Finite Group Databasebeta

← C73×#12269 #32921673

Subgroups — C73×#12269 #32921673

Order 18688.

372 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C73×#2764C211yesmaximal, characteristic
2C73×#2030C211yesmaximal, characteristic
3C73×#1608C211yesmaximal, characteristic
4C73×#1602C211yesmaximal, characteristic
5C73×#1351C211yesmaximal, characteristic
6C73×#1344C211yesmaximal, characteristic
7C73×#1317C211yesmaximal, characteristic
8#543×C73C2211yescharacteristic
9#483×C73—21no—
10#451×C73—21no—
11#400×C73—21no—
12#398×C73—21no—
13#397×C73C2211yescharacteristic
14#393×C73C2211yescharacteristic
15#391×C73—21no—
16#388×C73—21no—
17#385×C73—21no—
18#383×C73—21no—
19#381×C73—21no—
20#381×C73C2211yescharacteristic
21#342×C73—21no—
22#342×C73C2211yescharacteristic
23#328×C73—21no—
24#328×C73—21no—
25#323×C73C2211yescharacteristic
26#323×C73C2211yescharacteristic
27C22×Q8×C73D411yescharacteristic
28C23×C4×C73D411yescharacteristic
29C2×Q16×C73—41no—
30C22⋊Q8×C73—21no—
31C22⋊Q8×C73—21no—
32C22⋊Q8×C73—41no—
33C22⋊Q8×C73—41no—
34C2×C4⋊C4×C73—21no—
35C2×C4⋊C4×C73—21no—
36C2×C4⋊C4×C73—21no—
37C2×C4⋊C4×C73D411yescharacteristic
38C2×C22⋊C4×C73—21no—
39C2×C22⋊C4×C73—21no—
40C2×C22⋊C4×C73—21no—
41C2×C22⋊C4×C73—21no—
42C2×C22⋊C4×C73D411yescharacteristic
43C2×C22⋊C4×C73C2311yescharacteristic
44C2×C42×C73—21no—
45#106×C73—41no—
46#103×C73—41no—
47#103×C73—41no—
48C22⋊C8×C73—21no—
49C22⋊C8×C73—21no—
50#95×C73—21no—
51#95×C73—21no—
52#95×C73—21no—
53#95×C73—21no—
54#95×C73—21no—
55#95×C73—21no—
56#95×C73—21no—
57#95×C73—21no—
58#95×C73—41no—
59#95×C73—41no—
60#95×C73D411yescharacteristic
61#95×C73D411yescharacteristic
62C24×C73C2×D411yescharacteristic
63C2×Q8×C73—21no—
64C2×Q8×C73—21no—
65C2×Q8×C73—42no—
66C2×Q8×C73—41no—
67C22×C4×C73—21no—
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73—21no—
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73—41no—
78C22×C4×C73—41no—
79C22×C4×C73—41no—
80C22×C4×C73C2×D411yescharacteristic
81C22×C4×C73C2×D411yescharacteristic
82Q16×C73—82no—
83C2×C8×C73—41no—
84C2×C8×C73—41no—
85C4⋊C4×C73—21no—
86C4⋊C4×C73—21no—
87C4⋊C4×C73—41no—
88C4⋊C4×C73—41no—
89C4⋊C4×C73—41no—
90C4⋊C4×C73—81no—
91C4⋊C4×C73—81no—
92C4⋊C4×C73—81no—
93C22⋊C4×C73—41no—
94C22⋊C4×C73—42no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C22⋊C4×C73—41no—
98C22⋊C4×C73—41no—
99C22⋊C4×C73—41no—
100C22⋊C4×C73—41no—
101C22⋊C4×C73—41no—
102C42×C73—42no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—41no—
106C23×C73—41no—
107C23×C73#12011yescharacteristic
108C23×C73#13511yescharacteristic
109C23×C73#13711yescharacteristic
110Q8×C73—42no—
111Q8×C73—81no—
112Q8×C73—81no—
113Q8×C73—81no—
114C2×C4×C73—22no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—41no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
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×C73—42no—
128C2×C4×C73—41no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—81no—
140C2×C4×C73—81no—
141C2×C4×C73—81no—
142C2×C4×C73—81no—
143C2×C4×C73—81no—
144C2×C4×C73—81no—
145C8×C73—81no—
146C8×C73—81no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—81no—
156C22×C73#45211yescharacteristic
