Finite Group Databasebeta

← #34008138

Subgroups — #34008138

Order 18688.

680 conjugacy classes of subgroups.

The subgroup lattice has 416 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×#17988491C211yesmaximal, characteristic
6C2×#14556658—21no—
7C2×C22⋊#10596833C2212yes—
8C2×C22⋊#10596833C2212yes—
9C2×C4×#10596833—21no—
10#17989453—21no—
11#17989453—21no—
12C23×Dic146C411yescharacteristic
13C22×#11924007C411yescharacteristic
14C22×C4×Dic73C2211yescharacteristic
15#17988491—21no—
16#17988491—21no—
17#17988491—21no—
18#17988491—21no—
19C2×#14556498C411yescharacteristic
20C2×#14556498C2211yescharacteristic
21C2×#14556498C2211yescharacteristic
22C2×#95×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556658—42no—
26C22⋊#10596833—22no—
27C22⋊#10596833—24no—
28C22⋊#10596833Q814yescomplemented
29C4×#10596833—42no—
30C22×Dic146—21no—
31C22×Dic146—21no—
32C22×Dic146—22no—
33C22×Dic146—42no—
34C22×Dic146—42no—
35C22×Dic146C814yescomplemented
36C23×Dic73C2×C411yescharacteristic
37C23×Dic73C2×C411yescharacteristic
38C23×Dic73C2×C411yescharacteristic
39C23×Dic73C2311yescharacteristic
40C2×#11924007—21no—
41C2×#11924007—21no—
42C2×#11924007—42no—
43C2×C4×Dic73—42no—
44C2×C4×Dic73D411yescharacteristic
45C2×C4×Dic73D411yescharacteristic
46C2×C4×Dic73D411yescharacteristic
47C2×C4×Dic73D411yescharacteristic
48#14556498—21no—
49#14556498—21no—
50#14556498—21no—
51#14556498—21no—
52#14556498—21no—
53#14556498—21no—
54C23×C4×C73C2×C411yescharacteristic
55C23×C4×C73C2×C411yescharacteristic
56C23×C4×C73C2×C411yescharacteristic
57#95×C73—21no—
58#95×C73—21no—
59C2×#10596833—24no—
60C2×#10596833—42no—
61C2×#10596833—42no—
62C2×#10596833—42no—
63C2×#10596833—42no—
64C2×#10596833—42no—
65C2×Dic146—24no—
66C2×Dic146—24no—
67C2×Dic146—42no—
68C2×Dic146—42no—
69C2×Dic146—48no—
70C2×Dic146—42no—
71C2×Dic146—42no—
72C2×Dic146—48no—
73C22×Dic73—22no—
74C22×Dic73—22no—
75C22×Dic73—21no—
76C22×Dic73—21no—
77C22×Dic73—21no—
78C22×Dic73—22no—
79C22×Dic73—41no—
80C22×Dic73—41no—
81C22×Dic73—41no—
82C22×Dic73—41no—
83C22×Dic73—41no—
84C22×Dic73—41no—
85C22×Dic73C22⋊C411yescharacteristic
86C22×Dic73C22⋊C411yescharacteristic
87C22×Dic73C2×C812yes—
88C22×Dic73C2×C812yes—
89C22×Dic73M1612yes—
90C22×Dic73C2×D411yescharacteristic
91C22×Dic73C2×D411yescharacteristic
92C22×Dic73C2×Q812yes—
93C22×Dic73#4112yes—
94#11924007—42no—
95#11924007—42no—
96C4×Dic73—22no—
97C4×Dic73—22no—
98C4×Dic73—41no—
99C4×Dic73—41no—
100C24×C73C22×C411yescharacteristic
101C22×C4×C73—21no—
102C22×C4×C73—21no—
103C22×C4×C73—22no—
104C22×C4×C73—22no—
105C22×C4×C73—21no—
106C22×C4×C73—22no—
107C22×C4×C73—41no—
108C22×C4×C73—41no—
109C22×C4×C73—41no—
110C22×C4×C73—41no—
111C22×C4×C73—41no—
112C22×C4×C73C22⋊C411yescharacteristic
113C22×C4×C73C22⋊C411yescharacteristic
114C22×C4×C73C2×C812yes—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73C2×C22⋊C411yescharacteristic
