Finite Group Databasebeta

← C73×#18645 #32928049

Subgroups — C73×#18645 #32928049

Order 18688.

872 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3509C211yesmaximal, characteristic
2C73×#3230C211yesmaximal, characteristic, complemented
3C2×#487×C73C211yesmaximal, characteristic, complemented
4C73×#3079C211yesmaximal, characteristic
5C73×#1638C214yesmaximal, complemented
6C73×#1636C214yesmaximal, complemented
7C73×#1546C211yesmaximal, characteristic, complemented
8C73×#1493C211yesmaximal, characteristic, complemented
9C73×#1476C211yesmaximal, characteristic
10#557×C73—21no—
11#557×C73C2212yes—
12#556×C73—21no—
13#556×C73C2212yes—
14#552×C73—22no—
15#552×C73—22no—
16#541×C73—22no—
17#536×C73—21no—
18#533×C73—21no—
19#533×C73—21no—
20#533×C73C2211yescharacteristic
21C2×C4⋊Q8×C73C2211yescharacteristic
22C2×C4⋊Q8×C73C2211yescharacteristic
23#519×C73—21no—
24C4×#41×C73C2211yescharacteristic
25#500×C73—21no—
26#487×C73—21no—
27#487×C73—22no—
28#487×C73C2214yes—
29#484×C73—22no—
30#477×C73C2214yes—
31#477×C73C2212yes—
32#476×C73C2212yes—
33#475×C73—21no—
34#474×C73—21no—
35#431×C73C2211yescharacteristic
36#428×C73—21no—
37#423×C73C2211yescharacteristic
38#417×C73—21no—
39C2×#103×C73—22no—
40C2×C4×C8×C73C2211yescharacteristic
41#332×C73C2214yes—
42Q8⋊C8×C73C2212yes—
43Q8⋊C8×C73C2214yes—
44D4⋊C8×C73C2212yes—
45C2×#41×C73D411yescharacteristic
46C22×Q8×C73—21no—
47C22×Q8×C73—21no—
48C2×M16×C73—21no—
49C22×C8×C73—21no—
50C4⋊Q8×C73—22no—
51C4⋊Q8×C73—21no—
52C4⋊Q8×C73—21no—
53C4⋊Q8×C73—21no—
54C4⋊Q8×C73—21no—
55C4⋊Q8×C73—21no—
56C4⋊Q8×C73D411yescharacteristic
57C4⋊Q8×C73D412yes—
58C4⋊Q8×C73D411yescharacteristic
59C4⋊Q8×C73C2312yes—
60C4⋊Q8×C73C2312yes—
61#126×C73—24no—
62#126×C73—24no—
63#125×C73—22no—
64#125×C73—24no—
65#125×C73—22no—
66#125×C73—24no—
67#125×C73—21no—
68#124×C73—22no—
69#123×C73—24no—
70C22⋊Q8×C73—22no—
71C22⋊Q8×C73—22no—
72C22⋊Q8×C73—22no—
73C22⋊Q8×C73—22no—
74C22⋊Q8×C73—21no—
75C22⋊Q8×C73D412yes—
76C4×Q8×C73—22no—
77C4×Q8×C73—22no—
78C4×Q8×C73—22no—
79C4×Q8×C73—22no—
80C4×Q8×C73—22no—
81C4×Q8×C73—22no—
82C4×Q8×C73—21no—
83C4×Q8×C73D411yescharacteristic
84C4×Q8×C73C2311yescharacteristic
85C4×Q8×C73C2312yes—
86C4×D4×C73—21no—
87C4×D4×C73—21no—
88C4×D4×C73D411yescharacteristic
89C4×D4×C73C2311yescharacteristic
90#117×C73—24no—
91#117×C73—22no—
92#117×C73—21no—
93#117×C73—22no—
94#117×C73—21no—
95#117×C73D411yescharacteristic
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73D412yes—
100C2×C42×C73—21no—
101C2×C42×C73C2311yescharacteristic
102#107×C73—22no—
103#107×C73—24no—
104#106×C73—22no—
105C4⋊C8×C73—21no—
106C4⋊C8×C73C2312yes—
107C4⋊C8×C73C2312yes—
108#103×C73—22no—
109#103×C73—24no—
110#103×C73—28no—
111#102×C73—22no—
