Finite Group Databasebeta

← #32983687

Subgroups — #32983687

Order 18688.

432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619015C211yesmaximal, characteristic
2#22615146C211yesmaximal, characteristic
3#22608649C211yesmaximal, characteristic
4#22608647C211yesmaximal, characteristic
5#22608274C211yesmaximal, characteristic
6#22607787C211yesmaximal, characteristic
7C73×#1285C211yesmaximal, characteristic
8C2×#14556591C2211yescharacteristic
9C2×C4×Dic146C2211yescharacteristic
10#17988716—22no—
11#17988715—22no—
12#17988644C2211yescharacteristic
13#17988644C2211yescharacteristic
14#17988641—21no—
15#17988637—21no—
16#17988527—21no—
17#17988527—21no—
18#17988493C412yes—
19#17988492—21no—
20#17988492—21no—
21#17988453C412yes—
22#17988334—22no—
23#17988332—22no—
24#17988312—21no—
25#17988312—21no—
26#432×C73C2211yescharacteristic
27#432×C73C2211yescharacteristic
28C4×C4⋊C4×C73C2211yescharacteristic
29C22×Dic146—21no—
30C22×Dic146C2×C411yescharacteristic
31#14556591—21no—
32#14556591—21no—
33#14556591—21no—
34#14556591—21no—
35C4×Dic146—21no—
36C4×Dic146—21no—
37C4×Dic146—21no—
38C4×Dic146—21no—
39C2×C4⋊Dic73—21no—
40C2×C4⋊Dic73C2×C412yes—
41C2×C4⋊Dic73C2×C411yescharacteristic
42C2×#11924007D411yescharacteristic
43C2×#11924007D411yescharacteristic
44C2×C4×Dic73D411yescharacteristic
45C2×C4×Dic73D411yescharacteristic
46C4⋊#10596831—21no—
47C4⋊#10596831D412yes—
48#14556520—22no—
49#14556520—22no—
50C22⋊#10596831—21no—
51C22⋊#10596831—21no—
52#14556502—21no—
53#14556502—21no—
54#14556501—22no—
55C8×Dic73—22no—
56#14556498—22no—
57#14556498—22no—
58#14556498—22no—
59#14556498—22no—
60C2×C4⋊C4×C73—21no—
61C2×C42×C73C2×C412yes—
62C2×C42×C73C2311yescharacteristic
63C4⋊C8×C73—21no—
64C4⋊C8×C73D412yes—
65C22⋊C8×C73—21no—
66C22⋊C8×C73—21no—
67#97×C73—21no—
68#97×C73—21no—
69#95×C73—21no—
70C2×Dic146—21no—
71C2×Dic146—21no—
72C2×Dic146—22no—
73C2×Dic146—41no—
74C2×Dic146—44no—
75C2×Dic146—41no—
76C2×Dic146—41no—
77C22×Dic73—22no—
78C22×Dic73C22⋊C411yescharacteristic
79C22×Dic73C22⋊C411yescharacteristic
80C22×Dic73C22⋊C411yescharacteristic
81C22×Dic73C22⋊C411yescharacteristic
82C2×#10596831—22no—
83C2×#10596831—41no—
84C4⋊Dic73—21no—
85C4⋊Dic73—21no—
86C4⋊Dic73—22no—
87C4⋊Dic73—22no—
88C4⋊Dic73—41no—
89C4⋊Dic73—41no—
90#11924007—21no—
91#11924007—21no—
92#11924007—21no—
93#11924007—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C22×C4×C73—22no—
99C22×C4×C73C22×C411yescharacteristic
100C22×C4×C73C2×D411yescharacteristic
101C22×C4×C73C2×D411yescharacteristic
102C2×C8×C73—22no—
103C2×C8×C73—41no—
104C4⋊C4×C73—42no—
105C42×C73—42no—
106C42×C73C2×D411yescharacteristic
107C42×C73C2×D411yescharacteristic
108C42×C73#4111yescharacteristic
109C42×C73#4111yescharacteristic
110C23×C73C2×C22⋊C411yescharacteristic
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—22no—
114C2×C4×C73—41no—
115C2×C4×C73—42no—
116C2×C4×C73—42no—
117C2×C4×C73—42no—
118C2×C4×C73C4×D411yescharacteristic
119C2×C4×C73C4×D411yescharacteristic
120C2×C4×C73#12011yescharacteristic
121C2×C4×C73#12111yescharacteristic
122C2×C4×C73#12111yescharacteristic
123C2×C4×C73#12311yescharacteristic
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—44no—
134C2×Dic73—42no—
135C2×Dic73#10112yes—
136Dic146—42no—
137Dic146—42no—
138Dic146—82no—
139Dic146—82no—
140C8×C73—42no—
141C8×C73—81no—
142#10596831—42no—
143#10596831—81no—
144C22×C73—21no—
145C22×C73—21no—
146C22×C73#38611yescharacteristic
147C22×C73C2×#10111yescharacteristic
148C22×C73#41311yescharacteristic
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—82no—
155C4×C73#45412yes—
156Dic73—22no—
157Dic73—41no—
158Dic73—41no—
159Dic73—41no—
