Finite Group Databasebeta

← C73×#10553 #32919957

Subgroups — C73×#10553 #32919957

Order 18688.

416 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×#3138C211yesmaximal, characteristic
2C73×#1950C211yesmaximal, characteristic, complemented
3C73×#1550C211yesmaximal, characteristic, complemented
4C73×#1545C211yesmaximal, characteristic
5C2×#331×C73C211yesmaximal, characteristic
6C73×#1481C211yesmaximal, characteristic, complemented
7C73×#1283C211yesmaximal, characteristic, complemented
8#533×C73C2211yescharacteristic
9C2×#127×C73C2211yescharacteristic
10#490×C73—22no—
11#486×C73—21no—
12#486×C73—21no—
13#431×C73C2211yescharacteristic
14C2×#108×C73—21no—
15#423×C73C2211yescharacteristic
16C2×C4⋊C8×C73C2211yescharacteristic
17C2×C4⋊C8×C73C2211yescharacteristic
18#418×C73—21no—
19#418×C73—21no—
20C4×M16×C73C2211yescharacteristic
21#341×C73—21no—
22#333×C73—21no—
23#332×C73—21no—
24#331×C73—22no—
25#331×C73—22no—
26Q8⋊C8×C73—22no—
27C22×D4×C73—21no—
28C22×D4×C73—21no—
29C22×D4×C73—21no—
30C2×M16×C73—21no—
31C2×M16×C73D411yescharacteristic
32C2×M16×C73D411yescharacteristic
33C22×C8×C73—21no—
34C22×C8×C73—21no—
35C4⋊Q8×C73D411yescharacteristic
36C4⋊Q8×C73D411yescharacteristic
37#127×C73—21no—
38#127×C73—21no—
39#127×C73—21no—
40#127×C73D412yes—
41#125×C73—21no—
42C22⋊Q8×C73—21no—
43C22⋊Q8×C73—21no—
44C4×Q8×C73—21no—
45C4×Q8×C73—21no—
46#117×C73—21no—
47C2×C42×C73C2311yescharacteristic
48#108×C73—42no—
49C4⋊C8×C73—21no—
50C4⋊C8×C73—21no—
51C4⋊C8×C73—21no—
52C4⋊C8×C73—21no—
53C4⋊C8×C73—21no—
54C4⋊C8×C73—21no—
55C4⋊C8×C73D412yes—
56#102×C73—22no—
57#102×C73—22no—
58#102×C73—22no—
59#102×C73—22no—
60C22⋊C8×C73—21no—
61#97×C73—21no—
62C4×C8×C73—21no—
63C4×C8×C73—21no—
64C24×C73—41no—
65C2×Q8×C73—21no—
66C2×Q8×C73—21no—
67C2×D4×C73—22no—
68C2×D4×C73—22no—
69C2×D4×C73—22no—
70C2×D4×C73—41no—
71C2×D4×C73—41no—
72C2×D4×C73—41no—
73C2×D4×C73—41no—
74C2×D4×C73—41no—
75C2×D4×C73—41no—
76C2×D4×C73—41no—
77C2×D4×C73—81no—
78C2×D4×C73—81no—
79C2×D4×C73—82no—
80C22×C4×C73C2×D411yescharacteristic
81C22×C4×C73#4111yescharacteristic
82C22×C4×C73#4111yescharacteristic
83M16×C73—21no—
84M16×C73—21no—
85M16×C73—21no—
86M16×C73—21no—
87M16×C73—41no—
88M16×C73—41no—
89C2×C8×C73—21no—
90C2×C8×C73—21no—
91C2×C8×C73—22no—
92C2×C8×C73—41no—
93C2×C8×C73—41no—
94C2×C8×C73—41no—
95C2×C8×C73—41no—
96C2×C8×C73—41no—
97C2×C8×C73—81no—
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73—41no—
103C4⋊C4×C73—41no—
104C22⋊C4×C73—41no—
105C42×C73—41no—
106C42×C73C2×D411yescharacteristic
107C42×C73C2×D411yescharacteristic
108C42×C73C2×D411yescharacteristic
109C42×C73#4111yescharacteristic
110C23×C73—42no—
111C23×C73—82no—
112C23×C73—82no—
113C23×C73—81no—
114C23×C73—81no—
115C23×C73#12411yescharacteristic
116Q8×C73—41no—
117Q8×C73—41no—
118Q8×C73—81no—
119D4×C73—42no—
120D4×C73—42no—
121D4×C73—82no—
122D4×C73—82no—
123D4×C73—82no—
124D4×C73—81no—
125D4×C73—81no—
126D4×C73—81no—
127D4×C73—81no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73#12011yescharacteristic
134C2×C4×C73#12111yescharacteristic
135C2×C4×C73#12111yescharacteristic
136C2×C4×C73#12111yescharacteristic
137C2×C4×C73#12311yescharacteristic
138C2×C4×C73#12311yescharacteristic
139C2×C4×C73#13511yescharacteristic
140C2×C4×C73#13511yescharacteristic
141C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C73#13711yescharacteristic
143C8×C73—41no—
144C8×C73—41no—
145C8×C73—42no—
146C8×C73—81no—
147C8×C73—81no—
148C8×C73—81no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—82no—
152C22×C73—82no—
153C22×C73—82no—
154C22×C73—162no—
155C22×C73—162no—
156C22×C73#39411yescharacteristic
157C22×C73#48811yescharacteristic
158C22×C73#48911yescharacteristic
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—81no—
163C4×C73—81no—
164C4×C73#44911yescharacteristic
165C4×C73#45211yescharacteristic
166C4×C73#46311yescharacteristic
167C4×C73#46411yescharacteristic
168C4×C73#47111yescharacteristic
169C4×C73#47211yescharacteristic
