Finite Group Databasebeta

← #33095521

Subgroups — #33095521

Order 18688.

1010 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×#17989142C211yesmaximal, characteristic
2C2×#17988642C211yesmaximal, characteristic
3#22612324C211yesmaximal, characteristic
4#22610905C211yesmaximal, characteristic, complemented
5#22610904C211yesmaximal, characteristic, complemented
6#22610903C211yesmaximal, characteristic, complemented
7#22610885C214yesmaximal, complemented
8#22610024C214yesmaximal
9C73×#1993C211yesmaximal, characteristic, complemented
10#17989142—24no—
11#17989142C418yescomplemented
12C2×#14556591C2211yescharacteristic
13C2×#14556582C2212yes—
14C2×#14556571—21no—
15C2×#14556567—21no—
16C2×Q8×Dic73—21no—
17C2×#14556556—21no—
18C2×#14556549C2212yes—
19C2×C42×D73C2211yescharacteristic
20#17988642—24no—
21C2×#14556520C2212yes—
22C2×#14556503C2212yes—
23C2×#14556502C2211yescharacteristic
24#17988454—21no—
25#17988453C2211yescharacteristic
26#17988449—21no—
27#17988444C2212yes—
28C4⋊C4×Dic73C2212yes—
29#17988434—21no—
30#17988432—21no—
31#17988350C2214yes—
32#17988349C2214yes—
33#17988349C2214yes—
34C2×C4⋊Q8×C73C2211yescharacteristic
35C2×#97×C73C2211yescharacteristic
36#382×C73C2211yescharacteristic
37#340×C73C2214yes—
38C22×Dic146—21no—
39C22×C4×D73D411yescharacteristic
40C22×C4×D73D411yescharacteristic
41C22×C4×D73C2311yescharacteristic
42C22×#10596831C2312yes—
43#14556591—22no—
44#14556591C2×C414yes—
45#14556582—24no—
46#14556582C2×C418yes—
47#14556571—28no—
48#14556567—28no—
49Q8×Dic73—28no—
50#14556556—28no—
51#14556549—24no—
52#14556549C2×C418yes—
53C2×C4⋊Dic73—22no—
54C2×C4⋊Dic73—21no—
55C2×C4⋊Dic73C2312yes—
56C2×C4⋊Dic73C2312yes—
57C2×#11924007—22no—
58C2×#11924005—22no—
59C2×#11924005—22no—
60C2×C4×Dic73—22no—
61C2×C4×Dic73—22no—
62C2×C4×Dic73D411yescharacteristic
63C2×C4×Dic73D411yescharacteristic
64C2×C4×Dic73C2311yescharacteristic
65C42×D73C2×C414yes—
66C42×D73D414yes—
67#14556520—24no—
68#14556503—24no—
69#14556502—22no—
70#14556498—22no—
71#14556498—22no—
72#14556498—21no—
73#14556498—21no—
74C22×Q8×C73—21no—
75C22×C8×C73C2312yes—
76C4⋊Q8×C73—22no—
77C4⋊Q8×C73C2×C414yes—
78C2×C4⋊C4×C73—21no—
79C2×C4⋊C4×C73C2312yes—
80C2×C4⋊C4×C73C2312yes—
81C2×C42×C73C2311yescharacteristic
82#97×C73—22no—
83#95×C73—21no—
84#95×C73—21no—
85C23×D73C2×D411yescharacteristic
86C2×Dic146—24no—
87C2×Dic146—44no—
88C22×Dic73—22no—
89C22×Dic73—22no—
90C22×Dic73C2×D411yescharacteristic
91C22×Dic73C2×D411yescharacteristic
92C22×Dic73C2×D411yescharacteristic
93C2×C4×D73—22no—
94C2×C4×D73—22no—
95C2×C4×D73—42no—
96C2×C4×D73—42no—
97C2×C4×D73C22⋊C414yes—
98C2×C4×D73C22⋊C414yes—
99C2×C4×D73C22×C412yes—
100C2×C4×D73C2×D412yes—
101C2×#10596831—22no—
102C2×#10596831—22no—
103C2×#10596831—22no—
104C4⋊Dic73—24no—
105C4⋊Dic73—22no—
106C4⋊Dic73—28no—
107C4⋊Dic73—24no—
108C4⋊Dic73C22×C414yes—
109#11924007—28no—
110#11924005—28no—
111#11924005—44no—
112C4×Dic73—28no—
113C4×Dic73—44no—
114C4×Dic73C22⋊C414yes—
115C4×Dic73C22⋊C414yes—
116C4×Dic73C22×C412yes—
117C4×Dic73C2×D412yes—
118C2×Q8×C73—24no—
119C2×Q8×C73—44no—
120C22×C4×C73—22no—
