Finite Group Databasebeta

← C73×#9082 #32918486

Subgroups — C73×#9082 #32918486

Order 18688.

628 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#431×C73C211yesmaximal, characteristic
2C2×#387×C73C211yesmaximal, characteristic
3C73×#1817C211yesmaximal, characteristic
4C2×#324×C73C212yesmaximal
5C73×#1280C212yesmaximal
6C22×C4⋊C4×C73C411yescharacteristic
7C22×C4⋊C4×C73C2211yescharacteristic
8C22×C42×C73C2211yescharacteristic
9#431×C73—24no—
10C2×C4⋊C8×C73—21no—
11C2×C22⋊C8×C73C2212yes—
12C2×C22⋊C8×C73C2212yes—
13C2×C4×C8×C73—21no—
14#387×C73—21no—
15#387×C73—21no—
16#387×C73—21no—
17#387×C73—21no—
18C2×#95×C73C411yescharacteristic
19C2×#95×C73C411yescharacteristic
20C2×#95×C73C411yescharacteristic
21C2×#95×C73C2211yescharacteristic
22#336×C73—21no—
23#336×C73—21no—
24#324×C73—24no—
25C23×C4×C73C2×C411yescharacteristic
26C23×C4×C73C2×C411yescharacteristic
27C23×C4×C73C2×C411yescharacteristic
28C23×C4×C73C2×C411yescharacteristic
29C23×C4×C73C2×C411yescharacteristic
30C23×C4×C73C2×C411yescharacteristic
31C23×C4×C73C2311yescharacteristic
32C22×C8×C73—22no—
33C22×C8×C73—22no—
34C2×C4⋊C4×C73—21no—
35C2×C4⋊C4×C73—21no—
36C2×C4⋊C4×C73—22no—
37C2×C4⋊C4×C73—21no—
38C2×C4⋊C4×C73—21no—
39C2×C4⋊C4×C73—22no—
40C2×C4⋊C4×C73—22no—
41C2×C4⋊C4×C73C814yescomplemented
42C2×C42×C73—22no—
43C2×C42×C73—22no—
44C2×C42×C73D411yescharacteristic
45C2×C42×C73D411yescharacteristic
46C2×C42×C73D411yescharacteristic
47C2×C42×C73D411yescharacteristic
48C4⋊C8×C73—24no—
49C22⋊C8×C73—22no—
50C22⋊C8×C73—22no—
51C22⋊C8×C73—22no—
52C22⋊C8×C73D414yes—
53C4×C8×C73—24no—
54#95×C73—21no—
55#95×C73—21no—
56#95×C73—21no—
57#95×C73—21no—
58#95×C73—21no—
59#95×C73—21no—
60#95×C73—21no—
61#95×C73—21no—
62C24×C73C22×C411yescharacteristic
63C22×C4×C73—22no—
64C22×C4×C73—22no—
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73—22no—
68C22×C4×C73—22no—
69C22×C4×C73—21no—
70C22×C4×C73—21no—
71C22×C4×C73—22no—
72C22×C4×C73—22no—
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73—22no—
76C22×C4×C73—22no—
77C22×C4×C73—41no—
78C22×C4×C73—41no—
79C22×C4×C73—41no—
80C22×C4×C73—41no—
81C22×C4×C73—41no—
82C22×C4×C73—41no—
83C22×C4×C73—41no—
84C22×C4×C73—41no—
85C22×C4×C73—41no—
86C22×C4×C73C22⋊C411yescharacteristic
87C22×C4×C73C22⋊C411yescharacteristic
88C22×C4×C73C22⋊C411yescharacteristic
89C22×C4×C73C22⋊C411yescharacteristic
90C22×C4×C73C2×C812yes—
91C22×C4×C73C2×C812yes—
92C22×C4×C73C2×C812yes—
93C22×C4×C73M1612yes—
94C22×C4×C73C2×D411yescharacteristic
95C22×C4×C73C2×D411yescharacteristic
96C22×C4×C73C2×D412yes—
97C22×C4×C73#4112yes—
98C2×C8×C73—24no—
99C2×C8×C73—42no—
100C2×C8×C73—42no—
101C2×C8×C73—42no—
102C2×C8×C73—42no—
103C2×C8×C73—42no—
104C4⋊C4×C73—24no—
105C4⋊C4×C73—24no—
106C4⋊C4×C73—41no—
107C4⋊C4×C73—42no—
108C4⋊C4×C73—41no—
109C42×C73—21no—
110C42×C73—21no—
