Finite Group Databasebeta

← C73×#19351 #32928755

Subgroups — C73×#19351 #32928755

Order 18688.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3255C211yesmaximal, characteristic, complemented
2C73×#3254C211yesmaximal, characteristic
3C73×#3167C211yesmaximal, characteristic
4C73×#2960C211yesmaximal, characteristic, complemented
5C73×#1692C212yesmaximal, complemented
6C73×#1686C212yesmaximal, complemented
7C73×#1684C212yesmaximal, complemented
8C73×#1682C212yesmaximal, complemented
9C73×#1567C211yesmaximal, characteristic, complemented
10C73×#1561C211yesmaximal, characteristic, complemented
11C73×#1560C211yesmaximal, characteristic
12#533×C73C2211yescharacteristic
13#533×C73C2211yescharacteristic
14#532×C73C2211yescharacteristic
15#498×C73C2211yescharacteristic
16#492×C73C2211yescharacteristic
17#487×C73C2211yescharacteristic
18#486×C73C2211yescharacteristic
19#477×C73C2212yes—
20#475×C73—21no—
21#475×C73C2212yes—
22#474×C73—21no—
23#470×C73—22no—
24#468×C73—22no—
25#465×C73—21no—
26#465×C73—21no—
27#462×C73—21no—
28#462×C73C2212yes—
29#461×C73—21no—
30#460×C73C2212yes—
31#446×C73—21no—
32#446×C73C2212yes—
33C8×Q8×C73—21no—
34C8×Q8×C73C2212yes—
35C4×SD16×C73—21no—
36C4×SD16×C73—21no—
37#424×C73—21no—
38#423×C73C2211yescharacteristic
39#423×C73C2211yescharacteristic
40#423×C73C2211yescharacteristic
41#405×C73—21no—
42C2×C4×C8×C73C2211yescharacteristic
43#335×C73C2212yes—
44#335×C73C2212yes—
45#333×C73C2212yes—
46#332×C73C2212yes—
47#332×C73C2212yes—
48#331×C73C2212yes—
49C2×#41×C73—21no—
50C2×Q16×C73—22no—
51C2×SD16×C73—22no—
52C2×SD16×C73—21no—
53C2×SD16×C73—21no—
54C2×M16×C73—21no—
55C2×M16×C73—21no—
56C2×M16×C73—21no—
57C22×C8×C73D411yescharacteristic
58C22×C8×C73D411yescharacteristic
59C4⋊Q8×C73D411yescharacteristic
60C4⋊Q8×C73D411yescharacteristic
61C4⋊Q8×C73C2311yescharacteristic
62C4⋊Q8×C73C2311yescharacteristic
63C4⋊Q8×C73C2311yescharacteristic
64#127×C73C2311yescharacteristic
65#125×C73—21no—
66#125×C73—21no—
67#124×C73—21no—
68C22⋊Q8×C73—21no—
69C22⋊Q8×C73—21no—
70C22⋊Q8×C73—21no—
71C22⋊Q8×C73D412yes—
72#121×C73—21no—
73#121×C73—21no—
74C4×Q8×C73—21no—
75C4×Q8×C73—21no—
76C4×Q8×C73—21no—
77C4×Q8×C73C2312yes—
78C4×D4×C73—21no—
79C4×D4×C73—21no—
80#117×C73—21no—
81#117×C73—21no—
82C2×C42×C73C2311yescharacteristic
83#107×C73—22no—
84#106×C73—21no—
85#106×C73—21no—
86#106×C73—22no—
87C4⋊C8×C73—22no—
88C4⋊C8×C73—22no—
89C4⋊C8×C73—21no—
90C4⋊C8×C73—21no—
91C4⋊C8×C73—21no—
92C4⋊C8×C73C2312yes—
93C4⋊C8×C73C2312yes—
94C4⋊C8×C73C2312yes—
95#103×C73—22no—
96#103×C73—22no—
97#103×C73—21no—
98#103×C73—21no—
99#103×C73—22no—
100#102×C73—21no—
101#102×C73—21no—
102#102×C73—22no—
103#97×C73—22no—
104C4×C8×C73—22no—
105C4×C8×C73D411yescharacteristic
106C4×C8×C73D411yescharacteristic
107C4×C8×C73C2311yescharacteristic
108C4×C8×C73C2311yescharacteristic
109#41×C73—82no—
110C2×Q8×C73—21no—
111C2×Q8×C73—21no—
112C2×Q8×C73—21no—
113C2×Q8×C73—21no—
114C2×Q8×C73C2×D412yes—
115C2×D4×C73—21no—
116C2×D4×C73—21no—
117C2×D4×C73—21no—
118C2×D4×C73—41no—
119C22×C4×C73—41no—
120C22×C4×C73C2×D411yescharacteristic
121C22×C4×C73C2×D411yescharacteristic
122C22×C4×C73#4111yescharacteristic
123Q16×C73—82no—
124SD16×C73—42no—
125SD16×C73—42no—
126SD16×C73—82no—
127M16×C73—42no—
128M16×C73—81no—
129M16×C73—81no—
130C2×C8×C73—22no—
131C2×C8×C73—22no—
132C2×C8×C73—22no—
133C2×C8×C73—22no—
134C2×C8×C73—41no—
135C2×C8×C73C2×D411yescharacteristic
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C4⋊C4×C73—21no—
140C4⋊C4×C73—21no—
141C4⋊C4×C73—21no—
142C4⋊C4×C73—22no—
143C4⋊C4×C73—22no—
