Finite Group Databasebeta

← #33089656

Subgroups — #33089656

Order 18688.

1638 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989138C211yesmaximal, characteristic
2C2×#17988587C214yesmaximal, complemented
3C2×#17988539C211yesmaximal, characteristic, complemented
4#382×D73C211yesmaximal, characteristic, complemented
5#22610755C211yesmaximal, characteristic, complemented
6#22610754C211yesmaximal, characteristic, complemented
7#22610752C211yesmaximal, characteristic, complemented
8#22610739C214yesmaximal, complemented
9C73×#1960C211yesmaximal, characteristic, complemented
10C22×#11924029C2212yes—
11C22×#11924011C2212yes—
12#17989138—24no—
13#17989138C418yescomplemented
14C2×#14556588C2211yescharacteristic
15C2×#14556580C2212yes—
16C2×#14556566—22no—
17C2×#14556553—22no—
18C2×C4⋊C4×D73C2212yes—
19C2×C42×D73C2211yescharacteristic
20#17988587—216no—
21C2×#14556515C2214yes—
22C2×#14556513C2214yes—
23C2×#14556511C2214yes—
24#17988539—24no—
25C2×#14556502C2211yescharacteristic
26C2×C8×Dic73C2212yes—
27#17988453C2211yescharacteristic
28#17988452C2212yes—
29#17988451—22no—
30#95×D73—22no—
31C2×C4⋊Q8×C73C2211yescharacteristic
32C2×#103×C73C2214yes—
33C2×#97×C73C2211yescharacteristic
34#382×C73C2211yescharacteristic
35C2×#11924029—24no—
36C2×#11924029—28no—
37C2×#11924029—28no—
38C2×#11924029C2×C418yes—
39C22×D292—22no—
40C22×D292—22no—
41C22×D292C2312yes—
42C22×C4×D73—22no—
43C22×C4×D73—22no—
44C22×C4×D73D412yes—
45C22×C4×D73C2311yescharacteristic
46C2×#11924011—24no—
47C2×#11924011—24no—
48C2×#11924011D418yescomplemented
49C22×#10596831C2312yes—
50#14556588—22no—
51#14556588C2×C414yescomplemented
52#14556580—24no—
53#14556580C2×C418yescomplemented
54#14556566—216no—
55#14556553—216no—
56C2×C4⋊Dic73C2312yes—
57C2×#11924007—22no—
58C4⋊C4×D73—28no—
59C2×#11924005—24no—
60C2×C4×Dic73D412yes—
61C2×C4×Dic73C2311yescharacteristic
62C42×D73C2×C414yes—
63C42×D73D414yes—
64#14556515—28no—
65#14556513—28no—
66#14556511—28no—
67#14556502—22no—
68C8×Dic73—24no—
69#14556498—24no—
70#14556498—22no—
71C22×Q8×C73C2312yes—
72C22×C8×C73C2312yes—
73C4⋊Q8×C73—22no—
74C4⋊Q8×C73C2×C414yescomplemented
75C2×C4⋊C4×C73—22no—
76C2×C4⋊C4×C73C2312yes—
77C2×C42×C73C2311yescharacteristic
78#103×C73—28no—
79#97×C73—22no—
80#95×C73—22no—
81C23×D73—22no—
82C23×D73C2×D411yescharacteristic
83#11924029—232no—
84#11924029—416no—
85C2×D292—24no—
86C2×D292—24no—
87C2×D292—28no—
88C2×D292—28no—
89C2×D292—22no—
90C2×D292—48no—
91C2×D292—44no—
92C2×D292—44no—
93C2×D292C22×C414yes—
94C22×Dic73—22no—
95C22×Dic73C2×D412yes—
96C22×Dic73C2×D411yescharacteristic
97C2×C4×D73—28no—
98C2×C4×D73—44no—
99C2×C4×D73—44no—
100C2×C4×D73—44no—
101C2×C4×D73—48no—
102C2×C4×D73—44no—
103C2×C4×D73C22⋊C418yes—
104C2×C4×D73C22×C412yes—
105C2×C4×D73C2×D414yes—
106C2×C4×D73C2×D412yes—
107C2×C4×D73#4114yes—
108#11924011—216no—
109C2×#10596831—22no—
110C2×#10596831—22no—
111C2×#10596831C2×D414yes—
112C4⋊Dic73—24no—
113#11924007—44no—
114#11924005—216no—
115C4×Dic73C22⋊C418yes—
116C4×Dic73C22×C412yes—
117C4×Dic73C2×D412yes—
118C2×Q8×C73—22no—
119C2×Q8×C73—24no—
