Finite Group Databasebeta

← #34008141

Subgroups — #34008141

Order 18688.

616 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625787C211yesmaximal, characteristic
2C4×C22⋊#10596833C211yesmaximal, characteristic
3#22624769C212yesmaximal
4#22624769C212yesmaximal
5C2×#17988482C211yesmaximal, characteristic
6C2×#14556658—21no—
7C2×C22⋊#10596833C2212yes—
8C2×C22⋊#10596833C2212yes—
9C2×C4×#10596833—21no—
10#17989453—21no—
11#17989453—21no—
12C22×#11924007C411yescharacteristic
13C22×#11924007C411yescharacteristic
14C22×#11924007C411yescharacteristic
15C22×C4×Dic73C2211yescharacteristic
16#17988482—21no—
17#17988482—21no—
18#17988482—21no—
19#17988482—21no—
20C2×#14556498C2211yescharacteristic
21C2×#14556498C2211yescharacteristic
22C22×C4⋊C4×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556658—42no—
26C22⋊#10596833—22no—
27C22⋊#10596833—24no—
28C22⋊#10596833Q814yes—
29C4×#10596833—42no—
30C23×Dic73C2×C411yescharacteristic
31C23×Dic73C2×C411yescharacteristic
32C23×Dic73C2×C411yescharacteristic
33C23×Dic73C2311yescharacteristic
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×#11924007—22no—
37C2×#11924007—21no—
38C2×#11924007—21no—
39C2×#11924007—21no—
40C2×#11924007—21no—
41C2×#11924007—42no—
42C2×#11924007—42no—
43C2×#11924007C814yescomplemented
44C2×C4×Dic73—42no—
45C2×C4×Dic73D411yescharacteristic
46C2×C4×Dic73D411yescharacteristic
47C2×C4×Dic73D411yescharacteristic
48C2×C4×Dic73D411yescharacteristic
49#14556498—21no—
50#14556498—21no—
51#14556498—21no—
52#14556498—21no—
53C23×C4×C73C2×C411yescharacteristic
54C23×C4×C73C2×C411yescharacteristic
55C23×C4×C73C2×C411yescharacteristic
56C2×C4⋊C4×C73—21no—
57C2×C4⋊C4×C73—21no—
58C2×C4⋊C4×C73—42no—
59C2×#10596833—24no—
60C2×#10596833—42no—
61C2×#10596833—42no—
62C2×#10596833—42no—
63C2×#10596833—42no—
64C2×#10596833—42no—
65C22×Dic73—22no—
66C22×Dic73—22no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73—22no—
71C22×Dic73—41no—
72C22×Dic73—41no—
73C22×Dic73—41no—
74C22×Dic73—41no—
75C22×Dic73—41no—
76C22×Dic73—41no—
77C22×Dic73C22⋊C411yescharacteristic
78C22×Dic73C22⋊C411yescharacteristic
79C22×Dic73C2×C812yes—
80C22×Dic73C2×C812yes—
81C22×Dic73M1612yes—
82C22×Dic73C2×D411yescharacteristic
83C22×Dic73C2×D411yescharacteristic
84C22×Dic73C2×Q812yes—
85C22×Dic73#4112yes—
86#11924007—24no—
87#11924007—24no—
88#11924007—42no—
89#11924007—42no—
90#11924007—42no—
91#11924007—42no—
92C4×Dic73—22no—
93C4×Dic73—22no—
94C4×Dic73—41no—
95C4×Dic73—41no—
96C24×C73C22×C411yescharacteristic
97C22×C4×C73—21no—
98C22×C4×C73—21no—
99C22×C4×C73—22no—
100C22×C4×C73—22no—
101C22×C4×C73—21no—
102C22×C4×C73—22no—
103C22×C4×C73—41no—
104C22×C4×C73—41no—
105C22×C4×C73—41no—
106C22×C4×C73—41no—
107C22×C4×C73—41no—
108C22×C4×C73C22⋊C411yescharacteristic
109C22×C4×C73C22⋊C411yescharacteristic
110C22×C4×C73C2×C812yes—
111C4⋊C4×C73—42no—
112C4⋊C4×C73—42no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73C2×C22⋊C411yescharacteristic
