Finite Group Databasebeta

← C73×#19355 #32928759

Subgroups — C73×#19355 #32928759

Order 18688.

678 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3251C212yesmaximal, complemented
2C73×#3147C211yesmaximal, characteristic, complemented
3C73×#2966C211yesmaximal, characteristic, complemented
4C73×#1690C211yesmaximal, characteristic, complemented
5C73×#1689C211yesmaximal, characteristic, complemented
6C73×#1688C211yesmaximal, characteristic, complemented
7C73×#1687C211yesmaximal, characteristic, complemented
8C73×#1666C212yesmaximal, complemented
9C73×#1665C212yesmaximal, complemented
10C73×#1566C211yesmaximal, characteristic, complemented
11C73×#1557C212yesmaximal, complemented
12C2×#135×C73—21no—
13C2×#135×C73—21no—
14#532×C73C2212yes—
15#529×C73C2211yescharacteristic
16#495×C73—21no—
17#495×C73—21no—
18#494×C73C2211yescharacteristic
19#493×C73C2211yescharacteristic
20#492×C73C2212yes—
21#478×C73—22no—
22#475×C73C2212yes—
23#474×C73C2212yes—
24#469×C73—22no—
25#468×C73—22no—
26#463×C73—22no—
27#460×C73C2212yes—
28#459×C73C2212yes—
29#446×C73C2211yescharacteristic
30C8×Q8×C73C2211yescharacteristic
31#436×C73C2211yescharacteristic
32#435×C73—21no—
33C8×D4×C73—21no—
34C8×D4×C73C2211yescharacteristic
35#433×C73—21no—
36#432×C73C2211yescharacteristic
37#423×C73C2212yes—
38#405×C73—21no—
39C2×C4×C8×C73C2211yescharacteristic
40#334×C73C2211yescharacteristic
41#334×C73C2211yescharacteristic
42#334×C73C2212yes—
43#332×C73C2212yes—
44#332×C73C2212yes—
45#331×C73C2212yes—
46#331×C73C2212yes—
47C2×#41×C73—22no—
48#135×C73—44no—
49#135×C73—44no—
50C2×Q16×C73—21no—
51C2×Q16×C73—21no—
52C2×SD16×C73—22no—
53C2×SD16×C73—22no—
54C2×SD16×C73—22no—
55C2×D8×C73—22no—
56C2×D8×C73—21no—
57C2×D8×C73—21no—
58C2×M16×C73—22no—
59C2×M16×C73—21no—
60C22×C8×C73—21no—
61C22×C8×C73D411yescharacteristic
62C22×C8×C73D411yescharacteristic
63C4⋊Q8×C73C2312yes—
64#127×C73C2312yes—
65#126×C73—21no—
66#125×C73D411yescharacteristic
67#124×C73—22no—
68#124×C73D411yescharacteristic
69#123×C73—21no—
70C22⋊Q8×C73D411yescharacteristic
71#121×C73—22no—
72#121×C73—22no—
73#121×C73D411yescharacteristic
74C4×Q8×C73C2311yescharacteristic
75C4×D4×C73—21no—
76C4×D4×C73—22no—
77C4×D4×C73—22no—
78C4×D4×C73C2311yescharacteristic
79#117×C73—21no—
80C2×C42×C73C2311yescharacteristic
81#107×C73—22no—
82#106×C73—22no—
83C4⋊C8×C73—21no—
84C4⋊C8×C73—21no—
85C4⋊C8×C73—22no—
86C4⋊C8×C73C2312yes—
87C4⋊C8×C73C2312yes—
88C4⋊C8×C73C2311yescharacteristic
89C4⋊C8×C73C2311yescharacteristic
90#103×C73—22no—
91#102×C73—22no—
92#102×C73—22no—
93#102×C73—22no—
94C22⋊C8×C73—21no—
95C22⋊C8×C73—21no—
96C22⋊C8×C73—21no—
97#97×C73—21no—
98#97×C73—21no—
99C4×C8×C73—21no—
100C4×C8×C73D411yescharacteristic
101C4×C8×C73D411yescharacteristic
