Finite Group Databasebeta

← C73×#19088 #32928492

Subgroups — C73×#19088 #32928492

Order 18688.

884 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3559C211yesmaximal, characteristic, complemented
2C73×#3234C211yesmaximal, characteristic, complemented
3C73×#3219C211yesmaximal, characteristic, complemented
4C73×#3214C211yesmaximal, characteristic, complemented
5C73×#1664C212yesmaximal, complemented
6C73×#1661C212yesmaximal, complemented
7C73×#1657C212yesmaximal, complemented
8C73×#1656C212yesmaximal, complemented
9C73×#1536C211yesmaximal, characteristic, complemented
10C73×#1535C211yesmaximal, characteristic, complemented
11C73×#1534C211yesmaximal, characteristic, complemented
12#563×C73C2212yes—
13#562×C73C2212yes—
14#554×C73—21no—
15#553×C73—21no—
16#553×C73—21no—
17#547×C73—22no—
18#547×C73—21no—
19#544×C73—21no—
20#540×C73—21no—
21#539×C73—22no—
22#539×C73—21no—
23#537×C73—21no—
24#532×C73C2211yescharacteristic
25#532×C73C2211yescharacteristic
26#529×C73C2211yescharacteristic
27C2×#125×C73C2211yescharacteristic
28#501×C73C2212yes—
29#497×C73C2211yescharacteristic
30#496×C73C2212yes—
31#496×C73C2211yescharacteristic
32#491×C73C2211yescharacteristic
33#490×C73C2211yescharacteristic
34#490×C73C2212yes—
35#489×C73C2212yes—
36#481×C73—21no—
37#480×C73—21no—
38#478×C73—22no—
39#464×C73—21no—
40#463×C73—21no—
41#461×C73—21no—
42#459×C73—21no—
43#452×C73—21no—
44#449×C73—22no—
45#449×C73—21no—
46#432×C73C2211yescharacteristic
47#432×C73C2211yescharacteristic
48#432×C73C2211yescharacteristic
49#330×C73C2212yes—
50#330×C73C2212yes—
51#330×C73C2212yes—
52#329×C73C2212yes—
53#329×C73C2212yes—
54#329×C73C2212yes—
55C2×#41×C73—22no—
56C2×#41×C73—21no—
57C2×#41×C73D412yes—
58C2×Q16×C73—21no—
59C2×SD16×C73—22no—
60C2×SD16×C73—21no—
61C2×SD16×C73—21no—
62C2×D8×C73—22no—
63C2×D8×C73—21no—
64C4⋊Q8×C73—21no—
65C4⋊Q8×C73—22no—
66C4⋊Q8×C73D411yescharacteristic
67C4⋊Q8×C73C2311yescharacteristic
68#127×C73D411yescharacteristic
69#127×C73C2311yescharacteristic
70#126×C73—22no—
71#126×C73—22no—
72#126×C73—21no—
73#125×C73—22no—
74#125×C73—21no—
75#125×C73—21no—
76#125×C73—21no—
77#125×C73D412yes—
78#125×C73C2311yescharacteristic
79#125×C73C2312yes—
80#124×C73—21no—
81#124×C73C2312yes—
82#124×C73C2311yescharacteristic
83#123×C73—22no—
84#123×C73—22no—
85#123×C73—22no—
86#123×C73—22no—
87#123×C73—21no—
88#123×C73—22no—
89#123×C73—22no—
90C22⋊Q8×C73—22no—
91C22⋊Q8×C73—22no—
92C22⋊Q8×C73—22no—
93C22⋊Q8×C73—22no—
94C22⋊Q8×C73—22no—
95C22⋊Q8×C73—22no—
96C22⋊Q8×C73D411yescharacteristic
97#121×C73—22no—
98#121×C73—22no—
99#121×C73—21no—
100#121×C73—21no—
101#121×C73—22no—
102#121×C73—22no—
103#121×C73—21no—
104#121×C73—21no—
105#121×C73—21no—
106#121×C73—21no—
107#121×C73D411yescharacteristic
108C4×Q8×C73D411yescharacteristic
109C4×D4×C73—22no—
110C4×D4×C73—22no—
111C4×D4×C73—21no—
112C4×D4×C73—21no—
113C4×D4×C73—21no—
114C4×D4×C73—21no—
115C4×D4×C73—21no—
116C4×D4×C73—21no—
117C4×D4×C73—21no—
118C4×D4×C73D411yescharacteristic
119#117×C73—21no—
120#117×C73—21no—
121C2×C4⋊C4×C73—22no—
122C2×C4⋊C4×C73—21no—
123C2×C4⋊C4×C73—21no—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73D411yescharacteristic
126C2×C4⋊C4×C73D411yescharacteristic