120C23×C73C4×Q812yes—
121C23×C73C22×C811yescharacteristic
122C23×C73C2×M1611yescharacteristic
123C23×C73#13112yes—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—22no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—44no—
131C2×C4×C73—42no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—42no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—82no—
139C2×C4×C73#10112yes—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—24no—
147C2×Dic73—24no—
148C2×Dic73—22no—
149C2×Dic73—42no—
150C2×Dic73—42no—
151C2×Dic73—42no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—42no—
155C2×Dic73—41no—
156C2×Dic73—41no—
157C2×Dic73—41no—
158C2×Dic73—82no—
159C2×Dic73C22⋊C812yes—
160C2×Dic73C22⋊C812yes—
161C2×Dic73#9912yes—
162C2×Dic73#10012yes—
163C2×Dic73C22⋊Q812yes—
164C2×Dic73#12411yescharacteristic
165C2×Dic73C4⋊Q811yescharacteristic
166Dic146—48no—
167Dic146—48no—
168#10596833—44no—
169#10596833—82no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—22no—
175C22×C73—22no—
176C22×C73—22no—
177C22×C73—22no—
178C22×C73#39111yescharacteristic
179C22×C73C2×C22⋊C811yescharacteristic
180C22×C73#40811yescharacteristic
181C22×C73C2×#9911yescharacteristic
182C22×C73#41011yescharacteristic
183C22×C73C2×#10011yescharacteristic
184C22×C73C2×#10111yescharacteristic
185C22×C73C8×Q812yes—
186C22×C73#44612yes—
187C4×C73—22no—
188C4×C73—42no—
189C4×C73—41no—
190C4×C73—81no—
191Dic73—22no—
192Dic73—22no—
193Dic73—21no—
194Dic73—21no—
195Dic73—42no—
196Dic73—81no—
197Dic73#32314yes—
198#9878—731nomaximal, Sylow
199C2×C73—22no—
200C2×C73—22no—
201C2×C73C2×#32311yescharacteristic
202C2×C73#146111yescharacteristic
203C2×C73#146911yescharacteristic
204C2×C73#147211yescharacteristic
205C2×C73#198411yescharacteristic
206C2×C73#199611yescharacteristic
207C2×C73#199711yescharacteristic
208C2×#391—731no—
209#1797—731no—
210C4×C22⋊C8—731no—
211#1280—732no—
212#1280—732no—
213C73#987811yescharacteristic, complemented, Sylow
214C23×Q8—731no—
215C22×C4⋊C4—731no—
216C22×C42—731no—
217C2×C4⋊C8—1461no—
218C2×C22⋊C8—732no—
219C2×C22⋊C8—732no—
220C2×C4×C8—1461no—
221#391—1461no—
222#391—1461no—
223#391—1461no—
224#391—1461no—
225C2×#95—731no—
226C2×#95—731no—
227C2×#95—731no—
228C2×#95#6440811yescharacteristic
229#336—1461no—
230#336—1461no—
231C22×Q8—2922no—
232C22×Q8—2922no—
233C22×Q8—734no—
234C22×Q8—1461no—
235C22×Q8—1461no—
236C22×Q8—1462no—
237C23×C4—731no—
238C23×C4—731no—
239C23×C4—731no—
240C23×C4—731no—
241C23×C4C2×#6440811yescharacteristic
242C23×C4C2×#6440811yescharacteristic
243C23×C4C2×#6440811yescharacteristic
244C22×C8—1462no—
245C22×C8—1462no—
246C2×C4⋊C4—2922no—
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—21no—
260#95—21no—
261#95—1461no—
262#95—1461no—
263#95—1461no—
264#95—1461no—
265#95—1461no—
266#95—1461no—
