Finite Group Databasebeta

← C73×#19685 #32929089

Subgroups — C73×#19685 #32929089

Order 18688.

712 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3230C211yesmaximal, characteristic, complemented
2C73×#3206C211yesmaximal, characteristic
3C73×#3167C211yesmaximal, characteristic
4C73×#3165C211yesmaximal, characteristic, complemented
5C73×#3141C211yesmaximal, characteristic
6C2×#487×C73C211yesmaximal, characteristic, complemented
7C73×#1719C212yesmaximal, complemented
8C73×#1718C212yesmaximal, complemented
9C73×#1718C212yesmaximal, complemented
10C73×#1714C212yesmaximal, complemented
11C73×#1451C211yesmaximal, characteristic, complemented
12#533×C73C2211yescharacteristic
13#532×C73C2211yescharacteristic
14C2×C4⋊Q8×C73C2211yescharacteristic
15C2×C4⋊Q8×C73C2211yescharacteristic
16#501×C73—22no—
17#500×C73C2212yes—
18#500×C73C2212yes—
19#498×C73C2212yes—
20#498×C73C2211yescharacteristic
21#492×C73C2211yescharacteristic
22#492×C73C2212yes—
23#489×C73—22no—
24#487×C73—22no—
25#487×C73C2212yes—
26#487×C73C2212yes—
27#487×C73C2212yes—
28#487×C73C2211yescharacteristic
29#487×C73C2212yes—
30#487×C73C2212yes—
31#486×C73C2212yes—
32#486×C73C2211yescharacteristic
33#484×C73—22no—
34#477×C73—22no—
35#465×C73—22no—
36#461×C73—22no—
37#448×C73—22no—
38C4×SD16×C73—22no—
39#431×C73C2211yescharacteristic
40#428×C73—22no—
41#417×C73—22no—
42C2×#103×C73—22no—
43C4×M16×C73C2211yescharacteristic
44C2×C4×C8×C73C2211yescharacteristic
45#322×C73C2212yes—
46#322×C73C2212yes—
47C2×#41×C73—21no—
48C22×Q8×C73—21no—
49C22×Q8×C73—21no—
50C2×SD16×C73—22no—
51C2×SD16×C73—24no—
52C2×M16×C73D412yes—
53C22×C8×C73D412yes—
54C4⋊Q8×C73—21no—
55C4⋊Q8×C73—21no—
56C4⋊Q8×C73—21no—
57C4⋊Q8×C73—21no—
58C4⋊Q8×C73—21no—
59C4⋊Q8×C73—21no—
60C4⋊Q8×C73C2312yes—
61C4⋊Q8×C73C2311yescharacteristic
62C4⋊Q8×C73C2311yescharacteristic
63C4⋊Q8×C73C2312yes—
64C4⋊Q8×C73C2311yescharacteristic
65#127×C73C2311yescharacteristic
66#125×C73—21no—
67#124×C73—21no—
68C22⋊Q8×C73—21no—
69C22⋊Q8×C73—21no—
70#121×C73—21no—
71#121×C73—21no—
72C4×Q8×C73—21no—
73C4×Q8×C73—21no—
74C4×D4×C73—21no—
75C4×D4×C73—21no—
76#117×C73—21no—
77C2×C4⋊C4×C73—21no—
78C2×C4⋊C4×C73—21no—
79C2×C4⋊C4×C73—21no—
80C2×C4⋊C4×C73—21no—
81C2×C42×C73C2311yescharacteristic
82#107×C73—24no—
83#107×C73—24no—
84#106×C73—24no—
85#106×C73—22no—
86C4⋊C8×C73D412yes—
87#103×C73—24no—
88#103×C73—24no—
89#103×C73—24no—
90#103×C73—22no—
91#103×C73—24no—
92#103×C73—24no—
93#102×C73—24no—
94#102×C73—22no—
95C22⋊C8×C73D412yes—
96#97×C73D412yes—
97C4×C8×C73D412yes—
98C4×C8×C73C2311yescharacteristic
99C4×C8×C73C2311yescharacteristic
100C4×C8×C73C2312yes—
101C4×C8×C73C2312yes—
102#41×C73—44no—
103C2×Q8×C73—21no—
104C2×Q8×C73—21no—
105C2×Q8×C73—22no—
106C2×Q8×C73—21no—
107C2×Q8×C73—22no—
108C2×Q8×C73—44no—
109C2×Q8×C73—41no—
110C2×Q8×C73—41no—
111C2×Q8×C73—82no—
112C2×D4×C73—21no—
113C2×D4×C73—21no—
114C2×D4×C73—21no—
115C2×D4×C73—41no—
116C22×C4×C73—41no—
117C22×C4×C73—41no—
118C22×C4×C73—41no—
119C22×C4×C73C2×D411yescharacteristic
120C22×C4×C73C2×D411yescharacteristic
121C22×C4×C73C2×D411yescharacteristic
122SD16×C73—44no—
123SD16×C73—84no—
124M16×C73—24no—
125C2×C8×C73—42no—
126C2×C8×C73C2×D412yes—
127C2×C8×C73C2×D412yes—
128C2×C8×C73C2×D414yes—
129C2×C8×C73C2×D414yes—
