Finite Group Databasebeta

← #32989706

Subgroups — #32989706

Order 18688.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#22619738C211yesmaximal, characteristic
2#22609924C211yesmaximal, characteristic
3#22608622C211yesmaximal, characteristic
4#22608387C211yesmaximal, characteristic
5C2×#17988319C211yesmaximal, characteristic
6#22607805C211yesmaximal, characteristic
7C73×#1566C211yesmaximal, characteristic
8#17989144C2211yescharacteristic
9C2×C4×Dic146C2211yescharacteristic
10#17988895—22no—
11#17988883—21no—
12#17988873—21no—
13#17988629—21no—
14#17988611C2211yescharacteristic
15C2×C4⋊#10596831C2211yescharacteristic
16#17988597—21no—
17C2×#14556509—21no—
18#17988355—21no—
19#17988335—21no—
20#17988332—21no—
21#17988319—21no—
22#17988319—21no—
23#17988319—21no—
24#17988319—21no—
25#423×C73C2211yescharacteristic
26#423×C73C2211yescharacteristic
27C2×C4×C8×C73C2211yescharacteristic
28#334×C73—22no—
29C22×Dic146D411yescharacteristic
30C2×#11924012—21no—
31C22×#10596831—21no—
32#14556591D411yescharacteristic
33#14556591D411yescharacteristic
34#14556583—21no—
35#14556570—21no—
36#14556570—21no—
37C4×Dic146—21no—
38C4×Dic146—21no—
39C4×Dic146—21no—
40C4×Dic146—21no—
41C4×Dic146—21no—
42C4×Dic146—21no—
43#14556550—21no—
44C2×C4⋊Dic73D411yescharacteristic
45C2×#11924007—21no—
46C2×C4×Dic73—21no—
47#14556525—22no—
48#14556523—22no—
49C4⋊#10596831—21no—
50C4⋊#10596831—21no—
51C4⋊#10596831—21no—
52C4⋊#10596831—21no—
53#14556516—22no—
54#14556516—22no—
55#14556509—42no—
56C2×M16×C73—21no—
57C2×M16×C73—21no—
58C22×C8×C73—21no—
59C2×C42×C73C2311yescharacteristic
60C4⋊C8×C73—21no—
61C4⋊C8×C73—21no—
62C4⋊C8×C73—21no—
63C4⋊C8×C73D412yes—
64C4×C8×C73—21no—
65C4×C8×C73D411yescharacteristic
66C4×C8×C73D411yescharacteristic
67C2×Dic146—21no—
68C2×Dic146—21no—
69C2×Dic146—21no—
70C2×Dic146—21no—
71C2×Dic146—21no—
72C2×Dic146—21no—
73C2×Dic146—21no—
74C2×Dic146SD1612yes—
75C22×Dic73—21no—
76C22×Dic73—21no—
77#11924012—41no—
78#11924012—41no—
79C2×#10596831—41no—
80C2×#10596831—41no—
81C2×#10596831—81no—
82C4⋊Dic73—21no—
83C4⋊Dic73—21no—
84C4⋊Dic73—21no—
85C4⋊Dic73—21no—
86C4⋊Dic73—21no—
87C4⋊Dic73—21no—
88#11924007—41no—
89#11924007—41no—
90#11924007—41no—
91#11924007—41no—
92C22⋊Dic73—41no—
93C4×Dic73—41no—
94C4×Dic73—41no—
95C4×Dic73—41no—
96C22×C4×C73C2×D411yescharacteristic
97C22×C4×C73#4111yescharacteristic
98C22×C4×C73#4111yescharacteristic
99M16×C73—41no—
100M16×C73—41no—
101M16×C73—41no—
102M16×C73—41no—
103C2×C8×C73—21no—
104C2×C8×C73—22no—
105C2×C8×C73—21no—
106C2×C8×C73—42no—
107C2×C8×C73—41no—
108C42×C73C2×D411yescharacteristic
109C42×C73C2×D411yescharacteristic
110C42×C73C2×D411yescharacteristic
111C42×C73#4111yescharacteristic
112C23×C73#12311yescharacteristic
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—41no—
116C2×C4×C73#12011yescharacteristic
117C2×C4×C73#12111yescharacteristic
118C2×C4×C73#12111yescharacteristic
119C2×C4×C73#12111yescharacteristic
120C2×C4×C73#12311yescharacteristic
121C2×C4×C73#12411yescharacteristic
122C2×C4×C73C2×SD1611yescharacteristic
123C2×C4×C73#13511yescharacteristic
124C2×C4×C73#13711yescharacteristic
125C2×C4×C73#13711yescharacteristic
126C2×Dic73—22no—
127C2×Dic73—41no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—81no—
133Dic146—22no—
134Dic146—22no—
135Dic146—41no—
136Dic146—41no—
137Dic146—41no—
138Dic146—41no—
139Dic146—81no—
140C8×C73—22no—
141C8×C73—41no—
142C8×C73—42no—
143C8×C73—81no—
144#10596831—81no—
145#10596831—81no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73#39411yescharacteristic
149C22×C73#48311yescharacteristic
150C22×C73#48511yescharacteristic
151C4×C73—21no—
152C4×C73—21no—
153C4×C73—21no—
154C4×C73#44811yescharacteristic
155C4×C73#45211yescharacteristic
156C4×C73#46511yescharacteristic
157C4×C73#47011yescharacteristic
158C4×C73#47111yescharacteristic
159C4×C73#47311yescharacteristic
160Dic73—42no—
161Dic73—81no—
162Dic73—81no—
163Dic73—81no—
164#10462—731nomaximal, Sylow
