Finite Group Databasebeta

← #32995448

Subgroups — #32995448

Order 18688.

442 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 83 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#22612596C211yesmaximal, characteristic
2#22608269C211yesmaximal, characteristic
3#22607880C212yesmaximal, complemented
4#22607860C212yesmaximal, complemented
5C73×#1466C211yesmaximal, characteristic
6C2×#14556572C411yescharacteristic
7C22×#11924007C411yescharacteristic
8#17988551—21no—
9#17988482—21no—
10#17988481—21no—
11#17988471—21no—
12#17988467C411yescharacteristic
13#17988460—21no—
14#17988459C2211yescharacteristic
15#17988448C2211yescharacteristic
16C4×C22⋊Dic73C411yescharacteristic
17#17988313—21no—
18#17988311C2212yes—
19C2×C4×D4×C73C2211yescharacteristic
20#432×C73—21no—
21#323×C73—21no—
22#323×C73C2212yes—
23C23×Dic73C2×C411yescharacteristic
24C23×Dic73C2×C411yescharacteristic
25C2×#11924012—41no—
26#14556572—22no—
27#14556572—22no—
28C2×#11924007—21no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×#11924007—41no—
33C2×#11924007—41no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—21no—
36C2×C22⋊Dic73C2×C411yescharacteristic
37C2×C22⋊Dic73C2×C411yescharacteristic
38C2×C4×Dic73—21no—
39C22⋊#10596831—22no—
40C22⋊#10596831—41no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46C22×D4×C73C2×C411yescharacteristic
47C23×C4×C73C2×C411yescharacteristic
48C23×C4×C73D411yescharacteristic
49C4×D4×C73—41no—
50C4×D4×C73—41no—
51C2×C4⋊C4×C73D411yescharacteristic
52C2×C22⋊C4×C73D411yescharacteristic
53C2×C22⋊C4×C73C2311yescharacteristic
54C2×C42×C73D411yescharacteristic
55C4⋊C8×C73—41no—
56C22⋊C8×C73—22no—
57#97×C73—41no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—41no—
64C22×Dic73—41no—
65C22×Dic73—41no—
66C22×Dic73—81no—
67C22×Dic73M1612yescomplemented
68#11924012—82no—
69C2×#10596831—42no—
70#11924007—24no—
71#11924007—42no—
72#11924007—41no—
73#11924007—41no—
74#11924007—81no—
75C22⋊Dic73—24no—
76C22⋊Dic73—21no—
77C22⋊Dic73—41no—
78C22⋊Dic73—81no—
79C22⋊Dic73M1612yescomplemented
80C4×Dic73—81no—
81C24×C73C22⋊C411yescharacteristic
82C24×C73C22×C411yescharacteristic
83C2×D4×C73—21no—
84C2×D4×C73—21no—
85C2×D4×C73—41no—
86C2×D4×C73—41no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—81no—
92C22×C4×C73—81no—
93C22×C4×C73C22⋊C411yescharacteristic
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22⋊C411yescharacteristic
96C22×C4×C73C2×D411yescharacteristic
97C22×C4×C73C2×D411yescharacteristic
98C2×C8×C73—42no—
99C4⋊C4×C73—41no—
100C22⋊C4×C73—41no—
101C22⋊C4×C73—41no—
102C42×C73—21no—
103C42×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—41no—
110C23×C73—41no—
111C23×C73—41no—
112C23×C73—41no—
113C23×C73C2×C22⋊C411yescharacteristic
114C23×C73C2×M1611yescharacteristic
115C23×C73C2×M1611yescharacteristic
116D4×C73—42no—
117D4×C73—42no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—41no—
125C2×C4×C73—42no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—81no—
130C2×C4×C73—81no—
131C2×C4×C73—81no—
132C2×C4×C73#9911yescharacteristic
133C2×C4×C73#9911yescharacteristic
134C2×Dic73—22no—
135C2×Dic73—22no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—42no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—42no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73—82no—
149C8×C73—82no—
150#10596831—82no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—42no—
158C22×C73—42no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—81no—
165C22×C73#40711yescharacteristic
166C22×C73C2×#9911yescharacteristic
167C22×C73#41311yescharacteristic
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73—41no—
173C4×C73—41no—
174Dic73—42no—
175Dic73—42no—
176Dic73—81no—
177Dic73—81no—
178#11528—731nomaximal, Sylow
179C2×C73—21no—
180C2×C73—21no—