130C4⋊C4×C73—22no—
131C4⋊C4×C73—21no—
132C4⋊C4×C73—22no—
133C4⋊C4×C73—21no—
134C4⋊C4×C73—21no—
135C4⋊C4×C73—22no—
136C4⋊C4×C73—21no—
137C4⋊C4×C73—22no—
138C4⋊C4×C73—21no—
139C4⋊C4×C73—21no—
140C4⋊C4×C73—41no—
141C4⋊C4×C73—41no—
142C4⋊C4×C73—41no—
143C4⋊C4×C73—41no—
144C4⋊C4×C73—41no—
145C4⋊C4×C73—41no—
146C22⋊C4×C73—41no—
147C22⋊C4×C73—41no—
148C22⋊C4×C73—41no—
149C42×C73—41no—
150C42×C73C2×D411yescharacteristic
151C42×C73C2×D411yescharacteristic
152C42×C73C2×D411yescharacteristic
153C42×C73C2411yescharacteristic
154C23×C73—41no—
155C23×C73#12711yescharacteristic
156Q8×C73—42no—
157Q8×C73—42no—
158Q8×C73—44no—
159Q8×C73—44no—
160Q8×C73—42no—
161Q8×C73—82no—
162Q8×C73—82no—
163D4×C73—42no—
164D4×C73—42no—
165D4×C73—42no—
166D4×C73—82no—
167C2×C4×C73—22no—
168C2×C4×C73—22no—
169C2×C4×C73—41no—
170C2×C4×C73—41no—
171C2×C4×C73—41no—
172C2×C4×C73—42no—
173C2×C4×C73—42no—
174C2×C4×C73—82no—
175C2×C4×C73—82no—
176C2×C4×C73—82no—
177C2×C4×C73#12711yescharacteristic
178C2×C4×C73#12711yescharacteristic
179C2×C4×C73#12711yescharacteristic
180C2×C4×C73#13714yes—
181C2×C4×C73C22×D411yescharacteristic
182C2×C4×C73C22×D411yescharacteristic
183C2×C4×C73C22×D411yescharacteristic
184C8×C73—24no—
185C8×C73—22no—
186C8×C73—22no—
187C8×C73—24no—
188C22×C73—21no—
189C22×C73—21no—
190C22×C73—81no—
191C22×C73—81no—
192C22×C73—81no—
193C22×C73#49712yes—
194C22×C73C2×#12711yescharacteristic
195C4×C73—21no—
196C4×C73—21no—
197C4×C73—81no—
198C4×C73—82no—
199C4×C73—81no—
200C4×C73—82no—
201C4×C73—81no—
202C4×C73#49712yes—
203C4×C73C2×#13712yes—
204C4×C73#57512yes—
205C4×C73#57712yes—
206#19685C7311yesmaximal, characteristic, direct product factor, Sylow
207C2×C73—22no—
208C2×C73—161no—
209C2×C73C2×#49711yescharacteristic
210C2×C73#315311yescharacteristic
211C2×C73#315411yescharacteristic
212#3230C2×C7311yescharacteristic, complemented
213#3206C2×C7311yescharacteristic
214#3167C2×C7311yescharacteristic
215#3165C2×C7311yescharacteristic, complemented
216#3141C2×C7311yescharacteristic
217C2×#487C2×C7311yescharacteristic, complemented
218#1719C2×C7312yescomplemented
219#1718C2×C7312yescomplemented
220#1718C2×C7312yescomplemented
221#1714C2×C7312yescomplemented
222#1451C2×C7311yescharacteristic, complemented
223C73#1968511yescharacteristic, direct product factor, Sylow
224#533C22×C7311yescharacteristic
225#532C22×C7311yescharacteristic
226C2×C4⋊Q8C22×C7311yescharacteristic
227C2×C4⋊Q8C22×C7311yescharacteristic
228#501—22no—
229#500C22×C7312yes—
230#500C22×C7312yes—
231#498C22×C7312yes—
232#498C22×C7311yescharacteristic
233#492C22×C7311yescharacteristic
234#492C22×C7312yes—
235#489—22no—
236#487—22no—
237#487C22×C7312yes—
238#487C22×C7312yes—
239#487C22×C7312yes—
240#487C22×C7311yescharacteristic
241#487C22×C7312yes—
242#487C22×C7312yes—
243#486C22×C7312yes—
244#486C22×C7311yescharacteristic
245#484—22no—
246#477—22no—
247#465—22no—
248#461—22no—
249#448—22no—
250C4×SD16—22no—
251#431C22×C7311yescharacteristic
252#428—22no—
253#417—22no—
254C2×#103—22no—
255C4×M16C22×C7311yescharacteristic
256C2×C4×C8C22×C7311yescharacteristic
257#322C22×C7312yes—
258#322C22×C7312yes—
259C2×#41—21no—
260C22×Q8—21no—
261C22×Q8—21no—
262C2×SD16—22no—
263C2×SD16—24no—
264C2×M16D4×C7312yes—
