Finite Group Databasebeta

← #33239407

Subgroups — #33239407

Order 18688.

642 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989017C211yesmaximal, characteristic
2#22618848C211yesmaximal, characteristic, complemented
3#22618847C211yesmaximal, characteristic, complemented
4#22611814C214yesmaximal, complemented
5#22611809C214yesmaximal, complemented
6C2×#17988416C211yesmaximal, characteristic, complemented
7#22611660C211yesmaximal, characteristic, complemented
8#22611530C211yesmaximal, characteristic, complemented
9C73×#2143C211yesmaximal, characteristic, complemented
10C2×#14556613C2211yescharacteristic
11#17989354—21no—
12#17989353—21no—
13#17989017C412yescomplemented
14#17989017C412yescomplemented
15#17989017C2212yes—
16#17989017C2212yes—
17C2×#14556537C411yescharacteristic, complemented
18C2×#14556535C411yescharacteristic, complemented
19C2×#14556534C411yescharacteristic, complemented
20C2×#14556532C411yescharacteristic, complemented
21C22×#11924003C2211yescharacteristic
22#17988709—22no—
23#17988708—22no—
24#17988704C2214yescomplemented
25#17988703C2214yescomplemented
26C2×#14556527C2211yescharacteristic
27#17988604—21no—
28#17988603—21no—
29#17988542C2211yescharacteristic
30#17988416C2212yescomplemented
31#17988416C2212yescomplemented
32#17988395C2214yescomplemented
33#17988362C2212yescomplemented
34C16×Dic73C2212yescomplemented
35C2×#135×C73C2211yescharacteristic
36C2×M32×C73C2211yescharacteristic
37C2×#108×C73C2211yescharacteristic
38#359×C73C2214yescomplemented
39C2×#11924028—21no—
40#14556613—21no—
41#14556613—21no—
42#14556613C2×C412yes—
43#14556613C2312yes—
44C2×Dic292C2×C411yescharacteristic
45C2×#11924017—21no—
46C2×D584C2×C411yescharacteristic
47#14556599—24no—
48#14556598—24no—
49#14556598—42no—
50#14556597—42no—
51C2×#11924012—21no—
52C2×#11924012—42no—
53C2×#11924012D411yescharacteristic
54M16×D73—42no—
55#14556550D411yescharacteristic
56#14556537C2×C412yes—
57#14556537C2×C412yes—
58#14556535C2×C412yes—
59#14556535C2×C412yes—
60#14556534C2×C412yes—
61#14556534C2×C412yes—
62#14556532C2×C412yes—
63#14556532C2×C412yes—
64C2×#11924003C2×C411yescharacteristic
65C2×#11924003C2×C411yescharacteristic
66C2×#11924003C2×C411yescharacteristic
67C2×#11924003C2×C411yescharacteristic
68C2×#11924003C2311yescharacteristic
69C2×#11924003C2311yescharacteristic
70#14556527—21no—
71#14556527C2312yes—
72#14556518—24no—
73#14556517—24no—
74#14556501D412yes—
75C8×Dic73C2312yes—
76C2×#41×C73—21no—
77#135×C73—21no—
78#135×C73—21no—
79#135×C73C2×C412yes—
80#135×C73C2312yes—
81C2×Q16×C73C2×C411yescharacteristic
82C2×SD16×C73—21no—
83C2×D8×C73C2×C411yescharacteristic
84C2×M16×C73—21no—
85C22×C8×C73C2311yescharacteristic
86M32×C73—21no—
87M32×C73—21no—
88C2×C16×C73C2312yes—
89#108×C73—21no—
90#108×C73C2312yes—
91#11924028—22no—
92#11924028—22no—
93#11924028—41no—
94#11924028—41no—
95C2×Dic146—21no—
96C2×D292—21no—
97C2×C22⋊D73—41no—
98C2×C4×D73—41no—
99Dic292—21no—
100Dic292C22×C412yes—
101#11924017—22no—
102#11924017—22no—
103D584—21no—
104D584C22×C412yes—
105#11924012—22no—
106#11924012—41no—
107#11924012—44no—
108#11924012D812yes—
109#11924012D812yes—
110#11924011—44no—
111C2×#10596831—41no—
112C2×#10596831—44no—
113C2×#10596831C2×D412yes—
114C8×D73—44no—
115C4⋊Dic73—21no—
116C22⋊Dic73—21no—
117C4×Dic73C2×D412yes—
118#11924003C22×C411yescharacteristic
119#11924003C22×C411yescharacteristic
120#11924003C22×C411yescharacteristic
121#11924003C22×C411yescharacteristic
122#41×C73—22no—
