Finite Group Databasebeta

← #34004093

Subgroups — #34004093

Order 18688.

1158 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 160 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#22625822C212yesmaximal, complemented
2C2×#17989433C212yesmaximal, complemented
3C2×#17989430C212yesmaximal
4C22×#14556547C211yesmaximal, characteristic
5C2×C22⋊#10596833C2214yes—
6#17989453—24no—
7#17989433—24no—
8#17989430—24no—
9C24×Dic73C411yescharacteristic
10C2×#14556547—24no—
11C2×#14556547—24no—
12C2×#14556547—24no—
13C22×#11924007C411yescharacteristic
14C22×#11924007C2211yescharacteristic
15C22×C22⋊Dic73C2211yescharacteristic
16C22×C4×Dic73C411yescharacteristic
17C22×C4×Dic73C2211yescharacteristic
18C22×C22⋊C4×C73C411yescharacteristic
19C22×#10596833—24no—
20C22⋊#10596833—24no—
21C22⋊#10596833—24no—
22C23×Dic73—22no—
23C23×Dic73—22no—
24C23×Dic73—22no—
25C23×Dic73—22no—
26C23×Dic73—22no—
27C23×Dic73—22no—
28C23×Dic73C814yescomplemented
29C23×Dic73C2×C411yescharacteristic
30C23×Dic73C2×C411yescharacteristic
31C23×Dic73C2×C411yescharacteristic
32C23×Dic73C2311yescharacteristic
33#14556547—232no—
34C2×#11924007—22no—
35C2×#11924007—22no—
36C2×#11924007—22no—
37C2×#11924007—22no—
38C2×#11924007—22no—
39C2×#11924007D414yes—
40C2×C22⋊Dic73—22no—
41C2×C22⋊Dic73—22no—
42C2×C22⋊Dic73D414yes—
43C2×C4×Dic73—22no—
44C2×C4×Dic73—22no—
45C2×C4×Dic73—22no—
46C2×C4×Dic73—22no—
47C2×C4×Dic73—22no—
48C2×C4×Dic73D414yes—
49C25×C73C2×C411yescharacteristic
50C23×C4×C73C2×C411yescharacteristic
51C23×C4×C73C2×C411yescharacteristic
52C2×C22⋊C4×C73—22no—
53C2×C22⋊C4×C73—22no—
54C2×C22⋊C4×C73—22no—
55C2×#10596833—48no—
56C2×#10596833—44no—
57C22×Dic73—28no—
58C22×Dic73—28no—
59C22×Dic73—28no—
60C22×Dic73—28no—
61C22×Dic73—28no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73—28no—
71C22×Dic73—28no—
72C22×Dic73—21no—
73C22×Dic73—21no—
74C22×Dic73—42no—
75C22×Dic73—42no—
76C22×Dic73C22⋊C412yes—
77C22×Dic73C22⋊C412yes—
78C22×Dic73C22⋊C412yes—
79C22×Dic73C2×C812yes—
80C22×Dic73C2×C812yes—
81C22×Dic73M1612yes—
82C22×Dic73M1612yes—
83C22×Dic73C2×D412yes—
84C22×Dic73C2×D412yes—
85C22×Dic73C2×D412yes—
86#11924007—28no—
87#11924007—28no—
88C22⋊Dic73—28no—
89C4×Dic73—28no—
90C4×Dic73—28no—
91C24×C73—21no—
92C24×C73—21no—
93C24×C73—21no—
94C24×C73—21no—
95C24×C73—42no—
96C24×C73—42no—
97C24×C73C22⋊C412yes—
98C24×C73C2×C812yes—
99C24×C73M1612yes—
100C24×C73C22×C411yescharacteristic
101C22×C4×C73—21no—
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73—21no—
105C22×C4×C73—42no—
106C22×C4×C73—42no—
107C22×C4×C73C22⋊C412yes—
108C22×C4×C73C22⋊C412yes—
109C22⋊C4×C73—28no—
110C23×C73—22no—
111C23×C73—22no—
112C23×C73—22no—
113C23×C73—22no—
114C23×C73—22no—
115C23×C73—22no—
116C23×C73—22no—
117C23×C73—22no—
118C23×C73—42no—
119C23×C73—42no—
120C23×C73—44no—
121C23×C73—44no—
122C23×C73—44no—
123C23×C73—44no—
124C23×C73—42no—
125C23×C73—42no—
126C23×C73—42no—
127C23×C73—42no—
128C23×C73C22⋊C814yes—
129C23×C73C2×C22⋊C411yescharacteristic