120C2×Q8×C73—24no—
121C2×Q8×C73C22×C414yes—
122C22×C4×C73—22no—
123C22×C4×C73—22no—
124C22×C4×C73C2×D412yes—
125C22×C4×C73C2411yescharacteristic
126C2×C8×C73—22no—
127C2×C8×C73—22no—
128C2×C8×C73C2×D414yes—
129C4⋊C4×C73—28no—
130C4⋊C4×C73—24no—
131C42×C73C22×C412yes—
132C42×C73C2×D412yes—
133C23×C73C22×D411yescharacteristic
134C22×D73—24no—
135C22×D73—24no—
136C22×D73—42no—
137C22×D73—42no—
138C22×D73—48no—
139C22×D73C2×C22⋊C412yes—
140C22×D73#12412yes—
141C22×D73#12712yes—
142Q8×C73—28no—
143Q8×C73—44no—
144C2×C4×C73—24no—
145C2×C4×C73—24no—
146C2×C4×C73—42no—
147C2×C4×C73—42no—
148C2×C4×C73—42no—
149C2×C4×C73—44no—
150C2×C4×C73C2×C22⋊C414yes—
151C2×C4×C73C23×C411yescharacteristic
152C2×C4×C73C22×D412yes—
153C2×C4×C73C22×D411yescharacteristic
154C2×C4×C73C2×#4112yes—
155C2×Dic73—24no—
156C2×Dic73—42no—
157C2×Dic73—44no—
158C2×Dic73C2×C22⋊C414yes—
159C2×Dic73C2×C22⋊C412yes—
160C2×Dic73#12412yes—
161C2×Dic73#12712yes—
162D292—28no—
163D292—416no—
164D292—416no—
165D292—44no—
166C4×D73—48no—
167C4×D73—416no—
168C4×D73—88no—
169C4×D73C4×D418yes—
170C4×D73#12118yes—
171C8×C73—24no—
172#10596831—24no—
173C22×C73C22×C22⋊C411yescharacteristic
174C22×C73C2×#12411yescharacteristic
175C22×C73C2×#12711yescharacteristic
176C22×C73#57514yes—
177C2×D73—24no—
178C2×D73—24no—
179C2×D73—24no—
180C2×D73—48no—
181C2×D73—44no—
182C2×D73—84no—
183C2×D73—84no—
184C2×D73#39014yes—
185C4×C73—24no—
186C4×C73—44no—
187C4×C73—82no—
188C4×C73C2×C4×D412yes—
189C4×C73C2×#12112yes—
190Dic73—24no—
191Dic73—82no—
192Dic73#39014yes—
193#21201—731nomaximal, Sylow
194C2×C73C2×#39011yescharacteristic
195C2×C73#289612yes—
196C2×C73#314212yes—
197C2×C73#315312yes—
198D73—24no—
199D73—84no—
200C2×#532—731no—
201C2×#417—734no—
202C2×C4×M16—731no—
203C2×#382—731no—
204#1961—731no—
205#1961—731no—
206#1960—731no—
207#1960D7311yescharacteristic, complemented
208#1958—734no—
209C73#2120111yescharacteristic, complemented, Sylow
210C22×#41—732no—
211C22×M16—732no—
212#532—738no—
213#532—1464no—
214C2×C4⋊Q8C2×D7311yescharacteristic
215C2×#127—731no—
216C2×#124—732no—
217C2×#121—1462no—
218C2×C4×D4—1462no—
219C22×C4⋊C4—732no—
220C22×C42—731no—
221#417—14616no—
222C2×#103—734no—
223C2×#103C2×D7314yes—
224C2×#102—734no—
225C2×#102—734no—
226C4×M16—1464no—
227C2×#97—731no—
228C2×#97C2×D7311yescharacteristic
229C2×C4×C8—732no—
230#382—732no—
231#382—731no—
232#382—1462no—
233#382C2×D7311yescharacteristic
234C2×#95—1462no—
235C2×#41—738no—
236C2×#41—1468no—
237C2×#41—1468no—
238C2×#41—1464no—
239C22×Q8C22×D7312yes—
240C22×D4—732no—
241C22×D4—1462no—
242C22×D4—1462no—
243C23×C4—732no—
244C23×C4—731no—
245C23×C4—1462no—
246C23×C4—1462no—
247C2×M16—738no—
248C2×M16—1464no—
249C2×M16—1464no—
250C22×C8—732no—
251C22×C8C22×D7312yes—
252C4⋊Q8—22no—
253C4⋊Q8C4×D7314yescomplemented
254#127—734no—
255#127—1462no—
256#124—738no—
257#124—1464no—
258#121—14616no—
259C4×D4—14616no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—732no—
262C2×C4⋊C4—1468no—
263C2×C4⋊C4—1462no—
264C2×C4⋊C4C22×D7312yes—
265C2×C22⋊C4—1464no—
266C2×C42—732no—
267C2×C42—731no—
268C2×C42—734no—
