Finite Group Databasebeta

← #32984793

Subgroups — #32984793

Order 18688.

610 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
1C4×#14556580C211yesmaximal, characteristic
2#22610082C211yesmaximal, characteristic, complemented
3C4×#14556501C211yesmaximal, characteristic, complemented
4C2×Q8⋊#10596831C211yesmaximal, characteristic, complemented
5C2×#17988316C211yesmaximal, characteristic
6C2×#17988314C211yesmaximal, characteristic
7C2×Q8⋊C8×C73C211yesmaximal, characteristic, complemented
8C2×#14556580C411yescharacteristic
9C2×C4×D292C2211yescharacteristic
10C2×C4⋊#10596831C2211yescharacteristic
11C2×#14556520—22no—
12C2×#14556501—22no—
13C2×C4×#10596831C2211yescharacteristic
14#17988494C411yescharacteristic
15#17988488C411yescharacteristic
16#17988477—22no—
17#17988452C411yescharacteristic
18C4×#11924005—22no—
19C42×Dic73C2211yescharacteristic
20Q8⋊#10596831—22no—
21#17988316—22no—
22#17988314—22no—
23C2×C4×Q8×C73C2211yescharacteristic
24C2×C4⋊C8×C73C2211yescharacteristic
25C2×C4×C8×C73C2211yescharacteristic
26Q8⋊C8×C73—22no—
27C22×D292C2×C411yescharacteristic
28C22×C4×D73—21no—
29C22×#10596831—21no—
30C22×#10596831—21no—
31#14556580—22no—
32#14556580—22no—
33C4×D292—21no—
34C4×D292—21no—
35C4×D292—21no—
36C4×D292—21no—
37C2×C4⋊Dic73C2×C411yescharacteristic
38C2×#11924005—22no—
39C2×#11924005—22no—
40C2×#11924005—21no—
41C2×C4×Dic73C2×C411yescharacteristic
42C2×C4×Dic73C2×C411yescharacteristic
43C2×C4×Dic73D412yes—
44C2×C4×Dic73D412yes—
45C4⋊#10596831—21no—
46C4⋊#10596831—21no—
47#14556520—44no—
48#14556501—28no—
49C4×#10596831—21no—
50C4×#10596831D412yes—
51#14556498—22no—
52#14556498—22no—
53C22×Q8×C73C2×C411yescharacteristic
54C22×C8×C73—21no—
55C22×C8×C73—21no—
56C4×Q8×C73—21no—
57C4×Q8×C73—21no—
58C4×Q8×C73—21no—
59C4×Q8×C73—21no—
60C2×C4⋊C4×C73—21no—
61C2×C4⋊C4×C73C2×C411yescharacteristic
62C2×C42×C73—21no—
63C2×C42×C73C2311yescharacteristic
64C4⋊C8×C73—21no—
65C4⋊C8×C73—21no—
66C4×C8×C73—21no—
67C4×C8×C73D412yes—
68C23×D73—21no—
69C2×D292—21no—
70C2×D292—21no—
71C2×D292—21no—
72C2×D292—21no—
73C2×D292—21no—
74C2×D292M1612yes—
75C22×Dic73—21no—
76C22×Dic73C22⋊C412yes—
77C22×Dic73C22⋊C412yes—
78C2×C4×D73—41no—
79C2×C4×D73—41no—
80C2×C4×D73—42no—
81C2×C4×D73—42no—
82C2×#10596831—24no—
83C2×#10596831—22no—
84C2×#10596831—41no—
85C2×#10596831—42no—
86C4⋊Dic73—21no—
87C4⋊Dic73—21no—
88#11924005—28no—
89#11924005—41no—
90#11924005—41no—
91#11924005—44no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—22no—
97C4×Dic73—22no—
98C4×Dic73—24no—
99C2×Q8×C73—21no—
100C2×Q8×C73—21no—
101C2×Q8×C73—21no—
102C2×Q8×C73—21no—
103C2×Q8×C73—21no—
104C2×Q8×C73M1612yes—
105C22×C4×C73—21no—
106C22×C4×C73—21no—
107C22×C4×C73C22×C411yescharacteristic
108C22×C4×C73C2×D411yescharacteristic
109C22×C4×C73C2×D411yescharacteristic
110C2×C8×C73—24no—
111C2×C8×C73—22no—
112C2×C8×C73—41no—
113C2×C8×C73—42no—
114C4⋊C4×C73—21no—
115C4⋊C4×C73—21no—
116C4⋊C4×C73—41no—
117C4⋊C4×C73—41no—
118C42×C73—41no—
119C42×C73—41no—
120C42×C73C2×D411yescharacteristic
121C42×C73C2×D411yescharacteristic
122C42×C73#4111yescharacteristic
123C42×C73#4111yescharacteristic
124C23×C73C2×C22⋊C411yescharacteristic
125C22×D73—22no—
126C22×D73—41no—
