Finite Group Databasebeta

← #32974484

Subgroups — #32974484

Order 18688.

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

normal subgroups only

This group has 530 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#22618240C211yesmaximal, characteristic
2#22609692C211yesmaximal, characteristic
3#336×D73C211yesmaximal, characteristic
4#22607755C211yesmaximal, characteristic, complemented
5#22607754C211yesmaximal, characteristic, complemented
6#22607753C211yesmaximal, characteristic, complemented
7C73×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D73—21no—
9C2×#14556582C411yescharacteristic
10C2×C42×D73C2211yescharacteristic
11C2×#14556503—21no—
12C2×#14556501—21no—
13#17988485C2211yescharacteristic
14#17988473—21no—
15#17988469—21no—
16#17988461—21no—
17#17988458—21no—
18#17988452C411yescharacteristic
19#17988444C411yescharacteristic
20#17988444C411yescharacteristic
21#17988342C2211yescharacteristic
22#17988342C2211yescharacteristic
23#17988341—21no—
24#389×C73C2211yescharacteristic
25#336×C73C2211yescharacteristic
26#336×C73C2211yescharacteristic
27C22×C4×D73C2×C411yescharacteristic
28C22×C4×D73D411yescharacteristic
29C22×C4×D73D411yescharacteristic
30C22×#10596831—21no—
31C22×#10596831—21no—
32C2×C8×D73—24no—
33C2×C8×D73—42no—
34C2×C8×D73—42no—
35#14556582—42no—
36C2×C4⋊Dic73—21no—
37C2×C4⋊Dic73C2×C411yescharacteristic
38C2×C4⋊Dic73C2×C411yescharacteristic
39C2×#11924007—21no—
40C2×#11924007—21no—
41C2×#11924005—21no—
42C2×#11924005—21no—
43C2×C4×Dic73C2×C411yescharacteristic
44C2×C4×Dic73D411yescharacteristic
45C2×C4×Dic73D411yescharacteristic
46C42×D73—42no—
47#14556503—24no—
48#14556501—42no—
49#14556498—21no—
50#14556498—21no—
51#14556498—21no—
52#14556498—21no—
53#14556498—21no—
54C22×C8×C73—21no—
55C22×C8×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C4⋊C4×C73C2×C411yescharacteristic
58C2×C4⋊C4×C73C2×C411yescharacteristic
59C2×C42×C73C2311yescharacteristic
60#95×C73—21no—
61C23×D73C22⋊C411yescharacteristic
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73C22⋊C411yescharacteristic
65C22×Dic73C22⋊C411yescharacteristic
66C22×Dic73C22⋊C411yescharacteristic
67C2×C4×D73—22no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—22no—
71C2×C4×D73—22no—
72C2×C4×D73—22no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77C2×C4×D73—41no—
78C2×C4×D73—41no—
79C2×#10596831—22no—
80C2×#10596831—22no—
81C2×#10596831—41no—
82C2×#10596831—41no—
83C2×#10596831—41no—
84C2×#10596831—41no—
85C8×D73—48no—
86C4⋊Dic73—21no—
87C4⋊Dic73—21no—
88C4⋊Dic73—42no—
89C4⋊Dic73—41no—
90#11924007—41no—
91#11924007—41no—
92#11924007—42no—
93#11924005—42no—
94#11924005—42no—
95C4×Dic73—22no—
96C4×Dic73—22no—
97C4×Dic73—41no—
98C22×C4×C73—21no—
99C22×C4×C73—21no—
100C22×C4×C73C22×C411yescharacteristic
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73C2×D411yescharacteristic
103C2×C8×C73—22no—
104C2×C8×C73—22no—
105C2×C8×C73—41no—
106C2×C8×C73—41no—
107C2×C8×C73—41no—
108C2×C8×C73—41no—
109C4⋊C4×C73—21no—
110C4⋊C4×C73—21no—
111C4⋊C4×C73—41no—
112C4⋊C4×C73—41no—
113C4⋊C4×C73—41no—
114C42×C73—41no—
115C23×C73C2×C22⋊C411yescharacteristic
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—21no—
119C22×D73—21no—
120C22×D73#10112yes—
121C22×D73#10412yes—
122C22×D73#10412yes—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73#13111yescharacteristic
136C2×C4×C73#13111yescharacteristic
137C2×C4×C73#13511yescharacteristic
138C2×C4×C73#13511yescharacteristic
139C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C73#13711yescharacteristic
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—41no—
155C2×Dic73#9912yes—
156C4×D73—24no—
157C4×D73—24no—
158C4×D73—42no—
159C4×D73—42no—
160C4×D73—42no—
161C4×D73—42no—
162C8×C73—42no—
163C8×C73—42no—
164#10596831—42no—
165#10596831—42no—
166C22×C73#40811yescharacteristic
167C22×C73C2×#9911yescharacteristic
168C22×C73C2×#10111yescharacteristic
169C22×C73#41611yescharacteristic
170C22×C73#41711yescharacteristic
171C22×C73C2×#10411yescharacteristic
172C22×C73C2×#10411yescharacteristic
173C2×D73—22no—
174C2×D73—22no—
175C2×D73—22no—
176C2×D73—22no—
177C2×D73—22no—
178C2×D73—22no—
179C2×D73#33014yes—
180C4×C73—21no—
181C4×C73—21no—
182C4×C73—21no—
183C4×C73—21no—
184C4×C73—21no—
185C4×C73—21no—
186C4×C73—81no—
187C4×C73—81no—
188Dic73—22no—
189Dic73—41no—
190Dic73—41no—
191Dic73—81no—
192Dic73—81no—
