Finite Group Databasebeta

← C73×#10242 #32919646

Subgroups — C73×#10242 #32919646

Order 18688.

658 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×#3205C211yesmaximal, characteristic
2C73×#3037C211yesmaximal, characteristic, complemented
3C73×#2548C211yesmaximal, characteristic, complemented
4C73×#1545C211yesmaximal, characteristic, complemented
5C73×#1502C211yesmaximal, characteristic, complemented
6C73×#1479C211yesmaximal, characteristic, complemented
7C73×#1303C211yesmaximal, characteristic, complemented
8C2×#137×C73—21no—
9#532×C73C2211yescharacteristic
10C2×#127×C73C2211yescharacteristic
11C2×#124×C73—21no—
12C2×C4×Q8×C73C2211yescharacteristic
13#493×C73—21no—
14#486×C73—21no—
15#464×C73—22no—
16#462×C73—21no—
17#460×C73—21no—
18#459×C73—22no—
19#447×C73—22no—
20#431×C73C2211yescharacteristic
21#431×C73C2211yescharacteristic
22#423×C73C2211yescharacteristic
23#417×C73—21no—
24#394×C73—22no—
25#390×C73—22no—
26#390×C73—21no—
27C4×C4⋊C4×C73C2211yescharacteristic
28#331×C73—22no—
29#327×C73—22no—
30Q8⋊C8×C73—22no—
31C2×#41×C73—21no—
32C22×Q8×C73D411yescharacteristic
33C22×D4×C73—21no—
34C22×D4×C73—21no—
35C22×D4×C73D412yes—
36#137×C73—42no—
37#137×C73—42no—
38C2×Q16×C73—22no—
39C2×SD16×C73—22no—
40C2×D8×C73—24no—
41C2×M16×C73—21no—
42C4⋊Q8×C73D411yescharacteristic
43#127×C73—21no—
44#127×C73—21no—
45#127×C73—21no—
46#127×C73—21no—
47#127×C73D411yescharacteristic
48#124×C73—21no—
49#124×C73—42no—
50#124×C73—42no—
51#121×C73—21no—
52#121×C73—21no—
53C4×Q8×C73—21no—
54C4×Q8×C73—21no—
55C4×Q8×C73—21no—
56C4×Q8×C73—21no—
57C4×D4×C73—21no—
58C4×D4×C73—21no—
59C2×C4⋊C4×C73—21no—
60C2×C4⋊C4×C73—21no—
61C2×C4⋊C4×C73D411yescharacteristic
62C2×C22⋊C4×C73—24no—
63C2×C22⋊C4×C73—24no—
64C2×C42×C73—21no—
65C2×C42×C73—21no—
66C2×C42×C73C2311yescharacteristic
67C4⋊C8×C73—21no—
68C4⋊C8×C73—21no—
69C4⋊C8×C73D412yes—
70C4⋊C8×C73D412yes—
71#103×C73—22no—
72#102×C73—22no—
73#102×C73—24no—
74C22⋊C8×C73—21no—
75C22⋊C8×C73—21no—
76C4×C8×C73—21no—
77C4×C8×C73—21no—
78#95×C73D412yes—
79C24×C73—22no—
80#41×C73—41no—
81#41×C73—41no—
82#41×C73—41no—
83#41×C73—41no—
84C2×Q8×C73—21no—
85C2×Q8×C73—21no—
86C2×Q8×C73—21no—
87C2×Q8×C73—21no—
88C2×Q8×C73—21no—
89C2×Q8×C73—21no—
90C2×Q8×C73D812yescomplemented
91C2×D4×C73—21no—
92C2×D4×C73—22no—
93C2×D4×C73—21no—
94C2×D4×C73—21no—
95C2×D4×C73—22no—
96C2×D4×C73—44no—
97C2×D4×C73—41no—
98C2×D4×C73—41no—
99C2×D4×C73—41no—
100C2×D4×C73—41no—
101C2×D4×C73—41no—
102C2×D4×C73—41no—
103C2×D4×C73—41no—
104C2×D4×C73—41no—
105C2×D4×C73—41no—
106C2×D4×C73—82no—
107C22×C4×C73—21no—
108C22×C4×C73—22no—
109C22×C4×C73—21no—
110C22×C4×C73—41no—
111C22×C4×C73C2×D411yescharacteristic
112C22×C4×C73C2×D411yescharacteristic
113C22×C4×C73C2×D411yescharacteristic
114Q16×C73—44no—
115SD16×C73—44no—
116D8×C73—84no—
117M16×C73—41no—
118M16×C73—41no—
119C2×C8×C73—22no—
120C2×C8×C73—22no—
121C2×C8×C73—41no—
122C4⋊C4×C73—21no—
123C4⋊C4×C73—21no—
124C4⋊C4×C73—21no—
125C4⋊C4×C73—21no—
126C4⋊C4×C73—42no—
127C4⋊C4×C73—41no—
128C4⋊C4×C73—41no—
129C22⋊C4×C73—48no—
130C22⋊C4×C73—41no—
131C22⋊C4×C73—41no—
132C22⋊C4×C73—84no—
133C42×C73—41no—
134C42×C73—41no—
135C42×C73—41no—
136C42×C73—41no—
137C42×C73C2×D411yescharacteristic
138C42×C73C2×D411yescharacteristic
139C42×C73C2×D411yescharacteristic
140C42×C73#4111yescharacteristic
141C23×C73—44no—
142C23×C73—44no—
143C23×C73—41no—
