Finite Group Databasebeta

← #34004905

Subgroups — #34004905

Order 18688.

496 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625864C211yesmaximal, characteristic
2#22625847C211yesmaximal, characteristic
3C2×#17989447C212yesmaximal
4#22624809C212yesmaximal
5#22612500C211yesmaximal, characteristic
6C2×#14556658—21no—
7C2×#14556658C2212yes—
8C2×#14556658C2212yes—
9C2×C4⋊#10596833—21no—
10#17989453—21no—
11#17989453—21no—
12#17989447—24no—
13C2×#14556589C2211yescharacteristic
14C2×Q8×Dic73C411yescharacteristic
15C2×#14556556C411yescharacteristic
16#17988493C411yescharacteristic
17#17988484—21no—
18#17988484—21no—
19#17988456C2211yescharacteristic
20#17988438—21no—
21#17988438—21no—
22C42×Dic73C2211yescharacteristic
23#391×C73C411yescharacteristic
24C22×#10596833—22no—
25C22×#10596833—22no—
26#14556658—22no—
27#14556658—22no—
28#14556658—22no—
29#14556658—22no—
30#14556658—42no—
31C4⋊#10596833—42no—
32C22×Dic146C2×C411yescharacteristic
33#14556589—21no—
34#14556589—21no—
35#14556589D412yes—
36#14556589Q812yes—
37Q8×Dic73—42no—
38#14556556—42no—
39C2×C4⋊Dic73—21no—
40C2×C4⋊Dic73C2×C411yescharacteristic
41C2×#11924007—21no—
42C2×#11924007—21no—
43C2×#11924007—21no—
44C2×#11924007—21no—
45C2×#11924007—21no—
46C2×C4×Dic73—21no—
47C2×C4×Dic73—21no—
48C2×C4×Dic73C2×C411yescharacteristic
49C2×C4×Dic73D411yescharacteristic
50C2×C4×Dic73D411yescharacteristic
51C2×C4×Dic73D411yescharacteristic
52C2×C4×Dic73D411yescharacteristic
53C2×C4×Dic73C2311yescharacteristic
54#14556498—21no—
55#14556498—21no—
56C22×Q8×C73C2×C411yescharacteristic
57C2×C4⋊C4×C73C2×C411yescharacteristic
58C2×C42×C73C2×C411yescharacteristic
59#95×C73—21no—
60#95×C73—21no—
61C2×#10596833—42no—
62C2×#10596833—42no—
63C2×#10596833—42no—
64C2×#10596833—42no—
65C2×#10596833—42no—
66C2×#10596833—42no—
67C2×Dic146—21no—
68C2×Dic146—41no—
69C2×Dic146—41no—
70C2×Dic146C4⋊C412yes—
71C22×Dic73—21no—
72C22×Dic73—21no—
73C22×Dic73C22⋊C411yescharacteristic
74C22×Dic73C22⋊C411yescharacteristic
75C22×Dic73C2×D411yescharacteristic
76C22×Dic73C2×D411yescharacteristic
77C4⋊Dic73—42no—
78C4⋊Dic73—41no—
79#11924007—22no—
80#11924007—22no—
81#11924007—22no—
82#11924007—22no—
83#11924007—42no—
84#11924007—42no—
85#11924007—41no—
86#11924007—41no—
87C4×Dic73—22no—
88C4×Dic73—22no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—22no—
92C4×Dic73—42no—
93C4×Dic73—42no—
94C4×Dic73SD1612yes—
95C4×Dic73Q1612yes—
96C4×Dic73C2×D411yescharacteristic
97C4×Dic73C2×Q811yescharacteristic
98C4×Dic73#4111yescharacteristic
99C4×Dic73#4111yescharacteristic
100C2×Q8×C73—21no—
101C2×Q8×C73—41no—
102C2×Q8×C73—41no—
103C2×Q8×C73C4⋊C412yes—
104C22×C4×C73—21no—
105C22×C4×C73—21no—
106C22×C4×C73C22⋊C411yescharacteristic
107C22×C4×C73C22⋊C411yescharacteristic
108C22×C4×C73C22×C411yescharacteristic
109C4⋊C4×C73—41no—
110C42×C73—41no—
111C23×C73C2×C22⋊C411yescharacteristic
112Q8×C73—42no—
113Q8×C73—42no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—22no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73#10312yes—
128C2×C4×C73C2×C4⋊C411yescharacteristic
129C2×C4×C73#11711yescharacteristic
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—22no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73#10012yes—
141C2×Dic73#10312yes—
142C2×Dic73#12111yescharacteristic
143C2×Dic73#12111yescharacteristic
144C2×Dic73C22⋊Q811yescharacteristic
145C2×Dic73C22⋊Q811yescharacteristic
146C2×Dic73C2×SD1611yescharacteristic
147C2×Dic73C2×Q1611yescharacteristic
148C2×Dic73#13512yes—
149C2×Dic73AGL(1,ℤ/8)11yescharacteristic
150C2×Dic73#13711yescharacteristic
151C2×Dic73#13712yes—
152Dic146—42no—
153Dic146—42no—
154#10596833—82no—
155#10596833—82no—
156C22×C73#38011yescharacteristic
157C22×C73C2×#10011yescharacteristic
158C22×C73#41311yescharacteristic
159C22×C73C2×#10311yescharacteristic
160C22×C73#41611yescharacteristic
161C22×C73#41711yescharacteristic
162C22×C73#41911yescharacteristic
163C4×C73—22no—
164C4×C73—21no—
165C4×C73—21no—
166C4×C73—42no—
167C4×C73—41no—
168C4×C73—81no—
169Dic73—22no—
170Dic73—22no—
171Dic73—42no—
172Dic73—81no—
173Dic73#46011yescharacteristic