269C2×C42—734no—
270C2×C42C22×D7311yescharacteristic
271#103—28no—
272#103—1468no—
273#102—1468no—
274#102—1468no—
275#97—22no—
276#97—1462no—
277C4×C8—1464no—
278#95—22no—
279#95—1464no—
280#95—1462no—
281C24—731no—
282C24—1462no—
283#41—29216no—
284#41—14632no—
285C2×Q8—22no—
286C2×Q8—24no—
287C2×Q8—24no—
288C2×Q8C2×C4×D7314yes—
289C2×D4—2928no—
290C2×D4—2924no—
291C2×D4—2924no—
292C2×D4—734no—
293C2×D4—1468no—
294C2×D4—1468no—
295C2×D4—1462no—
296C2×D4—1464no—
297C2×D4—1464no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—2924no—
301C22×C4—2924no—
302C22×C4—2924no—
303C22×C4—2924no—
304C22×C4—2928no—
305C22×C4—738no—
306C22×C4—731no—
307C22×C4—732no—
308C22×C4—732no—
309C22×C4—734no—
310C22×C4—734no—
311C22×C4—732no—
312C22×C4—1468no—
313C22×C4—1462no—
314C22×C4D4×D7312yes—
315C22×C4C23×D7311yescharacteristic
316M16—14616no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—734no—
320C2×C8—1462no—
321C2×C8—1462no—
322C2×C8D4×D7314yes—
323C4⋊C4—28no—
324C4⋊C4—24no—
325C4⋊C4—2924no—
326C4⋊C4—1464no—
327C22⋊C4—14616no—
328C42—738no—
329C42—732no—
330C42—732no—
331C42C2×C4×D7312yes—
332C42D4×D7312yes—
333C23—2922no—
334C23—2928no—
335C23—2922no—
336C23—732no—
337C23—732no—
338C23—732no—
339C23—1464no—
340C23—1464no—
341C23C2×D4×D7311yescharacteristic
342Q8—28no—
343Q8—44no—
344D4—29216no—
345D4—29216no—
346D4—2924no—
347D4—1468no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—2928no—
355C2×C4—29216no—
356C2×C4—2922no—
357C2×C4—2924no—
358C2×C4—5848no—
359C2×C4—732no—
360C2×C4—732no—
361C2×C4—732no—
362C2×C4—738no—
363C2×C4—738no—
364C2×C4—734no—
365C2×C4—1464no—
366C2×C4C22⋊C4×D7314yes—
367C2×C4C22×C4×D7311yescharacteristic
368C2×C4C2×D4×D7312yes—
369C2×C4C2×D4×D7311yescharacteristic
370C2×C4#41×D7312yes—
371C8—24no—
372C8—1464no—
373C22—2928no—
374C22—2924no—
375C22—5844no—
376C22—5844no—
377C22—734no—
378C22—1464no—
379C22—1464no—
380C22—1464no—
381C22C2×C22⋊C4×D7311yescharacteristic
382C22#124×D7311yescharacteristic
383C22#127×D7311yescharacteristic
384C22#1798938614yes—
385C4—24no—
386C4—44no—
387C4—82no—
388C4—5842no—
389C4—734no—
390C4—1464no—
391C4C4×D4×D7312yes—
392C4#121×D7312yes—
393C2—5844no—
394C2—1464no—
395C2#390×D7311yescharacteristic
396C2#2261844912yes—
397C2#2262033312yes—
398C2#2262039412yes—
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1960C2
socleC23×C73C22×D4
prime radicalC2×#17989138C2
cosocleC22×C4×C73C24
hypercenter#1960D73
hypocenterC73#21201
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
2. C2×#17988587C2semidirect
3. C2×#17988539C2semidirect
4. #382×D73C2semidirect
5. #22610755C2semidirect
6. #22610754C2semidirect
7. #22610752C2semidirect
8. #22610739C2semidirect
9. C73×#1960C2semidirect
13. #17989138C4semidirect
48. C2×#11924011D4semidirect
51. #14556588C2×C4semidirect
53. #14556580C2×C4semidirect
74. C4⋊Q8×C73C2×C4semidirect
207. #1960D73semidirect
209. C73#21201semidirect
253. C4⋊Q8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891382
C2×#179885872
C2×#179885392
#382×D732
#226107552
#226107542
#226107522
#226107392
C73×#19602
#2120173