Finite Group Databasebeta

← #34016127

Subgroups — #34016127

Order 18688.

970 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626607C212yesmaximal
2#22625203C218yesmaximal, complemented
3#22625181C212yesmaximal
4#22625179C212yesmaximal
5C22×#14556581C211yesmaximal, characteristic
6#17989608—22no—
7#17989607C2214yes—
8#17989604—22no—
9#17989603C2214yes—
10#17989590—22no—
11#17989557C2214yes—
12C4×#11924037—22no—
13#17989433C2218yes—
14#17989432C2218yes—
15C2×#14556581—22no—
16C2×#14556581—22no—
17C2×#14556581—22no—
18C2×#14556581—22no—
19C2×#14556581C414yes—
20C2×#14556581C2214yes—
21C22×C4⋊Dic73C2211yescharacteristic
22C22×#11924007C411yescharacteristic
23C22×#11924007C411yescharacteristic
24C22×#11924007C411yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×C4×Dic73C2211yescharacteristic
27C22×C4⋊C4×C73C411yescharacteristic
28C2×#11924037—24no—
29#14556658—24no—
30C4⋊#10596833—24no—
31C22⋊#10596833—24no—
32C22⋊#10596833C2318yes—
33#14556646—24no—
34C4×#10596833—24no—
35C23×Dic73C2×C411yescharacteristic
36C23×Dic73C2×C411yescharacteristic
37C23×Dic73C2×C411yescharacteristic
38C23×Dic73C2311yescharacteristic
39#14556581—24no—
40#14556581—24no—
41#14556581—24no—
42#14556581—24no—
43#14556581—24no—
44#14556581—24no—
45#14556581—24no—
46#14556581—24no—
47C2×C4⋊Dic73—22no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73C2×C412yes—
50C2×C4⋊Dic73C2312yes—
51C2×#11924007—21no—
52C2×#11924007—22no—
53C2×#11924007—21no—
54C2×#11924007—22no—
55C2×#11924007—21no—
56C2×#11924007—21no—
57C2×#11924007—22no—
58C2×#11924007—22no—
59C2×#11924007—21no—
60C2×#11924007—21no—
61C2×#11924007—22no—
62C2×#11924007C2×C414yes—
63C2×#11924007C2×C414yes—
64C2×#11924007C2×C414yes—
65C2×#11924007C2×C412yes—
66C2×#11924007C2312yes—
67C2×C4×Dic73C2×C412yes—
68C2×C4×Dic73D412yes—
69C2×C4×Dic73D412yes—
70C2×C4×Dic73D412yes—
71C2×C4×Dic73D412yes—
72C2×C4×Dic73C2312yes—
73C23×C4×C73C2×C411yescharacteristic
74C23×C4×C73C2×C411yescharacteristic
75C23×C4×C73C2×C411yescharacteristic
76C2×C4⋊C4×C73—22no—
77C2×C4⋊C4×C73—21no—
78C2×C4⋊C4×C73—21no—
79C2×C4⋊C4×C73C2×C414yes—
80#11924037—48no—
81C2×#10596833—28no—
82C22×Dic73—24no—
83C22×Dic73—21no—
84C22×Dic73—21no—
85C22×Dic73—21no—
86C22×Dic73—21no—
87C22×Dic73—42no—
88C22×Dic73—42no—
89C22×Dic73—42no—
90C22×Dic73C22⋊C411yescharacteristic
91C22×Dic73C22⋊C412yes—
92C22×Dic73C22⋊C411yescharacteristic
93C22×Dic73C22×C412yes—
94C22×Dic73C22×C412yes—
95C22×Dic73C22×C412yes—
96C22×Dic73C22×C411yescharacteristic
97C22×Dic73C2×D412yes—
98C22×Dic73C2×D412yes—
99C22×Dic73C2411yescharacteristic
100C4⋊Dic73—24no—
101C4⋊Dic73—24no—
102#11924007—24no—
103#11924007—24no—
104#11924007—24no—
105#11924007—24no—
106#11924007—24no—
107#11924007—24no—
108#11924007—24no—
109#11924007—24no—
110C4×Dic73C22⋊C412yes—
111C4×Dic73C22⋊C412yes—
112C4×Dic73C22⋊C412yes—
113C4×Dic73C22⋊C412yes—
114C4×Dic73C2×D412yes—
115C4×Dic73C2×D412yes—