112C22⋊C8×C73—21no—
113C4×C8×C73—21no—
114C4×C8×C73—21no—
115C4×C8×C73C2312yes—
116#41×C73—22no—
117#41×C73—22no—
118C2×Q8×C73—21no—
119C2×Q8×C73—22no—
120C2×Q8×C73—22no—
121C2×Q8×C73—22no—
122C2×Q8×C73—44no—
123C2×Q8×C73—41no—
124C2×Q8×C73—42no—
125C2×Q8×C73—42no—
126C2×Q8×C73C2×D412yes—
127C2×Q8×C73C2×D411yescharacteristic
128C2×D4×C73—21no—
129C2×D4×C73C2×D411yescharacteristic
130C22×C4×C73—22no—
131C22×C4×C73—21no—
132C22×C4×C73—21no—
133C22×C4×C73—21no—
134C22×C4×C73—41no—
135C22×C4×C73C2×D411yescharacteristic
136C22×C4×C73C2×D411yescharacteristic
137C22×C4×C73C2×D411yescharacteristic
138M16×C73—42no—
139C2×C8×C73—22no—
140C2×C8×C73—22no—
141C2×C8×C73—22no—
142C2×C8×C73—42no—
143C4⋊C4×C73—24no—
144C4⋊C4×C73—24no—
145C4⋊C4×C73—24no—
146C4⋊C4×C73—24no—
147C4⋊C4×C73—22no—
148C4⋊C4×C73—22no—
149C4⋊C4×C73—21no—
150C4⋊C4×C73—21no—
151C4⋊C4×C73—21no—
152C4⋊C4×C73—21no—
153C4⋊C4×C73—22no—
154C4⋊C4×C73—22no—
155C4⋊C4×C73—21no—
156C4⋊C4×C73—22no—
157C4⋊C4×C73—22no—
158C4⋊C4×C73—22no—
159C4⋊C4×C73—41no—
160C4⋊C4×C73—41no—
161C4⋊C4×C73C2×D414yes—
162C4⋊C4×C73C2×D411yescharacteristic
163C4⋊C4×C73C2×D412yes—
164C4⋊C4×C73C2×D411yescharacteristic
165C22⋊C4×C73—24no—
166C22⋊C4×C73—24no—
167C22⋊C4×C73—21no—
168C22⋊C4×C73—22no—
169C22⋊C4×C73—21no—
170C22⋊C4×C73—21no—
171C42×C73—24no—
172C42×C73—24no—
173C42×C73—21no—
174C42×C73—21no—
175C42×C73—21no—
176C42×C73—22no—
177C42×C73C2×D411yescharacteristic
178C42×C73C2×D411yescharacteristic
179C42×C73C2×D411yescharacteristic
180C42×C73C2411yescharacteristic
181C23×C73—21no—
182C23×C73#12011yescharacteristic
183Q8×C73—21no—
184Q8×C73—21no—
185Q8×C73—24no—
186Q8×C73—44no—
187Q8×C73—42no—
188Q8×C73—42no—
189Q8×C73—44no—
190Q8×C73—42no—
191Q8×C73—82no—
192D4×C73—21no—
193D4×C73—21no—
194D4×C73—42no—
195C2×C4×C73—22no—
196C2×C4×C73—22no—
197C2×C4×C73—21no—
198C2×C4×C73—21no—
199C2×C4×C73—22no—
200C2×C4×C73—22no—
201C2×C4×C73—24no—
202C2×C4×C73—21no—
203C2×C4×C73—44no—
204C2×C4×C73—42no—
205C2×C4×C73—42no—
206C2×C4×C73—42no—
207C2×C4×C73—42no—
208C2×C4×C73—82no—
209C2×C4×C73#12011yescharacteristic
210C2×C4×C73#12011yescharacteristic
211C2×C4×C73#12011yescharacteristic
212C2×C4×C73#13512yes—
213C2×C4×C73#13712yes—
214C2×C4×C73C22×D411yescharacteristic
215C2×C4×C73C22×D411yescharacteristic
216C2×C4×C73C22×D411yescharacteristic
217C8×C73—42no—
218C8×C73—42no—
219C8×C73—42no—
220C22×C73—21no—
221C22×C73—21no—
222C22×C73—41no—
223C22×C73—41no—
224C22×C73—41no—
225C22×C73#45212yes—
226C22×C73C2×#12011yescharacteristic
227C4×C73—21no—
228C4×C73—21no—
229C4×C73—41no—
230C4×C73—44no—
231C4×C73—41no—
232C4×C73—42no—
233C4×C73—41no—
234C4×C73—42no—
235C4×C73—82no—
236C4×C73#45212yes—
237C4×C73#45412yes—