118C23×C73C4×Q812yes—
119C23×C73C22×C811yescharacteristic
120C23×C73C2×M1611yescharacteristic
121C23×C73#13112yes—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—22no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—44no—
129C2×C4×C73—42no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—42no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73—41no—
136C2×C4×C73—82no—
137C2×C4×C73#10012yes—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—24no—
145C2×Dic73—24no—
146C2×Dic73—22no—
147C2×Dic73—42no—
148C2×Dic73—42no—
149C2×Dic73—42no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152C2×Dic73—42no—
153C2×Dic73—41no—
154C2×Dic73—41no—
155C2×Dic73—41no—
156C2×Dic73—82no—
157C2×Dic73C22⋊C812yes—
158C2×Dic73C22⋊C812yes—
159C2×Dic73#9912yes—
160C2×Dic73#10112yes—
161C2×Dic73C22⋊Q812yes—
162C2×Dic73#12411yescharacteristic
163C2×Dic73C4⋊Q811yescharacteristic
164#10596833—44no—
165#10596833—82no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—22no—
171C22×C73—22no—
172C22×C73—22no—
173C22×C73—22no—
174C22×C73#39111yescharacteristic
175C22×C73C2×C22⋊C811yescharacteristic
176C22×C73#40811yescharacteristic
177C22×C73C2×#9911yescharacteristic
178C22×C73#41011yescharacteristic
179C22×C73C2×#10011yescharacteristic
180C22×C73C2×#10111yescharacteristic
181C22×C73C8×Q812yes—
182C22×C73#44612yes—
183C4×C73—22no—
184C4×C73—42no—
185C4×C73—41no—
186C4×C73—81no—
187Dic73—22no—
188Dic73—22no—
189Dic73—21no—
190Dic73—21no—
191Dic73—42no—
192Dic73—81no—
193Dic73#32414yes—
194#9879—731nomaximal, Sylow
195C2×C73—22no—
196C2×C73—22no—
197C2×C73C2×#32411yescharacteristic
198C2×C73#146011yescharacteristic
199C2×C73#147011yescharacteristic
200C2×C73#147111yescharacteristic
201C2×C73#198411yescharacteristic
202C2×C73#199611yescharacteristic
203C2×C73#199711yescharacteristic
204C2×#389—731no—
205#1797—731no—
206C4×C22⋊C8—731no—
207#1280—732no—
208#1280—732no—
209C73#987911yescharacteristic, complemented, Sylow
210C22×C4⋊C4—731no—
211C22×C4⋊C4—731no—
212C22×C4⋊C4—731no—
213C22×C4⋊C4#6440811yescharacteristic
214C22×C42—731no—
215C2×C4⋊C8—1461no—
216C2×C22⋊C8—732no—
217C2×C22⋊C8—732no—
218C2×C4×C8—1461no—
219#389—1461no—
220#389—1461no—
221#389—1461no—
222#389—1461no—
223C2×#95—731no—
224C2×#95—731no—
225#336—1461no—
226#336—1461no—
227C23×C4—731no—
228C23×C4—731no—
229C23×C4—731no—
230C23×C4—731no—
231C23×C4C2×#6440811yescharacteristic
232C23×C4C2×#6440811yescharacteristic
233C23×C4C2×#6440811yescharacteristic
234C22×C8—1462no—
235C22×C8—1462no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—42no—
239C2×C4⋊C4—2922no—
240C2×C4⋊C4—2922no—
241C2×C4⋊C4—734no—
242C2×C4⋊C4—1461no—
243C2×C4⋊C4—1461no—
244C2×C4⋊C4—1461no—
245C2×C4⋊C4—1461no—
246C2×C4⋊C4—1462no—
247C2×C4⋊C4—1461no—
248C2×C4⋊C4—1461no—
249C2×C42—2922no—
250C2×C42—731no—
251C2×C42—731no—
252C2×C42—731no—
253C2×C42—731no—
254C4⋊C8—2922no—
255C22⋊C8—734no—
256C22⋊C8—1464no—
257C22⋊C8—1462no—
