Finite Group Databasebeta

← #34008600

Subgroups — #34008600

Order 18688.

802 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989467C212yesmaximal
2C2×#17989467C212yesmaximal
3#22625594C212yesmaximal
4C2×C4×#11924007C211yesmaximal, characteristic
5C22×#11924037C2214yes—
6#17989467—24no—
7#17989467C418yescomplemented
8#17989453—22no—
9#17989453—22no—
10C22×#11924007C2211yescharacteristic
11C22×#11924007C2211yescharacteristic
12C22×C4×Dic73C411yescharacteristic
13C22×C4×Dic73C2211yescharacteristic
14C4×#11924007—22no—
15C4×#11924007—22no—
16C2×#14556498C411yescharacteristic
17C2×#14556498C411yescharacteristic
18C22×C42×C73C411yescharacteristic
19C2×#11924037—24no—
20C2×#11924037—24no—
21C2×#11924037—24no—
22C2×#11924037—24no—
23C2×#11924037—24no—
24C2×#11924037C2×C418yes—
25C22×#10596833—24no—
26C23×Dic73C2×C411yescharacteristic
27C23×Dic73C2×C411yescharacteristic
28C23×Dic73C2×C411yescharacteristic
29C23×Dic73C2311yescharacteristic
30C2×#11924007—22no—
31C2×#11924007—22no—
32C2×#11924007—22no—
33C2×#11924007—22no—
34C2×#11924007C2×C414yes—
35C2×#11924007D412yes—
36C2×#11924007Q812yes—
37C2×C4×Dic73—22no—
38C2×C4×Dic73—22no—
39C2×C4×Dic73—21no—
40C2×C4×Dic73—21no—
41C2×C4×Dic73—42no—
42C2×C4×Dic73D412yes—
43C2×C4×Dic73D412yes—
44#14556498—22no—
45#14556498—22no—
46C23×C4×C73C2×C411yescharacteristic
47C23×C4×C73C2×C411yescharacteristic
48C23×C4×C73C2×C411yescharacteristic
49C2×C42×C73—21no—
50C2×C42×C73—21no—
51C2×C42×C73—42no—
52#11924037—28no—
53#11924037—28no—
54#11924037—44no—
55#11924037—44no—
56C2×#10596833—28no—
57C2×#10596833—44no—
58C2×#10596833—44no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—41no—
66C22×Dic73—41no—
67C22×Dic73—41no—
68C22×Dic73—41no—
69C22×Dic73—41no—
70C22×Dic73—41no—
71C22×Dic73C4212yes—
72C22×Dic73C22⋊C412yes—
73C22×Dic73C4⋊C412yes—
74C22×Dic73C22×C412yes—
75C22×Dic73C2×D411yescharacteristic
76C22×Dic73C2×D412yes—
77C22×Dic73C2×Q811yescharacteristic
78C22×Dic73#4112yes—
79C22×Dic73#4112yes—
80C22×Dic73#4112yes—
81C22×Dic73#4112yes—
82#11924007—28no—
83#11924007—24no—
84#11924007—24no—
85C4×Dic73—24no—
86C4×Dic73—24no—
87C4×Dic73—42no—
88C4×Dic73—42no—
89C24×C73C22×C411yescharacteristic
90C22×C4×C73—21no—
91C22×C4×C73—21no—
92C22×C4×C73—22no—
93C22×C4×C73—22no—
94C22×C4×C73—21no—
95C22×C4×C73—21no—
96C22×C4×C73—21no—
97C22×C4×C73—21no—
98C22×C4×C73—41no—
99C22×C4×C73—41no—
100C22×C4×C73—41no—
101C22×C4×C73—41no—
102C22×C4×C73C4212yes—
103C22×C4×C73C22⋊C411yescharacteristic
104C22×C4×C73C22⋊C411yescharacteristic
105C22×C4×C73C4⋊C412yes—
106C42×C73—42no—
107C42×C73—42no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73C2×C4211yescharacteristic
113C23×C73C2×C22⋊C411yescharacteristic
114C23×C73C2×C4⋊C411yescharacteristic
115C23×C73#11711yescharacteristic
116C23×C73#11711yescharacteristic
117C23×C73#11711yescharacteristic
118C23×C73#11711yescharacteristic