238C4×C73C2×#13511yescharacteristic
239C4×C73C2×#13711yescharacteristic
240C4×C73#57812yes—
241#18645C7311yesmaximal, characteristic, direct product factor, Sylow
242C2×C73—22no—
243C2×C73—81no—
244C2×C73C2×#45211yescharacteristic
245C2×C73#301111yescharacteristic
246C2×C73C2×#45411yescharacteristic
247#3509C2×C7311yescharacteristic
248#3230C2×C7311yescharacteristic, complemented
249C2×#487C2×C7311yescharacteristic, complemented
250#3079C2×C7311yescharacteristic
251#1638C2×C7314yescomplemented
252#1636C2×C7314yescomplemented
253#1546C2×C7311yescharacteristic, complemented
254#1493C2×C7311yescharacteristic, complemented
255#1476C2×C7311yescharacteristic
256C73#1864511yescharacteristic, direct product factor, Sylow
257#557—21no—
258#557C22×C7312yes—
259#556—21no—
260#556C22×C7312yes—
261#552—22no—
262#552—22no—
263#541—22no—
264#536—21no—
265#533—21no—
266#533—21no—
267#533C22×C7311yescharacteristic
268C2×C4⋊Q8C22×C7311yescharacteristic
269C2×C4⋊Q8C22×C7311yescharacteristic
270#519—21no—
271C4×#41C22×C7311yescharacteristic
272#500—21no—
273#487—22no—
274#487—21no—
275#487C22×C7314yes—
276#484—22no—
277#477C22×C7312yes—
278#477C22×C7314yes—
279#476C22×C7312yes—
280#475—21no—
281#474—21no—
282#431C22×C7311yescharacteristic
283#428—21no—
284#423C22×C7311yescharacteristic
285#417—21no—
286C2×#103—22no—
287C2×C4×C8C22×C7311yescharacteristic
288#332C22×C7314yes—
289Q8⋊C8C22×C7312yes—
290Q8⋊C8C22×C7314yes—
291D4⋊C8C22×C7312yes—
292C2×#41D4×C7311yescharacteristic
293C22×Q8—21no—
294C22×Q8—21no—
295C2×M16—21no—
296C22×C8—21no—
297C4⋊Q8—22no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8D4×C7311yescharacteristic
304C4⋊Q8D4×C7312yes—
305C4⋊Q8D4×C7311yescharacteristic
306C4⋊Q8C23×C7312yes—
307C4⋊Q8C23×C7312yes—
308#126—24no—
309#126—24no—
310#125—22no—
311#125—24no—
312#125—22no—
313#125—24no—
314#125—21no—
315#124—22no—
316#123—24no—
317C22⋊Q8—22no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—21no—
322C22⋊Q8D4×C7312yes—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—21no—
330C4×Q8D4×C7311yescharacteristic
331C4×Q8C23×C7311yescharacteristic
332C4×Q8C23×C7312yes—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4D4×C7311yescharacteristic
336C4×D4C23×C7311yescharacteristic
337#117—24no—
338#117—22no—
339#117—21no—
340#117—22no—
341#117—21no—
342#117D4×C7311yescharacteristic
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4D4×C7312yes—
347C2×C42—21no—
348C2×C42C23×C7311yescharacteristic
349#107—22no—
350#107—24no—
351#106—22no—
352C4⋊C8—21no—
353C4⋊C8C23×C7312yes—
354C4⋊C8C23×C7312yes—
355#103—22no—
356#103—24no—
357#103—28no—
358#102—22no—
359C22⋊C8—21no—
360C4×C8—21no—
361C4×C8—21no—
362C4×C8C23×C7312yes—
363#41—22no—
