Finite Group Databasebeta

← C73×#10409 #32919813

Subgroups — C73×#10409 #32919813

Order 18688.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2541C211yesmaximal, characteristic
2C73×#1957C211yesmaximal, characteristic, complemented
3C73×#1948C211yesmaximal, characteristic, complemented
4C73×#1802C211yesmaximal, characteristic, complemented
5C2×#331×C73C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C73C211yesmaximal, characteristic, complemented
7C73×#1279C211yesmaximal, characteristic, complemented
8C2×#127×C73—21no—
9C2×#127×C73C2211yescharacteristic
10C2×#121×C73—21no—
11C2×#121×C73—21no—
12C2×C4×D4×C73C2211yescharacteristic
13C2×#106×C73—21no—
14C2×C4⋊C8×C73C2211yescharacteristic
15C2×C4⋊C8×C73C2211yescharacteristic
16C2×#102×C73—22no—
17C2×#102×C73—21no—
18C2×C4×C8×C73C2211yescharacteristic
19#392×C73—22no—
20#390×C73—21no—
21#384×C73C2211yescharacteristic
22C4×C4⋊C4×C73C2211yescharacteristic
23#340×C73—21no—
24#340×C73—21no—
25#331×C73—22no—
26D4⋊C8×C73—22no—
27C22×D4×C73—22no—
28C22×D4×C73—22no—
29C22×D4×C73—21no—
30C22×D4×C73—21no—
31C22×D4×C73D411yescharacteristic
32C22×D4×C73D412yes—
33C23×C4×C73—21no—
34C22×C8×C73—21no—
35C22×C8×C73—21no—
36C22×C8×C73—21no—
37#127×C73—21no—
38#127×C73—21no—
39#127×C73—21no—
40#127×C73—21no—
41#127×C73—42no—
42#127×C73—42no—
43#121×C73—42no—
44#121×C73—42no—
45#121×C73—42no—
46#121×C73—42no—
47C4×D4×C73—21no—
48C4×D4×C73—21no—
49C4×D4×C73—21no—
50C4×D4×C73—21no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73—21no—
53C2×C4⋊C4×C73—21no—
54C2×C4⋊C4×C73D411yescharacteristic
55C2×C4⋊C4×C73D411yescharacteristic
56C2×C4⋊C4×C73D411yescharacteristic
57C2×C22⋊C4×C73—22no—
58C2×C22⋊C4×C73—22no—
59C2×C22⋊C4×C73—21no—
60C2×C42×C73—21no—
61C2×C42×C73C2311yescharacteristic
62#106×C73—42no—
63C4⋊C8×C73—21no—
64C4⋊C8×C73—21no—
65C4⋊C8×C73—21no—
66C4⋊C8×C73D412yescomplemented
67#102×C73—44no—
68#102×C73—42no—
69C4×C8×C73—21no—
70C4×C8×C73—21no—
71#95×C73—21no—
72C24×C73—21no—
73C24×C73—22no—
74C2×D4×C73—21no—
75C2×D4×C73—22no—
76C2×D4×C73—21no—
77C2×D4×C73—22no—
78C2×D4×C73—21no—
79C2×D4×C73—21no—
80C2×D4×C73—21no—
81C2×D4×C73—42no—
82C2×D4×C73—42no—
83C2×D4×C73—44no—
84C2×D4×C73—44no—
85C2×D4×C73—44no—
86C2×D4×C73—44no—
87C2×D4×C73—41no—
88C2×D4×C73—41no—
89C2×D4×C73—41no—
90C2×D4×C73—41no—
91C2×D4×C73—41no—
92C2×D4×C73—41no—
93C2×D4×C73—41no—
94C2×D4×C73—41no—
95C2×D4×C73—41no—
96C2×D4×C73—41no—
97C2×D4×C73—41no—
98C2×D4×C73—41no—
99C2×D4×C73—82no—
100C2×D4×C73—82no—
101C2×D4×C73SD1612yes—
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73—21no—
105C22×C4×C73—41no—
106C22×C4×C73—41no—
107C22×C4×C73—41no—
108C22×C4×C73—41no—
109C22×C4×C73—41no—
110C22×C4×C73—41no—
111C22×C4×C73—41no—
112C22×C4×C73C2×D411yescharacteristic
113C22×C4×C73C2×D411yescharacteristic
114C22×C4×C73C2×D411yescharacteristic
115C2×C8×C73—22no—
116C2×C8×C73—22no—
117C2×C8×C73—41no—
118C2×C8×C73—41no—
119C2×C8×C73—41no—
120C2×C8×C73—41no—
121C2×C8×C73—41no—
122C2×C8×C73—41no—
123C2×C8×C73—41no—
124C4⋊C4×C73—21no—
125C4⋊C4×C73—21no—
126C4⋊C4×C73—21no—
127C4⋊C4×C73—21no—
128C4⋊C4×C73—42no—
129C4⋊C4×C73—41no—
130C4⋊C4×C73—41no—
131C4⋊C4×C73—41no—
132C4⋊C4×C73—41no—
133C4⋊C4×C73D812yes—
134C4⋊C4×C73SD1612yes—
135C22⋊C4×C73—44no—
136C22⋊C4×C73—44no—
137C22⋊C4×C73—41no—
138C22⋊C4×C73—41no—
139C42×C73—41no—
140C42×C73—41no—
141C42×C73C2×D411yescharacteristic
142C42×C73#4111yescharacteristic
143C42×C73#4111yescharacteristic
144C42×C73#4111yescharacteristic
145C23×C73—22no—
146C23×C73—41no—
147C23×C73—41no—
148C23×C73—41no—
149C23×C73—41no—
150C23×C73—41no—
151C23×C73—41no—
152C23×C73—42no—
153C23×C73—42no—
154C23×C73—42no—
155C23×C73—42no—
156C23×C73—42no—
157C23×C73—42no—
