Finite Group Databasebeta

← C73×#10246 #32919650

Subgroups — C73×#10246 #32919650

Order 18688.

740 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3208C211yesmaximal, characteristic, complemented
2C73×#3077C211yesmaximal, characteristic, complemented
3C73×#2541C211yesmaximal, characteristic
4C73×#1545C211yesmaximal, characteristic, complemented
5C73×#1503C211yesmaximal, characteristic, complemented
6C73×#1478C211yesmaximal, characteristic, complemented
7C73×#1303C211yesmaximal, characteristic, complemented
8#533×C73C2211yescharacteristic
9C2×#127×C73—21no—
10C2×#127×C73C2211yescharacteristic
11C2×#121×C73—22no—
12C2×C4×D4×C73C2211yescharacteristic
13#492×C73—21no—
14#486×C73—21no—
15#478×C73—22no—
16#476×C73—21no—
17#474×C73—21no—
18#460×C73—22no—
19#450×C73—22no—
20#431×C73C2211yescharacteristic
21#431×C73C2211yescharacteristic
22#428×C73—21no—
23#423×C73C2211yescharacteristic
24#418×C73—21no—
25#392×C73—22no—
26#390×C73—21no—
27C4×C4⋊C4×C73C2211yescharacteristic
28#331×C73—22no—
29#328×C73—22no—
30D4⋊C8×C73—22no—
31C22×D4×C73—24no—
32C22×D4×C73—21no—
33C22×D4×C73—21no—
34C22×D4×C73D411yescharacteristic
35C22×D4×C73D412yes—
36C23×C4×C73—21no—
37C2×SD16×C73—24no—
38C2×M16×C73—21no—
39C4⋊Q8×C73D411yescharacteristic, complemented
40C4⋊Q8×C73D411yescharacteristic, complemented
41#127×C73—21no—
42#127×C73—21no—
43#127×C73—21no—
44#127×C73—21no—
45#127×C73—42no—
46#127×C73—42no—
47#125×C73—21no—
48C22⋊Q8×C73—21no—
49C22⋊Q8×C73—21no—
50#121×C73—48no—
51C4×Q8×C73—21no—
52C4×Q8×C73—21no—
53C4×D4×C73—21no—
54C4×D4×C73—21no—
55C4×D4×C73—21no—
56C4×D4×C73—21no—
57#117×C73—21no—
58C2×C4⋊C4×C73—21no—
59C2×C4⋊C4×C73D411yescharacteristic
60C2×C22⋊C4×C73—24no—
61C2×C22⋊C4×C73—21no—
62C2×C42×C73—21no—
63C2×C42×C73C2311yescharacteristic
64#107×C73—22no—
65#106×C73—22no—
66C4⋊C8×C73—21no—
67C4⋊C8×C73—21no—
68C4⋊C8×C73D412yescomplemented
69C4⋊C8×C73D412yescomplemented
70#102×C73—22no—
71#102×C73—22no—
72#102×C73—24no—
73C22⋊C8×C73—21no—
74C22⋊C8×C73—21no—
75C4×C8×C73—21no—
76C4×C8×C73—21no—
77#95×C73D412yes—
78C24×C73—21no—
79C24×C73—22no—
80C2×Q8×C73—21no—
81C2×Q8×C73—21no—
82C2×D4×C73—21no—
83C2×D4×C73—22no—
84C2×D4×C73—21no—
85C2×D4×C73—22no—
86C2×D4×C73—21no—
87C2×D4×C73—21no—
88C2×D4×C73—21no—
89C2×D4×C73—44no—
90C2×D4×C73—48no—
91C2×D4×C73—48no—
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—41no—
100C2×D4×C73—82no—
101C2×D4×C73—84no—
102C2×D4×C73SD1612yescomplemented
103C22×C4×C73—22no—
104C22×C4×C73—21no—
105C22×C4×C73—44no—
106C22×C4×C73—41no—
107C22×C4×C73—41no—
108C22×C4×C73C2×D411yescharacteristic
109C22×C4×C73C2×D411yescharacteristic
110C22×C4×C73C2×D411yescharacteristic
111SD16×C73—84no—
112M16×C73—41no—
113M16×C73—41no—
114C2×C8×C73—22no—
115C2×C8×C73—22no—
116C2×C8×C73—41no—
117C4⋊C4×C73—24no—
118C4⋊C4×C73—21no—
119C4⋊C4×C73—21no—
120C4⋊C4×C73—21no—
121C4⋊C4×C73—21no—
122C4⋊C4×C73—21no—
123C4⋊C4×C73—21no—
124C4⋊C4×C73—41no—
125C4⋊C4×C73—41no—
126C22⋊C4×C73—48no—
127C22⋊C4×C73—41no—
128C22⋊C4×C73—41no—
129C22⋊C4×C73—41no—
130C42×C73—41no—
131C42×C73—41no—
132C42×C73—41no—
133C42×C73C2×D411yescharacteristic
134C42×C73C2×D411yescharacteristic
135C42×C73C2×D411yescharacteristic
136C42×C73#4111yescharacteristic
137C23×C73—22no—
138C23×C73—42no—
139C23×C73—42no—
140C23×C73—44no—
141C23×C73—44no—
142C23×C73—41no—
143C23×C73—41no—
144C23×C73—42no—
145C23×C73—42no—