258C4×C8—2922no—
259#95—1461no—
260#95—1461no—
261#95—1461no—
262#95—1461no—
263C24C22×#6440811yescharacteristic
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—2921no—
276C22×C4—2921no—
277C22×C4—2921no—
278C22×C4—2921no—
279C22×C4—2921no—
280C22×C4—2921no—
281C22×C4—732no—
282C22×C4—732no—
283C22×C4—732no—
284C22×C4—731no—
285C22×C4—732no—
286C22×C4—732no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—731no—
290C22×C4—1461no—
291C22×C4—1461no—
292C22×C4—1461no—
293C22×C4—1462no—
294C22×C4—1462no—
295C22×C4—1462no—
296C22×C4C22⋊#6440811yescharacteristic
297C22×C4C22⋊#6440811yescharacteristic
298C22×C4#1192403612yes—
299C2×C8—2922no—
300C2×C8—2922no—
301C2×C8—2922no—
302C2×C8—2922no—
303C2×C8—2922no—
304C2×C8—1464no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—2922no—
308C4⋊C4—2922no—
309C4⋊C4—2922no—
310C4⋊C4—2922no—
311C4⋊C4—1464no—
312C4⋊C4—1464no—
313C42—2921no—
314C42—2921no—
315C42—1462no—
316C42—1462no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C22⋊#6440811yescharacteristic
322C23Q8×#6440812yes—
323C23C2×#1192403611yescharacteristic
324C23D73⋊M1611yescharacteristic
325C23#1455667812yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—82no—
341C2×C4—2922no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—2922no—
345C2×C4—2921no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—2922no—
349C2×C4—2922no—
350C2×C4—5842no—
351C2×C4—732no—
352C2×C4—732no—
353C2×C4—732no—
354C2×C4—731no—
355C2×C4—732no—
356C2×C4—731no—
357C2×C4—732no—
358C2×C4—1462no—
359C2×C4—1464no—
360C2×C4—1464no—
361C2×C4—1461no—
362C2×C4—1461no—
363C2×C4—1461no—
364C2×C4—1461no—
365C2×C4—1461no—
366C2×C4—1461no—
367C2×C4#1455665112yes—
368C8—2924no—
369C8—5842no—
370C22—22no—
371C22—22no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22(C2×#64408)⋊Q811yescharacteristic
379C22#1798955511yescharacteristic
380C22#1798956011yescharacteristic
381C22D73⋊#9911yescharacteristic
382C22#1798956611yescharacteristic
383C22C2×#1455665111yescharacteristic
384C22D73⋊#10111yescharacteristic
385C22#1798963612yes—
386C22#1798963912yes—
387C4—22no—
388C4—42no—
389C4—41no—
390C4—81no—
391C4—2922no—
392C4—5841no—
393C4—734no—
394C4—1462no—
395C4—1461no—
396C4—1461no—
397C4—1462no—
398C2—22no—
399C2—22no—
400C2#2262516011yescharacteristic
401C2#2262517011yescharacteristic
402C2#2262520311yescharacteristic
403C2#2262520711yescharacteristic
404C2#2262610211yescharacteristic
405C2#2262612211yescharacteristic
406C2#2262612311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC23×C73C22×C8
FrattiniC24C22×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC23×Dic73C23
hypercenterC22×C4⋊C4#64408
hypocenterC73#9879
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
43. C2×#11924007C8semidirect
209. C73#9879semidirect

Maximal subgroups

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

subgroupindex
#226257872
C4×C22⋊#105968332
#226247692
C2×#179884822
#987973