158C23×C73—42no—
159C23×C73#12011yescharacteristic
160D4×C73—22no—
161D4×C73—22no—
162D4×C73—44no—
163D4×C73—41no—
164D4×C73—41no—
165D4×C73—82no—
166D4×C73—88no—
167D4×C73—88no—
168D4×C73—81no—
169D4×C73—81no—
170D4×C73—81no—
171D4×C73—81no—
172D4×C73—81no—
173D4×C73—81no—
174D4×C73—81no—
175D4×C73—81no—
176C2×C4×C73—21no—
177C2×C4×C73—21no—
178C2×C4×C73—22no—
179C2×C4×C73—22no—
180C2×C4×C73—41no—
181C2×C4×C73—41no—
182C2×C4×C73—41no—
183C2×C4×C73—41no—
184C2×C4×C73—41no—
185C2×C4×C73—41no—
186C2×C4×C73—41no—
187C2×C4×C73—81no—
188C2×C4×C73—81no—
189C2×C4×C73—81no—
190C2×C4×C73—81no—
191C2×C4×C73—81no—
192C2×C4×C73—81no—
193C2×C4×C73—81no—
194C2×C4×C73#12111yescharacteristic
195C2×C4×C73#12111yescharacteristic
196C2×C4×C73#12111yescharacteristic
197C2×C4×C73#12311yescharacteristic
198C2×C4×C73#12311yescharacteristic
199C2×C4×C73#12411yescharacteristic
200C2×C4×C73C2×D811yescharacteristic
201C2×C4×C73C2×SD1611yescharacteristic
202C2×C4×C73C2×SD1611yescharacteristic
203C2×C4×C73#13511yescharacteristic
204C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
207C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
208C8×C73—42no—
209C8×C73—42no—
210C8×C73—81no—
211C22×C73—42no—
212C22×C73—42no—
213C22×C73—42no—
214C22×C73—81no—
215C22×C73—81no—
216C22×C73—81no—
217C22×C73—81no—
218C22×C73—82no—
219C22×C73—82no—
220C22×C73—82no—
221C22×C73—82no—
222C22×C73—82no—
223C22×C73—82no—
224C22×C73—82no—
225C22×C73#39411yescharacteristic
226C22×C73#44711yescharacteristic
227C22×C73#44911yescharacteristic
228C22×C73#45011yescharacteristic
229C22×C73#45011yescharacteristic
230C22×C73#45311yescharacteristic
231C22×C73#45511yescharacteristic
232C4×C73—21no—
233C4×C73—21no—
234C4×C73—42no—
235C4×C73—42no—
236C4×C73—81no—
237C4×C73—161no—
238C4×C73#45911yescharacteristic
239C4×C73#46011yescharacteristic
240C4×C73#46511yescharacteristic
241C4×C73#46911yescharacteristic
242C4×C73#48111yescharacteristic
243C4×C73#48211yescharacteristic
244C4×C73#48611yescharacteristic
245C4×C73#49011yescharacteristic
246#10409C7311yesmaximal, characteristic, direct product factor, Sylow
247C2×C73—82no—
248C2×C73—162no—
249C2×C73#162111yescharacteristic
250C2×C73#162911yescharacteristic
251C2×C73#163911yescharacteristic
252C2×C73#164211yescharacteristic
253C2×C73#203411yescharacteristic
254C2×C73#203711yescharacteristic
255C2×C73#204111yescharacteristic
256#2541C2×C7311yescharacteristic
257#1957C2×C7311yescharacteristic, complemented
258#1948C2×C7311yescharacteristic, complemented
259#1802C2×C7311yescharacteristic, complemented
260C2×#331C2×C7311yescharacteristic, complemented
261C2×D4⋊C8C2×C7311yescharacteristic, complemented
262#1279C2×C7311yescharacteristic, complemented
263C73#1040911yescharacteristic, direct product factor, Sylow
264C2×#127—21no—
265C2×#127C22×C7311yescharacteristic
266C2×#121—21no—
267C2×#121—21no—
268C2×C4×D4C22×C7311yescharacteristic
269C2×#106—21no—
270C2×C4⋊C8C22×C7311yescharacteristic
271C2×C4⋊C8C22×C7311yescharacteristic
272C2×#102—21no—
273C2×#102—22no—
274C2×C4×C8C22×C7311yescharacteristic
275#392—22no—
276#390—21no—
277#384C22×C7311yescharacteristic
278C4×C4⋊C4C22×C7311yescharacteristic
279#340—21no—
280#340—21no—
281#331—22no—
282D4⋊C8—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4D4×C7311yescharacteristic
288C22×D4D4×C7312yes—
289C23×C4—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293#127—21no—
294#127—21no—
295#127—21no—
296#127—21no—
297#127—42no—
298#127—42no—
299#121—42no—
300#121—42no—
301#121—42no—
302#121—42no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4D4×C7311yescharacteristic
311C2×C4⋊C4D4×C7311yescharacteristic
312C2×C4⋊C4D4×C7311yescharacteristic
