Finite Group Databasebeta

← C73×#19344 #32928748

Subgroups — C73×#19344 #32928748

Order 18688.

612 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3254C212yesmaximal, complemented
2C73×#3169C211yesmaximal, characteristic
3C73×#2960C211yesmaximal, characteristic, complemented
4C73×#1698C214yesmaximal, complemented
5C73×#1676C212yesmaximal, complemented
6C73×#1668C212yesmaximal, complemented
7C73×#1567C211yesmaximal, characteristic, complemented
8C73×#1560C212yesmaximal, complemented
9#533×C73C2211yescharacteristic
10#532×C73C2212yes—
11#500×C73C2211yescharacteristic
12#493×C73C2211yescharacteristic
13#486×C73C2212yes—
14#477×C73C2214yes—
15#474×C73—22no—
16#468×C73—24no—
17#466×C73—21no—
18#466×C73—21no—
19#461×C73—22no—
20#460×C73C2214yes—
21#446×C73—21no—
22#446×C73C2212yes—
23C8×Q8×C73—21no—
24C8×Q8×C73C2212yes—
25C4×D8×C73—21no—
26C4×D8×C73—21no—
27#424×C73—21no—
28#423×C73C2211yescharacteristic
29#423×C73C2212yes—
30#405×C73—21no—
31C2×C4×C8×C73C2211yescharacteristic
32#335×C73C2212yes—
33#335×C73C2212yes—
34#333×C73C2214yes—
35#331×C73C2214yes—
36C2×#41×C73—22no—
37C2×SD16×C73—24no—
38C2×D8×C73—21no—
39C2×D8×C73—21no—
40C2×M16×C73—21no—
41C2×M16×C73—22no—
42C22×C8×C73D411yescharacteristic
43C22×C8×C73D411yescharacteristic
44C4⋊Q8×C73D411yescharacteristic
45C4⋊Q8×C73D411yescharacteristic
46C4⋊Q8×C73C2312yes—
47#127×C73C2312yes—
48#125×C73—21no—
49#124×C73—22no—
50C22⋊Q8×C73—21no—
51C22⋊Q8×C73D412yes—
52#121×C73—22no—
53#121×C73—22no—
54C4×Q8×C73—21no—
55C4×Q8×C73C2312yes—
56C4×D4×C73—22no—
57C4×D4×C73—22no—
58#117×C73—21no—
59C2×C42×C73C2311yescharacteristic
60#107×C73—21no—
61#107×C73—21no—
62#107×C73—24no—
63C4⋊C8×C73—22no—
64C4⋊C8×C73—22no—
65C4⋊C8×C73—21no—
66C4⋊C8×C73—22no—
67C4⋊C8×C73C2312yes—
68C4⋊C8×C73C2314yes—
69#103×C73—24no—
70#102×C73—22no—
71#102×C73—22no—
72#102×C73—24no—
73#97×C73—22no—
74C4×C8×C73—22no—
75C4×C8×C73D411yescharacteristic
76C4×C8×C73D411yescharacteristic
77C4×C8×C73C2311yescharacteristic
78C4×C8×C73C2311yescharacteristic
79#41×C73—84no—
80C2×Q8×C73—21no—
81C2×Q8×C73—22no—
82C2×Q8×C73C2×D412yes—
83C2×D4×C73—22no—
84C2×D4×C73—22no—
85C2×D4×C73—22no—
86C2×D4×C73—42no—
87C22×C4×C73—42no—
88C22×C4×C73C2×D411yescharacteristic
89C22×C4×C73C2×D411yescharacteristic
90C22×C4×C73#4111yescharacteristic
91SD16×C73—84no—
92D8×C73—42no—
93D8×C73—42no—
94M16×C73—42no—
95M16×C73—82no—
96C2×C8×C73—22no—
97C2×C8×C73—22no—
98C2×C8×C73—24no—
99C2×C8×C73—41no—
100C2×C8×C73C2×D411yescharacteristic
101C2×C8×C73C2×D411yescharacteristic
102C2×C8×C73C2×D411yescharacteristic
103C2×C8×C73C2×D411yescharacteristic
104C4⋊C4×C73—21no—
105C4⋊C4×C73—21no—
106C4⋊C4×C73—21no—
107C4⋊C4×C73—22no—
108C4⋊C4×C73—22no—
109C4⋊C4×C73—22no—
110C4⋊C4×C73—22no—
111C4⋊C4×C73C2×D412yes—
112C22⋊C4×C73—22no—
113C22⋊C4×C73—42no—
114C22⋊C4×C73—42no—
