Finite Group Databasebeta

← C73×#13387 #32922791

Subgroups — C73×#13387 #32922791

Order 18688.

428 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3058C211yesmaximal, characteristic
2C73×#2159C211yesmaximal, characteristic, complemented
3C2×#361×C73C211yesmaximal, characteristic, complemented
4C2×#357×C73C211yesmaximal, characteristic, complemented
5C2×#350×C73C211yesmaximal, characteristic, complemented
6C73×#1816C211yesmaximal, characteristic, complemented
7C73×#1382C211yesmaximal, characteristic, complemented
8C22×D8×C73C2211yescharacteristic
9C2×#131×C73C2211yescharacteristic
10#535×C73—21no—
11C2×M32×C73C2211yescharacteristic
12C22×C16×C73C2211yescharacteristic
13#469×C73—22no—
14#466×C73—21no—
15#466×C73—21no—
16C2×#108×C73C2211yescharacteristic
17#427×C73C2211yescharacteristic
18C2×#107×C73C2211yescharacteristic
19#418×C73—21no—
20#417×C73—21no—
21#367×C73—21no—
22#366×C73—21no—
23#361×C73—22no—
24#357×C73—22no—
25#350×C73—22no—
26#343×C73—21no—
27C2×#41×C73D411yescharacteristic
28C22×D4×C73—21no—
29C2×D8×C73—21no—
30C2×D8×C73—21no—
31C2×D8×C73—21no—
32C2×D8×C73—21no—
33C2×D8×C73—21no—
34C2×D8×C73D412yes—
35#131×C73—21no—
36#131×C73—21no—
37#131×C73—21no—
38#131×C73—21no—
39C2×M16×C73—21no—
40C2×M16×C73—21no—
41C2×M16×C73D411yescharacteristic
42C22×C8×C73—21no—
43C22×C8×C73C2311yescharacteristic
44#127×C73—41no—
45#124×C73—41no—
46#121×C73—22no—
47#121×C73—22no—
48#120×C73—42no—
49#117×C73—21no—
50C2×C4⋊C4×C73—21no—
51M32×C73—21no—
52M32×C73D412yescomplemented
53C2×C16×C73—21no—
54C2×C16×C73—21no—
55C2×C16×C73—21no—
56C2×C16×C73—21no—
57#108×C73—21no—
58#108×C73—21no—
59#107×C73—21no—
60#107×C73—21no—
61#107×C73D411yescharacteristic
62#107×C73D411yescharacteristic
63#106×C73—21no—
64#103×C73—41no—
65#102×C73—22no—
66#102×C73—22no—
67#102×C73—41no—
68C24×C73—41no—
69#41×C73—21no—
70#41×C73—21no—
71#41×C73—21no—
72#41×C73—21no—
73C2×Q8×C73D811yescharacteristic
74C2×D4×C73—21no—
75C2×D4×C73—22no—
76C2×D4×C73—42no—
77C2×D4×C73—42no—
78C2×D4×C73—41no—
79C2×D4×C73—41no—
80C2×D4×C73—41no—
81C2×D4×C73—41no—
82C2×D4×C73—41no—
83C2×D4×C73D811yescharacteristic
84C22×C4×C73—21no—
85C22×C4×C73—41no—
86C22×C4×C73C2×D411yescharacteristic
87D8×C73—22no—
88D8×C73—22no—
89D8×C73—41no—
90D8×C73—41no—
91M16×C73—21no—
92M16×C73—21no—
93M16×C73—41no—
94M16×C73—41no—
95M16×C73—41no—
96M16×C73—41no—
97C2×C8×C73—21no—
98C2×C8×C73—41no—
99C2×C8×C73—41no—
100C2×C8×C73—41no—
101C2×C8×C73C2×D411yescharacteristic
102C2×C8×C73C2×D411yescharacteristic
103C2×C8×C73C2×D411yescharacteristic
104C2×C8×C73#4111yescharacteristic
105C2×C8×C73#4111yescharacteristic
106C2×C8×C73#4111yescharacteristic
107C4⋊C4×C73—21no—
108C4⋊C4×C73—21no—
109C4⋊C4×C73—41no—
110C4⋊C4×C73—41no—
111C22⋊C4×C73—42no—
112C22⋊C4×C73—42no—
113C22⋊C4×C73—41no—
114C42×C73—41no—
115C16×C73—22no—
116C16×C73—41no—
117C23×C73—21no—
118C23×C73—42no—
119C23×C73—81no—
120C23×C73—81no—
121C23×C73—161no—
122C23×C73—161no—
123C23×C73AGL(1,ℤ/8)11yescharacteristic
124Q8×C73—21no—
125Q8×C73—21no—
126D4×C73—21no—
127D4×C73—21no—
128D4×C73—41no—
129D4×C73—41no—
130D4×C73—42no—
131D4×C73—42no—
132D4×C73—81no—
133D4×C73—81no—
134D4×C73—162no—
135D4×C73—162no—
136C2×C4×C73—21no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—41no—
141C2×C4×C73—81no—
142C2×C4×C73—161no—
143C2×C4×C73#12011yescharacteristic
144C2×C4×C73#12111yescharacteristic
145C2×C4×C73#12311yescharacteristic
146C2×C4×C73C2×D811yescharacteristic
147C2×C4×C73#13511yescharacteristic
148C2×C4×C73#13711yescharacteristic
149C8×C73—41no—
150C8×C73—81no—
151C8×C73#12111yescharacteristic
152C8×C73#12111yescharacteristic
153C8×C73#12311yescharacteristic
154C8×C73#12411yescharacteristic
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—82no—
161C22×C73—82no—
162C22×C73—82no—
163C22×C73—162no—
164C22×C73—162no—
165C22×C73#44711yescharacteristic
166C22×C73#46811yescharacteristic
167C22×C73#48211yescharacteristic
168C4×C73—41no—
169C4×C73—81no—
170C4×C73—81no—
171C4×C73—161no—
172C4×C73#39411yescharacteristic
173C4×C73#45211yescharacteristic
174C4×C73#46611yescharacteristic
175C4×C73#48011yescharacteristic
176#13387C7311yesmaximal, characteristic, direct product factor, Sylow
177C2×C73—21no—
178C2×C73—21no—
179C2×C73—81no—
180C2×C73—162no—
181C2×C73#203311yescharacteristic
182C2×C73#219211yescharacteristic