170#10553C7311yesmaximal, characteristic, direct product factor, Sylow
171C2×C73—21no—
172C2×C73—21no—
173C2×C73—162no—
174C2×C73#204211yescharacteristic
175C2×C73#204811yescharacteristic
176C2×C73#205111yescharacteristic
177#3138C2×C7311yescharacteristic
178#1950C2×C7311yescharacteristic, complemented
179#1550C2×C7311yescharacteristic, complemented
180#1545C2×C7311yescharacteristic
181C2×#331C2×C7311yescharacteristic
182#1481C2×C7311yescharacteristic, complemented
183#1283C2×C7311yescharacteristic, complemented
184C73#1055311yescharacteristic, direct product factor, Sylow
185#533C22×C7311yescharacteristic
186C2×#127C22×C7311yescharacteristic
187#490—22no—
188#486—21no—
189#486—21no—
190#431C22×C7311yescharacteristic
191C2×#108—21no—
192#423C22×C7311yescharacteristic
193C2×C4⋊C8C22×C7311yescharacteristic
194C2×C4⋊C8C22×C7311yescharacteristic
195#418—21no—
196#418—21no—
197C4×M16C22×C7311yescharacteristic
198#341—21no—
199#333—21no—
200#332—21no—
201#331—22no—
202#331—22no—
203Q8⋊C8—22no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C2×M16—21no—
208C2×M16D4×C7311yescharacteristic
209C2×M16D4×C7311yescharacteristic
210C22×C8—21no—
211C22×C8—21no—
212C4⋊Q8D4×C7311yescharacteristic
213C4⋊Q8D4×C7311yescharacteristic
214#127—21no—
215#127—21no—
216#127—21no—
217#127D4×C7312yes—
218#125—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223#117—21no—
224C2×C42C23×C7311yescharacteristic
225#108—42no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8D4×C7312yes—
233#102—22no—
234#102—22no—
235#102—22no—
236#102—22no—
237C22⋊C8—21no—
238#97—21no—
239C4×C8—21no—
240C4×C8—21no—
241C24—41no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—81no—
255C2×D4—81no—
256C2×D4—82no—
257C22×C4C2×D4×C7311yescharacteristic
258C22×C4#41×C7311yescharacteristic
259C22×C4#41×C7311yescharacteristic
260M16—21no—
261M16—21no—
262M16—21no—
263M16—21no—
264M16—41no—
265M16—41no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—81no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42C2×D4×C7311yescharacteristic
284C42C2×D4×C7311yescharacteristic
285C42C2×D4×C7311yescharacteristic
286C42#41×C7311yescharacteristic
287C23—42no—
288C23—82no—
289C23—82no—
290C23—81no—
291C23—81no—
292C23#124×C7311yescharacteristic
293Q8—41no—
294Q8—41no—
295Q8—81no—
296D4—42no—
297D4—42no—
298D4—82no—
299D4—82no—
300D4—82no—
301D4—81no—
302D4—81no—
303D4—81no—
304D4—81no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4#120×C7311yescharacteristic
311C2×C4#121×C7311yescharacteristic
312C2×C4#121×C7311yescharacteristic
313C2×C4#121×C7311yescharacteristic
314C2×C4#123×C7311yescharacteristic
315C2×C4#123×C7311yescharacteristic
316C2×C4#135×C7311yescharacteristic
317C2×C4#135×C7311yescharacteristic
318C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
319C2×C4#137×C7311yescharacteristic
320C8—41no—
321C8—41no—
322C8—42no—
323C8—81no—
324C8—81no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22—162no—
332C22—162no—
333C22#394×C7311yescharacteristic
334C22#488×C7311yescharacteristic
335C22#489×C7311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4#449×C7311yescharacteristic
342C4#452×C7311yescharacteristic
343C4#463×C7311yescharacteristic
344C4#464×C7311yescharacteristic
345C4#471×C7311yescharacteristic
346C4#472×C7311yescharacteristic
347C2—21no—
348C2—21no—
349C2—162no—
350C2C73×#204211yescharacteristic
351C2C73×#204811yescharacteristic
352C2C73×#205111yescharacteristic
subgroupG/H
center, socleC22×C73#394
commutator, Frattini, cosocleC2×C42C23×C73
prime radicalC2×#127×C73C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#1950C2semidirect
3. C73×#1550C2semidirect
6. C73×#1481C2semidirect
7. C73×#1283C2semidirect
170. #10553C73direct (N × H)
178. #1950C2×C73semidirect
179. #1550C2×C73semidirect
182. #1481C2×C73semidirect
183. #1283C2×C73semidirect
184. C73#10553direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#31382
C73×#19502
C73×#15502
C73×#15452
C2×#331×C732
C73×#14812
C73×#12832
#1055373