144C4⋊C4×C73—21no—
145C4⋊C4×C73—21no—
146C4⋊C4×C73—21no—
147C4⋊C4×C73—21no—
148C4⋊C4×C73—21no—
149C4⋊C4×C73—21no—
150C4⋊C4×C73—41no—
151C4⋊C4×C73—41no—
152C4⋊C4×C73C2×D412yes—
153C22⋊C4×C73—22no—
154C22⋊C4×C73—41no—
155C22⋊C4×C73—41no—
156C22⋊C4×C73—41no—
157C42×C73—22no—
158C42×C73—41no—
159C42×C73C2×D411yescharacteristic
160C42×C73C2×D411yescharacteristic
161C42×C73#4111yescharacteristic
162C42×C73C2411yescharacteristic
163C23×C73—41no—
164C23×C73#12111yescharacteristic
165Q8×C73—22no—
166Q8×C73—22no—
167Q8×C73—42no—
168Q8×C73—41no—
169Q8×C73—41no—
170Q8×C73—41no—
171Q8×C73—41no—
172Q8×C73—81no—
173D4×C73—41no—
174D4×C73—41no—
175D4×C73—41no—
176D4×C73—41no—
177D4×C73—81no—
178D4×C73—82no—
179C2×C4×C73—21no—
180C2×C4×C73—21no—
181C2×C4×C73—21no—
182C2×C4×C73—21no—
183C2×C4×C73—22no—
184C2×C4×C73—22no—
185C2×C4×C73—22no—
186C2×C4×C73—41no—
187C2×C4×C73—41no—
188C2×C4×C73—41no—
189C2×C4×C73—82no—
190C2×C4×C73#12111yescharacteristic
191C2×C4×C73#12111yescharacteristic
192C2×C4×C73#12111yescharacteristic
193C2×C4×C73C22×D411yescharacteristic
194C2×C4×C73C22×D411yescharacteristic
195C2×C4×C73C2×#4111yescharacteristic
196C8×C73—21no—
197C8×C73—21no—
198C8×C73—21no—
199C8×C73—42no—
200C8×C73—42no—
201C8×C73—42no—
202C8×C73#13712yes—
203C22×C73—21no—
204C22×C73—21no—
205C22×C73—21no—
206C22×C73—81no—
207C22×C73—81no—
208C22×C73—81no—
209C22×C73C2×#12111yescharacteristic
210C4×C73—21no—
211C4×C73—21no—
212C4×C73—21no—
213C4×C73—42no—
214C4×C73—42no—
215C4×C73—81no—
216C4×C73—81no—
217C4×C73—81no—
218C4×C73#47112yes—
219C4×C73C2×#13711yescharacteristic
220C4×C73#57511yescharacteristic
221C4×C73#57611yescharacteristic
222C4×C73#57811yescharacteristic
223#19351C7311yesmaximal, characteristic, direct product factor, Sylow
224C2×C73—41no—
225C2×C73—161no—
226C2×C73#303711yescharacteristic
227C2×C73#306111yescharacteristic
228C2×C73C2×#47111yescharacteristic
229#3255C2×C7311yescharacteristic, complemented
230#3254C2×C7311yescharacteristic
231#3167C2×C7311yescharacteristic
232#2960C2×C7311yescharacteristic, complemented
233#1692C2×C7312yescomplemented
234#1686C2×C7312yescomplemented
235#1684C2×C7312yescomplemented
236#1682C2×C7312yescomplemented
237#1567C2×C7311yescharacteristic, complemented
238#1561C2×C7311yescharacteristic, complemented
239#1560C2×C7311yescharacteristic
240C73#1935111yescharacteristic, direct product factor, Sylow
241#533C22×C7311yescharacteristic
242#533C22×C7311yescharacteristic
243#532C22×C7311yescharacteristic
244#498C22×C7311yescharacteristic
245#492C22×C7311yescharacteristic
246#487C22×C7311yescharacteristic
247#486C22×C7311yescharacteristic
248#477C22×C7312yes—
249#475—21no—
250#475C22×C7312yes—
251#474—21no—
252#470—22no—
253#468—22no—
254#465—21no—
255#465—21no—
256#462—21no—
257#462C22×C7312yes—
258#461—21no—
259#460C22×C7312yes—
260#446—21no—
261#446C22×C7312yes—
262C8×Q8—21no—
263C8×Q8C22×C7312yes—
264C4×SD16—21no—
265C4×SD16—21no—
266#424—21no—
267#423C22×C7311yescharacteristic
268#423C22×C7311yescharacteristic
269#423C22×C7311yescharacteristic
270#405—21no—
271C2×C4×C8C22×C7311yescharacteristic
272#335C22×C7312yes—
273#335C22×C7312yes—
274#333C22×C7312yes—
275#332C22×C7312yes—
276#332C22×C7312yes—
277#331C22×C7312yes—
278C2×#41—21no—
279C2×Q16—22no—
280C2×SD16—22no—
281C2×SD16—21no—
282C2×SD16—21no—
283C2×M16—21no—
284C2×M16—21no—
285C2×M16—21no—
286C22×C8D4×C7311yescharacteristic
287C22×C8D4×C7311yescharacteristic
288C4⋊Q8D4×C7311yescharacteristic
289C4⋊Q8D4×C7311yescharacteristic
290C4⋊Q8C23×C7311yescharacteristic