160Dic73—82no—
161#9456—731nomaximal, Sylow
162C2×C73—21no—
163C2×C73—21no—
164C2×C73#188811yescharacteristic
165C2×C73#190111yescharacteristic
166C2×C73#190911yescharacteristic
167#2983—731no—
168#2568—731no—
169#1556—731no—
170#1556—731no—
171#1467—731no—
172#1285—731no—
173#1285D7311yescharacteristic
174C73#945611yescharacteristic, complemented, Sylow
175C2×C4⋊Q8—731no—
176C2×C4×Q8—731no—
177#446—1462no—
178#446—1462no—
179#432—731no—
180#432—731no—
181#432—1461no—
182#432C2×D7311yescharacteristic
183#432C2×D7311yescharacteristic
184#431—1461no—
185#400—1461no—
186#400—1461no—
187#391—732no—
188#391—1461no—
189#391—1461no—
190#382—732no—
191C4×C4⋊C4C2×D7311yescharacteristic
192#332—1462no—
193#332—1462no—
194#324—1461no—
195#324—1461no—
196C22×Q8—731no—
197C22×Q8—1461no—
198C4⋊Q8—1461no—
199C4⋊Q8—1461no—
200C4⋊Q8—1461no—
201C4⋊Q8—1461no—
202C4×Q8—1461no—
203C4×Q8—1461no—
204C4×Q8—1461no—
205C4×Q8—1461no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—731no—
208C2×C4⋊C4—731no—
209C2×C4⋊C4—731no—
210C2×C4⋊C4—732no—
211C2×C4⋊C4—1461no—
212C2×C42—731no—
213C2×C42—731no—
214C2×C42C4×D7312yes—
215C2×C42C22×D7311yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—732no—
218C4⋊C8—1462no—
219C4⋊C8—1462no—
220C4⋊C8—1461no—
221C4⋊C8D29212yes—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C22⋊C8—1461no—
225C22⋊C8—1461no—
226#97—21no—
227#97—21no—
228#97—1462no—
229#97—1461no—
230#97—1461no—
231C4×C8—1462no—
232#95—21no—
233#95—1462no—
234#95—1462no—
235#95—1462no—
236#95—1462no—
237C2×Q8—2924no—
238C2×Q8—2921no—
239C2×Q8—2921no—
240C2×Q8—2921no—
241C2×Q8—1462no—
242C2×Q8—1461no—
243C2×Q8—1461no—
244C22×C4—22no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—731no—
248C22×C4—731no—
249C22×C4—1462no—
250C22×C4C2×C4×D7311yescharacteristic
251C22×C4D4×D7311yescharacteristic
252C22×C4D4×D7311yescharacteristic
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—2921no—
256C2×C8—1462no—
257C4⋊C4—42no—
258C4⋊C4—2921no—
259C4⋊C4—2921no—
260C4⋊C4—1462no—
261C4⋊C4—1462no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C42—42no—
269C42—1461no—
270C42—1461no—
271C42—1461no—
272C42—1461no—
273C42D4×D7311yescharacteristic
274C42C2×D29211yescharacteristic
275C42#1192402811yescharacteristic
276C42#1192402911yescharacteristic
277C23C22⋊C4×D7311yescharacteristic
278Q8—2922no—
279Q8—2922no—
280Q8—5842no—
281Q8—5842no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—2921no—
290C2×C4—2921no—
291C2×C4—2924no—
292C2×C4—2922no—
293C2×C4—732no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4#1455655311yescharacteristic
302C2×C4C4×D29211yescharacteristic
303C2×C4#1455656111yescharacteristic
304C2×C4#1455656411yescharacteristic
305C2×C4#1455656611yescharacteristic
306C2×C4#1455657611yescharacteristic
307C8—42no—
308C8—81no—
309C8—2922no—
310C8—5841no—
311C22—21no—
312C22—21no—
313C22#1798846511yescharacteristic
314C22#101×D7311yescharacteristic
315C22#1798856811yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—2921no—
323C4—2921no—
324C4—2921no—
325C4—5842no—
326C4—1462no—
327C4#1798876112yes—
328C2—21no—
329C2—21no—
330C2#2261033311yescharacteristic
331C2#2261039811yescharacteristic
332C2#2261045211yescharacteristic
subgroupG/H
centerC22#17988465
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1285C2
socleC22×C73#386
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1285D73
hypocenterC73#9456
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
174. C73#9456semidirect

Maximal subgroups

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

subgroupindex
#226190152
#226151462
#226086492
#226086472
#226082742
#226077872
C73×#12852
#945673