144C23×C73—42no—
145C23×C73—42no—
146C23×C73—42no—
147C23×C73#12011yescharacteristic
148Q8×C73—22no—
149Q8×C73—22no—
150Q8×C73—41no—
151Q8×C73—41no—
152Q8×C73—41no—
153Q8×C73—41no—
154D4×C73—41no—
155D4×C73—41no—
156D4×C73—42no—
157D4×C73—44no—
158D4×C73—81no—
159D4×C73—82no—
160D4×C73—82no—
161D4×C73—82no—
162D4×C73—81no—
163D4×C73—81no—
164D4×C73—81no—
165D4×C73—81no—
166D4×C73—81no—
167D4×C73—81no—
168C2×C4×C73—22no—
169C2×C4×C73—22no—
170C2×C4×C73—41no—
171C2×C4×C73—41no—
172C2×C4×C73—41no—
173C2×C4×C73—42no—
174C2×C4×C73—42no—
175C2×C4×C73—42no—
176C2×C4×C73—41no—
177C2×C4×C73—41no—
178C2×C4×C73—42no—
179C2×C4×C73—81no—
180C2×C4×C73—81no—
181C2×C4×C73#12011yescharacteristic
182C2×C4×C73#12011yescharacteristic
183C2×C4×C73#12111yescharacteristic
184C2×C4×C73#12111yescharacteristic
185C2×C4×C73#12111yescharacteristic
186C2×C4×C73#12711yescharacteristic
187C2×C4×C73C2×D811yescharacteristic
188C2×C4×C73#13511yescharacteristic
189C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
191C8×C73—42no—
192C8×C73—42no—
193C8×C73—81no—
194C22×C73—21no—
195C22×C73—21no—
196C22×C73—84no—
197C22×C73—84no—
198C22×C73—81no—
199C22×C73—82no—
200C22×C73—82no—
201C22×C73—81no—
202C22×C73—82no—
203C22×C73—81no—
204C22×C73#39211yescharacteristic
205C22×C73#44711yescharacteristic
206C22×C73#44911yescharacteristic
207C4×C73—21no—
208C4×C73—21no—
209C4×C73—21no—
210C4×C73—42no—
211C4×C73—82no—
212C4×C73—81no—
213C4×C73—81no—
214C4×C73#44711yescharacteristic
215C4×C73#44911yescharacteristic
216C4×C73#45512yes—
217C4×C73#46611yescharacteristic
218C4×C73#46911yescharacteristic
219#10242C7311yesmaximal, characteristic, direct product factor, Sylow
220C2×C73—21no—
221C2×C73—21no—
222C2×C73—161no—
223C2×C73—162no—
224C2×C73#199911yescharacteristic
225C2×C73#200411yescharacteristic
226C2×C73#200811yescharacteristic
227#3205C2×C7311yescharacteristic
228#3037C2×C7311yescharacteristic, complemented
229#2548C2×C7311yescharacteristic, complemented
230#1545C2×C7311yescharacteristic, complemented
231#1502C2×C7311yescharacteristic, complemented
232#1479C2×C7311yescharacteristic, complemented
233#1303C2×C7311yescharacteristic, complemented
234C73#1024211yescharacteristic, direct product factor, Sylow
235C2×#137—21no—
236#532C22×C7311yescharacteristic
237C2×#127C22×C7311yescharacteristic
238C2×#124—21no—
239C2×C4×Q8C22×C7311yescharacteristic
240#493—21no—
241#486—21no—
242#464—22no—
243#462—21no—
244#460—21no—
245#459—22no—
246#447—22no—
247#431C22×C7311yescharacteristic
248#431C22×C7311yescharacteristic
249#423C22×C7311yescharacteristic
250#417—21no—
251#394—22no—
252#390—22no—
253#390—21no—
254C4×C4⋊C4C22×C7311yescharacteristic
255#331—22no—
256#327—22no—
257Q8⋊C8—22no—
258C2×#41—21no—
259C22×Q8D4×C7311yescharacteristic
260C22×D4—21no—
261C22×D4—21no—
262C22×D4D4×C7312yes—
263#137—42no—
264#137—42no—
265C2×Q16—22no—
266C2×SD16—22no—
267C2×D8—24no—
268C2×M16—21no—
269C4⋊Q8D4×C7311yescharacteristic
270#127—21no—
271#127—21no—
272#127—21no—
273#127—21no—
274#127D4×C7311yescharacteristic
275#124—21no—
276#124—42no—
277#124—42no—
278#121—21no—
279#121—21no—
280C4×Q8—21no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×D4—21no—
285C4×D4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4D4×C7311yescharacteristic
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42C23×C7311yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8D4×C7312yes—