102C4×C8×C73C2311yescharacteristic
103C4×C8×C73C2311yescharacteristic
104#41×C73—44no—
105#41×C73—44no—
106C2×Q8×C73—22no—
107C2×Q8×C73C2×D411yescharacteristic
108C2×D4×C73—21no—
109C2×D4×C73—22no—
110C2×D4×C73—22no—
111C2×D4×C73—22no—
112C2×D4×C73—42no—
113C2×D4×C73C2×D411yescharacteristic
114C22×C4×C73—21no—
115C22×C4×C73—42no—
116C22×C4×C73C2×D411yescharacteristic
117C22×C4×C73C2×D411yescharacteristic
118C22×C4×C73#4111yescharacteristic
119Q16×C73—42no—
120Q16×C73—42no—
121SD16×C73—44no—
122SD16×C73—44no—
123SD16×C73—82no—
124D8×C73—42no—
125D8×C73—42no—
126D8×C73—82no—
127M16×C73—42no—
128M16×C73—82no—
129C2×C8×C73—22no—
130C2×C8×C73—22no—
131C2×C8×C73—21no—
132C2×C8×C73—21no—
133C2×C8×C73—22no—
134C2×C8×C73—22no—
135C2×C8×C73—42no—
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73C2×D411yescharacteristic
140C4⋊C4×C73—21no—
141C4⋊C4×C73—21no—
142C4⋊C4×C73—21no—
143C4⋊C4×C73—21no—
144C4⋊C4×C73—22no—
145C4⋊C4×C73—22no—
146C4⋊C4×C73C2×D411yescharacteristic
147C4⋊C4×C73C2×D411yescharacteristic
148C22⋊C4×C73—21no—
149C22⋊C4×C73—21no—
150C22⋊C4×C73—21no—
151C22⋊C4×C73—21no—
152C22⋊C4×C73—21no—
153C22⋊C4×C73—42no—
154C22⋊C4×C73—42no—
155C42×C73—21no—
156C42×C73C2×D411yescharacteristic
157C42×C73C2×D411yescharacteristic
158C42×C73#4111yescharacteristic
159C42×C73C2411yescharacteristic
160C23×C73—21no—
161C23×C73—42no—
162C23×C73#12111yescharacteristic
163Q8×C73—22no—
164Q8×C73—42no—
165Q8×C73—42no—
166D4×C73—22no—
167D4×C73—42no—
168D4×C73—42no—
169D4×C73—42no—
170D4×C73—42no—
171D4×C73—42no—
172D4×C73—82no—
173D4×C73—84no—
174C2×C4×C73—21no—
175C2×C4×C73—21no—
176C2×C4×C73—22no—
177C2×C4×C73—21no—
178C2×C4×C73—21no—
179C2×C4×C73—21no—
180C2×C4×C73—41no—
181C2×C4×C73—41no—
182C2×C4×C73—41no—
183C2×C4×C73—42no—
184C2×C4×C73—84no—
185C2×C4×C73#12111yescharacteristic
186C2×C4×C73#12111yescharacteristic
187C2×C4×C73#12111yescharacteristic
188C2×C4×C73C22×D411yescharacteristic
189C2×C4×C73C22×D411yescharacteristic
190C2×C4×C73C2×#4111yescharacteristic
191C8×C73—21no—
192C8×C73—21no—
193C8×C73—41no—
194C8×C73—41no—
195C8×C73—42no—
196C8×C73—42no—
197C8×C73AGL(1,ℤ/8)12yes—
198C8×C73AGL(1,ℤ/8)12yes—
199C22×C73—21no—
200C22×C73—21no—
201C22×C73—21no—
202C22×C73—41no—
203C22×C73—41no—
204C22×C73—41no—
205C22×C73—82no—
206C22×C73—82no—
207C22×C73—82no—
208C22×C73C2×#12111yescharacteristic
209C4×C73—21no—
210C4×C73—21no—
211C4×C73—21no—
212C4×C73—21no—
213C4×C73—41no—
214C4×C73—41no—
215C4×C73—41no—
216C4×C73—82no—
217C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
218C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
219C4×C73#57712yes—
220#19355C7311yesmaximal, characteristic, direct product factor, Sylow
221C2×C73—41no—
222C2×C73—81no—
223C2×C73—162no—
224C2×C73#303811yescharacteristic