265C22×C8D4×C7312yes—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8C23×C7312yes—
273C4⋊Q8C23×C7312yes—
274C4⋊Q8C23×C7311yescharacteristic
275C4⋊Q8C23×C7311yescharacteristic
276C4⋊Q8C23×C7311yescharacteristic
277#127C23×C7311yescharacteristic
278#125—21no—
279#124—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282#121—21no—
283#121—21no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—21no—
287C4×D4—21no—
288#117—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C42C23×C7311yescharacteristic
294#107—24no—
295#107—24no—
296#106—24no—
297#106—22no—
298C4⋊C8D4×C7312yes—
299#103—24no—
300#103—24no—
301#103—24no—
302#103—22no—
303#103—24no—
304#103—24no—
305#102—24no—
306#102—22no—
307C22⋊C8D4×C7312yes—
308#97D4×C7312yes—
309C4×C8D4×C7312yes—
310C4×C8C23×C7311yescharacteristic
311C4×C8C23×C7311yescharacteristic
312C4×C8C23×C7312yes—
313C4×C8C23×C7312yes—
314#41—44no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—22no—
318C2×Q8—21no—
319C2×Q8—22no—
320C2×Q8—44no—
321C2×Q8—41no—
322C2×Q8—41no—
323C2×Q8—82no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C2×D4×C7311yescharacteristic
332C22×C4C2×D4×C7311yescharacteristic
333C22×C4C2×D4×C7311yescharacteristic
334SD16—44no—
335SD16—84no—
336M16—24no—
337C2×C8—42no—
338C2×C8C2×D4×C7312yes—
339C2×C8C2×D4×C7312yes—
340C2×C8C2×D4×C7314yes—
341C2×C8C2×D4×C7314yes—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C42—41no—
362C42C2×D4×C7311yescharacteristic
363C42C2×D4×C7311yescharacteristic
364C42C2×D4×C7311yescharacteristic
365C42C24×C7311yescharacteristic
366C23—41no—
367C23#127×C7311yescharacteristic
368Q8—42no—
369Q8—42no—
370Q8—44no—
371Q8—44no—
372Q8—42no—
373Q8—82no—
374Q8—82no—
375D4—42no—
376D4—42no—
377D4—42no—
378D4—82no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4#127×C7311yescharacteristic
390C2×C4#127×C7311yescharacteristic
391C2×C4#127×C7311yescharacteristic
392C2×C4#137×C7314yes—
393C2×C4C22×D4×C7311yescharacteristic
394C2×C4C22×D4×C7311yescharacteristic
395C2×C4C22×D4×C7311yescharacteristic
396C8—24no—
397C8—22no—
398C8—22no—
399C8—24no—
400C22—21no—
401C22—21no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22#497×C7312yes—
406C22C2×#127×C7311yescharacteristic
407C4—21no—
408C4—21no—
409C4—81no—
410C4—82no—
411C4—81no—
412C4—82no—
413C4—81no—
414C4#497×C7312yes—
415C4C2×#137×C7312yes—
416C4#575×C7312yes—
417C4#577×C7312yes—
418C2—22no—
419C2—161no—
420C2C2×#497×C7311yescharacteristic
421C2C73×#315311yescharacteristic
422C2C73×#315411yescharacteristic
subgroupG/H
center, socleC22×C73C2×#127
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×#3230C2semidirect
4. C73×#3165C2semidirect
6. C2×#487×C73C2semidirect
7. C73×#1719C2semidirect
8. C73×#1718C2semidirect
9. C73×#1718C2semidirect
10. C73×#1714C2semidirect
11. C73×#1451C2semidirect
206. #19685C73direct (N × H)
212. #3230C2×C73semidirect
215. #3165C2×C73semidirect
217. C2×#487C2×C73semidirect
218. #1719C2×C73semidirect
219. #1718C2×C73semidirect
220. #1718C2×C73semidirect
221. #1714C2×C73semidirect
222. #1451C2×C73semidirect
223. C73#19685direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32302
C73×#32062
C73×#31672
C73×#31652
C73×#31412
C2×#487×C732
C73×#17192
C73×#17182
C73×#17142
C73×#14512
#1968573