116C4×Dic73C2×D412yes—
117C4×Dic73C2×D412yes—
118C24×C73C22×C411yescharacteristic
119C22×C4×C73—21no—
120C22×C4×C73—21no—
121C22×C4×C73—21no—
122C22×C4×C73—21no—
123C22×C4×C73—42no—
124C22×C4×C73—42no—
125C22×C4×C73—42no—
126C22×C4×C73C22⋊C411yescharacteristic
127C22×C4×C73C22⋊C411yescharacteristic
128C22×C4×C73C22⋊C412yes—
129C22×C4×C73C22×C412yes—
130C22×C4×C73C22×C412yes—
131C22×C4×C73C22×C412yes—
132C4⋊C4×C73—24no—
133C4⋊C4×C73—24no—
134C23×C73—22no—
135C23×C73—22no—
136C23×C73—22no—
137C23×C73C2×C22⋊C411yescharacteristic
138C23×C73C2×C22⋊C411yescharacteristic
139C23×C73C23×C411yescharacteristic
140C2×C4×C73—24no—
141C2×C4×C73—22no—
142C2×C4×C73—22no—
143C2×C4×C73—24no—
144C2×C4×C73—41no—
145C2×C4×C73—41no—
146C2×C4×C73—42no—
147C2×C4×C73—42no—
148C2×C4×C73—42no—
149C2×C4×C73—42no—
150C2×C4×C73—42no—
151C2×C4×C73—42no—
152C2×C4×C73C2×C22⋊C412yes—
153C2×C4×C73C2×C22⋊C412yes—
154C2×Dic73—24no—
155C2×Dic73—22no—
156C2×Dic73—24no—
157C2×Dic73—24no—
158C2×Dic73—22no—
159C2×Dic73—22no—
160C2×Dic73—24no—
161C2×Dic73—41no—
162C2×Dic73—42no—
163C2×Dic73—41no—
164C2×Dic73—42no—
165C2×Dic73—42no—
166C2×Dic73—42no—
167C2×Dic73—42no—
168C2×Dic73—42no—
169C2×Dic73#10114yes—
170C2×Dic73C2×C22⋊C412yes—
171C2×Dic73C2×C22⋊C412yes—
172C2×Dic73C2×C22⋊C412yes—
173C2×Dic73C22×D412yes—
174#10596833—48no—
175C22×C73—28no—
176C22×C73—21no—
177C22×C73—21no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73#41012yes—
183C22×C73C2×#10112yes—
184C22×C73C22×C22⋊C411yescharacteristic
185C22×C73#56812yes—
186C4×C73—22no—
187C4×C73—22no—
188C4×C73—42no—
189C4×C73—42no—
190Dic73—22no—
191Dic73—22no—
192Dic73—22no—
193Dic73—42no—
194Dic73—42no—
195Dic73C2×#10114yes—
196#17394—731nomaximal, Sylow
197C2×C73—22no—
198C2×C73—22no—
199C2×C73—22no—
200C2×C73#287911yescharacteristic
201C2×C73C2×#41011yescharacteristic
202C2×C73C22×#10111yescharacteristic
203C22×#125—731no—
204#2920—732no—
205#1470—738no—
206#1463—732no—
207#1463—732no—
208C73#1739411yescharacteristic, complemented, Sylow
209C2×#125—734no—
210C2×#125—734no—
211C2×#125—1462no—
212C2×#125—1462no—
213C2×#125—1462no—
214C2×#125—1462no—
215C22×C4⋊C4—731no—
216C22×C4⋊C4—731no—
217C22×C4⋊C4—731no—
218C22×C4⋊C4—731no—
219C22×C4⋊C4—731no—
220C22×C4⋊C4#6440811yescharacteristic
221C22×C42—731no—
222#432—734no—
223#432—1462no—
224#431—734no—
225#431—1462no—
226#423—1462no—
227#407—734no—
228C4×M16—1462no—
229#324—738no—
230#324—738no—
231C23×C4—731no—
232C23×C4—731no—
233C23×C4—731no—
234C23×C4—731no—
235C23×C4C2×#6440811yescharacteristic
236C23×C4C2×#6440811yescharacteristic
237C23×C4C2×#6440811yescharacteristic
238C2×M16—1464no—
239#125—1464no—
240#125—1464no—
241#125—1464no—
242#125—1464no—
243#125—1464no—
244#125—1464no—
245#125—1464no—
246#125—1464no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—732no—
251C2×C4⋊C4—732no—
252C2×C4⋊C4—732no—
253C2×C4⋊C4—734no—
254C2×C4⋊C4—734no—
255C2×C4⋊C4—734no—
256C2×C4⋊C4—732no—