123#41×C73—22no—
124#41×C73—41no—
125#41×C73—41no—
126C2×Q8×C73—21no—
127C2×D4×C73—21no—
128C2×D4×C73—41no—
129C22×C4×C73—41no—
130C22×C4×C73C2×D411yescharacteristic
131Q16×C73—21no—
132Q16×C73C22×C412yes—
133SD16×C73—22no—
134SD16×C73—22no—
135D8×C73—21no—
136D8×C73C22×C412yes—
137M16×C73—22no—
138M16×C73—41no—
139C2×C8×C73—41no—
140C2×C8×C73C22×C411yescharacteristic
141C2×C8×C73C22×C411yescharacteristic
142C2×C8×C73C2×D411yescharacteristic
143C2×C8×C73#4111yescharacteristic
144C2×C8×C73#4111yescharacteristic
145C2×C8×C73C2411yescharacteristic
146C16×C73—22no—
147C23×C73—41no—
148C23×C73#13511yescharacteristic
149C22×D73—41no—
150Q8×C73—22no—
151Q8×C73—41no—
152D4×C73—22no—
153D4×C73—42no—
154D4×C73—42no—
155D4×C73—41no—
156C2×C4×C73—41no—
157C2×C4×C73—42no—
158C2×C4×C73—42no—
159C2×C4×C73C4×D411yescharacteristic
160C2×C4×C73C4×D411yescharacteristic
161C2×C4×C73C2×D811yescharacteristic
162C2×C4×C73C2×D811yescharacteristic
163C2×C4×C73#13511yescharacteristic
164C2×C4×C73C22×D411yescharacteristic
165C22⋊D73—42no—
166C22⋊D73—42no—
167C2×Dic73—22no—
168C2×Dic73—41no—
169D292—22no—
170D292—41no—
171C4×D73—42no—
172C4×D73—42no—
173Dic146—22no—
174Dic146—41no—
175C8×C73—42no—
176C8×C73C4×D411yescharacteristic
177C8×C73C4×D411yescharacteristic
178C8×C73C23×C411yescharacteristic
179C8×C73C2×#4111yescharacteristic
180#10596831—42no—
181#10596831C2×D814yes—
182C22×C73—41no—
183C22×C73—42no—
184C22×C73—161no—
185C22×C73C4×D811yescharacteristic
186C22×C73C4×D811yescharacteristic
187C22×C73C2×#13511yescharacteristic
188C2×D73—42no—
189C2×D73—161no—
190C4×C73—42no—
191C4×C73C4×D811yescharacteristic
192C4×C73C4×D811yescharacteristic
193C4×C73C2×C4×D411yescharacteristic
194C4×C73C22×D811yescharacteristic
195Dic73—42no—
196Dic73—42no—
197#33465—731nomaximal, Sylow
198C2×C73—21no—
199C2×C73—21no—
200C2×C73—21no—
201C2×C73—82no—
202C2×C73C2×C4×D811yescharacteristic
203D73—82no—
204C2×#508—731no—
205#2957—731no—
206#2957—731no—
207#2179—734no—
208#2178—734no—
209C2×#368—731no—
210#2143—731no—
211#2143D7311yescharacteristic, complemented
212#2108—731no—
213C73#3346511yescharacteristic, complemented, Sylow
214C2×#135—731no—
215C2×#135C2×D7311yescharacteristic
216#568—1461no—
217#568—1461no—
218#508—732no—
219#508—732no—
220#508—732no—
221#508—732no—
222C2×Q32—731no—
223C2×SD32—731no—
224C2×SD32—731no—
225C2×D16—731no—
226C2×M32C2×D7311yescharacteristic
227C22×C16—731no—
228#444—1462no—
229#444—1462no—
230#443—734no—
231#443—734no—
232C2×#108—731no—
233C2×#108C2×D7311yescharacteristic
234#421—1461no—
235#421—1461no—
236#405—731no—
237#368—732no—
238#368—732no—
239#359—734no—
240#359C2×D7314yescomplemented
241#346—732no—
242C4×C16—732no—
243C2×#41—21no—
244C2×#41—1461no—
245#135—21no—
246#135—21no—
247#135—732no—
248#135—732no—
249#135—1461no—
250#135—1461no—
251#135C4×D7312yes—
252#135C22×D7312yes—
253C2×Q16—731no—
254C2×Q16C4×D7311yescharacteristic
255C2×SD16—21no—
256C2×SD16—1461no—
257C2×D8—731no—
258C2×D8C4×D7311yescharacteristic
259#131—2922no—
260#131—2922no—
261#131—1464no—
262#131—1464no—
263C2×M16—21no—
264C2×M16—2922no—
265C2×M16—2922no—
266C2×M16—731no—
267C2×M16—1461no—
268C22×C8C22×D7311yescharacteristic
269#117—731no—
270Q32—732no—
271Q32—732no—
272SD32—732no—
273SD32—732no—
274SD32—732no—
275SD32—732no—
276D16—732no—
277D16—732no—
278M32—21no—
279M32—21no—
280C2×C16—731no—
281C2×C16—731no—
282C2×C16—731no—
283C2×C16—731no—
284C2×C16—731no—
285C2×C16—731no—
286C2×C16C22×D7312yes—
287#108—21no—
288#108—732no—
