Finite Group Databasebeta

← #32996758

Subgroups — #32996758

Order 18688.

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

normal subgroups only

This group has 446 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#22613215C211yesmaximal, characteristic
2#22608269C211yesmaximal, characteristic
3#22607951C212yesmaximal, complemented
4#22607930C212yesmaximal, complemented
5C73×#1799C211yesmaximal, characteristic
6C2×C4×Dic146C411yescharacteristic, complemented
7#17988551—21no—
8#17988525—21no—
9#17988512C411yescharacteristic, complemented
10#17988512C2211yescharacteristic
11#17988501—21no—
12#17988499C411yescharacteristic, complemented
13#17988499C2211yescharacteristic
14C4×C22⋊Dic73—21no—
15C4×C22⋊Dic73—21no—
16#17988433C411yescharacteristic, complemented
17#17988313—21no—
18#17988311C2212yes—
19C2×C4×D4×C73C2211yescharacteristic
20C2×#99×C73—21no—
21#380×C73—21no—
22#342×C73C2212yes—
23C22×Dic146C2×C411yescharacteristic
24C2×#11924012—41no—
25C4×Dic146—41no—
26C4×Dic146—41no—
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×#11924007—21no—
29C2×C22⋊Dic73—21no—
30C2×C22⋊Dic73—21no—
31C2×C22⋊Dic73—21no—
32C2×C22⋊Dic73—21no—
33C2×C4×Dic73—21no—
34C2×C4×Dic73—21no—
35C22⋊#10596831—22no—
36C22⋊#10596831—41no—
37#14556498—21no—
38#14556498—21no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498C2×C411yescharacteristic
43#14556498C2×C411yescharacteristic
44C22×D4×C73D411yescharacteristic
45C23×C4×C73D411yescharacteristic
46C23×C4×C73D411yescharacteristic
47C4×D4×C73—41no—
48C4×D4×C73—41no—
49C2×C4⋊C4×C73—41no—
50C2×C4⋊C4×C73D411yescharacteristic
51C2×C22⋊C4×C73—22no—
52C2×C22⋊C4×C73C2×C411yescharacteristic
53C2×C22⋊C4×C73C2311yescharacteristic
54C2×C42×C73C2×C411yescharacteristic
55#99×C73—42no—
56#95×C73—41no—
57C2×Dic146—41no—
58C2×Dic146—42no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63#11924012—82no—
64C2×#10596831—42no—
65C4⋊Dic73—41no—
66#11924007—42no—
67C22⋊Dic73—42no—
68C22⋊Dic73—42no—
69C22⋊Dic73—42no—
70C22⋊Dic73—41no—
71C22⋊Dic73—41no—
72C4×Dic73—42no—
73C4×Dic73—41no—
74C4×Dic73—41no—
75C24×C73C22⋊C411yescharacteristic
76C24×C73C2×D411yescharacteristic
77C2×D4×C73—21no—
78C2×D4×C73—21no—
79C2×D4×C73—41no—
80C2×D4×C73—41no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—42no—
86C22×C4×C73—42no—
87C22×C4×C73—42no—
88C22×C4×C73C22⋊C411yescharacteristic
89C22×C4×C73C22⋊C411yescharacteristic
90C22×C4×C73C22⋊C411yescharacteristic
91C22×C4×C73C22×C411yescharacteristic
92C22×C4×C73C2×D411yescharacteristic
93C4⋊C4×C73—41no—
94C4⋊C4×C73—82no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C22⋊C4×C73—42no—
98C22⋊C4×C73—42no—
99C42×C73—21no—
100C42×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—41no—
107C23×C73—41no—
108C23×C73—41no—
109C23×C73—41no—
110C23×C73C2×C22⋊C411yescharacteristic
111C23×C73AGL(1,ℤ/8)11yescharacteristic
112C23×C73#13711yescharacteristic
113D4×C73—42no—
114D4×C73—42no—
115C2×C4×C73—22no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—42no—
123C2×C4×C73—42no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—81no—
128C2×C4×C73—81no—
129C2×C4×C73—82no—
130C2×C4×C73—82no—
131C2×C4×C73—82no—
132C2×C4×C73#9911yescharacteristic
133C2×C4×C73#9911yescharacteristic
134C2×Dic73—22no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146Dic146—42no—
147Dic146—42no—
148#10596831—82no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—42no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—81no—
162C22×C73—81no—
163C22×C73C2×#9911yescharacteristic
164C22×C73#41711yescharacteristic
165C22×C73#42111yescharacteristic
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73—41no—
171C4×C73—162no—
172C4×C73#35412yes—
173Dic73—42no—