181C2×C73—41no—
182C2×C73—41no—
183C2×C73—81no—
184C2×C73#146511yescharacteristic
185C2×C73#212111yescharacteristic
186C2×C73#212311yescharacteristic
187#2322—731no—
188#1466D7311yescharacteristic
189#1465—731no—
190#1326—732no—
191#1317—732no—
192C73#1152811yescharacteristic, complemented, Sylow
193C2×#123—731no—
194C2×C4×D4C2×D7311yescharacteristic
195C22×C4⋊C4—731no—
196#432—21no—
197#407—1461no—
198#389—1461no—
199#388—1461no—
200#387—1461no—
201#386—731no—
202#385—731no—
203#385—1461no—
204#381—731no—
205C4×C22⋊C4—731no—
206#324—1461no—
207#323—21no—
208#323—732no—
209#323C2×D7312yes—
210C22×D4C4×D7311yescharacteristic
211C23×C4—731no—
212C23×C4—731no—
213C23×C4C4×D7311yescharacteristic
214C23×C4D29211yescharacteristic
215C2×M16—2921no—
216#123—1462no—
217#123—1462no—
218C4×D4—41no—
219C4×D4—41no—
220C2×C4⋊C4—2921no—
221C2×C4⋊C4—2921no—
222C2×C4⋊C4—1461no—
223C2×C4⋊C4—1461no—
224C2×C4⋊C4—1461no—
225C2×C4⋊C4—1461no—
226C2×C4⋊C4D29211yescharacteristic
227C2×C22⋊C4—731no—
228C2×C22⋊C4—731no—
229C2×C22⋊C4—1461no—
230C2×C22⋊C4—1461no—
231C2×C22⋊C4C22⋊D7311yescharacteristic
232C2×C22⋊C4C22×D7311yescharacteristic
233C2×C42—1461no—
234C2×C42C22⋊D7311yescharacteristic
235C4⋊C8—41no—
236C22⋊C8—22no—
237C22⋊C8—2921no—
238C22⋊C8—1462no—
239#97—41no—
240#95—1461no—
241#95—1461no—
242#95—1461no—
243#95—1461no—
244#95—1461no—
245C24#1192400511yescharacteristic
246C24C2×C4×D7311yescharacteristic
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—2921no—
258C22×C4—2921no—
259C22×C4—2921no—
260C22×C4—5841no—
261C22×C4—732no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266C22×C4—1461no—
267C22×C4#1192400511yescharacteristic
268C22×C4#1192400511yescharacteristic
269C22×C4#1192400511yescharacteristic
270C22×C4C2×C22⋊D7311yescharacteristic
271C22×C4C2×D29211yescharacteristic
272M16—5842no—
273C2×C8—42no—
274C2×C8—2922no—
275C4⋊C4—41no—
276C4⋊C4—2922no—
277C4⋊C4—2921no—
278C4⋊C4—2921no—
279C4⋊C4—5841no—
280C4⋊C4—1464no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—2921no—
284C22⋊C4—5841no—
285C22⋊C4—732no—
286C22⋊C4—1464no—
287C22⋊C4—1461no—
288C42—21no—
289C42—21no—
290C42—5841no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23C2×#1192400511yescharacteristic
301C23M16×D7311yescharacteristic
302C23M16×D7311yescharacteristic
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—2921no—
320C2×C4—2922no—
321C2×C4—2921no—
322C2×C4—2921no—
323C2×C4—2921no—
324C2×C4—2922no—
325C2×C4—2921no—
326C2×C4—2921no—
327C2×C4—2921no—
328C2×C4—2921no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—5842no—
332C2×C4—1462no—
333C2×C4—1462no—
334C2×C4#1455650511yescharacteristic
335C2×C4#1455650511yescharacteristic
336C8—82no—
337C8—5842no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—42no—
345C22—42no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22#1798855011yescharacteristic
353C22C2×#1455650511yescharacteristic
354C22#1798856911yescharacteristic
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—2922no—
362C4—2922no—
363C4—5841no—
364C4—5841no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—41no—
369C2—81no—
370C2#2260826711yescharacteristic
371C2#2261157811yescharacteristic
372C2#2261158411yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC24×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1466C2
socleC22×C73C2×#99
prime radicalC22×D4×C73C2×C4
cosocleC2×C22⋊C4×C73C23
hypercenter#1466D73
hypocenterC73#11528
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #22607880C2semidirect
4. #22607860C2semidirect
67. C22×Dic73M16semidirect
79. C22⋊Dic73M16semidirect
192. C73#11528semidirect

Maximal subgroups

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

subgroupindex
#226125962
#226082692
#226078802
#226078602
C73×#14662
#1152873