Finite Group Databasebeta

← #32981325

Subgroups — #32981325

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×#14556570C211yesmaximal, characteristic
2#22609911C211yesmaximal, characteristic
3C2×#17988319C212yesmaximal, complemented
4#22607771C212yesmaximal, complemented
5C2×#431×C73C211yesmaximal, characteristic
6C2×#14556570C411yescharacteristic
7C2×C4×Dic146C2211yescharacteristic
8C2×C4⋊#10596831C2212yes—
9C2×C22⋊#10596831—21no—
10#17988493C411yescharacteristic
11#17988485C411yescharacteristic
12#17988471—21no—
13#17988460—21no—
14#17988447C411yescharacteristic
15C4×#11924007—21no—
16C4×C4⋊Dic73C2211yescharacteristic
17C4×C22⋊Dic73—21no—
18#17988342—21no—
19#17988319—24no—
20C22×C42×C73C2211yescharacteristic
21#431×C73—24no—
22C2×C4⋊C8×C73—21no—
23C2×C22⋊C8×C73—21no—
24C2×C4×C8×C73C2212yes—
25C22×Dic146C2×C411yescharacteristic
26C22×#10596831—22no—
27#14556570—22no—
28#14556570C814yescomplemented
29C4×Dic146—22no—
30C4×Dic146—22no—
31C2×C4⋊Dic73C2×C411yescharacteristic
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×C22⋊Dic73—21no—
38C2×C22⋊Dic73—21no—
39C2×C4×Dic73—21no—
40C2×C4×Dic73—21no—
41C4⋊#10596831—22no—
42C4⋊#10596831—22no—
43C22⋊#10596831—42no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49C23×C4×C73C2×C411yescharacteristic
50C23×C4×C73D411yescharacteristic
51C23×C4×C73D411yescharacteristic
52C22×C8×C73—22no—
53C2×C42×C73—22no—
54C2×C42×C73—22no—
55C2×C42×C73C2×C411yescharacteristic
56C2×C42×C73D411yescharacteristic
57C2×C42×C73D411yescharacteristic
58C2×C42×C73C2311yescharacteristic
59C4⋊C8×C73—24no—
60C22⋊C8×C73—24no—
61C4×C8×C73—22no—
62C4×C8×C73D414yes—
63C2×Dic146—22no—
64C2×Dic146—22no—
65C2×Dic146—21no—
66C2×Dic146C2×C812yes—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73—21no—
71C2×#10596831—42no—
72C2×#10596831—42no—
73C2×#10596831—42no—
74C4⋊Dic73—21no—
75C4⋊Dic73—22no—
76C4⋊Dic73—22no—
77C4⋊Dic73C2×C812yes—
78#11924007—24no—
79#11924007—42no—
80#11924007—41no—
81#11924007—41no—
82C22⋊Dic73—24no—
83C22⋊Dic73—42no—
84C4×Dic73—42no—
85C4×Dic73—41no—
86C4×Dic73—41no—
87C24×C73C22⋊C411yescharacteristic
88C22×C4×C73—22no—
89C22×C4×C73—22no—
90C22×C4×C73—21no—
91C22×C4×C73—22no—
92C22×C4×C73—21no—
93C22×C4×C73—21no—
94C22×C4×C73—21no—
95C22×C4×C73—22no—
96C22×C4×C73—41no—
97C22×C4×C73—41no—
98C22×C4×C73C22⋊C411yescharacteristic
99C22×C4×C73C22⋊C411yescharacteristic
100C22×C4×C73C22⋊C411yescharacteristic
101C22×C4×C73C2×C812yes—
102C22×C4×C73M1612yes—
103C22×C4×C73C22×C411yescharacteristic
104C22×C4×C73C2×D411yescharacteristic
105C22×C4×C73C2×D411yescharacteristic
106C2×C8×C73—24no—
107C2×C8×C73—42no—
108C2×C8×C73—42no—
109C42×C73—22no—
110C42×C73—21no—
111C42×C73—22no—
112C42×C73—21no—
113C42×C73C2×D412yes—
114C42×C73#4112yes—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73C22⋊C812yes—
122C23×C73C2×C22⋊C411yescharacteristic
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—24no—
128C2×C4×C73—24no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—42no—