174Dic73#46211yescharacteristic
175Dic73#46412yes—
176Dic73#47511yescharacteristic
177Dic73#47711yescharacteristic
178Dic73#47912yes—
179#8590—731nomaximal, Sylow
180C2×C73#154211yescharacteristic
181C2×C73#154811yescharacteristic
182C2×C73#155111yescharacteristic
183C2×C73#155911yescharacteristic
184C2×C73#180011yescharacteristic
185C2×C73#180311yescharacteristic
186C2×C73#180511yescharacteristic
187C4×C4⋊Q8—731no—
188#1842—731no—
189#1831—731no—
190C2×#333—732no—
191#1296—732no—
192C73#859011yescharacteristic, complemented, Sylow
193C2×C4⋊Q8—731no—
194C2×C4×Q8—731no—
195C2×C4×Q8—731no—
196C2×C4⋊C8—732no—
197C2×C4⋊C8—732no—
198C2×C4⋊C8—1461no—
199C2×C4⋊C8—1461no—
200#391—731no—
201#391#6440811yescharacteristic
202#389—1461no—
203#389—1461no—
204#384—731no—
205C4×C4⋊C4—1461no—
206C4×C4⋊C4—1461no—
207C43—731no—
208#336—1461no—
209#336—1461no—
210#333—1464no—
211C22×Q8—731no—
212C22×Q8C2×#6440811yescharacteristic
213C22×C8—1462no—
214C22×C8—1462no—
215C4⋊Q8—732no—
216C4⋊Q8—732no—
217C4⋊Q8—1461no—
218C4⋊Q8—1461no—
219C4×Q8—2922no—
220C4×Q8—2922no—
221C2×C4⋊C4—731no—
222C2×C4⋊C4—1461no—
223C2×C4⋊C4—1461no—
224C2×C4⋊C4—1461no—
225C2×C4⋊C4—1461no—
226C2×C4⋊C4—1461no—
227C2×C4⋊C4—1461no—
228C2×C4⋊C4C2×#6440811yescharacteristic
229C2×C42—731no—
230C2×C42—731no—
231C2×C42—731no—
232C2×C42—731no—
233C2×C42—731no—
234C2×C42—731no—
235C2×C42—1461no—
236C2×C42—1461no—
237C2×C42C2×#6440811yescharacteristic
238C4⋊C8—2922no—
239C4⋊C8—2922no—
240C4⋊C8—1462no—
241C4⋊C8—1462no—
242C4⋊C8—1462no—
243C4⋊C8—1462no—
244#95—21no—
245#95—21no—
246#95—1461no—
247#95—1461no—
248C2×Q8—21no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—2921no—
252C2×Q8—2921no—
253C2×Q8—732no—
254C2×Q8—1461no—
255C2×Q8C4⋊#6440812yes—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—731no—
259C22×C4—731no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4C22⋊#6440811yescharacteristic
265C22×C4C22⋊#6440811yescharacteristic
266C22×C4C22×#6440811yescharacteristic
267C2×C8—2922no—
268C2×C8—2922no—
269C2×C8—2922no—
270C2×C8—2922no—
271C2×C8—2922no—
272C2×C8—2922no—
273C4⋊C4—41no—
274C4⋊C4—2921no—
275C4⋊C4—2922no—
276C4⋊C4—2921no—
277C4⋊C4—2921no—
278C4⋊C4—2922no—
279C4⋊C4—2922no—
280C4⋊C4—1462no—
281C4⋊C4—1462no—
282C4⋊C4—1462no—
283C4⋊C4—1462no—
284C42—41no—
285C42—2922no—
286C42—2922no—
287C42—732no—
288C42—732no—
289C42—731no—
290C42—731no—
291C42—731no—
292C42—731no—
293C42—1461no—
294C42—1462no—
295C42—1461no—
296C42—1462no—
297C42—1462no—
298C23C2×C22⋊#6440811yescharacteristic
299Q8—42no—
300Q8—42no—
301Q8—2922no—
302Q8—2922no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—2921no—
317C2×C4—2921no—
318C2×C4—2921no—
319C2×C4—2921no—
320C2×C4—2921no—
321C2×C4—731no—
322C2×C4—731no—
323C2×C4—731no—
324C2×C4—731no—
325C2×C4—731no—
326C2×C4—731no—
327C2×C4—732no—
328C2×C4—731no—
329C2×C4—731no—
330C2×C4—732no—
331C2×C4—732no—
332C2×C4—732no—
333C2×C4—1462no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4#1455665412yes—
339C2×C4C2×C4⋊#6440811yescharacteristic
340C2×C4#1455667011yescharacteristic
341C8—5842no—
342C8—5842no—
343C22#1798952911yescharacteristic
344C22D73⋊#10011yescharacteristic
345C22#1798957411yescharacteristic
346C22C2×#1455665411yescharacteristic
347C22#1798957711yescharacteristic
348C22#1798957811yescharacteristic
349C22#1798958011yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—42no—
354C4—41no—
355C4—81no—
356C4—2922no—
357C4—5841no—
358C4—731no—
359C4—731no—
360C4—731no—
361C4—731no—
362C4—732no—
363C4—732no—
364C4—1462no—
365C4—1462no—
366C2#2262543311yescharacteristic
367C2#2262544511yescharacteristic
368C2#2262545111yescharacteristic
369C2#2262546711yescharacteristic
370C2#2262579611yescharacteristic
371C2#2262580011yescharacteristic
372C2#2262580211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#391×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#391#64408
hypocenterC73#8590
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
192. C73#8590semidirect

Maximal subgroups

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

subgroupindex
#226258642
#226258472
C2×#179894472
#226248092
#226125002
#859073