119C2×C4×C73—24no—
120C2×C4×C73—24no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—22no—
126C2×C4×C73—22no—
127C2×C4×C73—42no—
128C2×C4×C73—42no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—42no—
134C2×C4×C73—42no—
135C2×C4×C73#10012yes—
136C2×C4×C73#10112yes—
137C2×Dic73—22no—
138C2×Dic73—22no—
139C2×Dic73—22no—
140C2×Dic73—22no—
141C2×Dic73—22no—
142C2×Dic73—42no—
143C2×Dic73—42no—
144C2×Dic73—42no—
145C2×Dic73—42no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—42no—
151C2×Dic73—42no—
152C2×Dic73#11714yes—
153C2×Dic73C4×D414yes—
154C2×Dic73C4×D412yes—
155C2×Dic73C4×Q812yes—
156C2×Dic73#12112yes—
157C2×Dic73C22⋊Q812yes—
158C2×Dic73#12314yes—
159C2×Dic73#12412yes—
160C2×Dic73#12512yes—
161C2×Dic73#12614yes—
162#10596833—48no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—21no—
175C22×C73#37611yescharacteristic
176C22×C73C4×C22⋊C411yescharacteristic
177C22×C73C4×C4⋊C411yescharacteristic
178C22×C73#38011yescharacteristic
179C22×C73#38111yescharacteristic
180C22×C73#38211yescharacteristic
181C22×C73#38311yescharacteristic
182C22×C73C2×#10011yescharacteristic
183C22×C73C2×#10111yescharacteristic
184C22×C73#41311yescharacteristic
185C22×C73#41311yescharacteristic
186C4×C73—22no—
187C4×C73—22no—
188C4×C73—42no—
189C4×C73—42no—
190Dic73—42no—
191Dic73—42no—
192Dic73—42no—
193Dic73#38714yes—
194Dic73#38814yes—
195#10802—731nomaximal, Sylow
196C2×C73—21no—
197C2×C73—21no—
198C2×C73—21no—
199C2×C73—21no—
200C2×C73#143411yescharacteristic
201C2×C73C4×#10011yescharacteristic
202C2×C73C4×#10111yescharacteristic
203C2×C73#180011yescharacteristic
204C2×C73#180111yescharacteristic
205C2×C73#182111yescharacteristic
206C2×C73#182211yescharacteristic
207C2×C4×C4⋊C4—731no—
208C2×#343—732no—
209C2×#343—732no—
210#1728—732no—
211C73#1080211yescharacteristic, complemented, Sylow
212C22×M16—734no—
213C22×C4⋊C4—731no—
214C22×C4⋊C4—731no—
215C22×C42—731no—
216C22×C42—731no—
217C22×C42#6440811yescharacteristic
218C4×C4⋊C4—1462no—
219C4×C4⋊C4—1462no—
220C2×#95—731no—
221C2×#95—731no—
222#343—738no—
223#343—1464no—
224#336—1462no—
225#336—1462no—
226C23×C4—731no—
227C23×C4—731no—
228C23×C4—731no—
229C23×C4—731no—
230C23×C4C2×#6440811yescharacteristic
231C23×C4C2×#6440811yescharacteristic
232C23×C4C2×#6440811yescharacteristic
233C2×M16—738no—
234C2×M16—1464no—
235C2×M16—1464no—
236C2×M16—1464no—
237C2×M16—1464no—
238C2×M16—1464no—
239C22×C8—1464no—
240C2×C4⋊C4—734no—
241C2×C4⋊C4—732no—
242C2×C4⋊C4—732no—
243C2×C4⋊C4—1462no—
244C2×C4⋊C4—1462no—
245C2×C4⋊C4—1462no—
246C2×C4⋊C4—1462no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42—42no—
250C2×C42—2922no—
251C2×C42—732no—
252C2×C42—732no—
253C2×C42—1461no—
254C2×C42—1461no—
255C2×C42—1462no—
256C2×C42—1462no—
257#95—1462no—
258#95—1462no—
259C24C22×#6440811yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—2921no—
273C22×C4—2921no—
274C22×C4—2921no—