121C22×C4×C73—22no—
122C22×C4×C73C2×D411yescharacteristic
123C22×C4×C73C2×D411yescharacteristic
124C22×C4×C73C2411yescharacteristic
125C2×C8×C73—22no—
126C2×C8×C73—22no—
127C2×C8×C73—22no—
128C4⋊C4×C73—24no—
129C4⋊C4×C73—22no—
130C4⋊C4×C73—24no—
131C4⋊C4×C73C22×C414yes—
132C42×C73C22×C412yes—
133C42×C73C2×D412yes—
134C23×C73C22×D411yescharacteristic
135C22×D73—21no—
136C22×D73—21no—
137C22×D73—22no—
138C22×D73—22no—
139C22×D73C2×C22⋊C412yes—
140Q8×C73—48no—
141C2×C4×C73—22no—
142C2×C4×C73—22no—
143C2×C4×C73—24no—
144C2×C4×C73—44no—
145C2×C4×C73—42no—
146C2×C4×C73—42no—
147C2×C4×C73—42no—
148C2×C4×C73C2×C22⋊C412yes—
149C2×C4×C73C2×C22⋊C412yes—
150C2×C4×C73C23×C411yescharacteristic
151C2×C4×C73C22×D411yescharacteristic
152C2×C4×C732−1+412yes—
153C2×C4×C732−1+412yes—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73—22no—
157C2×Dic73—22no—
158C2×Dic73—24no—
159C2×Dic73—44no—
160C2×Dic73—42no—
161C2×Dic73—42no—
162C2×Dic73—42no—
163C2×Dic73C2×C22⋊C412yes—
164C2×Dic73C2×C22⋊C412yes—
165C2×Dic73C2×C22⋊C412yes—
166C4×D73—24no—
167C4×D73—24no—
168C4×D73—44no—
169C4×D73—44no—
170Dic146—48no—
171C8×C73—42no—
172#10596831—42no—
173C22×C73C22×C22⋊C411yescharacteristic
174C22×C73#53611yescharacteristic
175C22×C73#53611yescharacteristic
176C22×C73#57512yes—
177C22×C73#57512yes—
178C2×D73—22no—
179C2×D73—22no—
180C2×D73—22no—
181C2×D73—42no—
182C2×D73—42no—
183C4×C73—22no—
184C4×C73—22no—
185C4×C73—44no—
186C4×C73—82no—
187C4×C73#51912yes—
188C4×C73#53612yes—
189Dic73—22no—
190Dic73—22no—
191Dic73—22no—
192Dic73—44no—
193Dic73—82no—
194#21842—731nomaximal, Sylow
195C2×C73#231011yescharacteristic
196C2×C73#289611yescharacteristic
197C2×C73#289611yescharacteristic
198C2×C73#324012yes—
199C2×C73#324012yes—
200D73—42no—
201C2×#533—731no—
202C2×#432—731no—
203#2283—731no—
204#1993—731no—
205#1993—731no—
206#1993—731no—
207#1993D7311yescharacteristic, complemented
208#1989—734no—
209#1825—734no—
210C73#2184211yescharacteristic, complemented, Sylow
211#533—738no—
212#533—1464no—
213C2×C4⋊Q8—731no—
214C2×C4⋊Q8C2×D7311yescharacteristic
215C2×#125—732no—
216C2×C22⋊Q8—1461no—
217C2×C22⋊Q8—1461no—
218C2×C4×Q8—1461no—
219C2×C4×Q8—1461no—
220C2×#117—732no—
221C22×C42—731no—
222#432—1464no—
223C2×C4⋊C8—732no—
224C2×C22⋊C8—732no—
225C2×#97—731no—
226C2×#97C2×D7311yescharacteristic
227#383—1461no—
228#382—731no—
229#382C2×D7311yescharacteristic
230#381—1461no—
231#380—732no—
232C4×C4⋊C4—732no—
233C4×C22⋊C4—1461no—
234#376—1461no—
235#340—734no—
236#340—734no—
237#340—734no—
238#340C2×D7314yes—
239C22×Q8—21no—
240C22×Q8—1461no—
241C23×C4—731no—
242C23×C4—731no—
243C23×C4—731no—
244C22×C8—732no—
245C22×C8C22×D7312yes—
246C4⋊Q8—22no—
247C4⋊Q8—734no—
248C4⋊Q8—1462no—
249C4⋊Q8C4×D7314yes—
250#125—738no—
251#125—1464no—
252C22⋊Q8—1468no—
253C22⋊Q8—1468no—
254C4×Q8—1468no—
255C4×Q8—1468no—
256#117—738no—
257#117—1464no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—732no—
260C2×C4⋊C4—732no—
261C2×C4⋊C4—1462no—
262C2×C4⋊C4—1462no—
263C2×C4⋊C4—1461no—
264C2×C4⋊C4C22×D7312yes—
265C2×C4⋊C4C22×D7312yes—
266C2×C22⋊C4—1462no—