225C2×C73#306011yescharacteristic
226C2×C73#306711yescharacteristic
227#3251C2×C7312yescomplemented
228#3147C2×C7311yescharacteristic, complemented
229#2966C2×C7311yescharacteristic, complemented
230#1690C2×C7311yescharacteristic, complemented
231#1689C2×C7311yescharacteristic, complemented
232#1688C2×C7311yescharacteristic, complemented
233#1687C2×C7311yescharacteristic, complemented
234#1666C2×C7312yescomplemented
235#1665C2×C7312yescomplemented
236#1566C2×C7311yescharacteristic, complemented
237#1557C2×C7312yescomplemented
238C73#1935511yescharacteristic, direct product factor, Sylow
239C2×#135—21no—
240C2×#135—21no—
241#532C22×C7312yes—
242#529C22×C7311yescharacteristic
243#495—21no—
244#495—21no—
245#494C22×C7311yescharacteristic
246#493C22×C7311yescharacteristic
247#492C22×C7312yes—
248#478—22no—
249#475C22×C7312yes—
250#474C22×C7312yes—
251#469—22no—
252#468—22no—
253#463—22no—
254#460C22×C7312yes—
255#459C22×C7312yes—
256#446C22×C7311yescharacteristic
257C8×Q8C22×C7311yescharacteristic
258#436C22×C7311yescharacteristic
259#435—21no—
260C8×D4—21no—
261C8×D4C22×C7311yescharacteristic
262#433—21no—
263#432C22×C7311yescharacteristic
264#423C22×C7312yes—
265#405—21no—
266C2×C4×C8C22×C7311yescharacteristic
267#334C22×C7312yes—
268#334C22×C7311yescharacteristic
269#334C22×C7311yescharacteristic
270#332C22×C7312yes—
271#332C22×C7312yes—
272#331C22×C7312yes—
273#331C22×C7312yes—
274C2×#41—22no—
275#135—44no—
276#135—44no—
277C2×Q16—21no—
278C2×Q16—21no—
279C2×SD16—22no—
280C2×SD16—22no—
281C2×SD16—22no—
282C2×D8—22no—
283C2×D8—21no—
284C2×D8—21no—
285C2×M16—22no—
286C2×M16—21no—
287C22×C8—21no—
288C22×C8D4×C7311yescharacteristic
289C22×C8D4×C7311yescharacteristic
290C4⋊Q8C23×C7312yes—
291#127C23×C7312yes—
292#126—21no—
293#125D4×C7311yescharacteristic
294#124—22no—
295#124D4×C7311yescharacteristic
296#123—21no—
297C22⋊Q8D4×C7311yescharacteristic
298#121—22no—
299#121—22no—
300#121D4×C7311yescharacteristic
301C4×Q8C23×C7311yescharacteristic
302C4×D4—21no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4C23×C7311yescharacteristic
306#117—21no—
307C2×C42C23×C7311yescharacteristic
308#107—22no—
309#106—22no—
310C4⋊C8—21no—
311C4⋊C8—21no—
312C4⋊C8—22no—
313C4⋊C8C23×C7311yescharacteristic
314C4⋊C8C23×C7311yescharacteristic
315C4⋊C8C23×C7312yes—
316C4⋊C8C23×C7312yes—
317#103—22no—
318#102—22no—
319#102—22no—
320#102—22no—
321C22⋊C8—21no—
322C22⋊C8—21no—
323C22⋊C8—21no—
324#97—21no—
325#97—21no—
326C4×C8—21no—
327C4×C8D4×C7311yescharacteristic
328C4×C8D4×C7311yescharacteristic
329C4×C8C23×C7311yescharacteristic
330C4×C8C23×C7311yescharacteristic
331#41—44no—
332#41—44no—
333C2×Q8—22no—
334C2×Q8C2×D4×C7311yescharacteristic
335C2×D4—21no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—42no—