136C2×C4×C73—42no—
137C2×C4×C73—42no—
138C2×C4×C73—42no—
139C2×C4×C73C22⋊C812yes—
140C2×C4×C73C4×D412yes—
141C2×C4×C73#12011yescharacteristic
142C2×C4×C73#12112yes—
143C2×C4×C73#12311yescharacteristic
144C2×C4×C73C22×C811yescharacteristic
145C2×C4×C73C2×M1611yescharacteristic
146C2×C4×C73#13112yes—
147C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C73#13712yes—
149C2×C4×C73#13711yescharacteristic
150C2×Dic73—22no—
151C2×Dic73—22no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—41no—
155C2×Dic73—41no—
156C2×Dic73—41no—
157C2×Dic73—41no—
158C2×Dic73—41no—
159C2×Dic73—41no—
160C2×Dic73—41no—
161C2×Dic73—41no—
162Dic146—24no—
163Dic146—42no—
164C8×C73—44no—
165#10596831—82no—
166C22×C73—22no—
167C22×C73—22no—
168C22×C73—22no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73—41no—
172C22×C73—41no—
173C22×C73#38611yescharacteristic
174C22×C73C2×C22⋊C811yescharacteristic
175C22×C73#40811yescharacteristic
176C22×C73#41711yescharacteristic
177C22×C73#41911yescharacteristic
178C22×C73#42111yescharacteristic
179C22×C73#42111yescharacteristic
180C4×C73—22no—
181C4×C73—21no—
182C4×C73—21no—
183C4×C73—41no—
184C4×C73—41no—
185C4×C73C8×D412yes—
186C4×C73#43512yes—
187C4×C73#46812yes—
188C4×C73#47012yes—
189Dic73—42no—
190Dic73—42no—
191Dic73—81no—
192Dic73—81no—
193#9073—731nomaximal, Sylow
194C2×C73—42no—
195C2×C73#147711yescharacteristic
196C2×C73#147911yescharacteristic
197C2×C73#149511yescharacteristic
198C2×C73#149711yescharacteristic
199C2×C73#186911yescharacteristic
200C2×C73#189411yescharacteristic
201C2×C73#189711yescharacteristic
202C2×#431D7311yescharacteristic
203C4×C22⋊Q8—731no—
204#1797—731no—
205C2×Q8⋊C8—732no—
206#1279—732no—
207C73#907311yescharacteristic, complemented, Sylow
208C2×C22⋊Q8—731no—
209C2×C4×Q8—731no—
210C22×C42C2×D7311yescharacteristic
211#431—24no—
212C2×C4⋊C8—21no—
213C2×C4⋊C8—732no—
214C2×C22⋊C8—21no—
215C2×C22⋊C8—1461no—
216C2×C4×C8C2×D7312yes—
217#391—731no—
218#389—731no—
219#387—1461no—
220#385—1461no—
221#380—731no—
222C4×C4⋊C4—731no—
223C4×C4⋊C4—1461no—
224C4×C22⋊C4—1461no—
225#336—1461no—
226Q8⋊C8—1464no—
227C22×Q8—731no—
228C23×C4C4×D7311yescharacteristic
229C23×C4D29211yescharacteristic
230C23×C4C22⋊D7311yescharacteristic
231C22×C8—22no—
232C22×C8—1462no—
233C22⋊Q8—734no—
234C22⋊Q8—1462no—
235C4×Q8—1462no—
236C4×Q8—1462no—
237C2×C4⋊C4—731no—
238C2×C4⋊C4—731no—
239C2×C4⋊C4—731no—
240C2×C4⋊C4—1461no—
241C2×C4⋊C4—1461no—
242C2×C4⋊C4—1461no—
243C2×C22⋊C4—1461no—
244C2×C22⋊C4—1461no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—1461no—
248C2×C42—1461no—
249C2×C42C4×D7311yescharacteristic
250C2×C42D29211yescharacteristic
251C2×C42C22⋊D7311yescharacteristic
252C2×C42C22×D7311yescharacteristic
253C4⋊C8—24no—
254C4⋊C8—1462no—
255C4⋊C8—1462no—
256C22⋊C8—24no—
257C22⋊C8—2922no—
258C4×C8—22no—
259C4×C8C22⋊D7314yes—
260#95—1461no—
261#95—1461no—
262#95—1461no—
263#95—1461no—
264#95—1461no—