174Dic73—81no—
175Dic73—81no—
176Dic73—81no—
177#11823—731nomaximal, Sylow
178C2×C73—21no—
179C2×C73—21no—
180C2×C73—41no—
181C2×C73—41no—
182C2×C73—81no—
183C2×C73#151311yescharacteristic
184C2×C73#212011yescharacteristic
185C2×C73C2×#35411yescharacteristic
186#2398—731no—
187#1799D7311yescharacteristic
188#1465—731no—
189#1351—732no—
190#1344—732no—
191C73#1182311yescharacteristic, complemented, Sylow
192C2×C4×Q8—731no—
193C2×C4×D4C2×D7311yescharacteristic
194C2×#99—21no—
195#407—1461no—
196#400—1461no—
197#397—731no—
198#397—731no—
199#394—1461no—
200#393—731no—
201#393—731no—
202#380—21no—
203C4×C22⋊C4—1461no—
204C4×C22⋊C4—1461no—
205#376—731no—
206#342C2×D7312yes—
207#324—1461no—
208#323—732no—
209C22×Q8—731no—
210C22×D4C22⋊D7311yescharacteristic
211C23×C4D29211yescharacteristic
212C23×C4C22⋊D7311yescharacteristic
213C2×M16—2921no—
214C4×Q8—2921no—
215C4×Q8—2921no—
216C4×D4—41no—
217C4×D4—41no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—1461no—
221C2×C4⋊C4D29211yescharacteristic
222C2×C22⋊C4—22no—
223C2×C22⋊C4—1461no—
224C2×C22⋊C4—1461no—
225C2×C22⋊C4—1461no—
226C2×C22⋊C4—1461no—
227C2×C22⋊C4C4×D7311yescharacteristic
228C2×C22⋊C4C22×D7311yescharacteristic
229C2×C42—1461no—
230C2×C42—1461no—
231C2×C42C4×D7311yescharacteristic
232#99—42no—
233C22⋊C8—2921no—
234C22⋊C8—1462no—
235#95—41no—
236#95—731no—
237#95—731no—
238#95—1461no—
239#95—1461no—
240#95—1461no—
241#95—1461no—
242#95—1461no—
243C24#1192400511yescharacteristic
244C24C2×C22⋊D7311yescharacteristic
245C2×Q8—2921no—
246C2×Q8—2922no—
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—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4#1192400511yescharacteristic
263C22×C4#1192400511yescharacteristic
264C22×C4#1192400511yescharacteristic
265C22×C4C2×C4×D7311yescharacteristic
266C22×C4C2×D29211yescharacteristic
267M16—5842no—
268C2×C8—2922no—
269C4⋊C4—41no—
270C4⋊C4—82no—
271C4⋊C4—2921no—
272C4⋊C4—2922no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—2922no—
278C22⋊C4—2921no—
279C22⋊C4—2921no—
280C22⋊C4—2922no—
281C22⋊C4—2922no—
282C42—21no—
283C42—21no—
284C42—2922no—
285C42—2921no—
286C42—2921no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23C2×#1192400511yescharacteristic
297C23#1455661711yescharacteristic
298C23#1455662211yescharacteristic
299Q8—2922no—
300Q8—2922no—
301D4—42no—
302D4—42no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—2921no—
321C2×C4—2921no—
322C2×C4—2921no—
323C2×C4—2921no—
324C2×C4—2921no—
325C2×C4—2921no—
326C2×C4—2921no—
327C2×C4—2921no—
328C2×C4—2921no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—1462no—
332C2×C4#1455650511yescharacteristic
333C2×C4#1455650511yescharacteristic
334C8—5842no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—81no—
348C22—81no—
349C22C2×#1455650511yescharacteristic
350C22#1798858611yescharacteristic
351C22#1798860511yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—162no—
358C4—2922no—
359C4—5841no—
360C4—5841no—
361C4—5841no—
362C4#1798838112yes—
363C2—21no—
364C2—21no—
365C2—41no—
366C2—41no—
367C2—81no—
368C2#2260847211yescharacteristic
369C2#2261157011yescharacteristic
370C2C2×#1798838111yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1799C2
socleC22×C73C2×#99
prime radicalC22×D4×C73D4
cosocleC2×C22⋊C4×C73C23
hypercenter#1799D73
hypocenterC73#11823
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #22607951C2semidirect
4. #22607930C2semidirect
6. C2×C4×Dic146C4semidirect
9. #17988512C4semidirect
12. #17988499C4semidirect
16. #17988433C4semidirect
191. C73#11823semidirect

Maximal subgroups

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

subgroupindex
#226132152
#226082692
#226079512
#226079302
C73×#17992
#1182373