127C22×D73—41no—
128C22×D73—42no—
129C22×D73—42no—
130Q8×C73—22no—
131Q8×C73—22no—
132Q8×C73—41no—
133Q8×C73—41no—
134C2×C4×C73—22no—
135C2×C4×C73—22no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—42no—
140C2×C4×C73C4×D411yescharacteristic
141C2×C4×C73C4×D411yescharacteristic
142C2×C4×C73#12111yescharacteristic
143C2×C4×C73#12111yescharacteristic
144C2×C4×C73#12411yescharacteristic
145C2×C4×C73#12711yescharacteristic
146C2×C4×C73C2×M1611yescharacteristic
147C2×C4×C73C2×M1611yescharacteristic
148C2×C4×C73#13111yescharacteristic
149C2×C4×C73#13111yescharacteristic
150C2×C4×C73AGL(1,ℤ/8)12yes—
151C2×C4×C73#13712yes—
152C2×Dic73—22no—
153C2×Dic73—22no—
154C2×Dic73—22no—
155C2×Dic73—22no—
156C2×Dic73—22no—
157C2×Dic73—41no—
158C2×Dic73—42no—
159C2×Dic73#10414yes—
160D292—22no—
161D292—22no—
162D292—41no—
163D292—41no—
164C4×D73—82no—
165C4×D73—81no—
166C4×D73—81no—
167C8×C73—24no—
168C8×C73—81no—
169#10596831—24no—
170#10596831—81no—
171C22×C73#39011yescharacteristic
172C22×C73#40711yescharacteristic
173C22×C73#40811yescharacteristic
174C22×C73#41712yes—
175C22×C73C2×#10412yes—
176C2×D73—42no—
177C2×D73—44no—
178C2×D73—81no—
179C2×D73—81no—
180C2×D73—82no—
181C4×C73—21no—
182C4×C73—21no—
183C4×C73—42no—
184C4×C73—81no—
185C4×C73#43511yescharacteristic
186C4×C73#43511yescharacteristic
187C4×C73#43511yescharacteristic
188C4×C73#43511yescharacteristic
189C4×C73#48912yes—
190C4×C73#49611yescharacteristic
191C4×C73#49711yescharacteristic
192Dic73—24no—
193Dic73—42no—
194Dic73—81no—
195#9646—731nomaximal, Sylow
196C2×C73#148312yes—
197C2×C73#148912yes—
198C2×C73#195511yescharacteristic
199C2×C73#195911yescharacteristic
200C2×C73#196211yescharacteristic
201D73—82no—
202C4×#124—731no—
203#1842—731no—
204C4×#97—731no—
205C2×Q8⋊C8—731no—
206C2×Q8⋊C8D7311yescharacteristic, complemented
207C2×D4⋊C8—731no—
208C2×D4⋊C8—731no—
209C73#964611yescharacteristic, complemented, Sylow
210C2×#124—731no—
211C2×C4×Q8C2×D7311yescharacteristic
212C2×C4×D4—731no—
213C2×C4⋊C8—731no—
214C2×C4⋊C8—1462no—
215C2×C4⋊C8C2×D7311yescharacteristic
216C2×#97—1462no—
217C2×C4×C8—731no—
218C2×C4×C8C2×D7311yescharacteristic
219#391—731no—
220#390—731no—
221#388—1462no—
222#382—731no—
223C4×C22⋊C4—1462no—
224C43—731no—
225Q8⋊C8—22no—
226Q8⋊C8—1462no—
227D4⋊C8—1462no—
228D4⋊C8—1462no—
229C22×Q8C4×D7311yescharacteristic
230C22×D4—731no—
231C23×C4—1461no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—1461no—
235C22×C8—1461no—
236#124—1462no—
237#124—1462no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×D4—1461no—
243C4×D4—1461no—
244C4×D4—1461no—
245C4×D4—1461no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—731no—
248C2×C4⋊C4C4×D7311yescharacteristic
249C2×C22⋊C4—1462no—
250C2×C22⋊C4—1461no—
251C2×C22⋊C4—1462no—
252C2×C42—21no—
253C2×C42—731no—
254C2×C42—731no—
255C2×C42—732no—
256C2×C42—732no—
257C2×C42C22×D7311yescharacteristic
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—2924no—
261C4⋊C8—1461no—
262C4⋊C8—1461no—
263#97—1468no—
264C4×C8—21no—
265C4×C8—732no—
266C4×C8—1461no—
267C4×C8C22⋊D7312yes—
268#95—1462no—
269#95—1462no—
270C24—1461no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8#1192401112yes—
277C2×D4—732no—
