Finite Group Databasebeta

← #33004663

Subgroups — #33004663

Order 18688.

492 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22615127C211yesmaximal, characteristic
2#22609919C211yesmaximal, characteristic
3#22608055C212yesmaximal
4#22608055C212yesmaximal
5C4×#99×C73C211yesmaximal, characteristic
6C2×#14556583C411yescharacteristic, complemented
7C2×#14556506C2212yes—
8#17988510—21no—
9#17988510—21no—
10#17988490C2211yescharacteristic
11#17988490C2211yescharacteristic
12#17988460—21no—
13#17988460—21no—
14#17988456C411yescharacteristic, complemented
15#17988452C411yescharacteristic, complemented
16#17988447—21no—
17C4×C4⋊Dic73C411yescharacteristic, complemented
18#17988354—21no—
19C2×C4×D4×C73C2211yescharacteristic
20C2×#99×C73C2212yes—
21C4×C22⋊C4×C73—21no—
22#342×C73—21no—
23#14556583—41no—
24#14556583—41no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73—41no—
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×C22⋊Dic73—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—22no—
36C2×C22⋊Dic73—21no—
37C2×C22⋊Dic73—21no—
38C2×C4×Dic73C2×C411yescharacteristic
39C2×C4×Dic73C2×C411yescharacteristic
40#14556506—24no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—41no—
45C22×D4×C73C2311yescharacteristic
46C23×C4×C73D411yescharacteristic
47C23×C4×C73D411yescharacteristic
48C4×D4×C73—41no—
49C4×D4×C73—41no—
50C2×C4⋊C4×C73C2×C411yescharacteristic
51C2×C22⋊C4×C73—22no—
52C2×C22⋊C4×C73D411yescharacteristic
53C2×C22⋊C4×C73D411yescharacteristic
54C2×C42×C73—41no—
55C2×C42×C73C2×C411yescharacteristic
56#99×C73—22no—
57#99×C73Q814yes—
58#95×C73—41no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—42no—
64C4⋊Dic73—42no—
65C4⋊Dic73—41no—
66C4⋊Dic73—41no—
67C4⋊Dic73—82no—
68#11924007—42no—
69#11924007—41no—
70#11924007—41no—
71#11924007—81no—
72#11924007—81no—
73C22⋊Dic73—42no—
74C22⋊Dic73—42no—
75C22⋊Dic73—42no—
76C22⋊Dic73—42no—
77C22⋊Dic73—81no—
78C22⋊Dic73—81no—
79C4×Dic73—41no—
80C4×Dic73—41no—
81C24×C73C2×D411yescharacteristic
82C24×C73C2×D411yescharacteristic
83C2×D4×C73—41no—
84C2×D4×C73—41no—
85C2×D4×C73C2×Q812yes—
86C2×D4×C73#4112yes—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—42no—
92C22×C4×C73—81no—
93C22×C4×C73—81no—
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22⋊C411yescharacteristic
96C22×C4×C73C22⋊C411yescharacteristic
97C22×C4×C73C22⋊C411yescharacteristic
98C22×C4×C73C22×C411yescharacteristic
99C4⋊C4×C73—41no—
100C22⋊C4×C73—24no—
101C22⋊C4×C73—41no—
102C22⋊C4×C73—41no—
103C22⋊C4×C73—42no—
104C42×C73—21no—
105C42×C73—21no—
106C42×C73—82no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—41no—
112C23×C73—41no—
113C23×C73—41no—
114C23×C73—41no—
115C23×C73C2×C22⋊C411yescharacteristic
116C23×C73C22⋊Q812yes—
117C23×C73#12411yescharacteristic
118C23×C73C4⋊Q811yescharacteristic
119D4×C73—42no—
120D4×C73—42no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—41no—
127C2×C4×C73—42no—
128C2×C4×C73—42no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—44no—
133C2×C4×C73—81no—
134C2×C4×C73—81no—
135C2×C4×C73—82no—
136C2×C4×C73—82no—
137C2×C4×C73#9911yescharacteristic
138C2×C4×C73#9911yescharacteristic
139C2×C4×C73C4×Q812yes—
140C2×Dic73—22no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152C2×Dic73—82no—
153C2×Dic73—82no—
154C2×Dic73—82no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—22no—
159C22×C73—21no—
160C22×C73—42no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—81no—
168C22×C73—81no—
169C22×C73#39111yescharacteristic
170C22×C73C2×#9911yescharacteristic
171C22×C73#41011yescharacteristic
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—22no—
175C4×C73—41no—
176C4×C73—41no—
177C4×C73—41no—
178C4×C73—84no—
179Dic73—42no—
180Dic73—81no—
181Dic73—81no—
182Dic73—81no—
183Dic73—162no—
184#13300—731nomaximal, Sylow
185C2×C73—21no—
186C2×C73—21no—
187C2×C73—41no—
188C2×C73—42no—
189C2×C73—41no—