340C2×D4C2×D4×C7311yescharacteristic
341C22×C4—21no—
342C22×C4—42no—
343C22×C4C2×D4×C7311yescharacteristic
344C22×C4C2×D4×C7311yescharacteristic
345C22×C4#41×C7311yescharacteristic
346Q16—42no—
347Q16—42no—
348SD16—44no—
349SD16—44no—
350SD16—82no—
351D8—42no—
352D8—42no—
353D8—82no—
354M16—42no—
355M16—82no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—42no—
363C2×C8C2×D4×C7311yescharacteristic
364C2×C8C2×D4×C7311yescharacteristic
365C2×C8C2×D4×C7311yescharacteristic
366C2×C8C2×D4×C7311yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4C2×D4×C7311yescharacteristic
374C4⋊C4C2×D4×C7311yescharacteristic
375C22⋊C4—21no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C42—21no—
383C42C2×D4×C7311yescharacteristic
384C42C2×D4×C7311yescharacteristic
385C42#41×C7311yescharacteristic
386C42C24×C7311yescharacteristic
387C23—21no—
388C23—42no—
389C23#121×C7311yescharacteristic
390Q8—22no—
391Q8—42no—
392Q8—42no—
393D4—22no—
394D4—42no—
395D4—42no—
396D4—42no—
397D4—42no—
398D4—42no—
399D4—82no—
400D4—84no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—84no—
412C2×C4#121×C7311yescharacteristic
413C2×C4#121×C7311yescharacteristic
414C2×C4#121×C7311yescharacteristic
415C2×C4C22×D4×C7311yescharacteristic
416C2×C4C22×D4×C7311yescharacteristic
417C2×C4C2×#41×C7311yescharacteristic
418C8—21no—
419C8—21no—
420C8—41no—
421C8—41no—
422C8—42no—
423C8—42no—
424C8AGL(1,ℤ/8)×C7312yes—
425C8AGL(1,ℤ/8)×C7312yes—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—82no—
433C22—82no—
434C22—82no—
435C22C2×#121×C7311yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—82no—
444C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
445C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
446C4#577×C7312yes—
447C2—41no—
448C2—81no—
449C2—162no—
450C2C73×#303811yescharacteristic
451C2C73×#306011yescharacteristic
452C2C73×#306711yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3251C2semidirect
2. C73×#3147C2semidirect
3. C73×#2966C2semidirect
4. C73×#1690C2semidirect
5. C73×#1689C2semidirect
6. C73×#1688C2semidirect
7. C73×#1687C2semidirect
8. C73×#1666C2semidirect
9. C73×#1665C2semidirect
10. C73×#1566C2semidirect
11. C73×#1557C2semidirect
220. #19355C73direct (N × H)
227. #3251C2×C73semidirect
228. #3147C2×C73semidirect
229. #2966C2×C73semidirect
230. #1690C2×C73semidirect
231. #1689C2×C73semidirect
232. #1688C2×C73semidirect
233. #1687C2×C73semidirect
234. #1666C2×C73semidirect
235. #1665C2×C73semidirect
236. #1566C2×C73semidirect
237. #1557C2×C73semidirect
238. C73#19355direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32512
C73×#31472
C73×#29662
C73×#16902
C73×#16892
C73×#16882
C73×#16872
C73×#16662
C73×#16652
C73×#15662
C73×#15572
#1935573