130C23×C73C2×C22⋊C411yescharacteristic
131C23×C73C2×C22⋊C411yescharacteristic
132C23×C73C22×C811yescharacteristic
133C23×C73C2×M1611yescharacteristic
134C23×C73C2×M1611yescharacteristic
135C23×C73C2×M1611yescharacteristic
136C2×C4×C73—22no—
137C2×C4×C73—22no—
138C2×C4×C73—24no—
139C2×C4×C73—42no—
140C2×C4×C73—42no—
141C2×C4×C73—42no—
142C2×C4×C73—42no—
143C2×C4×C73—42no—
144C2×Dic73—232no—
145C2×Dic73—22no—
146C2×Dic73—22no—
147C2×Dic73—22no—
148C2×Dic73—22no—
149C2×Dic73—22no—
150C2×Dic73—22no—
151C2×Dic73—22no—
152C2×Dic73—22no—
153C2×Dic73—22no—
154C2×Dic73—22no—
155C2×Dic73—22no—
156C2×Dic73—22no—
157C2×Dic73—24no—
158C2×Dic73—22no—
159C2×Dic73—42no—
160C2×Dic73—42no—
161C2×Dic73—42no—
162C2×Dic73—42no—
163C2×Dic73—42no—
164C2×Dic73C22⋊C814yes—
165C2×Dic73C22⋊C814yes—
166C2×Dic73#12014yes—
167#10596833—84no—
168C22×C73—22no—
169C22×C73—22no—
170C22×C73—22no—
171C22×C73—22no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—21no—
175C22×C73—21no—
176C22×C73—24no—
177C22×C73—44no—
178C22×C73—44no—
179C22×C73—44no—
180C22×C73—44no—
181C22×C73—44no—
182C22×C73—44no—
183C22×C73—42no—
184C22×C73—42no—
185C22×C73#37911yescharacteristic
186C22×C73C2×C22⋊C811yescharacteristic
187C22×C73C2×C22⋊C811yescharacteristic
188C22×C73C2×C22⋊C811yescharacteristic
189C22×C73#40711yescharacteristic
190C22×C73#40711yescharacteristic
191C22×C73#40711yescharacteristic
192C22×C73#41012yes—
193C22×C73#41312yes—
194C4×C73—42no—
195C4×C73—42no—
196Dic73—24no—
197Dic73—24no—
198Dic73—24no—
199Dic73—42no—
200#8300—731nomaximal, Sylow
201C2×C73—21no—
202C2×C73—21no—
203C2×C73—21no—
204C2×C73—21no—
205C2×C73—44no—
206C2×C73#145812yes—
207C2×C73#146412yes—
208C2×C73#177911yescharacteristic
209C2×C73#178211yescharacteristic
210C2×C73#178511yescharacteristic
211C22×#117—731no—
212#1817—732no—
213C2×#324—732no—
214C2×#323—732no—
215C73#830011yescharacteristic, complemented, Sylow
216C24×C4—731no—
217C2×#117—1464no—
218C2×#117—1464no—
219C2×#117—1464no—
220C22×C4⋊C4—731no—
221C22×C4⋊C4—731no—
222C22×C22⋊C4—731no—
223C22×C22⋊C4#6440811yescharacteristic
224C22×C42—731no—
225C22×C42—731no—
226C2×C22⋊C8—734no—
227#336—1464no—
228#324—1464no—
229#323—1464no—
230C25C2×#6440811yescharacteristic
231C23×C4—731no—
232C23×C4—731no—
233C23×C4—731no—
234C23×C4—731no—
235C23×C4—734no—
236C23×C4—1462no—
237C23×C4—1462no—
238C23×C4—1462no—
239C23×C4—1462no—
240C23×C4—1462no—
241C23×C4—1462no—
242C23×C4C2×#6440811yescharacteristic
243C23×C4C2×#6440811yescharacteristic
244C22×C8—1464no—
245#117—14632no—
246C2×C4⋊C4—734no—
247C2×C4⋊C4—1462no—
248C2×C4⋊C4—1462no—
249C2×C4⋊C4—1462no—
250C2×C4⋊C4—1462no—
251C2×C4⋊C4—1462no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—734no—
256C2×C22⋊C4—1462no—
257C2×C22⋊C4—1462no—
258C2×C42—734no—
259C2×C42—1462no—
260C2×C42—1462no—
261C2×C42—1462no—
262C2×C42—1462no—
263C2×C42—1462no—
264C22⋊C8—1464no—
265C22⋊C8—1464no—
266C24—21no—
267C24—21no—
268C24—21no—
269C24—21no—
270C24—42no—
271C24—42no—
272C24C22⋊#6440812yes—
273C24#1192403612yes—