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—21no—
316C2×C42—21no—
317C2×C42C23×C7311yescharacteristic
318#106—42no—
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8D4×C7312yescomplemented
323#102—44no—
324#102—42no—
325C4×C8—21no—
326C4×C8—21no—
327#95—21no—
328C24—21no—
329C24—22no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—44no—
340C2×D4—44no—
341C2×D4—44no—
342C2×D4—44no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—82no—
356C2×D4—82no—
357C2×D4SD16×C7312yes—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4C2×D4×C7311yescharacteristic
369C22×C4C2×D4×C7311yescharacteristic
370C22×C4C2×D4×C7311yescharacteristic
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—41no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—42no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4D8×C7312yes—
390C4⋊C4SD16×C7312yes—
391C22⋊C4—44no—
392C22⋊C4—44no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—41no—
396C42—41no—
397C42C2×D4×C7311yescharacteristic
398C42#41×C7311yescharacteristic
399C42#41×C7311yescharacteristic
400C42#41×C7311yescharacteristic
401C23—22no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23#120×C7311yescharacteristic
416D4—22no—
417D4—22no—
418D4—44no—
419D4—41no—
420D4—41no—
421D4—82no—
422D4—88no—
423D4—88no—
424D4—81no—
425D4—81no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—81no—
430D4—81no—
431D4—81no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4#121×C7311yescharacteristic
451C2×C4#121×C7311yescharacteristic
452C2×C4#121×C7311yescharacteristic
453C2×C4#123×C7311yescharacteristic
454C2×C4#123×C7311yescharacteristic
455C2×C4#124×C7311yescharacteristic
456C2×C4C2×D8×C7311yescharacteristic
457C2×C4C2×SD16×C7311yescharacteristic
458C2×C4C2×SD16×C7311yescharacteristic
459C2×C4#135×C7311yescharacteristic
460C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
461C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
462C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
463C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
464C8—42no—
465C8—42no—
466C8—81no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22#394×C7311yescharacteristic
482C22#447×C7311yescharacteristic
483C22#449×C7311yescharacteristic
484C22#450×C7311yescharacteristic
485C22#450×C7311yescharacteristic
486C22#453×C7311yescharacteristic
487C22#455×C7311yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—81no—
493C4—161no—
494C4#459×C7311yescharacteristic
495C4#460×C7311yescharacteristic
496C4#465×C7311yescharacteristic
497C4#469×C7311yescharacteristic
498C4#481×C7311yescharacteristic
499C4#482×C7311yescharacteristic
500C4#486×C7311yescharacteristic
501C4#490×C7311yescharacteristic
502C2—82no—
503C2—162no—
504C2C73×#162111yescharacteristic
505C2C73×#162911yescharacteristic
506C2C73×#163911yescharacteristic
507C2C73×#164211yescharacteristic
508C2C73×#203411yescharacteristic
509C2C73×#203711yescharacteristic
510C2C73×#204111yescharacteristic
subgroupG/H
center, socleC23×C73#120
commutator, Frattini, cosocleC2×C42C23×C73
prime radicalC73×#2541C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#1957C2semidirect
3. C73×#1948C2semidirect
4. C73×#1802C2semidirect
5. C2×#331×C73C2semidirect
6. C2×D4⋊C8×C73C2semidirect
7. C73×#1279C2semidirect
66. C4⋊C8×C73D4semidirect
246. #10409C73direct (N × H)
257. #1957C2×C73semidirect
258. #1948C2×C73semidirect
259. #1802C2×C73semidirect
260. C2×#331C2×C73semidirect
261. C2×D4⋊C8C2×C73semidirect
262. #1279C2×C73semidirect
263. C73#10409direct (N × H)
322. C4⋊C8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#25412
C73×#19572
C73×#19482
C73×#18022
C2×#331×C732
C2×D4⋊C8×C732
C73×#12792
#1040973