×#107C2×D7311yescharacteristic
221C2×#106—731no—
222C2×#106C2×D7311yescharacteristic
223C2×#102—732no—
224C2×#102—732no—
225C2×#102—732no—
226C2×#97—731no—
227C2×#97—731no—
228C2×#97C2×D7311yescharacteristic
229C2×C4×C8—731no—
230C2×C4×C8—731no—
231C2×C4×C8—731no—
232#390—732no—
233#390—732no—
234#389—732no—
235#389C2×D7312yes—
236#388—1462no—
237#388—1462no—
238#381—1462no—
239#380—1462no—
240C4×C4⋊C4—732no—
241#376—731no—
242#340—732no—
243#340—732no—
244#340C2×D7312yes—
245C22×D4—732no—
246C23×C4—1462no—
247C2×D8—734no—
248C2×D8—1462no—
249C2×D8—1462no—
250C22×C8—731no—
251C22×C8—731no—
252C22×C8C22×D7311yescharacteristic
253C22×C8C22×D7311yescharacteristic
254C4×D4—738no—
255C4×D4—1464no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—732no—
258C2×C4⋊C4—1462no—
259C2×C4⋊C4C22×D7312yes—
260C2×C4⋊C4C22×D7312yes—
261C2×C22⋊C4—1462no—
262C2×C22⋊C4—1462no—
263C2×C22⋊C4—1462no—
264C2×C22⋊C4—1462no—
265C2×C22⋊C4—1462no—
266C2×C42—731no—
267C2×C42—731no—
268C2×C42—1462no—
269C2×C42C22×D7311yescharacteristic
270#107—22no—
271#106—1462no—
272#106C4×D7314yes—
273#102—738no—
274#102—1464no—
275#102—1464no—
276#97—22no—
277#97—734no—
278#97—1462no—
279C4×C8—1462no—
280C4×C8—1462no—
281C4×C8—1462no—
282#95—22no—
283#95—732no—
284#95—732no—
285#95—1462no—
286#95—1462no—
287C24—1462no—
288C2×D4—734no—
289C2×D4—1462no—
290C2×D4—1462no—
291C2×D4—1462no—
292C2×D4—1462no—
293C2×D4—1462no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—5842no—
297C22×C4—5842no—
298C22×C4—732no—
299C22×C4—732no—
300C22×C4—1468no—
301C22×C4—1462no—
302C22×C4D4×D7311yescharacteristic
303C22×C4D4×D7311yescharacteristic
304C22×C4C23×D7311yescharacteristic
305D8—1468no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—732no—
309C2×C8—732no—
310C2×C8—1461no—
311C2×C8—1461no—
312C2×C8—1461no—
313C2×C8—1461no—
314C2×C8C2×C4×D7312yes—
315C2×C8#1192402712yes—
316C2×C8#1192402912yes—
317C2×C8#1192402912yes—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—82no—
322C4⋊C4—5842no—
323C4⋊C4—1462no—
324C4⋊C4—1462no—
325C4⋊C4C2×C4×D7314yes—
326C22⋊C4—5842no—
327C22⋊C4—5842no—
328C22⋊C4—5842no—
329C22⋊C4—5842no—
330C22⋊C4—1468no—
331C42—21no—
332C42—21no—
333C42—5842no—
334C42—732no—
335C42—732no—
336C42—1461no—
337C42—1461no—
338C23—2922no—
339C23—2922no—
340C23—2922no—
341C23—2922no—
342C23—2922no—
343C23—2922no—
344C23—1464no—
345C23C2×D4×D7311yescharacteristic
346D4—2922no—
347D4—2922no—
348D4—1464no—
349D4—1464no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—2922no—
361C2×C4—2922no—
362C2×C4—2922no—
363C2×C4—5848no—
364C2×C4—734no—
365C2×C4—1462no—
366C2×C4—1462no—
367C2×C4—1462no—
368C2×C4—1462no—
369C2×C4—1462no—
370C2×C4C22×C4×D7311yescharacteristic
371C2×C4#41×D7311yescharacteristic
372C2×C4#41×D7311yescharacteristic
373C2×C4C2×#1192402711yescharacteristic
374C2×C4C2×#1192402911yescharacteristic
375C2×C4C2×#1192402911yescharacteristic
376C8—22no—
377C8—1462no—
378C8—1462no—
379C8#1455654914yes—
380C22—2924no—
381C22—2924no—
382C22—2924no—
383C22—5842no—
384C22—5842no—
385C22—5842no—
386C22—5842no—
387C22C4×D4×D7311yescharacteristic
388C22#1798913211yescharacteristic
389C22#1798913811yescharacteristic
390C22#1798939112yes—
391C22#1798939612yes—
392C4—41no—
393C4—44no—
394C4—41no—
395C4—82no—
396C4—2922no—
397C4—5842no—
398C4—1464no—
399C4C2×#1455654911yescharacteristic
400C4C4×#1192402911yescharacteristic
401C4#1798912211yescharacteristic
402C4#1798912311yescharacteristic
403C2—5844no—
404C2#2261238911yescharacteristic
405C2#2261876212yes—
406C2#2262054911yescharacteristic
407C2#2262057611yescharacteristic
408C2#2262061912yes—
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1944C2
socleC23×C73C22×D4
prime radicalC22×D584C22
cosocleC22×C4×C73C24
hypercenter#1944D73
hypocenterC73#21290
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
2. #22612570C2semidirect
5. #22610660C2semidirect
6. #22610629C2semidirect
7. #22610613C2semidirect
8. #22609830C2semidirect
9. #22609745C2semidirect
10. #22609619C2semidirect
11. C73×#1944C2semidirect
14. #17988698C4semidirect
209. #1944D73semidirect
216. C73#21290semidirect

Maximal subgroups

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

subgroupindex
C2×#179886982
#226125702
#226108072
#226107952
#226106602
#226106292
#226106132
#226098302
#226097452
#226096192
C73×#19442
#2129073