364#41—22no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—44no—
370C2×Q8—41no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8C2×D4×C7312yes—
374C2×Q8C2×D4×C7311yescharacteristic
375C2×D4—21no—
376C2×D4C2×D4×C7311yescharacteristic
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—41no—
382C22×C4C2×D4×C7311yescharacteristic
383C22×C4C2×D4×C7311yescharacteristic
384C22×C4C2×D4×C7311yescharacteristic
385M16—42no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—42no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4C2×D4×C7314yes—
409C4⋊C4C2×D4×C7311yescharacteristic
410C4⋊C4C2×D4×C7312yes—
411C4⋊C4C2×D4×C7311yescharacteristic
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—21no—
415C22⋊C4—22no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C42—24no—
419C42—24no—
420C42—21no—
421C42—21no—
422C42—21no—
423C42—22no—
424C42C2×D4×C7311yescharacteristic
425C42C2×D4×C7311yescharacteristic
426C42C2×D4×C7311yescharacteristic
427C42C24×C7311yescharacteristic
428C23—21no—
429C23#120×C7311yescharacteristic
430Q8—21no—
431Q8—21no—
432Q8—24no—
433Q8—44no—
434Q8—44no—
435Q8—42no—
436Q8—42no—
437Q8—42no—
438Q8—82no—
439D4—21no—
440D4—21no—
441D4—42no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—21no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—82no—
456C2×C4#120×C7311yescharacteristic
457C2×C4#120×C7311yescharacteristic
458C2×C4#120×C7311yescharacteristic
459C2×C4#135×C7312yes—
460C2×C4#137×C7312yes—
461C2×C4C22×D4×C7311yescharacteristic
462C2×C4C22×D4×C7311yescharacteristic
463C2×C4C22×D4×C7311yescharacteristic
464C8—42no—
465C8—42no—
466C8—42no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22#452×C7312yes—
473C22C2×#120×C7311yescharacteristic
474C4—21no—
475C4—21no—
476C4—41no—
477C4—44no—
478C4—41no—
479C4—42no—
480C4—41no—
481C4—42no—
482C4—82no—
483C4#452×C7312yes—
484C4#454×C7312yes—
485C4C2×#135×C7311yescharacteristic
486C4C2×#137×C7311yescharacteristic
487C4#578×C7312yes—
488C2—22no—
489C2—81no—
490C2C2×#452×C7311yescharacteristic
491C2C73×#301111yescharacteristic
492C2C2×#454×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC2×#41×C73D4
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
2. C73×#3230C2semidirect
3. C2×#487×C73C2semidirect
5. C73×#1638C2semidirect
6. C73×#1636C2semidirect
7. C73×#1546C2semidirect
8. C73×#1493C2semidirect
241. #18645C73direct (N × H)
248. #3230C2×C73semidirect
249. C2×#487C2×C73semidirect
251. #1638C2×C73semidirect
252. #1636C2×C73semidirect
253. #1546C2×C73semidirect
254. #1493C2×C73semidirect
256. C73#18645direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35092
C73×#32302
C2×#487×C732
C73×#30792
C73×#16382
C73×#16362
C73×#15462
C73×#14932
C73×#14762
#1864573