297C4⋊C8D4×C7312yes—
298#103—22no—
299#102—22no—
300#102—24no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C4×C8—21no—
304C4×C8—21no—
305#95D4×C7312yes—
306C24—22no—
307#41—41no—
308#41—41no—
309#41—41no—
310#41—41no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8D8×C7312yescomplemented
318C2×D4—21no—
319C2×D4—22no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—22no—
323C2×D4—44no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—82no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—41no—
338C22×C4C2×D4×C7311yescharacteristic
339C22×C4C2×D4×C7311yescharacteristic
340C22×C4C2×D4×C7311yescharacteristic
341Q16—44no—
342SD16—44no—
343D8—84no—
344M16—41no—
345M16—41no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—41no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—42no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C22⋊C4—48no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—84no—
360C42—41no—
361C42—41no—
362C42—41no—
363C42—41no—
364C42C2×D4×C7311yescharacteristic
365C42C2×D4×C7311yescharacteristic
366C42C2×D4×C7311yescharacteristic
367C42#41×C7311yescharacteristic
368C23—44no—
369C23—44no—
370C23—41no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23#120×C7311yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—41no—
380Q8—41no—
381D4—41no—
382D4—41no—
383D4—42no—
384D4—44no—
385D4—82no—
386D4—81no—
387D4—82no—
388D4—82no—
389D4—81no—
390D4—81no—
391D4—81no—
392D4—81no—
393D4—81no—
394D4—81no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4#120×C7311yescharacteristic
409C2×C4#120×C7311yescharacteristic
410C2×C4#121×C7311yescharacteristic
411C2×C4#121×C7311yescharacteristic
412C2×C4#121×C7311yescharacteristic
413C2×C4#127×C7311yescharacteristic
414C2×C4C2×D8×C7311yescharacteristic
415C2×C4#135×C7311yescharacteristic
416C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
417C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
418C8—42no—
419C8—42no—
420C8—81no—
421C22—21no—
422C22—21no—
423C22—84no—
424C22—84no—
425C22—81no—
426C22—82no—
427C22—82no—
428C22—81no—
429C22—82no—
430C22—81no—
431C22#392×C7311yescharacteristic
432C22#447×C7311yescharacteristic
433C22#449×C7311yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—82no—
439C4—81no—
440C4—81no—
441C4#447×C7311yescharacteristic
442C4#449×C7311yescharacteristic
443C4#455×C7312yes—
444C4#466×C7311yescharacteristic
445C4#469×C7311yescharacteristic
446C2—21no—
447C2—21no—
448C2—162no—
449C2—161no—
450C2C73×#199911yescharacteristic
451C2C73×#200411yescharacteristic
452C2C73×#200811yescharacteristic
subgroupG/H
center, socleC22×C73#392
commutator, Frattini, cosocleC2×C42C23×C73
prime radicalC73×#3205C2
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
2. C73×#3037C2semidirect
3. C73×#2548C2semidirect
4. C73×#1545C2semidirect
5. C73×#1502C2semidirect
6. C73×#1479C2semidirect
7. C73×#1303C2semidirect
90. C2×Q8×C73D8semidirect
219. #10242C73direct (N × H)
228. #3037C2×C73semidirect
229. #2548C2×C73semidirect
230. #1545C2×C73semidirect
231. #1502C2×C73semidirect
232. #1479C2×C73semidirect
233. #1303C2×C73semidirect
234. C73#10242direct (N × H)
317. C2×Q8D8×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#32052
C73×#30372
C73×#25482
C73×#15452
C73×#15022
C73×#14792
C73×#13032
#1024273