111C42×C73—22no—
112C42×C73—22no—
113C42×C73—21no—
114C42×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73C2×C22⋊C411yescharacteristic
120C23×C73C4×D412yes—
121C23×C73C22×C811yescharacteristic
122C23×C73C2×M1611yescharacteristic
123C23×C73#13112yes—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—24no—
135C2×C4×C73—24no—
136C2×C4×C73—21no—
137C2×C4×C73—22no—
138C2×C4×C73—22no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—24no—
142C2×C4×C73—42no—
143C2×C4×C73—42no—
144C2×C4×C73—44no—
145C2×C4×C73—42no—
146C2×C4×C73—41no—
147C2×C4×C73—41no—
148C2×C4×C73—41no—
149C2×C4×C73—41no—
150C2×C4×C73—42no—
151C2×C4×C73—42no—
152C2×C4×C73—41no—
153C2×C4×C73—41no—
154C2×C4×C73—41no—
155C2×C4×C73—41no—
156C2×C4×C73—41no—
157C2×C4×C73—41no—
158C2×C4×C73—82no—
159C2×C4×C73—82no—
160C2×C4×C73C22⋊C812yes—
161C2×C4×C73C22⋊C812yes—
162C2×C4×C73#10112yes—
163C2×C4×C73#12011yescharacteristic
164C2×C4×C73#12112yes—
165C2×C4×C73#12311yescharacteristic
166C8×C73—44no—
167C8×C73—82no—
168C22×C73—22no—
169C22×C73—22no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—22no—
175C22×C73—22no—
176C22×C73#38611yescharacteristic
177C22×C73C2×C22⋊C811yescharacteristic
178C22×C73#40811yescharacteristic
179C22×C73#41011yescharacteristic
180C22×C73#41011yescharacteristic
181C22×C73C2×#10111yescharacteristic
182C22×C73#41311yescharacteristic
183C22×C73C8×D412yes—
184C22×C73#43512yes—
185C4×C73—22no—
186C4×C73—22no—
187C4×C73—21no—
188C4×C73—22no—
189C4×C73—21no—
190C4×C73—22no—
191C4×C73—42no—
192C4×C73—41no—
193C4×C73—42no—
194C4×C73—81no—
195C4×C73—81no—
196#9082C7311yesmaximal, characteristic, direct product factor, Sylow
197C2×C73—22no—
198C2×C73—22no—
199C2×C73#145811yescharacteristic
200C2×C73#146111yescharacteristic
201C2×C73#147011yescharacteristic
202C2×C73#147311yescharacteristic
203C2×C73#186911yescharacteristic
204C2×C73#189911yescharacteristic
205C2×C73#190111yescharacteristic
206C2×#431C2×C7311yescharacteristic
207C2×#387C2×C7311yescharacteristic
208#1817C2×C7311yescharacteristic
209C2×#324C2×C7312yes—
210#1280C2×C7312yes—
211C73#908211yescharacteristic, direct product factor, Sylow
212C22×C4⋊C4C4×C7311yescharacteristic
213C22×C4⋊C4C22×C7311yescharacteristic
214C22×C42C22×C7311yescharacteristic
215#431—24no—
216C2×C4⋊C8—21no—
217C2×C22⋊C8C22×C7312yes—
218C2×C22⋊C8C22×C7312yes—
219C2×C4×C8—21no—
220#387—21no—
221#387—21no—
222#387—21no—
223#387—21no—
224C2×#95C4×C7311yescharacteristic
225C2×#95C4×C7311yescharacteristic
226C2×#95C4×C7311yescharacteristic
227C2×#95C22×C7311yescharacteristic
228#336—21no—
229#336—21no—
230#324—24no—
231C23×C4C2×C4×C7311yescharacteristic
232C23×C4C2×C4×C7311yescharacteristic
233C23×C4C2×C4×C7311yescharacteristic
234C23×C4C2×C4×C7311yescharacteristic
235C23×C4C2×C4×C7311yescharacteristic
236C23×C4C2×C4×C7311yescharacteristic
