Finite Group Databasebeta

← C73×#13400 #32922804

Subgroups — C73×#13400 #32922804

Order 18688.

402 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3060C211yesmaximal, characteristic
2C2×#365×C73C211yesmaximal, characteristic, complemented
3C73×#2148C211yesmaximal, characteristic, complemented
4C73×#2145C211yesmaximal, characteristic, complemented
5C73×#2117C211yesmaximal, characteristic, complemented
6C73×#1814C211yesmaximal, characteristic, complemented
7C73×#1386C211yesmaximal, characteristic, complemented
8C2×#135×C73C2211yescharacteristic
9C2×#131×C73C2211yescharacteristic
10#537×C73—21no—
11C2×M32×C73C2211yescharacteristic
12C2×M32×C73C2211yescharacteristic
13#470×C73—21no—
14#469×C73—21no—
15#465×C73—22no—
16C2×#108×C73C2211yescharacteristic
17#427×C73C2211yescharacteristic
18C2×#106×C73C2211yescharacteristic
19#421×C73—21no—
20#417×C73—21no—
21#365×C73—22no—
22#362×C73—21no—
23#361×C73—21no—
24#360×C73—22no—
25#350×C73—22no—
26#344×C73—21no—
27C2×#41×C73—21no—
28C2×#41×C73D411yescharacteristic
29#135×C73—21no—
30#135×C73—21no—
31#135×C73—21no—
32#135×C73—21no—
33C2×Q16×C73D411yescharacteristic
34C2×SD16×C73—21no—
35C2×D8×C73D411yescharacteristic
36#131×C73—21no—
37#131×C73—21no—
38#131×C73—21no—
39#131×C73—21no—
40C2×M16×C73—21no—
41C2×M16×C73—21no—
42C2×M16×C73D411yescharacteristic
43C22×C8×C73—21no—
44C22×C8×C73C2311yescharacteristic
45C22⋊Q8×C73—22no—
46C22⋊Q8×C73—41no—
47#121×C73—22no—
48#121×C73—42no—
49#121×C73—41no—
50#117×C73—21no—
51C2×C4⋊C4×C73—21no—
52M32×C73—21no—
53M32×C73—21no—
54M32×C73—21no—
55M32×C73D412yescomplemented
56C2×C16×C73—21no—
57C2×C16×C73—21no—
58#108×C73—21no—
59#108×C73—21no—
60#107×C73—21no—
61#106×C73—21no—
62#106×C73—21no—
63#106×C73D412yes—
64#104×C73—42no—
65#103×C73—22no—
66#102×C73—22no—
67#41×C73—21no—
68#41×C73—21no—
69#41×C73—21no—
70#41×C73—21no—
71#41×C73—41no—
72#41×C73—41no—
73#41×C73—41no—
74#41×C73—41no—
75C2×Q8×C73—21no—
76C2×Q8×C73SD1611yescharacteristic
77C2×D4×C73—21no—
78C2×D4×C73—21no—
79C2×D4×C73—41no—
80C2×D4×C73—42no—
81C2×D4×C73SD1611yescharacteristic
82C22×C4×C73—21no—
83C22×C4×C73—41no—
84C22×C4×C73—41no—
85C22×C4×C73C2×D411yescharacteristic
86Q16×C73—21no—
87Q16×C73—21no—
88SD16×C73—41no—
89SD16×C73—41no—
90D8×C73—21no—
91D8×C73—21no—
92M16×C73—21no—
93M16×C73—21no—
94M16×C73—41no—
95M16×C73—41no—
96M16×C73—41no—
97M16×C73—41no—
98C2×C8×C73—21no—
99C2×C8×C73—41no—
100C2×C8×C73—41no—
101C2×C8×C73—41no—
102C2×C8×C73C2×D411yescharacteristic
103C2×C8×C73C2×D411yescharacteristic
104C2×C8×C73C2×D411yescharacteristic
105C2×C8×C73#4111yescharacteristic
106C2×C8×C73#4111yescharacteristic
107C2×C8×C73#4111yescharacteristic
108C4⋊C4×C73—22no—
109C4⋊C4×C73—42no—
110C4⋊C4×C73—41no—
111C4⋊C4×C73—41no—
112C22⋊C4×C73—42no—
113C22⋊C4×C73—42no—
114C22⋊C4×C73—41no—
115C42×C73—41no—
116C16×C73—22no—
117C16×C73—41no—
118C23×C73—21no—
119C23×C73—41no—
120C23×C73AGL(1,ℤ/8)11yescharacteristic
121Q8×C73—21no—
122Q8×C73—21no—
123Q8×C73—41no—
124Q8×C73—41no—
125D4×C73—21no—
126D4×C73—21no—
127D4×C73—41no—
128D4×C73—41no—
129D4×C73—41no—
130D4×C73—41no—
131D4×C73—81no—
132D4×C73—81no—
133D4×C73—162no—
134C2×C4×C73—21no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73—42no—
138C2×C4×C73—41no—
139C2×C4×C73—81no—
140C2×C4×C73—81no—
141C2×C4×C73—81no—
142C2×C4×C73—161no—
143C2×C4×C73#12011yescharacteristic
144C2×C4×C73#12111yescharacteristic
145C2×C4×C73#12311yescharacteristic
146C2×C4×C73C2×SD1611yescharacteristic
147C2×C4×C73#13511yescharacteristic
148C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
149C8×C73—41no—
150C8×C73—81no—
151C8×C73#12111yescharacteristic
152C8×C73#12111yescharacteristic
153C8×C73#12311yescharacteristic
154C8×C73#12411yescharacteristic
155C22×C73—41no—
156C22×C73—42no—
157C22×C73—41no—
158C22×C73—81no—
159C22×C73—81no—
160C22×C73—81no—
161C22×C73#45011yescharacteristic
162C22×C73#46911yescharacteristic
163C22×C73#48211yescharacteristic
164C4×C73—41no—
165C4×C73—82no—
166C4×C73—81no—
167C4×C73—161no—
168C4×C73#39411yescharacteristic
169C4×C73#44911yescharacteristic
170C4×C73#46511yescharacteristic
171C4×C73#48111yescharacteristic
172#13400C7311yesmaximal, characteristic, direct product factor, Sylow
173C2×C73—21no—
174C2×C73—21no—
175C2×C73—21no—
176C2×C73—81no—