165C2×C73—21no—
166C2×C73—21no—
167C2×C73#203511yescharacteristic
168C2×C73#205011yescharacteristic
169C2×C73#205211yescharacteristic
170#3078—731no—
171#1801—731no—
172#1566D7311yescharacteristic
173#1550—731no—
174#1493—731no—
175C2×Q8⋊C8—731no—
176#1292—731no—
177C73#1046211yescharacteristic, complemented, Sylow
178#533—731no—
179C2×C4×Q8—731no—
180#479—1462no—
181#477—1461no—
182#475—1461no—
183#428—1461no—
184#423—731no—
185#423C2×D7311yescharacteristic
186#423C2×D7311yescharacteristic
187C2×C4⋊C8—731no—
188#419—1461no—
189C2×#101—1461no—
190C2×C4×C8C2×D7311yescharacteristic
191#343—1461no—
192#334—22no—
193#333—1461no—
194#332—1461no—
195Q8⋊C8—1461no—
196Q8⋊C8—1461no—
197Q8⋊C8—1461no—
198Q8⋊C8—1461no—
199C22×Q8—731no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—1461no—
203C22×C8—21no—
204C22×C8—1461no—
205C4⋊Q8—731no—
206C4⋊Q8—731no—
207#125—1461no—
208C22⋊Q8—1461no—
209C22⋊Q8—1461no—
210C4×Q8—1461no—
211C4×Q8—1461no—
212C4×Q8—1461no—
213C4×Q8—1461no—
214C4×Q8—1461no—
215C4×Q8—1461no—
216#117—1461no—
217C2×C4⋊C4—731no—
218C2×C4⋊C4—1461no—
219C2×C42—1461no—
220C2×C42C22×D7311yescharacteristic
221#107—1462no—
222#106—1462no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—1461no—
227C4⋊C8—1461no—
228C4⋊C8—1461no—
229C4⋊C8—1461no—
230C4⋊C8C22⋊D7312yes—
231#103—1462no—
232#103—1462no—
233#101—2922no—
234C4×C8—21no—
235C4×C8D29211yescharacteristic
236C4×C8D29211yescharacteristic
237C2×Q8—732no—
238C2×Q8—1461no—
239C2×Q8—1461no—
240C2×Q8—1461no—
241C2×Q8—1461no—
242C2×Q8—1461no—
243C2×Q8—1461no—
244C2×Q8—1461no—
245C22×C4—1461no—
246C22×C4—1461no—
247C22×C4D4×D7311yescharacteristic
248C22×C4#1192402811yescharacteristic
249C22×C4#1192402911yescharacteristic
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—2921no—
255M16—2921no—
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—2921no—
262C2×C8—2921no—
263C2×C8—5841no—
264C4⋊C4—2921no—
265C4⋊C4—2921no—
266C4⋊C4—2921no—
267C4⋊C4—2921no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C22⋊C4—2921no—
275C42—2921no—
276C42—2921no—
277C42—2921no—
278C42D4×D7311yescharacteristic
279C42C2×C22⋊D7311yescharacteristic
280C42C2×D29211yescharacteristic
281C42#1192402911yescharacteristic
282C23#1455657611yescharacteristic
283Q8—2921no—
284Q8—2921no—
285Q8—2921no—
286Q8—2921no—
287Q8—5841no—
288Q8—1462no—
289Q8—1462no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—2921no—
294C2×C4—2921no—
295C2×C4—2921no—
296C2×C4—2921no—
297C2×C4—2921no—
298C2×C4—5841no—
299C2×C4—1462no—
300C2×C4#1455655911yescharacteristic
301C2×C4#1455656511yescharacteristic
302C2×C4#1455656611yescharacteristic
303C2×C4#1455656611yescharacteristic
304C2×C4#1455657611yescharacteristic
305C2×C4#1455658011yescharacteristic
306C2×C4SD16×D7311yescharacteristic
307C2×C4#1455661211yescharacteristic
308C2×C4#1455662011yescharacteristic
309C2×C4#1455662011yescharacteristic
310C8—22no—
311C8—41no—
312C8—42no—
313C8—81no—
314C8—5841no—
315C8—5841no—
316C22—21no—
317C22—21no—
318C22#1798850411yescharacteristic
319C22#1798891911yescharacteristic
320C22#1798893111yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—2922no—
325C4—5841no—
326C4—5841no—
327C4—5841no—
328C4#1798872411yescharacteristic
329C4#1798874611yescharacteristic
330C4#1798881711yescharacteristic
331C4#1798884611yescharacteristic
332C4#1798885111yescharacteristic
333C4#1798886311yescharacteristic
334C2—21no—
335C2—21no—
336C2#2261112911yescharacteristic
337C2#2261121811yescharacteristic
338C2#2261123211yescharacteristic
subgroupG/H
centerC22#17988504
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1566C2
socleC22×C73#394
prime radicalC23×C73#123
hypercenter#1566D73
hypocenterC73#10462
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
177. C73#10462semidirect

Maximal subgroups

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

subgroupindex
#226197382
#226099242
#226086222
#226083872
C2×#179883192
#226078052
C73×#15662
#1046273