289#108—1461no—
290#108C22×D7312yes—
291#104—1464no—
292#104—1464no—
293#97—732no—
294C4×C8—732no—
295#41—22no—
296#41—22no—
297#41—41no—
298#41—41no—
299#41—2921no—
300#41—2921no—
301#41—1462no—
302#41—1462no—
303C2×Q8—21no—
304C2×Q8—1461no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—2921no—
308C2×D4—1461no—
309C22×C4—41no—
310C22×C4—2921no—
311C22×C4D4×D7311yescharacteristic
312Q16—21no—
313Q16—732no—
314Q16—1461no—
315Q16C2×C4×D7312yes—
316SD16—22no—
317SD16—22no—
318SD16—1462no—
319SD16—1462no—
320D8—21no—
321D8—732no—
322D8—1461no—
323D8C2×C4×D7312yes—
324M16—22no—
325M16—41no—
326M16—2924no—
327M16—2921no—
328M16—2924no—
329M16—732no—
330M16—732no—
331M16—1462no—
332C2×C8—41no—
333C2×C8—2924no—
334C2×C8—2921no—
335C2×C8—2924no—
336C2×C8—732no—
337C2×C8C2×C4×D7311yescharacteristic
338C2×C8C2×C4×D7311yescharacteristic
339C2×C8D4×D7311yescharacteristic
340C2×C8#1192402711yescharacteristic
341C2×C8#1192402711yescharacteristic
342C2×C8C23×D7311yescharacteristic
343C4⋊C4—1461no—
344C22⋊C4—1461no—
345C42—732no—
346C16—22no—
347C16—731no—
348C16—731no—
349C16—731no—
350C16—731no—
351C23—41no—
352C23—2921no—
353C23#1455661211yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—2921no—
357Q8—1462no—
358D4—22no—
359D4—42no—
360D4—42no—
361D4—41no—
362D4—2922no—
363D4—2922no—
364D4—2921no—
365D4—1462no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—2921no—
370C2×C4—2922no—
371C2×C4—2922no—
372C2×C4—1462no—
373C2×C4#1455655111yescharacteristic
374C2×C4#1455655111yescharacteristic
375C2×C4D8×D7311yescharacteristic
376C2×C4D8×D7311yescharacteristic
377C2×C4#1455661211yescharacteristic
378C2×C4C2×D4×D7311yescharacteristic
379C8—42no—
380C8—2922no—
381C8—734no—
382C8#1455655111yescharacteristic
383C8#1455655111yescharacteristic
384C8C22×C4×D7311yescharacteristic
385C8C2×#1192402711yescharacteristic
386C22—41no—
387C22—42no—
388C22—161no—
389C22—2922no—
390C22—11681no—
391C22#1798866711yescharacteristic
392C22#1798866711yescharacteristic
393C22C2×#1455661211yescharacteristic
394C4—42no—
395C4—2922no—
396C4—2922no—
397C4#1798866711yescharacteristic
398C4#1798866711yescharacteristic
399C4C2×#1455655111yescharacteristic
400C4C2×D8×D7311yescharacteristic
401C2—21no—
402C2—21no—
403C2—21no—
404C2—82no—
405C2—5842no—
406C2C2×#1798866711yescharacteristic
subgroupG/H
centerC4C2×D8×D73
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC73×#2143C2
socleC2×C73C2×C4×D8
prime radicalC2×#17989017C2
cosocleC2×C8×C73C24
hypercenter#2143D73
hypocenterC73#33465
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2143

Complements

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

NH ≅ G/Ntype
2. #22618848C2semidirect
3. #22618847C2semidirect
4. #22611814C2semidirect
5. #22611809C2semidirect
6. C2×#17988416C2semidirect
7. #22611660C2semidirect
8. #22611530C2semidirect
9. C73×#2143C2semidirect
13. #17989017C4semidirect
14. #17989017C4semidirect
17. C2×#14556537C4semidirect
18. C2×#14556535C4semidirect
19. C2×#14556534C4semidirect
20. C2×#14556532C4semidirect
24. #17988704C22semidirect
25. #17988703C22semidirect
30. #17988416C22semidirect
31. #17988416C22semidirect
32. #17988395C22semidirect
33. #17988362C22semidirect
34. C16×Dic73C22semidirect
38. #359×C73C22semidirect
211. #2143D73semidirect
213. C73#33465semidirect
240. #359C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179890172
#226188482
#226188472
#226118142
#226118092
C2×#179884162
#226116602
#226115302
C73×#21432
#3346573