278C2×D4—1461no—
279C2×D4—1461no—
280C2×D4—1461no—
281C2×D4—1461no—
282C2×D4—1461no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—2921no—
286C22×C4—2921no—
287C22×C4—2922no—
288C22×C4—2922no—
289C22×C4—732no—
290C22×C4—732no—
291C22×C4—1461no—
292C22×C4C2×C4×D7311yescharacteristic
293C22×C4D4×D7311yescharacteristic
294C22×C4D4×D7311yescharacteristic
295C2×C8—24no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—42no—
299C2×C8—2921no—
300C2×C8—2922no—
301C2×C8—1464no—
302C2×C8—1462no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—1461no—
308C4⋊C4—1461no—
309C22⋊C4—2924no—
310C22⋊C4—2921no—
311C22⋊C4—2921no—
312C22⋊C4—1468no—
313C42—41no—
314C42—41no—
315C42—1464no—
316C42—1461no—
317C42—1461no—
318C42—1461no—
319C42—1461no—
320C42—1462no—
321C42—1462no—
322C42D4×D7311yescharacteristic
323C42C2×C22⋊D7311yescharacteristic
324C42#1192402711yescharacteristic
325C42#1192402811yescharacteristic
326C23—2921no—
327C23—2921no—
328C23—2922no—
329C23—2922no—
330C23—1462no—
331C23C22⋊C4×D7311yescharacteristic
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336D4—2921no—
337D4—2921no—
338D4—1462no—
339D4—1462no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—2921no—
347C2×C4—2922no—
348C2×C4—5842no—
349C2×C4—5841no—
350C2×C4—5841no—
351C2×C4—734no—
352C2×C4—1462no—
353C2×C4—1462no—
354C2×C4—1462no—
355C2×C4—1462no—
356C2×C4—1462no—
357C2×C4#1455655111yescharacteristic
358C2×C4C4×C22⋊D7311yescharacteristic
359C2×C4#1455656311yescharacteristic
360C2×C4#1455656411yescharacteristic
361C2×C4#1455657711yescharacteristic
362C2×C4#1455658711yescharacteristic
363C2×C4M16×D7311yescharacteristic
364C2×C4C2×#1192401111yescharacteristic
365C2×C4#1455659711yescharacteristic
366C2×C4#1455659911yescharacteristic
367C2×C4#1455661812yes—
368C2×C4#1455662312yes—
369C8—24no—
370C8—81no—
371C8—5841no—
372C8—1464no—
373C22—2922no—
374C22—2924no—
375C22—5841no—
376C22—5841no—
377C22—5842no—
378C22#1798848711yescharacteristic
379C22#1798854911yescharacteristic
380C22#1798855211yescharacteristic
381C22#1798858712yes—
382C22#104×D7312yes—
383C4—21no—
384C4—21no—
385C4—42no—
386C4—81no—
387C4—2922no—
388C4—5841no—
389C4—1464no—
390C4#1798865511yescharacteristic
391C4#1798865611yescharacteristic
392C4#1798865811yescharacteristic
393C4#1798866111yescharacteristic
394C4#1798894812yes—
395C4#1798897311yescharacteristic
396C4#1798898011yescharacteristic
397C2—5842no—
398C2#2260834312yes—
399C2#2260836912yes—
400C2#2261072711yescharacteristic
401C2#2261074411yescharacteristic
402C2#2261075711yescharacteristic
subgroupG/H
centerC22×C4D4×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC2×Q8⋊C8×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC22×D292C2×C4
cosocleC2×C42×C73C23
hypercenterC2×Q8⋊C8D73
hypocenterC73#9646
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #22610082C2semidirect
3. C4×#14556501C2semidirect
4. C2×Q8⋊#10596831C2semidirect
7. C2×Q8⋊C8×C73C2semidirect
206. C2×Q8⋊C8D73semidirect
209. C73#9646semidirect

Maximal subgroups

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

subgroupindex
C4×#145565802
#226100822
C4×#145565012
C2×Q8⋊#105968312
C2×#179883162
C2×#179883142
C2×Q8⋊C8×C732
#964673