267C24C22×#6440811yescharacteristic
268C2×Q8—2922no—
269C2×Q8—2922no—
270C2×Q8—2928no—
271C2×Q8—2928no—
272C2×Q8—2922no—
273C2×Q8—2922no—
274C2×Q8—1464no—
275C2×Q8—1464no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—2921no—
288C22×C4—2921no—
289C22×C4—2921no—
290C22×C4—2921no—
291C22×C4—2921no—
292C22×C4—2921no—
293C22×C4—732no—
294C22×C4—732no—
295C22×C4—732no—
296C22×C4—731no—
297C22×C4—732no—
298C22×C4—732no—
299C22×C4—731no—
300C22×C4—731no—
301C22×C4—731no—
302C22×C4—1461no—
303C22×C4—1461no—
304C22×C4—1461no—
305C22×C4—1462no—
306C22×C4—1462no—
307C22×C4—1462no—
308C22×C4C22⋊#6440811yescharacteristic
309C22×C4C22⋊#6440811yescharacteristic
310C22×C4#1192403612yes—
311C2×C8—2922no—
312C2×C8—2922no—
313C2×C8—2922no—
314C2×C8—2922no—
315C2×C8—2922no—
316C2×C8—1464no—
317C4⋊C4—2922no—
318C4⋊C4—2922no—
319C42—2921no—
320C42—2921no—
321C42—1462no—
322C42—1462no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23C2×C22⋊#6440811yescharacteristic
328C23Q8×#6440812yes—
329C23C2×#1192403611yescharacteristic
330C23D73⋊M1611yescharacteristic
331C23#1455667812yes—
332Q8—2928no—
333Q8—2928no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—2922no—
350C2×C4—2921no—
351C2×C4—2921no—
352C2×C4—2922no—
353C2×C4—2921no—
354C2×C4—2921no—
355C2×C4—2921no—
356C2×C4—2922no—
357C2×C4—2922no—
358C2×C4—5842no—
359C2×C4—732no—
360C2×C4—732no—
361C2×C4—732no—
362C2×C4—731no—
363C2×C4—732no—
364C2×C4—731no—
365C2×C4—732no—
366C2×C4—1462no—
367C2×C4—1464no—
368C2×C4—1464no—
369C2×C4—1461no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4—1461no—
374C2×C4—1461no—
375C2×C4#1455665212yes—
376C8—2924no—
377C8—5842no—
378C22—22no—
379C22—22no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22(C2×#64408)⋊Q811yescharacteristic
387C22#1798955511yescharacteristic
388C22#1798956011yescharacteristic
389C22D73⋊#9911yescharacteristic
390C22#1798956611yescharacteristic
391C22D73⋊#10011yescharacteristic
392C22C2×#1455665211yescharacteristic
393C22#1798963612yes—
394C22#1798963912yes—
395C4—22no—
396C4—42no—
397C4—41no—
398C4—81no—
399C4—2922no—
400C4—5841no—
401C4—734no—
402C4—1462no—
403C4—1461no—
404C4—1461no—
405C4—1462no—
406C2—22no—
407C2—22no—
408C2#2262515711yescharacteristic
409C2#2262517311yescharacteristic
410C2#2262520011yescharacteristic
411C2#2262521011yescharacteristic
412C2#2262610211yescharacteristic
413C2#2262612211yescharacteristic
414C2#2262612411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC23×C73C22×C8
FrattiniC24C22×#64408
FittingC2×#95×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC23×Dic73C23
hypercenterC2×#95#64408
hypocenterC73#9878
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
28. C22⋊#10596833Q8semidirect
35. C22×Dic146C8semidirect
213. C73#9878semidirect

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×#179884912
#987873