274C24#1192403812yes—
275C24C22×#6440811yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—2922no—
283C22×C4—2922no—
284C22×C4—732no—
285C22×C4—732no—
286C22×C4—732no—
287C22×C4—732no—
288C22×C4—732no—
289C22×C4—732no—
290C22×C4—732no—
291C22×C4—732no—
292C22×C4—732no—
293C22×C4—732no—
294C22×C4—1461no—
295C22×C4—1461no—
296C22×C4—1468no—
297C22×C4—1468no—
298C22×C4—1468no—
299C22×C4—1468no—
300C22×C4—1468no—
301C22×C4—1468no—
302C22×C4—1461no—
303C22×C4—1461no—
304C22×C4—1461no—
305C22×C4—1461no—
306C22×C4—1468no—
307C22×C4—1461no—
308C22×C4—1461no—
309C22×C4—1461no—
310C22×C4—1461no—
311C22×C4C22⋊#6440812yes—
312C22×C4C22⋊#6440812yes—
313C2×C8—2924no—
314C2×C8—2928no—
315C4⋊C4—1468no—
316C4⋊C4—1468no—
317C22⋊C4—28no—
318C22⋊C4—1468no—
319C42—1468no—
320C42—1468no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—42no—
330C23—42no—
331C23—44no—
332C23—44no—
333C23—44no—
334C23—44no—
335C23—42no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23#1455664814yes—
340C23C2×C22⋊#6440811yescharacteristic
341C23C2×C22⋊#6440811yescharacteristic
342C23C2×C22⋊#6440811yescharacteristic
343C23C2×#1192403611yescharacteristic
344C23D73⋊M1611yescharacteristic
345C23D73⋊M1611yescharacteristic
346C23C2×#1192403811yescharacteristic
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—2922no—
356C2×C4—2922no—
357C2×C4—2922no—
358C2×C4—2922no—
359C2×C4—2922no—
360C2×C4—734no—
361C2×C4—734no—
362C2×C4—734no—
363C2×C4—1462no—
364C2×C4—14632no—
365C2×C4—1462no—
366C2×C4—1462no—
367C2×C4—1462no—
368C2×C4—1462no—
369C2×C4—1462no—
370C2×C4—1462no—
371C2×C4—1462no—
372C2×C4—1462no—
373C2×C4—1462no—
374C2×C4—1462no—
375C2×C4—1462no—
376C2×C4—1462no—
377C2×C4—1464no—
378C8—5844no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—24no—
388C22—44no—
389C22—44no—
390C22—44no—
391C22—44no—
392C22—44no—
393C22—44no—
394C22—42no—
395C22—42no—
396C22#1798952811yescharacteristic
397C22#1798955511yescharacteristic
398C22#1798955511yescharacteristic
399C22C2×#1455664811yescharacteristic
400C22#1798955811yescharacteristic
401C22#1798955811yescharacteristic
402C22#1798955911yescharacteristic
403C22#1798956712yes—
404C22#1798957412yes—
405C4—42no—
406C4—42no—
407C4—2922no—
408C4—1464no—
409C4—1464no—
410C4—1464no—
411C2—21no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—44no—
416C2#2262516312yes—
417C2#2262518312yes—
418C2#2262575411yescharacteristic
419C2#2262576111yescharacteristic
420C2#2262576811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC23×C73C22×C8
FrattiniC24C22×#64408
FittingC22×C22⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC25×C73C2×C4
cosocleC23×Dic73C23
hypercenterC22×C22⋊C4#64408
hypocenterC73#8300
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #22625822C2semidirect
2. C2×#17989433C2semidirect
28. C23×Dic73C8semidirect
215. C73#8300semidirect

Maximal subgroups

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

subgroupindex
#226258222
C2×#179894332
C2×#179894302
C22×#145565472
#830073