115C42×C73—22no—
116C42×C73C2×D411yescharacteristic
117C42×C73C2×D411yescharacteristic
118C42×C73#4111yescharacteristic
119C42×C73C2411yescharacteristic
120C23×C73—42no—
121C23×C73#12111yescharacteristic
122Q8×C73—22no—
123Q8×C73—22no—
124Q8×C73—42no—
125Q8×C73—82no—
126D4×C73—42no—
127D4×C73—42no—
128D4×C73—42no—
129D4×C73—42no—
130D4×C73—82no—
131D4×C73—84no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—22no—
137C2×C4×C73—22no—
138C2×C4×C73—22no—
139C2×C4×C73—42no—
140C2×C4×C73—84no—
141C2×C4×C73#12111yescharacteristic
142C2×C4×C73#12111yescharacteristic
143C2×C4×C73#12111yescharacteristic
144C2×C4×C73C22×D411yescharacteristic
145C2×C4×C73C22×D411yescharacteristic
146C2×C4×C73C2×#4111yescharacteristic
147C8×C73—21no—
148C8×C73—21no—
149C8×C73—21no—
150C8×C73—42no—
151C8×C73—44no—
152C8×C73#13712yes—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—82no—
157C22×C73—82no—
158C22×C73—82no—
159C22×C73C2×#12111yescharacteristic
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—42no—
164C4×C73—42no—
165C4×C73—82no—
166C4×C73#47212yes—
167C4×C73C2×#13711yescharacteristic
168C4×C73#57511yescharacteristic
169C4×C73#57611yescharacteristic
170C4×C73#57811yescharacteristic
171#19344C7311yesmaximal, characteristic, direct product factor, Sylow
172C2×C73—41no—
173C2×C73—162no—
174C2×C73#303711yescharacteristic
175C2×C73#306111yescharacteristic
176C2×C73C2×#47211yescharacteristic
177#3254C2×C7312yescomplemented
178#3169C2×C7311yescharacteristic
179#2960C2×C7311yescharacteristic, complemented
180#1698C2×C7314yescomplemented
181#1676C2×C7312yescomplemented
182#1668C2×C7312yescomplemented
183#1567C2×C7311yescharacteristic, complemented
184#1560C2×C7312yescomplemented
185C73#1934411yescharacteristic, direct product factor, Sylow
186#533C22×C7311yescharacteristic
187#532C22×C7312yes—
188#500C22×C7311yescharacteristic
189#493C22×C7311yescharacteristic
190#486C22×C7312yes—
191#477C22×C7314yes—
192#474—22no—
193#468—24no—
194#466—21no—
195#466—21no—
196#461—22no—
197#460C22×C7314yes—
198#446—21no—
199#446C22×C7312yes—
200C8×Q8—21no—
201C8×Q8C22×C7312yes—
202C4×D8—21no—
203C4×D8—21no—
204#424—21no—
205#423C22×C7311yescharacteristic
206#423C22×C7312yes—
207#405—21no—
208C2×C4×C8C22×C7311yescharacteristic
209#335C22×C7312yes—
210#335C22×C7312yes—
211#333C22×C7314yes—
212#331C22×C7314yes—
213C2×#41—22no—
214C2×SD16—24no—
215C2×D8—21no—
216C2×D8—21no—
217C2×M16—21no—
218C2×M16—22no—
219C22×C8D4×C7311yescharacteristic
220C22×C8D4×C7311yescharacteristic
221C4⋊Q8D4×C7311yescharacteristic
222C4⋊Q8D4×C7311yescharacteristic
223C4⋊Q8C23×C7312yes—
224#127C23×C7312yes—
225#125—21no—
226#124—22no—
227C22⋊Q8—21no—
228C22⋊Q8D4×C7312yes—
229#121—22no—
230#121—22no—
231C4×Q8—21no—
232C4×Q8C23×C7312yes—
233C4×D4—22no—
234C4×D4—22no—
235#117—21no—
236C2×C42C23×C7311yescharacteristic