146C23×C73—42no—
147C23×C73#12011yescharacteristic
148Q8×C73—42no—
149Q8×C73—81no—
150D4×C73—22no—
151D4×C73—22no—
152D4×C73—41no—
153D4×C73—44no—
154D4×C73—41no—
155D4×C73—82no—
156D4×C73—82no—
157D4×C73—82no—
158D4×C73—816no—
159D4×C73—81no—
160D4×C73—81no—
161D4×C73—81no—
162D4×C73—81no—
163C2×C4×C73—22no—
164C2×C4×C73—24no—
165C2×C4×C73—41no—
166C2×C4×C73—42no—
167C2×C4×C73—42no—
168C2×C4×C73—42no—
169C2×C4×C73—41no—
170C2×C4×C73—41no—
171C2×C4×C73—41no—
172C2×C4×C73—82no—
173C2×C4×C73—82no—
174C2×C4×C73#12011yescharacteristic
175C2×C4×C73#12011yescharacteristic
176C2×C4×C73#12111yescharacteristic
177C2×C4×C73#12111yescharacteristic
178C2×C4×C73#12111yescharacteristic
179C2×C4×C73#12711yescharacteristic
180C2×C4×C73C2×SD1611yescharacteristic
181C2×C4×C73#13511yescharacteristic
182C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C73#13711yescharacteristic
184C8×C73—42no—
185C8×C73—42no—
186C8×C73—81no—
187C22×C73—21no—
188C22×C73—21no—
189C22×C73—44no—
190C22×C73—42no—
191C22×C73—82no—
192C22×C73—84no—
193C22×C73—84no—
194C22×C73—81no—
195C22×C73—81no—
196C22×C73—82no—
197C22×C73—82no—
198C22×C73—82no—
199C22×C73#39211yescharacteristic
200C22×C73#45011yescharacteristic
201C22×C73#45211yescharacteristic
202C4×C73—21no—
203C4×C73—21no—
204C4×C73—21no—
205C4×C73—44no—
206C4×C73—81no—
207C4×C73—81no—
208C4×C73—81no—
209C4×C73#44811yescharacteristic
210C4×C73#44911yescharacteristic
211C4×C73#45312yes—
212C4×C73#46511yescharacteristic
213C4×C73#46811yescharacteristic
214#10246C7311yesmaximal, characteristic, direct product factor, Sylow
215C2×C73—21no—
216C2×C73—21no—
217C2×C73—82no—
218C2×C73—162no—
219C2×C73#200011yescharacteristic
220C2×C73#200211yescharacteristic
221C2×C73#200811yescharacteristic
222#3208C2×C7311yescharacteristic, complemented
223#3077C2×C7311yescharacteristic, complemented
224#2541C2×C7311yescharacteristic
225#1545C2×C7311yescharacteristic, complemented
226#1503C2×C7311yescharacteristic, complemented
227#1478C2×C7311yescharacteristic, complemented
228#1303C2×C7311yescharacteristic, complemented
229C73#1024611yescharacteristic, direct product factor, Sylow
230#533C22×C7311yescharacteristic
231C2×#127—21no—
232C2×#127C22×C7311yescharacteristic
233C2×#121—22no—
234C2×C4×D4C22×C7311yescharacteristic
235#492—21no—
236#486—21no—
237#478—22no—
238#476—21no—
239#474—21no—
240#460—22no—
241#450—22no—
242#431C22×C7311yescharacteristic
243#431C22×C7311yescharacteristic
244#428—21no—
245#423C22×C7311yescharacteristic
246#418—21no—
247#392—22no—
248#390—21no—
249C4×C4⋊C4C22×C7311yescharacteristic
250#331—22no—
251#328—22no—
252D4⋊C8—22no—
253C22×D4—24no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4D4×C7311yescharacteristic
257C22×D4D4×C7312yes—
258C23×C4—21no—
259C2×SD16—24no—
260C2×M16—21no—
261C4⋊Q8D4×C7311yescharacteristic, complemented
262C4⋊Q8D4×C7311yescharacteristic, complemented
263#127—21no—
264#127—21no—
265#127—21no—
266#127—21no—
267#127—42no—
268#127—42no—
269#125—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272#121—48no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279#117—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4D4×C7311yescharacteristic
282C2×C22⋊C4—24no—
283C2×C22⋊C4—21no—
284C2×C42—21no—
285C2×C42C23×C7311yescharacteristic
286#107—22no—
287#106—22no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8D4×C7312yescomplemented
