Finite Group Databasebeta

← #34001409

Subgroups — #34001409

Order 18688.

578 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625785C211yesmaximal, characteristic
2C2×#17989453C211yesmaximal, characteristic
3#22624752C212yesmaximal, complemented
4#22624750C212yesmaximal, complemented
5#22612459C211yesmaximal, characteristic
6C23×#10596833—21no—
7C2×C4⋊#10596833—21no—
8C2×C22⋊#10596833—21no—
9#17989453—21no—
10#17989453C2212yes—
11#17989453C2212yes—
12C2×#14556570C411yescharacteristic
13C2×#14556556C411yescharacteristic
14C22×C4×Dic73C2211yescharacteristic
15#17988492C2211yescharacteristic
16#17988483C2211yescharacteristic
17#17988469—21no—
18#17988459—21no—
19C4⋊C4×Dic73C411yescharacteristic
20#17988438—21no—
21C22⋊C4×Dic73—21no—
22#380×C73C411yescharacteristic
23C22×#10596833—24no—
24C22×#10596833—22no—
25C22×#10596833—22no—
26C22×#10596833—42no—
27C22×#10596833—42no—
28C4⋊#10596833—42no—
29C22⋊#10596833—42no—
30C22×Dic146C2×C411yescharacteristic
31C23×Dic73D411yescharacteristic
32C23×Dic73D411yescharacteristic
33#14556570—22no—
34#14556570C814yescomplemented
35#14556556—42no—
36C2×C4⋊Dic73C2×C411yescharacteristic
37C2×#11924007—21no—
38C2×#11924007—21no—
39C2×#11924007—21no—
40C2×C22⋊Dic73—21no—
41C2×C4×Dic73—21no—
42C2×C4×Dic73—21no—
43C2×C4×Dic73—42no—
44C2×C4×Dic73C2×C411yescharacteristic
45C2×C4×Dic73D411yescharacteristic
46C2×C4×Dic73D411yescharacteristic
47C2×C4×Dic73C2311yescharacteristic
48#14556498—21no—
49#14556498—21no—
50#14556498—21no—
51#14556498—21no—
52C23×C4×C73C2×C411yescharacteristic
53C2×C4⋊C4×C73C2×C411yescharacteristic
54C2×C4⋊C4×C73C2×C411yescharacteristic
55C2×C22⋊C4×C73—21no—
56#95×C73—21no—
57C2×#10596833—24no—
58C2×#10596833—48no—
59C2×#10596833—42no—
60C2×#10596833—42no—
61C2×#10596833—42no—
62C2×#10596833—42no—
63C2×#10596833—42no—
64C2×Dic146—21no—
65C2×Dic146—41no—
66C2×Dic146—41no—
67C2×Dic146C2×C812yescomplemented
68C22×Dic73—22no—
69C22×Dic73—22no—
70C22×Dic73—21no—
71C22×Dic73—21no—
72C22×Dic73—21no—
73C22×Dic73—21no—
74C22×Dic73—41no—
75C22×Dic73—41no—
76C22×Dic73C22⋊C411yescharacteristic
77C22×Dic73C22⋊C411yescharacteristic
78C22×Dic73SD1612yes—
79C22×Dic73Q1612yes—
80C22×Dic73C2×D411yescharacteristic
81C22×Dic73C2×D411yescharacteristic
82C4⋊Dic73—21no—
83C4⋊Dic73C2×C812yescomplemented
84#11924007—24no—
85#11924007—42no—
86#11924007—41no—
87#11924007—41no—
88C22⋊Dic73—24no—
89C4×Dic73—22no—
90C4×Dic73—22no—
91C4×Dic73—41no—
92C4×Dic73—41no—
93C4×Dic73—42no—
94C4×Dic73—42no—
95C24×C73C22⋊C411yescharacteristic
96C22×C4×C73—21no—
97C22×C4×C73—21no—
98C22×C4×C73—41no—
99C22×C4×C73—41no—
100C22×C4×C73C22⋊C411yescharacteristic
101C22×C4×C73C2×C812yes—
102C22×C4×C73M1612yes—
103C22×C4×C73C22×C411yescharacteristic
104C4⋊C4×C73—41no—
105C4⋊C4×C73—41no—
106C22⋊C4×C73—42no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73C22⋊C812yes—
112C23×C73#10312yes—
113C23×C73#10412yes—
114C23×C73C2×C22⋊C411yescharacteristic
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—42no—
120C2×C4×C73—42no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73C22⋊C812yes—
128C2×C4×C73C22×C811yescharacteristic
129C2×C4×C73C2×M1611yescharacteristic
130C2×Dic73—24no—
131C2×Dic73—24no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—22no—
141C2×Dic73—22no—
142C2×Dic73—42no—
143C2×Dic73—42no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73#9912yes—
149C2×Dic73#10312yes—
150C2×Dic73C2×SD1611yescharacteristic
151C2×Dic73C2×Q1611yescharacteristic
152C2×Dic73AGL(1,ℤ/8)11yescharacteristic
153C2×Dic73#13711yescharacteristic
154Dic146—42no—
155Dic146—42no—
156#10596833—44no—
157#10596833—82no—
158C22×C73—22no—
159C22×C73—22no—
160C22×C73—22no—
161C22×C73—22no—
162C22×C73—22no—
163C22×C73—22no—
164C22×C73Q8⋊C814yes—
165C22×C73C2×C22⋊C811yescharacteristic
166C22×C73C2×#9911yescharacteristic
167C22×C73#41311yescharacteristic
168C22×C73C2×#10311yescharacteristic
169C22×C73#41711yescharacteristic
170C22×C73C2×#10411yescharacteristic
171C22×C73#42111yescharacteristic
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—22no—
175C4×C73—81no—
176C4×C73—81no—
177Dic73—21no—
178Dic73—22no—
179Dic73—21no—
180Dic73—21no—
181Dic73—22no—
182Dic73—21no—
183Dic73—42no—
184Dic73—42no—
185#7589—731nomaximal, Sylow