157C22×C73#45511yescharacteristic
158C22×C73B(4,𝔽2)11yescharacteristic
159C4×C73—41no—
160C4×C73—42no—
161C4×C73—41no—
162C4×C73—81no—
163C4×C73—81no—
164C4×C73—81no—
165C4×C73—81no—
166C4×C73—81no—
167C4×C73—81no—
168C4×C73—81no—
169C4×C73—161no—
170#12269C7311yesmaximal, characteristic, direct product factor, Sylow
171C2×C73—21no—
172C2×C73—21no—
173C2×C73—41no—
174C2×C73—41no—
175C2×C73#160611yescharacteristic
176C2×C73#219711yescharacteristic
177C2×C73#220111yescharacteristic
178#2764C2×C7311yescharacteristic
179#2030C2×C7311yescharacteristic
180#1608C2×C7311yescharacteristic
181#1602C2×C7311yescharacteristic
182#1351C2×C7311yescharacteristic
183#1344C2×C7311yescharacteristic
184#1317C2×C7311yescharacteristic
185C73#1226911yescharacteristic, direct product factor, Sylow
186#543C22×C7311yescharacteristic
187#483—21no—
188#451—21no—
189#400—21no—
190#398—21no—
191#397C22×C7311yescharacteristic
192#393C22×C7311yescharacteristic
193#391—21no—
194#388—21no—
195#385—21no—
196#383—21no—
197#381—21no—
198#381C22×C7311yescharacteristic
199#342—21no—
200#342C22×C7311yescharacteristic
201#328—21no—
202#328—21no—
203#323C22×C7311yescharacteristic
204#323C22×C7311yescharacteristic
205C22×Q8D4×C7311yescharacteristic
206C23×C4D4×C7311yescharacteristic
207C2×Q16—41no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—41no—
211C22⋊Q8—41no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4D4×C7311yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4D4×C7311yescharacteristic
221C2×C22⋊C4C23×C7311yescharacteristic
222C2×C42—21no—
223#106—41no—
224#103—41no—
225#103—41no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—41no—
237#95—41no—
238#95D4×C7311yescharacteristic
239#95D4×C7311yescharacteristic
240C24C2×D4×C7311yescharacteristic
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—42no—
244C2×Q8—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4C2×D4×C7311yescharacteristic
259C22×C4C2×D4×C7311yescharacteristic
260Q16—82no—
261C2×C8—41no—
262C2×C8—41no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42—42no—
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23#120×C7311yescharacteristic
286C23#135×C7311yescharacteristic
287C23#137×C7311yescharacteristic
288Q8—42no—
289Q8—81no—
290Q8—81no—
291Q8—81no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C8—81no—
324C8—81no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22#452×C7311yescharacteristic
335C22#455×C7311yescharacteristic
336C22B(4,𝔽2)×C7311yescharacteristic
337C4—41no—
338C4—42no—
339C4—41no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—161no—
348C2—21no—
349C2—21no—
350C2—41no—
351C2—41no—
352C2C73×#160611yescharacteristic
353C2C73×#219711yescharacteristic
354C2C73×#220111yescharacteristic
subgroupG/H
center, socleC22×C73B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C73
prime radicalC24×C73C2×D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C73 ◁ C2×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
170. #12269C73direct (N × H)
185. C73#12269direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#27642
C73×#20302
C73×#16082
C73×#16022
C73×#13512
C73×#13442
C73×#13172
#1226973