275C22×C4—2921no—
276C22×C4—2921no—
277C22×C4—2921no—
278C22×C4—732no—
279C22×C4—732no—
280C22×C4—732no—
281C22×C4—732no—
282C22×C4—731no—
283C22×C4—731no—
284C22×C4—732no—
285C22×C4—732no—
286C22×C4—732no—
287C22×C4—732no—
288C22×C4—732no—
289C22×C4—1461no—
290C22×C4—1461no—
291C22×C4—1461no—
292C22×C4—1461no—
293C22×C4—1461no—
294C22×C4—1461no—
295C22×C4C4×#6440812yes—
296C22×C4C22⋊#6440811yescharacteristic
297C22×C4C22⋊#6440811yescharacteristic
298C22×C4C4⋊#6440812yes—
299M16—2924no—
300M16—2924no—
301M16—1468no—
302M16—1468no—
303C2×C8—2924no—
304C2×C8—2924no—
305C2×C8—1468no—
306C4⋊C4—1468no—
307C4⋊C4—1464no—
308C4⋊C4—1464no—
309C42—42no—
310C42—42no—
311C42—2922no—
312C42—2922no—
313C42—1464no—
314C42—1464no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23C2×C4×#6440811yescharacteristic
320C23C2×C22⋊#6440811yescharacteristic
321C23C2×C4⋊#6440811yescharacteristic
322C23#1455667011yescharacteristic
323C23#1455667011yescharacteristic
324C23#1455667011yescharacteristic
325C23#1455667011yescharacteristic
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—2922no—
343C2×C4—2922no—
344C2×C4—2922no—
345C2×C4—2922no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—2921no—
349C2×C4—2921no—
350C2×C4—2922no—
351C2×C4—2922no—
352C2×C4—734no—
353C2×C4—734no—
354C2×C4—732no—
355C2×C4—732no—
356C2×C4—732no—
357C2×C4—732no—
358C2×C4—734no—
359C2×C4—732no—
360C2×C4—732no—
361C2×C4—734no—
362C2×C4—1462no—
363C2×C4—1462no—
364C2×C4—1462no—
365C2×C4—1462no—
366C2×C4—1462no—
367C2×C4#1455665112yes—
368C2×C4#1455665212yes—
369C8—2928no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22#1798952311yescharacteristic
383C22C4×C22⋊#6440811yescharacteristic
384C22C4×C4⋊#6440811yescharacteristic
385C22#1798952911yescharacteristic
386C22#1798953011yescharacteristic
387C22#1798953111yescharacteristic
388C22#1798953211yescharacteristic
389C22C2×#1455665111yescharacteristic
390C22C2×#1455665211yescharacteristic
391C22#1798957311yescharacteristic
392C22#1798957311yescharacteristic
393C4—22no—
394C4—22no—
395C4—42no—
396C4—42no—
397C4—2922no—
398C4—2922no—
399C4—2922no—
400C4—734no—
401C4—734no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#2262510711yescharacteristic
407C2C4×#1455665111yescharacteristic
408C2C4×#1455665211yescharacteristic
409C2#2262579511yescharacteristic
410C2#2262579711yescharacteristic
411C2#2262583011yescharacteristic
412C2#2262583211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC23×C73C2×C42
FrattiniC24C22×#64408
FittingC22×C42×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC23×Dic73C23
hypercenterC22×C42#64408
hypocenterC73#10802
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
7. #17989467C4semidirect
211. C73#10802semidirect

Maximal subgroups

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

subgroupindex
C2×#179894672
#226255942
C2×C4×#119240072
#1080273