265C24#1192400511yescharacteristic
266C2×Q8—732no—
267C2×Q8—1462no—
268C2×Q8—1462no—
269C2×Q8—1461no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—1461no—
281C22×C4—1461no—
282C22×C4—1461no—
283C22×C4—1461no—
284C22×C4#1192400511yescharacteristic
285C22×C4#1192400511yescharacteristic
286C22×C4#1192400511yescharacteristic
287C22×C4C8×D7312yes—
288C22×C4#1192401112yes—
289C22×C4C2×C4×D7311yescharacteristic
290C22×C4C2×C22⋊D7311yescharacteristic
291C22×C4C2×D29211yescharacteristic
292C2×C8—24no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—2922no—
296C2×C8—2922no—
297C2×C8—2922no—
298C4⋊C4—2922no—
299C4⋊C4—2921no—
300C4⋊C4—2921no—
301C4⋊C4—732no—
302C4⋊C4—1462no—
303C4⋊C4—1462no—
304C4⋊C4—1464no—
305C4⋊C4—1461no—
306C22⋊C4—2922no—
307C22⋊C4—1464no—
308C42—22no—
309C42—21no—
310C42—22no—
311C42—21no—
312C42—2922no—
313C42—2921no—
314C42—2921no—
315C42C2×C22⋊D7312yes—
316C42#1192402812yes—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23#1455650312yes—
324C23C2×#1192400511yescharacteristic
325Q8—2922no—
326Q8—1464no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—2921no—
344C2×C4—2921no—
345C2×C4—2921no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—2921no—
349C2×C4—2921no—
350C2×C4—2921no—
351C2×C4—2921no—
352C2×C4—2921no—
353C2×C4—1462no—
354C2×C4—1462no—
355C2×C4#1455650312yes—
356C2×C4C4×C22⋊D7312yes—
357C2×C4#1455656011yescharacteristic
358C2×C4#1455656512yes—
359C2×C4#1455657411yescharacteristic
360C2×C4C2×C8×D7311yescharacteristic
361C2×C4C2×#1192401111yescharacteristic
362C2×C4#1455659712yes—
363C2×C4#1455661911yescharacteristic
364C2×C4#1455662412yes—
365C2×C4#1455662411yescharacteristic
366C8—44no—
367C8—5842no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22#1798846611yescharacteristic
376C22C2×#1455650311yescharacteristic
377C22#1798855311yescharacteristic
378C22#1798858911yescharacteristic
379C22#1798859711yescharacteristic
380C22#1798860511yescharacteristic
381C22#1798860511yescharacteristic
382C4—22no—
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—2922no—
388C4—2922no—
389C4—5841no—
390C4—5841no—
391C4C8×C22⋊D7312yes—
392C4#1798865812yes—
393C4#1798883312yes—
394C4#1798884512yes—
395C2—42no—
396C2#2260831911yescharacteristic
397C2#2260832711yescharacteristic
398C2#2260839711yescharacteristic
399C2#2260840511yescharacteristic
400C2#2261022311yescharacteristic
401C2#2261036411yescharacteristic
402C2#2261037911yescharacteristic
subgroupG/H
centerC22×C4C2×D292
commutatorC2×C4×C73C22×C8
FrattiniC2×C42C22×D73
FittingC2×#431×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C42×C73C23
hypercenterC2×#431D73
hypocenterC73#9073
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. C2×#17988319C2semidirect
4. #22607771C2semidirect
28. #14556570C8semidirect
207. C73#9073semidirect

Maximal subgroups

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

subgroupindex
C4×#145565702
#226099112
C2×#179883192
#226077712
C2×#431×C732
#907373