291C4⋊C8D4×C7312yescomplemented
292#102—22no—
293#102—22no—
294#102—24no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C4×C8—21no—
298C4×C8—21no—
299#95D4×C7312yes—
300C24—21no—
301C24—22no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—44no—
312C2×D4—48no—
313C2×D4—48no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—82no—
323C2×D4—84no—
324C2×D4SD16×C7312yescomplemented
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—44no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4C2×D4×C7311yescharacteristic
331C22×C4C2×D4×C7311yescharacteristic
332C22×C4C2×D4×C7311yescharacteristic
333SD16—84no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C4⋊C4—24no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C22⋊C4—48no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—41no—
353C42—41no—
354C42—41no—
355C42C2×D4×C7311yescharacteristic
356C42C2×D4×C7311yescharacteristic
357C42C2×D4×C7311yescharacteristic
358C42#41×C7311yescharacteristic
359C23—22no—
360C23—42no—
361C23—42no—
362C23—44no—
363C23—44no—
364C23—41no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23#120×C7311yescharacteristic
370Q8—42no—
371Q8—81no—
372D4—22no—
373D4—22no—
374D4—41no—
375D4—44no—
376D4—41no—
377D4—82no—
378D4—82no—
379D4—82no—
380D4—816no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4#120×C7311yescharacteristic
397C2×C4#120×C7311yescharacteristic
398C2×C4#121×C7311yescharacteristic
399C2×C4#121×C7311yescharacteristic
400C2×C4#121×C7311yescharacteristic
401C2×C4#127×C7311yescharacteristic
402C2×C4C2×SD16×C7311yescharacteristic
403C2×C4#135×C7311yescharacteristic
404C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
405C2×C4#137×C7311yescharacteristic
406C8—42no—
407C8—42no—
408C8—81no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—42no—
413C22—82no—
414C22—84no—
415C22—84no—
416C22—81no—
417C22—81no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22#392×C7311yescharacteristic
422C22#450×C7311yescharacteristic
423C22#452×C7311yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—44no—
428C4—81no—
429C4—81no—
430C4—81no—
431C4#448×C7311yescharacteristic
432C4#449×C7311yescharacteristic
433C4#453×C7312yes—
434C4#465×C7311yescharacteristic
435C4#468×C7311yescharacteristic
436C2—21no—
437C2—21no—
438C2—82no—
439C2—162no—
440C2C73×#200011yescharacteristic
441C2C73×#200211yescharacteristic
442C2C73×#200811yescharacteristic
subgroupG/H
center, socleC22×C73#392
commutator, Frattini, cosocleC2×C42C23×C73
prime radicalC73×#2541C2
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
1. C73×#3208C2semidirect
2. C73×#3077C2semidirect
4. C73×#1545C2semidirect
5. C73×#1503C2semidirect
6. C73×#1478C2semidirect
7. C73×#1303C2semidirect
39. C4⋊Q8×C73D4semidirect
40. C4⋊Q8×C73D4semidirect
68. C4⋊C8×C73D4semidirect
69. C4⋊C8×C73D4semidirect
102. C2×D4×C73SD16semidirect
214. #10246C73direct (N × H)
222. #3208C2×C73semidirect
223. #3077C2×C73semidirect
225. #1545C2×C73semidirect
226. #1503C2×C73semidirect
227. #1478C2×C73semidirect
228. #1303C2×C73semidirect
229. C73#10246direct (N × H)
261. C4⋊Q8D4×C73semidirect
262. C4⋊Q8D4×C73semidirect
290. C4⋊C8D4×C73semidirect
291. C4⋊C8D4×C73semidirect
324. C2×D4SD16×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#32082
C73×#30772
C73×#25412
C73×#15452
C73×#15032
C73×#14782
C73×#13032
#1024673