237C23×C4C23×C7311yescharacteristic
238C22×C8—22no—
239C22×C8—22no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4C8×C7314yescomplemented
248C2×C42—22no—
249C2×C42—22no—
250C2×C42D4×C7311yescharacteristic
251C2×C42D4×C7311yescharacteristic
252C2×C42D4×C7311yescharacteristic
253C2×C42D4×C7311yescharacteristic
254C4⋊C8—24no—
255C22⋊C8—22no—
256C22⋊C8—22no—
257C22⋊C8—22no—
258C22⋊C8D4×C7314yes—
259C4×C8—24no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268C24C22×C4×C7311yescharacteristic
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4C22⋊C4×C7311yescharacteristic
293C22×C4C22⋊C4×C7311yescharacteristic
294C22×C4C22⋊C4×C7311yescharacteristic
295C22×C4C22⋊C4×C7311yescharacteristic
296C22×C4C2×C8×C7312yes—
297C22×C4C2×C8×C7312yes—
298C22×C4C2×C8×C7312yes—
299C22×C4M16×C7312yes—
300C22×C4C2×D4×C7311yescharacteristic
301C22×C4C2×D4×C7311yescharacteristic
302C22×C4C2×D4×C7312yes—
303C22×C4#41×C7312yes—
304C2×C8—24no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—42no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C42—21no—
316C42—21no—
317C42—22no—
318C42—22no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C2×C22⋊C4×C7311yescharacteristic
326C23C4×D4×C7312yes—
327C23C22×C8×C7311yescharacteristic
328C23C2×M16×C7311yescharacteristic
329C23#131×C7312yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—24no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4C22⋊C8×C7312yes—
367C2×C4C22⋊C8×C7312yes—
368C2×C4#101×C7312yes—
369C2×C4#120×C7311yescharacteristic
370C2×C4#121×C7312yes—
371C2×C4#123×C7311yescharacteristic
372C8—44no—
373C8—82no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22#386×C7311yescharacteristic
383C22C2×C22⋊C8×C7311yescharacteristic
384C22#408×C7311yescharacteristic
385C22#410×C7311yescharacteristic
386C22#410×C7311yescharacteristic
387C22C2×#101×C7311yescharacteristic
388C22#413×C7311yescharacteristic
389C22C8×D4×C7312yes—
390C22#435×C7312yes—
391C4—22no—
392C4—22no—
393C4—21no—
394C4—22no—
395C4—21no—
396C4—22no—
397C4—42no—
398C4—42no—
399C4—41no—
400C4—81no—
401C4—81no—
402C2—22no—
403C2—22no—
404C2C73×#145811yescharacteristic
405C2C73×#146111yescharacteristic
406C2C73×#147011yescharacteristic
407C2C73×#147311yescharacteristic
408C2C73×#186911yescharacteristic
409C2C73×#189911yescharacteristic
410C2C73×#190111yescharacteristic
subgroupG/H
center, socleC23×C73C2×C22⋊C4
commutatorC23C22×C8×C73
Frattini, cosocleC23×C4C23×C73
prime radicalC24×C73C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C22×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
41. C2×C4⋊C4×C73C8semidirect
196. #9082C73direct (N × H)
211. C73#9082direct (N × H)
247. C2×C4⋊C4C8×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#431×C732
C2×#387×C732
C73×#18172
C2×#324×C732
C73×#12802
#908273