Finite Group Databasebeta

← C73×#10196 #32919600

Subgroups — C73×#10196 #32919600

Order 18688.

546 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3245C211yesmaximal, characteristic
2C73×#3206C211yesmaximal, characteristic, complemented
3C73×#3141C211yesmaximal, characteristic, complemented
4C73×#1987C211yesmaximal, characteristic, complemented
5C73×#1980C211yesmaximal, characteristic, complemented
6C73×#1502C211yesmaximal, characteristic, complemented
7C73×#1283C211yesmaximal, characteristic, complemented
8#532×C73C2211yescharacteristic
9#532×C73C2211yescharacteristic
10C2×C4⋊Q8×C73C2211yescharacteristic
11#492×C73—21no—
12#489×C73—22no—
13#487×C73—21no—
14#487×C73—21no—
15#486×C73—21no—
16#474×C73—21no—
17#474×C73—21no—
18#466×C73—22no—
19#461×C73—22no—
20#459×C73—21no—
21#459×C73—21no—
22#448×C73—22no—
23#431×C73C2211yescharacteristic
24C2×C4⋊C8×C73C2211yescharacteristic
25C2×#104×C73—22no—
26#417×C73—22no—
27C4×M16×C73C2211yescharacteristic
28C4×C4⋊C4×C73C2211yescharacteristic
29#340×C73—22no—
30#327×C73—22no—
31C2×#41×C73—21no—
32C2×#41×C73—21no—
33C22×Q8×C73—21no—
34C2×SD16×C73—24no—
35C2×D8×C73—22no—
36C2×M16×C73D412yes—
37C22×C8×C73D412yes—
38C4⋊Q8×C73—21no—
39C4⋊Q8×C73—21no—
40C4⋊Q8×C73—21no—
41C4⋊Q8×C73D412yes—
42C4⋊Q8×C73D411yescharacteristic
43C4⋊Q8×C73D411yescharacteristic
44#127×C73D411yescharacteristic
45#127×C73D411yescharacteristic
46#124×C73—21no—
47#124×C73—21no—
48#121×C73—21no—
49#121×C73—21no—
50#121×C73—21no—
51#121×C73—21no—
52C4×D4×C73—21no—
53C4×D4×C73—21no—
54C4×D4×C73—21no—
55C4×D4×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C4⋊C4×C73—21no—
58C2×C4⋊C4×C73—21no—
59C2×C42×C73—21no—
60C2×C42×C73C2311yescharacteristic
61#107×C73—22no—
62C4⋊C8×C73—21no—
63C4⋊C8×C73—21no—
64C4⋊C8×C73—21no—
65#104×C73—44no—
66#103×C73—24no—
67#103×C73—24no—
68#102×C73—24no—
69#102×C73—22no—
70#102×C73—22no—
71C22⋊C8×C73D412yes—
72#97×C73—21no—
73C4×C8×C73—21no—
74C4×C8×C73—21no—
75#95×C73—21no—
76#41×C73—42no—
77#41×C73—42no—
78#41×C73—42no—
79#41×C73—42no—
80C2×Q8×C73—21no—
81C2×Q8×C73—22no—
82C2×Q8×C73—21no—
83C2×Q8×C73—41no—
84C2×Q8×C73—82no—
85C2×D4×C73—21no—
86C2×D4×C73—21no—
87C2×D4×C73—21no—
88C2×D4×C73—21no—
89C2×D4×C73—21no—
90C2×D4×C73—21no—
91C2×D4×C73—41no—
92C2×D4×C73—41no—
93C22×C4×C73—41no—
94C22×C4×C73—41no—
95C22×C4×C73—41no—
96C22×C4×C73—41no—
97C22×C4×C73C2×D411yescharacteristic
98C22×C4×C73C2×D411yescharacteristic
99C22×C4×C73C2×D411yescharacteristic
100SD16×C73—84no—
101D8×C73—82no—
102M16×C73—22no—
103M16×C73—22no—
104C2×C8×C73—22no—
105C2×C8×C73—22no—
106C2×C8×C73—22no—
107C2×C8×C73—42no—
108C4⋊C4×C73—22no—
109C4⋊C4×C73—22no—
110C4⋊C4×C73—21no—
111C4⋊C4×C73—21no—
112C4⋊C4×C73—21no—
113C4⋊C4×C73—22no—
114C4⋊C4×C73—21no—
115C4⋊C4×C73—41no—
116C4⋊C4×C73—41no—
117C4⋊C4×C73—41no—
118C22⋊C4×C73—41no—
119C22⋊C4×C73—41no—
120C22⋊C4×C73—41no—