267C2×C22⋊C4—1462no—
268C2×C42—731no—
269C2×C42—731no—
270C2×C42—731no—
271C2×C42—734no—
272C2×C42—734no—
273C2×C42—1462no—
274C2×C42—1462no—
275C2×C42C22×D7311yescharacteristic
276C4⋊C8—1464no—
277C22⋊C8—1464no—
278#97—22no—
279#97—1462no—
280#95—21no—
281#95—21no—
282#95—1462no—
283#95—1462no—
284#95—1461no—
285#95—1461no—
286C24—731no—
287C2×Q8—24no—
288C2×Q8—44no—
289C2×Q8—2924no—
290C2×Q8—1464no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—2922no—
294C22×C4—2922no—
295C22×C4—734no—
296C22×C4—734no—
297C22×C4—731no—
298C22×C4—731no—
299C22×C4—731no—
300C22×C4—732no—
301C22×C4—732no—
302C22×C4—1462no—
303C22×C4—1462no—
304C22×C4—1462no—
305C22×C4—1462no—
306C22×C4D4×D7311yescharacteristic
307C22×C4D4×D7311yescharacteristic
308C22×C4C23×D7311yescharacteristic
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—1462no—
313C2×C8—1462no—
314C2×C8—1462no—
315C4⋊C4—24no—
316C4⋊C4—22no—
317C4⋊C4—24no—
318C4⋊C4—734no—
319C4⋊C4—1468no—
320C4⋊C4—1468no—
321C4⋊C4—1464no—
322C4⋊C4—1464no—
323C4⋊C4—1462no—
324C4⋊C4C2×C4×D7314yes—
325C22⋊C4—2924no—
326C22⋊C4—1468no—
327C42—2924no—
328C42—734no—
329C42—734no—
330C42—732no—
331C42—732no—
332C42—1468no—
333C42C2×C4×D7312yes—
334C42D4×D7312yes—
335C23—732no—
336C23—1462no—
337C23—1462no—
338C23—1461no—
339C23—1461no—
340C23C2×D4×D7311yescharacteristic
341Q8—48no—
342Q8—2928no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—24no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—2924no—
351C2×C4—2924no—
352C2×C4—2924no—
353C2×C4—2922no—
354C2×C4—2922no—
355C2×C4—2922no—
356C2×C4—732no—
357C2×C4—732no—
358C2×C4—732no—
359C2×C4—1464no—
360C2×C4—1462no—
361C2×C4—1462no—
362C2×C4—1461no—
363C2×C4—1461no—
364C2×C4—1464no—
365C2×C4—1464no—
366C2×C4C22⋊C4×D7312yes—
367C2×C4C22⋊C4×D7312yes—
368C2×C4C22×C4×D7311yescharacteristic
369C2×C4C2×D4×D7311yescharacteristic
370C2×C4#1455663812yes—
371C2×C4#1455663912yes—
372C8—42no—
373C8—2922no—
374C22—2922no—
375C22—2922no—
376C22—1462no—
377C22—1462no—
378C22—1462no—
379C22C2×C22⋊C4×D7311yescharacteristic
380C22#1798915711yescharacteristic
381C22#1798916211yescharacteristic
382C22#1798938312yes—
383C22#1798938612yes—
384C4—22no—
385C4—22no—
386C4—44no—
387C4—82no—
388C4—2924no—
389C4—5842no—
390C4—1462no—
391C4—1462no—
392C4—1462no—
393C4#1798906312yes—
394C4#1798916012yes—
395C2—2922no—
396C2#2261251411yescharacteristic
397C2#2261844511yescharacteristic
398C2#2261844911yescharacteristic
399C2#2262116612yes—
400C2#2262117212yes—
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1993C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1993D73
hypocenterC73#21842
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
4. #22610905C2semidirect
5. #22610904C2semidirect
6. #22610903C2semidirect
7. #22610885C2semidirect
9. C73×#1993C2semidirect
11. #17989142C4semidirect
207. #1993D73semidirect
210. C73#21842semidirect

Maximal subgroups

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

subgroupindex
C2×#179891422
C2×#179886422
#226123242
#226109052
#226109042
#226109032
#226108852
#226100242
C73×#19932
#2184273