237#107—21no—
238#107—21no—
239#107—24no—
240C4⋊C8—22no—
241C4⋊C8—22no—
242C4⋊C8—21no—
243C4⋊C8—22no—
244C4⋊C8C23×C7312yes—
245C4⋊C8C23×C7314yes—
246#103—24no—
247#102—22no—
248#102—22no—
249#102—24no—
250#97—22no—
251C4×C8—22no—
252C4×C8D4×C7311yescharacteristic
253C4×C8D4×C7311yescharacteristic
254C4×C8C23×C7311yescharacteristic
255C4×C8C23×C7311yescharacteristic
256#41—84no—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8C2×D4×C7312yes—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—42no—
264C22×C4—42no—
265C22×C4C2×D4×C7311yescharacteristic
266C22×C4C2×D4×C7311yescharacteristic
267C22×C4#41×C7311yescharacteristic
268SD16—84no—
269D8—42no—
270D8—42no—
271M16—42no—
272M16—82no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—24no—
276C2×C8—41no—
277C2×C8C2×D4×C7311yescharacteristic
278C2×C8C2×D4×C7311yescharacteristic
279C2×C8C2×D4×C7311yescharacteristic
280C2×C8C2×D4×C7311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4C2×D4×C7312yes—
289C22⋊C4—22no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C42—22no—
293C42C2×D4×C7311yescharacteristic
294C42C2×D4×C7311yescharacteristic
295C42#41×C7311yescharacteristic
296C42C24×C7311yescharacteristic
297C23—42no—
298C23#121×C7311yescharacteristic
299Q8—22no—
300Q8—22no—
301Q8—42no—
302Q8—82no—
303D4—42no—
304D4—42no—
305D4—42no—
306D4—42no—
307D4—82no—
308D4—84no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—84no—
318C2×C4#121×C7311yescharacteristic
319C2×C4#121×C7311yescharacteristic
320C2×C4#121×C7311yescharacteristic
321C2×C4C22×D4×C7311yescharacteristic
322C2×C4C22×D4×C7311yescharacteristic
323C2×C4C2×#41×C7311yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—42no—
328C8—44no—
329C8#137×C7312yes—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—82no—
334C22—82no—
335C22—82no—
336C22C2×#121×C7311yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—82no—
343C4#472×C7312yes—
344C4C2×#137×C7311yescharacteristic
345C4#575×C7311yescharacteristic
346C4#576×C7311yescharacteristic
347C4#578×C7311yescharacteristic
348C2—41no—
349C2—162no—
350C2C73×#303711yescharacteristic
351C2C73×#306111yescharacteristic
352C2C2×#472×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3169C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3254C2semidirect
3. C73×#2960C2semidirect
4. C73×#1698C2semidirect
5. C73×#1676C2semidirect
6. C73×#1668C2semidirect
7. C73×#1567C2semidirect
8. C73×#1560C2semidirect
171. #19344C73direct (N × H)
177. #3254C2×C73semidirect
179. #2960C2×C73semidirect
180. #1698C2×C73semidirect
181. #1676C2×C73semidirect
182. #1668C2×C73semidirect
183. #1567C2×C73semidirect
184. #1560C2×C73semidirect
185. C73#19344direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32542
C73×#31692
C73×#29602
C73×#16982
C73×#16762
C73×#16682
C73×#15672
C73×#15602
#1934473