186C2×C73—24no—
187C2×C73#145911yescharacteristic
188C2×C73C2×Q8⋊C811yescharacteristic
189C2×C73#147711yescharacteristic
190C2×C73#150411yescharacteristic
191C2×C73#152011yescharacteristic
192C2×C73#153211yescharacteristic
193C2×C73#155011yescharacteristic
194C4×C22⋊Q8—731no—
195#1797—731no—
196C2×#336—731no—
197#1272—732no—
198#1271—732no—
199C73#758911yescharacteristic, complemented, Sylow
200C23×C8—1461no—
201C2×C22⋊Q8—731no—
202C2×C4×Q8—731no—
203C22×C42—731no—
204C2×C4⋊C8—1461no—
205C2×C22⋊C8—1461no—
206#391—731no—
207#389—731no—
208#387—1461no—
209#385—1461no—
210#380#6440811yescharacteristic
211C4×C4⋊C4—731no—
212C4×C4⋊C4—1461no—
213C4×C22⋊C4—1461no—
214#336—732no—
215#336—732no—
216#336—1461no—
217C22×Q8—731no—
218C23×C4—731no—
219C23×C4—731no—
220C23×C4C2×#6440811yescharacteristic
221C22×C8—2922no—
222C22×C8—2922no—
223C22×C8—1462no—
224C22×C8—1462no—
225C22×C8—1464no—
226C22⋊Q8—734no—
227C22⋊Q8—1462no—
228C4×Q8—2922no—
229C2×C4⋊C4—731no—
230C2×C4⋊C4—1461no—
231C2×C4⋊C4—1461no—
232C2×C4⋊C4—1461no—
233C2×C4⋊C4C2×#6440811yescharacteristic
234C2×C4⋊C4C2×#6440811yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—1461no—
237C2×C42—2922no—
238C2×C42—731no—
239C2×C42—731no—
240C2×C42—731no—
241C2×C42—731no—
242C2×C42—1461no—
243C2×C42—1461no—
244C4⋊C8—2922no—
245C22⋊C8—2922no—
246#95—21no—
247#95—1461no—
248#95—1461no—
249#95—1461no—
250#95—1461no—
251C24C22⋊#6440811yescharacteristic
252C2×Q8—2921no—
253C2×Q8—2921no—
254C2×Q8—732no—
255C2×Q8—1461no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—2921no—
261C22×C4—2921no—
262C22×C4—732no—
263C22×C4—732no—
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—1461no—
269C22×C4—1461no—
270C22×C4—1462no—
271C22×C4—1461no—
272C22×C4—1461no—
273C22×C4—1462no—
274C22×C4C22⋊#6440811yescharacteristic
275C22×C4#1192403612yes—
276C22×C4#1192403812yes—
277C22×C4C22×#6440811yescharacteristic
278C2×C8—2922no—
279C2×C8—2928no—
280C2×C8—2922no—
281C2×C8—2922no—
282C2×C8—2922no—
283C2×C8—2922no—
284C2×C8—1464no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—2921no—
288C4⋊C4—2921no—
289C4⋊C4—2922no—
290C4⋊C4—732no—
291C4⋊C4—1461no—
292C4⋊C4—1464no—
293C22⋊C4—42no—
294C22⋊C4—1464no—
295C42—2921no—
296C42—2921no—
297C42—2922no—
298C42—2922no—
299C42—1462no—
300C42—1462no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23#1455664812yes—
306C23#1455665412yes—
307C23#1455665512yes—
308C23C2×C22⋊#6440811yescharacteristic
309Q8—2922no—
310Q8—2922no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—2921no—
324C2×C4—2921no—
325C2×C4—2921no—
326C2×C4—2921no—
327C2×C4—2922no—
328C2×C4—2922no—
329C2×C4—732no—
330C2×C4—731no—
331C2×C4—732no—
332C2×C4—731no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—1462no—
336C2×C4—1462no—
337C2×C4—1464no—
338C2×C4—1464no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4#1455664812yes—
348C2×C4C2×#1192403611yescharacteristic
349C2×C4C2×#1192403811yescharacteristic
350C8—2924no—
351C8—5842no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22#1798943714yes—
359C22C2×#1455664811yescharacteristic
360C22D73⋊#9911yescharacteristic
361C22#1798957411yescharacteristic
362C22C2×#1455665411yescharacteristic
363C22#1798957811yescharacteristic
364C22C2×#1455665511yescharacteristic
365C22#1798958411yescharacteristic
366C4—21no—
367C4—21no—
368C4—22no—
369C4—81no—
370C4—81no—
371C4—2922no—
372C4—2922no—
373C4—1461no—
374C4—1462no—
375C4—1461no—
376C4—1461no—
377C4—1462no—
378C4—1461no—
379C2—24no—
380C2#2262516911yescharacteristic
381C2C2×#1798943711yescharacteristic
382C2#2262522811yescharacteristic
383C2#2262531611yescharacteristic
384C2#2262536911yescharacteristic
385C2#2262540711yescharacteristic
386C2#2262544911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting#380×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#380#64408
hypocenterC73#7589
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #22624752C2semidirect
4. #22624750C2semidirect
34. #14556570C8semidirect
67. C2×Dic146C2×C8semidirect
83. C4⋊Dic73C2×C8semidirect
199. C73#7589semidirect

Maximal subgroups

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

subgroupindex
#226257852
C2×#179894532
#226247522
#226247502
#226124592
#758973