190C2×C73#199611yescharacteristic
191C2×C73#212611yescharacteristic
192C2×C73#212711yescharacteristic
193#2566—731no—
194#1799—731no—
195C4×#99D7311yescharacteristic
196#1393—732no—
197#1393—732no—
198C73#1330011yescharacteristic, complemented, Sylow
199C2×#125—731no—
200C2×C4×D4C2×D7311yescharacteristic
201C2×#99—732no—
202C2×#99C2×D7312yes—
203#396—1461no—
204#396—1461no—
205#390—731no—
206#390—731no—
207#385—1461no—
208#385—1461no—
209#384—731no—
210#382—731no—
211#380—1461no—
212C4×C4⋊C4—731no—
213C4×C22⋊C4—21no—
214#342—21no—
215#342—1461no—
216C22×D4C22×D7311yescharacteristic
217C23×C4D29211yescharacteristic
218C23×C4C22⋊D7311yescharacteristic
219#125—2921no—
220#125—2921no—
221C4×D4—41no—
222C4×D4—41no—
223C2×C4⋊C4—2921no—
224C2×C4⋊C4—731no—
225C2×C4⋊C4—731no—
226C2×C4⋊C4—1461no—
227C2×C4⋊C4—1461no—
228C2×C4⋊C4—1461no—
229C2×C4⋊C4—1461no—
230C2×C4⋊C4—1461no—
231C2×C4⋊C4C4×D7311yescharacteristic
232C2×C22⋊C4—22no—
233C2×C22⋊C4—1462no—
234C2×C22⋊C4—1461no—
235C2×C22⋊C4—1461no—
236C2×C22⋊C4—1461no—
237C2×C22⋊C4—1461no—
238C2×C22⋊C4D29211yescharacteristic
239C2×C22⋊C4C22⋊D7311yescharacteristic
240C2×C42—41no—
241C2×C42—731no—
242C2×C42—731no—
243C2×C42C4×D7311yescharacteristic
244#99—22no—
245#99—1464no—
246#99Dic14614yes—
247#95—41no—
248#95—2921no—
249#95—1461no—
250#95—1461no—
251#95—1461no—
252C24C2×C22⋊D7311yescharacteristic
253C24C2×D29211yescharacteristic
254C2×D4—41no—
255C2×D4—41no—
256C2×D4C2×Dic14612yes—
257C2×D4#1192402812yes—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4—2922no—
266C22×C4—1461no—
267C22×C4—1461no—
268C22×C4—1461no—
269C22×C4—1461no—
270C22×C4#1192400511yescharacteristic
271C22×C4#1192400511yescharacteristic
272C22×C4#1192400511yescharacteristic
273C22×C4#1192400511yescharacteristic
274C22×C4C2×C4×D7311yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—2921no—
277C4⋊C4—2921no—
278C4⋊C4—2922no—
279C4⋊C4—2922no—
280C4⋊C4—2921no—
281C4⋊C4—2921no—
282C4⋊C4—5841no—
283C4⋊C4—5841no—
284C4⋊C4—5842no—
285C22⋊C4—24no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—2922no—
290C22⋊C4—2922no—
291C22⋊C4—2922no—
292C22⋊C4—2922no—
293C22⋊C4—5841no—
294C22⋊C4—5841no—
295C42—21no—
296C42—21no—
297C42—82no—
298C42—2921no—
299C42—2921no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23C2×#1192400511yescharacteristic
309C23#1455657012yes—
310C23#1455657911yescharacteristic
311C23#1455659111yescharacteristic
312D4—42no—
313D4—42no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—44no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—2921no—
331C2×C4—2921no—
332C2×C4—2921no—
333C2×C4—2921no—
334C2×C4—2921no—
335C2×C4—2921no—
336C2×C4—2921no—
337C2×C4—2921no—
338C2×C4—2921no—
339C2×C4—2921no—
340C2×C4—2921no—
341C2×C4—5842no—
342C2×C4—5842no—
343C2×C4—5842no—
344C2×C4—1462no—
345C2×C4#1455650511yescharacteristic
346C2×C4#1455650511yescharacteristic
347C2×C4C4×Dic14612yes—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22#1798849311yescharacteristic
363C22C2×#1455650511yescharacteristic
364C22#1798856011yescharacteristic
365C4—21no—
366C4—21no—
367C4—22no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—84no—
372C4—2922no—
373C4—5841no—
374C4—5841no—
375C4—5841no—
376C4—11682no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—41no—
381C2—41no—
382C2#2261091611yescharacteristic
383C2#2261159411yescharacteristic
384C2#2261159811yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC22×D4C22×D73
FittingC4×#99×C73C2
socleC22×C73C2×#99
prime radical, cosocleC22×D4×C73C23
hypercenterC4×#99D73
hypocenterC73#13300
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
6. C2×#14556583C4semidirect
14. #17988456C4semidirect
15. #17988452C4semidirect
17. C4×C4⋊Dic73C4semidirect
198. C73#13300semidirect

Maximal subgroups

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

subgroupindex
#226151272
#226099192
#226080552
C4×#99×C732
#1330073