121C22⋊C4×C73—41no—
122C42×C73—42no—
123C42×C73C2×D411yescharacteristic
124C42×C73C2×D411yescharacteristic
125C42×C73C2×D411yescharacteristic
126C42×C73#4111yescharacteristic
127C23×C73—41no—
128C23×C73—41no—
129C23×C73#12711yescharacteristic
130Q8×C73—44no—
131Q8×C73—42no—
132Q8×C73—42no—
133Q8×C73—82no—
134D4×C73—42no—
135D4×C73—42no—
136D4×C73—41no—
137D4×C73—41no—
138D4×C73—41no—
139D4×C73—41no—
140D4×C73—42no—
141D4×C73—81no—
142D4×C73—81no—
143D4×C73—81no—
144D4×C73—81no—
145D4×C73—81no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—41no—
149C2×C4×C73—42no—
150C2×C4×C73—41no—
151C2×C4×C73—41no—
152C2×C4×C73—42no—
153C2×C4×C73—81no—
154C2×C4×C73—82no—
155C2×C4×C73—81no—
156C2×C4×C73—82no—
157C2×C4×C73—82no—
158C2×C4×C73#12011yescharacteristic
159C2×C4×C73#12011yescharacteristic
160C2×C4×C73#12011yescharacteristic
161C2×C4×C73#12111yescharacteristic
162C2×C4×C73#12111yescharacteristic
163C2×C4×C73#12111yescharacteristic
164C2×C4×C73#13512yes—
165C2×C4×C73AGL(1,ℤ/8)12yes—
166C8×C73—42no—
167C8×C73—42no—
168C8×C73—42no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—81no—
172C22×C73—81no—
173C22×C73—81no—
174C22×C73—81no—
175C22×C73—81no—
176C22×C73—81no—
177C22×C73#39211yescharacteristic
178C22×C73#49511yescharacteristic
179C22×C73#49611yescharacteristic
180C4×C73—21no—
181C4×C73—21no—
182C4×C73—21no—
183C4×C73—82no—
184C4×C73—82no—
185C4×C73—81no—
186C4×C73—81no—
187C4×C73#44912yes—
188C4×C73#45511yescharacteristic
189C4×C73#45611yescharacteristic
190C4×C73#46312yes—
191#10196C7311yesmaximal, characteristic, direct product factor, Sylow
192C2×C73—21no—
193C2×C73—21no—
194C2×C73—161no—
195C2×C73—161no—
196C2×C73#200711yescharacteristic
197C2×C73#200811yescharacteristic
198C2×C73#201211yescharacteristic
199#3245C2×C7311yescharacteristic
200#3206C2×C7311yescharacteristic, complemented
201#3141C2×C7311yescharacteristic, complemented
202#1987C2×C7311yescharacteristic, complemented
203#1980C2×C7311yescharacteristic, complemented
204#1502C2×C7311yescharacteristic, complemented
205#1283C2×C7311yescharacteristic, complemented
206C73#1019611yescharacteristic, direct product factor, Sylow
207#532C22×C7311yescharacteristic
208#532C22×C7311yescharacteristic
209C2×C4⋊Q8C22×C7311yescharacteristic
210#492—21no—
211#489—22no—
212#487—21no—
213#487—21no—
214#486—21no—
215#474—21no—
216#474—21no—
217#466—22no—
218#461—22no—
219#459—21no—
220#459—21no—
221#448—22no—
222#431C22×C7311yescharacteristic
223C2×C4⋊C8C22×C7311yescharacteristic
224C2×#104—22no—
225#417—22no—
226C4×M16C22×C7311yescharacteristic
227C4×C4⋊C4C22×C7311yescharacteristic
228#340—22no—
229#327—22no—
230C2×#41—21no—
231C2×#41—21no—
232C22×Q8—21no—
233C2×SD16—24no—
234C2×D8—22no—
235C2×M16D4×C7312yes—
236C22×C8D4×C7312yes—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8D4×C7312yes—
241C4⋊Q8D4×C7311yescharacteristic