291C4⋊Q8C23×C7311yescharacteristic
292C4⋊Q8C23×C7311yescharacteristic
293#127C23×C7311yescharacteristic
294#125—21no—
295#125—21no—
296#124—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8D4×C7312yes—
301#121—21no—
302#121—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8C23×C7312yes—
307C4×D4—21no—
308C4×D4—21no—
309#117—21no—
310#117—21no—
311C2×C42C23×C7311yescharacteristic
312#107—22no—
313#106—21no—
314#106—21no—
315#106—22no—
316C4⋊C8—22no—
317C4⋊C8—22no—
318C4⋊C8—21no—
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8C23×C7312yes—
322C4⋊C8C23×C7312yes—
323C4⋊C8C23×C7312yes—
324#103—22no—
325#103—22no—
326#103—21no—
327#103—21no—
328#103—22no—
329#102—21no—
330#102—21no—
331#102—22no—
332#97—22no—
333C4×C8—22no—
334C4×C8D4×C7311yescharacteristic
335C4×C8D4×C7311yescharacteristic
336C4×C8C23×C7311yescharacteristic
337C4×C8C23×C7311yescharacteristic
338#41—82no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8C2×D4×C7312yes—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—41no—
348C22×C4—41no—
349C22×C4C2×D4×C7311yescharacteristic
350C22×C4C2×D4×C7311yescharacteristic
351C22×C4#41×C7311yescharacteristic
352Q16—82no—
353SD16—42no—
354SD16—42no—
355SD16—82no—
356M16—42no—
357M16—81no—
358M16—81no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8C2×D4×C7311yescharacteristic
365C2×C8C2×D4×C7311yescharacteristic
366C2×C8C2×D4×C7311yescharacteristic
367C2×C8C2×D4×C7311yescharacteristic
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4C2×D4×C7312yes—
382C22⋊C4—22no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C42—22no—
387C42—41no—
388C42C2×D4×C7311yescharacteristic
389C42C2×D4×C7311yescharacteristic
390C42#41×C7311yescharacteristic
391C42C24×C7311yescharacteristic
392C23—41no—
393C23#121×C7311yescharacteristic
394Q8—22no—
395Q8—22no—
396Q8—42no—
397Q8—41no—
398Q8—41no—
399Q8—41no—
400Q8—41no—
401Q8—81no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—81no—
407D4—82no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—82no—
419C2×C4#121×C7311yescharacteristic
420C2×C4#121×C7311yescharacteristic
421C2×C4#121×C7311yescharacteristic
422C2×C4C22×D4×C7311yescharacteristic
423C2×C4C22×D4×C7311yescharacteristic
424C2×C4C2×#41×C7311yescharacteristic
425C8—21no—
426C8—21no—
427C8—21no—
428C8—42no—
429C8—42no—
430C8—42no—
431C8#137×C7312yes—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22C2×#121×C7311yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—42no—
443C4—42no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4#471×C7312yes—
448C4C2×#137×C7311yescharacteristic
449C4#575×C7311yescharacteristic
450C4#576×C7311yescharacteristic
451C4#578×C7311yescharacteristic
452C2—41no—
453C2—161no—
454C2C73×#303711yescharacteristic
455C2C73×#306111yescharacteristic
456C2C2×#471×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radical#532×C73C22
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×#3255C2semidirect
4. C73×#2960C2semidirect
5. C73×#1692C2semidirect
6. C73×#1686C2semidirect
7. C73×#1684C2semidirect
8. C73×#1682C2semidirect
9. C73×#1567C2semidirect
10. C73×#1561C2semidirect
223. #19351C73direct (N × H)
229. #3255C2×C73semidirect
232. #2960C2×C73semidirect
233. #1692C2×C73semidirect
234. #1686C2×C73semidirect
235. #1684C2×C73semidirect
236. #1682C2×C73semidirect
237. #1567C2×C73semidirect
238. #1561C2×C73semidirect
240. C73#19351direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32552
C73×#32542
C73×#31672
C73×#29602
C73×#16922
C73×#16862
C73×#16842
C73×#16822
C73×#15672
C73×#15612
C73×#15602
#1935173