177C2×C73—161no—
178C2×C73#203411yescharacteristic
179#3060C2×C7311yescharacteristic
180C2×#365C2×C7311yescharacteristic, complemented
181#2148C2×C7311yescharacteristic, complemented
182#2145C2×C7311yescharacteristic, complemented
183#2117C2×C7311yescharacteristic, complemented
184#1814C2×C7311yescharacteristic, complemented
185#1386C2×C7311yescharacteristic, complemented
186C73#1340011yescharacteristic, direct product factor, Sylow
187C2×#135C22×C7311yescharacteristic
188C2×#131C22×C7311yescharacteristic
189#537—21no—
190C2×M32C22×C7311yescharacteristic
191C2×M32C22×C7311yescharacteristic
192#470—21no—
193#469—21no—
194#465—22no—
195C2×#108C22×C7311yescharacteristic
196#427C22×C7311yescharacteristic
197C2×#106C22×C7311yescharacteristic
198#421—21no—
199#417—21no—
200#365—22no—
201#362—21no—
202#361—21no—
203#360—22no—
204#350—22no—
205#344—21no—
206C2×#41—21no—
207C2×#41D4×C7311yescharacteristic
208#135—21no—
209#135—21no—
210#135—21no—
211#135—21no—
212C2×Q16D4×C7311yescharacteristic
213C2×SD16—21no—
214C2×D8D4×C7311yescharacteristic
215#131—21no—
216#131—21no—
217#131—21no—
218#131—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16D4×C7311yescharacteristic
222C22×C8—21no—
223C22×C8C23×C7311yescharacteristic
224C22⋊Q8—22no—
225C22⋊Q8—41no—
226#121—22no—
227#121—42no—
228#121—41no—
229#117—21no—
230C2×C4⋊C4—21no—
231M32—21no—
232M32—21no—
233M32—21no—
234M32D4×C7312yescomplemented
235C2×C16—21no—
236C2×C16—21no—
237#108—21no—
238#108—21no—
239#107—21no—
240#106—21no—
241#106—21no—
242#106D4×C7312yes—
243#104—42no—
244#103—22no—
245#102—22no—
246#41—21no—
247#41—21no—
248#41—21no—
249#41—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8SD16×C7311yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4SD16×C7311yescharacteristic
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C2×D4×C7311yescharacteristic
265Q16—21no—
266Q16—21no—
267SD16—41no—
268SD16—41no—
269D8—21no—
270D8—21no—
271M16—21no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277C2×C8—21no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8C2×D4×C7311yescharacteristic
282C2×C8C2×D4×C7311yescharacteristic
283C2×C8C2×D4×C7311yescharacteristic
284C2×C8#41×C7311yescharacteristic
285C2×C8#41×C7311yescharacteristic
286C2×C8#41×C7311yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C42—41no—
295C16—22no—
296C16—41no—
297C23—21no—
298C23—41no—
299C23AGL(1,ℤ/8)×C7311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—41no—
303Q8—41no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—41no—
310D4—81no—
311D4—81no—
312D4—162no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—161no—
322C2×C4#120×C7311yescharacteristic
323C2×C4#121×C7311yescharacteristic
324C2×C4#123×C7311yescharacteristic
325C2×C4C2×SD16×C7311yescharacteristic
326C2×C4#135×C7311yescharacteristic
327C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
328C8—41no—
329C8—81no—
330C8#121×C7311yescharacteristic
331C8#121×C7311yescharacteristic
332C8#123×C7311yescharacteristic
333C8#124×C7311yescharacteristic
334C22—41no—
335C22—42no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22#450×C7311yescharacteristic
341C22#469×C7311yescharacteristic
342C22#482×C7311yescharacteristic
343C4—41no—
344C4—82no—
345C4—81no—
346C4—161no—
347C4#394×C7311yescharacteristic
348C4#449×C7311yescharacteristic
349C4#465×C7311yescharacteristic
350C4#481×C7311yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—81no—
355C2—161no—
356C2C73×#203411yescharacteristic
subgroupG/H
center, socleC2×C73#2034
commutator, Frattini, cosocleC22×C8C23×C73
prime radicalC73×#3060C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C73 ◁ C22×C4×C73 ◁ C2×#131×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#365×C73C2semidirect
3. C73×#2148C2semidirect
4. C73×#2145C2semidirect
5. C73×#2117C2semidirect
6. C73×#1814C2semidirect
7. C73×#1386C2semidirect
55. M32×C73D4semidirect
172. #13400C73direct (N × H)
180. C2×#365C2×C73semidirect
181. #2148C2×C73semidirect
182. #2145C2×C73semidirect
183. #2117C2×C73semidirect
184. #1814C2×C73semidirect
185. #1386C2×C73semidirect
186. C73#13400direct (N × H)
234. M32D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#30602
C2×#365×C732
C73×#21482
C73×#21452
C73×#21172
C73×#18142
C73×#13862
#1340073