193#7691—731nomaximal, Sylow
194C2×C73#147211yescharacteristic
195C2×C73#148311yescharacteristic
196C2×C73#149411yescharacteristic
197C2×C73#150111yescharacteristic
198C2×C73#150411yescharacteristic
199C2×C73C2×#33011yescharacteristic
200C2×C73#155211yescharacteristic
201D73—24no—
202#2851—731no—
203#1749—731no—
204C2×#336—731no—
205#1271—731no—
206#1271—731no—
207#1271—731no—
208#1271D7311yescharacteristic, complemented
209C73#769111yescharacteristic, complemented, Sylow
210C23×C8—1461no—
211C2×#125—731no—
212C22×C42—731no—
213C2×C22⋊C8—1461no—
214C2×#97—1461no—
215#389—731no—
216#389C2×D7311yescharacteristic
217#387—1461no—
218#387—1461no—
219#385—1461no—
220#385—1461no—
221#382—731no—
222#380—731no—
223#380—731no—
224#336—731no—
225#336—731no—
226#336—1461no—
227#336C2×D7311yescharacteristic
228#336C2×D7311yescharacteristic
229C23×C4—731no—
230C23×C4—731no—
231C23×C4—731no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—2922no—
235C22×C8—2922no—
236C22×C8—1464no—
237C22×C8—1461no—
238C22×C8—1461no—
239#125—2922no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—731no—
242C2×C4⋊C4—731no—
243C2×C4⋊C4—1461no—
244C2×C4⋊C4—1461no—
245C2×C4⋊C4—1461no—
246C2×C4⋊C4C4×D7311yescharacteristic
247C2×C4⋊C4C4×D7311yescharacteristic
248C2×C22⋊C4—1461no—
249C2×C22⋊C4—1461no—
250C2×C42—2922no—
251C2×C42—731no—
252C2×C42—731no—
253C2×C42—731no—
254C2×C42C22×D7311yescharacteristic
255C22⋊C8—1464no—
256#97—2922no—
257#95—21no—
258#95—1461no—
259#95—1461no—
260#95—1461no—
261#95—1461no—
262#95—1461no—
263C24—731no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—2921no—
267C22×C4—2921no—
268C22×C4—731no—
269C22×C4—731no—
270C22×C4—731no—
271C22×C4—1462no—
272C22×C4—1462no—
273C22×C4—1462no—
274C22×C4—1462no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4—1461no—
278C22×C4—1461no—
279C22×C4—1461no—
280C22×C4—1461no—
281C22×C4—1461no—
282C22×C4—1461no—
283C22×C4C2×C4×D7311yescharacteristic
284C22×C4D4×D7311yescharacteristic
285C22×C4D4×D7311yescharacteristic
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—2928no—
293C2×C8—2921no—
294C2×C8—2921no—
295C2×C8—2921no—
296C2×C8—2921no—
297C2×C8—1462no—
298C2×C8—1462no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—2921no—
305C4⋊C4—2922no—
306C4⋊C4—2922no—
307C4⋊C4—2921no—
308C4⋊C4—2921no—
309C4⋊C4—1461no—
310C4⋊C4—1461no—
311C22⋊C4—2922no—
312C22⋊C4—2922no—
313C42—41no—
314C42—2921no—
315C42—1462no—
316C42—1462no—
317C23—732no—
318C23—732no—
319C23—732no—
320C23—1461no—
321C23—1461no—
322C23—1461no—
323C23—1461no—
324C23C22⋊C4×D7311yescharacteristic
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—2922no—
338C2×C4—2922no—
339C2×C4—2922no—
340C2×C4—2922no—
341C2×C4—2921no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—2921no—
345C2×C4—2921no—
346C2×C4—2921no—
347C2×C4—732no—
348C2×C4—1464no—
349C2×C4—1464no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4#1455659711yescharacteristic
359C2×C4#1455659911yescharacteristic
360C2×C4#1455661211yescharacteristic
361C2×C4#1455661411yescharacteristic
362C2×C4#1455661511yescharacteristic
363C2×C4#1455662011yescharacteristic
364C8—42no—
365C8—42no—
366C8—2922no—
367C8—2922no—
368C22—734no—
369C22—1462no—
370C22—1462no—
371C22—1462no—
372C22—1462no—
373C22—1462no—
374C22—1462no—
375C22#1798855211yescharacteristic
376C22#99×D7311yescharacteristic
377C22#101×D7311yescharacteristic
378C22#1798858211yescharacteristic
379C22#1798858511yescharacteristic
380C22#104×D7311yescharacteristic
381C22#104×D7311yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—81no—
389C4—81no—
390C4—2921no—
391C4—2921no—
392C4—5841no—
393C4—5841no—
394C4—1462no—
395C2—1464no—
396C2#2260829311yescharacteristic
397C2#2260834111yescharacteristic
398C2#2260839011yescharacteristic
399C2#2260842111yescharacteristic
400C2#2260843211yescharacteristic
401C2#330×D7311yescharacteristic
402C2#2260863011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1271C2
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1271D73
hypocenterC73#7691
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #22607755C2semidirect
5. #22607754C2semidirect
6. #22607753C2semidirect
7. C73×#1271C2semidirect
208. #1271D73semidirect
209. C73#7691semidirect

Maximal subgroups

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

subgroupindex
#226182402
#226096922
#336×D732
#226077552
#226077542
#226077532
C73×#12712
#769173