257C2×C4⋊C4—1462no—
258C2×C4⋊C4—1461no—
259C2×C4⋊C4—1461no—
260C2×C4⋊C4—1462no—
261C2×C4⋊C4—1462no—
262C2×C4⋊C4—1461no—
263C2×C4⋊C4—1461no—
264C2×C4⋊C4—1462no—
265C2×C4⋊C4—1462no—
266C2×C4⋊C4—1462no—
267C2×C4⋊C4—1461no—
268C2×C4⋊C4—1461no—
269C2×C4⋊C4—1462no—
270C2×C4⋊C4C2×#6440814yes—
271C2×C42—732no—
272C2×C42—732no—
273C2×C42—732no—
274C2×C42—732no—
275C2×C42—732no—
276C2×C42—732no—
277C4⋊C8—1464no—
278C4⋊C8—1464no—
279C22⋊C8—738no—
280C22⋊C8—1464no—
281#97—1464no—
282C4×C8—1464no—
283C24C22×#6440811yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—2922no—
292C22×C4—2922no—
293C22×C4—2922no—
294C22×C4—731no—
295C22×C4—731no—
296C22×C4—732no—
297C22×C4—732no—
298C22×C4—731no—
299C22×C4—732no—
300C22×C4—732no—
301C22×C4—731no—
302C22×C4—732no—
303C22×C4—732no—
304C22×C4—1461no—
305C22×C4—1461no—
306C22×C4—1461no—
307C22×C4—1461no—
308C22×C4—1464no—
309C22×C4C22⋊#6440811yescharacteristic
310C22×C4C22⋊#6440811yescharacteristic
311C22×C4C22⋊#6440812yes—
312C22×C4C22×#6440812yes—
313C22×C4C22×#6440812yes—
314C22×C4C22×#6440812yes—
315M16—2928no—
316C2×C8—1468no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—1464no—
320C4⋊C4—1464no—
321C4⋊C4—1464no—
322C4⋊C4—1464no—
323C4⋊C4—1464no—
324C4⋊C4—1464no—
325C4⋊C4—1464no—
326C4⋊C4—1464no—
327C4⋊C4—1464no—
328C4⋊C4—1464no—
329C42—732no—
330C42—732no—
331C42—732no—
332C42—732no—
333C42—732no—
334C42—732no—
335C42—732no—
336C42—732no—
337C23—22no—
338C23—22no—
339C23—22no—
340C23C2×C22⋊#6440811yescharacteristic
341C23C2×C22⋊#6440811yescharacteristic
342C23C23×#6440811yescharacteristic
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
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—2921no—
361C2×C4—2922no—
362C2×C4—2921no—
363C2×C4—732no—
364C2×C4—734no—
365C2×C4—732no—
366C2×C4—732no—
367C2×C4—732no—
368C2×C4—1462no—
369C2×C4—1462no—
370C2×C4—1464no—
371C2×C4—1464no—
372C2×C4—1464no—
373C2×C4—1464no—
374C2×C4—1462no—
375C2×C4C2×C22⋊#6440812yes—
376C2×C4C2×C22⋊#6440812yes—
377C8—2928no—
378C22—28no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22#1798956612yes—
386C22D73⋊#10112yes—
387C22C22×C22⋊#6440811yescharacteristic
388C22#1798966512yes—
389C4—22no—
390C4—22no—
391C4—42no—
392C4—42no—
393C4—2922no—
394C4—2922no—
395C4—734no—
396C4—1462no—
397C4—1462no—
398C4—1462no—
399C2—22no—
400C2—22no—
401C2—22no—
402C2#2262651511yescharacteristic
403C2C2×#1798956611yescharacteristic
404C2C2×D73⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#64408
commutatorC23×C73C23×C4
FrattiniC23C23×#64408
FittingC22×C4⋊C4×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC22×Dic73C24
hypercenterC22×C4⋊C4#64408
hypocenterC73#17394
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #22625203C2semidirect
208. C73#17394semidirect

Maximal subgroups

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

subgroupindex
#226266072
#226252032
#226251812
#226251792
C22×#145565812
#1739473