183C2×C73#219411yescharacteristic
184#3058C2×C7311yescharacteristic
185#2159C2×C7311yescharacteristic, complemented
186C2×#361C2×C7311yescharacteristic, complemented
187C2×#357C2×C7311yescharacteristic, complemented
188C2×#350C2×C7311yescharacteristic, complemented
189#1816C2×C7311yescharacteristic, complemented
190#1382C2×C7311yescharacteristic, complemented
191C73#1338711yescharacteristic, direct product factor, Sylow
192C22×D8C22×C7311yescharacteristic
193C2×#131C22×C7311yescharacteristic
194#535—21no—
195C2×M32C22×C7311yescharacteristic
196C22×C16C22×C7311yescharacteristic
197#469—22no—
198#466—21no—
199#466—21no—
200C2×#108C22×C7311yescharacteristic
201#427C22×C7311yescharacteristic
202C2×#107C22×C7311yescharacteristic
203#418—21no—
204#417—21no—
205#367—21no—
206#366—21no—
207#361—22no—
208#357—22no—
209#350—22no—
210#343—21no—
211C2×#41D4×C7311yescharacteristic
212C22×D4—21no—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8D4×C7312yes—
219#131—21no—
220#131—21no—
221#131—21no—
222#131—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16D4×C7311yescharacteristic
226C22×C8—21no—
227C22×C8C23×C7311yescharacteristic
228#127—41no—
229#124—41no—
230#121—22no—
231#121—22no—
232#120—42no—
233#117—21no—
234C2×C4⋊C4—21no—
235M32—21no—
236M32D4×C7312yescomplemented
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241#108—21no—
242#108—21no—
243#107—21no—
244#107—21no—
245#107D4×C7311yescharacteristic
246#107D4×C7311yescharacteristic
247#106—21no—
248#103—41no—
249#102—22no—
250#102—22no—
251#102—41no—
252C24—41no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—21no—
257C2×Q8D8×C7311yescharacteristic
258C2×D4—21no—
259C2×D4—22no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4D8×C7311yescharacteristic
268C22×C4—21no—
269C22×C4—41no—
270C22×C4C2×D4×C7311yescharacteristic
271D8—22no—
272D8—22no—
273D8—41no—
274D8—41no—
275M16—21no—
276M16—21no—
277M16—41no—
278M16—41no—
279M16—41no—
280M16—41no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8C2×D4×C7311yescharacteristic
286C2×C8C2×D4×C7311yescharacteristic
287C2×C8C2×D4×C7311yescharacteristic
288C2×C8#41×C7311yescharacteristic
289C2×C8#41×C7311yescharacteristic
290C2×C8#41×C7311yescharacteristic
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C42—41no—
299C16—22no—
300C16—41no—
301C23—21no—
302C23—42no—
303C23—81no—
304C23—81no—
305C23—161no—
306C23—161no—
307C23AGL(1,ℤ/8)×C7311yescharacteristic
308Q8—21no—
309Q8—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—81no—
317D4—81no—
318D4—162no—
319D4—162no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—161no—
327C2×C4#120×C7311yescharacteristic
328C2×C4#121×C7311yescharacteristic
329C2×C4#123×C7311yescharacteristic
330C2×C4C2×D8×C7311yescharacteristic
331C2×C4#135×C7311yescharacteristic
332C2×C4#137×C7311yescharacteristic
333C8—41no—
334C8—81no—
335C8#121×C7311yescharacteristic
336C8#121×C7311yescharacteristic
337C8#123×C7311yescharacteristic
338C8#124×C7311yescharacteristic
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—82no—
345C22—82no—
346C22—82no—
347C22—162no—
348C22—162no—
349C22#447×C7311yescharacteristic
350C22#468×C7311yescharacteristic
351C22#482×C7311yescharacteristic
352C4—41no—
353C4—81no—
354C4—81no—
355C4—161no—
356C4#394×C7311yescharacteristic
357C4#452×C7311yescharacteristic
358C4#466×C7311yescharacteristic
359C4#480×C7311yescharacteristic
360C2—21no—
361C2—21no—
362C2—81no—
363C2—162no—
364C2C73×#203311yescharacteristic
365C2C73×#219211yescharacteristic
366C2C73×#219411yescharacteristic
subgroupG/H
center, socleC22×C73#447
commutator, Frattini, cosocleC22×C8C23×C73
prime radicalC73×#3058C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×#131×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2159C2semidirect
3. C2×#361×C73C2semidirect
4. C2×#357×C73C2semidirect
5. C2×#350×C73C2semidirect
6. C73×#1816C2semidirect
7. C73×#1382C2semidirect
52. M32×C73D4semidirect
176. #13387C73direct (N × H)
185. #2159C2×C73semidirect
186. C2×#361C2×C73semidirect
187. C2×#357C2×C73semidirect
188. C2×#350C2×C73semidirect
189. #1816C2×C73semidirect
190. #1382C2×C73semidirect
191. C73#13387direct (N × H)
236. M32D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#30582
C73×#21592
C2×#361×C732
C2×#357×C732
C2×#350×C732
C73×#18162
C73×#13822
#1338773