242C4⋊Q8D4×C7311yescharacteristic
243#127D4×C7311yescharacteristic
244#127D4×C7311yescharacteristic
245#124—21no—
246#124—21no—
247#121—21no—
248#121—21no—
249#121—21no—
250#121—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C42—21no—
259C2×C42C23×C7311yescharacteristic
260#107—22no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264#104—44no—
265#103—24no—
266#103—24no—
267#102—24no—
268#102—22no—
269#102—22no—
270C22⋊C8D4×C7312yes—
271#97—21no—
272C4×C8—21no—
273C4×C8—21no—
274#95—21no—
275#41—42no—
276#41—42no—
277#41—42no—
278#41—42no—
279C2×Q8—21no—
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—41no—
283C2×Q8—82no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4C2×D4×C7311yescharacteristic
297C22×C4C2×D4×C7311yescharacteristic
298C22×C4C2×D4×C7311yescharacteristic
299SD16—84no—
300D8—82no—
301M16—22no—
302M16—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—42no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C42—42no—
322C42C2×D4×C7311yescharacteristic
323C42C2×D4×C7311yescharacteristic
324C42C2×D4×C7311yescharacteristic
325C42#41×C7311yescharacteristic
326C23—41no—
327C23—41no—
328C23#127×C7311yescharacteristic
329Q8—44no—
330Q8—42no—
331Q8—42no—
332Q8—82no—
333D4—42no—
334D4—42no—
335D4—41no—
336D4—41no—
337D4—41no—
338D4—41no—
339D4—42no—
340D4—81no—
341D4—81no—
342D4—81no—
343D4—81no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4#120×C7311yescharacteristic
358C2×C4#120×C7311yescharacteristic
359C2×C4#120×C7311yescharacteristic
360C2×C4#121×C7311yescharacteristic
361C2×C4#121×C7311yescharacteristic
362C2×C4#121×C7311yescharacteristic
363C2×C4#135×C7312yes—
364C2×C4AGL(1,ℤ/8)×C7312yes—
365C8—42no—
366C8—42no—
367C8—42no—
368C22—21no—
369C22—21no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22#392×C7311yescharacteristic
377C22#495×C7311yescharacteristic
378C22#496×C7311yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—82no—
384C4—81no—
385C4—81no—
386C4#449×C7312yes—
387C4#455×C7311yescharacteristic
388C4#456×C7311yescharacteristic
389C4#463×C7312yes—
390C2—21no—
391C2—21no—
392C2—161no—
393C2—161no—
394C2C73×#200711yescharacteristic
395C2C73×#200811yescharacteristic
396C2C73×#201211yescharacteristic
subgroupG/H
center, socleC22×C73#392
commutator, Frattini, cosocleC2×C42C23×C73
prime radicalC73×#3245C2
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×#3206C2semidirect
3. C73×#3141C2semidirect
4. C73×#1987C2semidirect
5. C73×#1980C2semidirect
6. C73×#1502C2semidirect
7. C73×#1283C2semidirect
191. #10196C73direct (N × H)
200. #3206C2×C73semidirect
201. #3141C2×C73semidirect
202. #1987C2×C73semidirect
203. #1980C2×C73semidirect
204. #1502C2×C73semidirect
205. #1283C2×C73semidirect
206. C73#10196direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32452
C73×#32062
C73×#31412
C73×#19872
C73×#19802
C73×#15022
C73×#12832
#1019673