127C2×C42×C73C2311yescharacteristic
128#107×C73—22no—
129#106×C73—22no—
130C4⋊C8×C73—21no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73—21no—
133#103×C73—22no—
134#103×C73—21no—
135#103×C73—21no—
136#102×C73—22no—
137#102×C73—21no—
138#102×C73—21no—
139#102×C73—22no—
140#102×C73—22no—
141C22⋊C8×C73—21no—
142C22⋊C8×C73—21no—
143C22⋊C8×C73—21no—
144#97×C73C2312yes—
145#97×C73C2311yescharacteristic
146#97×C73C2312yes—
147#97×C73C2311yescharacteristic
148#41×C73—84no—
149#41×C73—81no—
150#41×C73—81no—
151#41×C73—82no—
152C2×Q8×C73—22no—
153C2×Q8×C73—21no—
154C2×Q8×C73C2×D412yes—
155C2×Q8×C73C2×D411yescharacteristic
156C2×D4×C73—22no—
157C2×D4×C73—21no—
158C2×D4×C73—22no—
159C2×D4×C73—22no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—41no—
166C2×D4×C73C2×D412yes—
167C2×D4×C73C2×D411yescharacteristic
168C22×C4×C73—21no—
169C22×C4×C73—22no—
170C22×C4×C73—22no—
171C22×C4×C73—22no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—22no—
175C22×C4×C73—41no—
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179Q16×C73—81no—
180SD16×C73—82no—
181SD16×C73—81no—
182SD16×C73—81no—
183D8×C73—81no—
184D8×C73—82no—
185C2×C8×C73—22no—
186C2×C8×C73—21no—
187C2×C8×C73—22no—
188C2×C8×C73—21no—
189C4⋊C4×C73—22no—
190C4⋊C4×C73—22no—
191C4⋊C4×C73—22no—
192C4⋊C4×C73—22no—
193C4⋊C4×C73—22no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—22no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—22no—
202C4⋊C4×C73—22no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73C2×D411yescharacteristic
208C4⋊C4×C73C2×D411yescharacteristic
209C4⋊C4×C73C2×D412yes—
210C4⋊C4×C73C2×D412yes—
211C22⋊C4×C73—22no—
212C22⋊C4×C73—22no—
213C22⋊C4×C73—22no—
214C22⋊C4×C73—22no—
215C22⋊C4×C73—22no—
216C22⋊C4×C73—21no—
217C22⋊C4×C73—21no—
218C22⋊C4×C73—21no—
219C22⋊C4×C73—21no—
220C22⋊C4×C73—22no—
221C22⋊C4×C73—22no—
222C22⋊C4×C73—21no—
223C22⋊C4×C73—41no—
224C22⋊C4×C73—41no—
225C42×C73—22no—
226C42×C73—21no—
227C42×C73C2×D411yescharacteristic
228C42×C73C2×D411yescharacteristic
229C42×C73C2×D411yescharacteristic
230C42×C73C2411yescharacteristic
231C23×C73—22no—
232C23×C73—21no—
233C23×C73—41no—
234C23×C73#12011yescharacteristic
235Q8×C73—41no—
236Q8×C73—42no—
237Q8×C73—41no—
238Q8×C73—41no—
239Q8×C73—82no—
240D4×C73—41no—
241D4×C73—42no—
242D4×C73—42no—
243D4×C73—41no—
244D4×C73—41no—
245D4×C73—41no—
246D4×C73—41no—
247D4×C73—42no—
248D4×C73—44no—
249D4×C73—42no—
250D4×C73—81no—
251D4×C73—82no—
252D4×C73—82no—
253D4×C73—82no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—21no—
259C2×C4×C73—22no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—42no—
264C2×C4×C73—42no—
265C2×C4×C73—41no—
266C2×C4×C73—82no—
267C2×C4×C73—82no—
268C2×C4×C73—81no—
269C2×C4×C73—82no—
270C2×C4×C73—82no—
271C2×C4×C73—82no—
272C2×C4×C73#12011yescharacteristic
273C2×C4×C73#12011yescharacteristic
274C2×C4×C73#12011yescharacteristic
275C2×C4×C73C22×D411yescharacteristic
276C2×C4×C73C22×D411yescharacteristic
277C2×C4×C73C22×D411yescharacteristic
278C8×C73—42no—
279C8×C73—42no—
280C8×C73—41no—
281C8×C73—41no—
282C22×C73—21no—
283C22×C73—21no—
284C22×C73—21no—
285C22×C73—42no—
286C22×C73—41no—
287C22×C73—41no—
288C22×C73—42no—
289C22×C73—42no—
290C22×C73—41no—
291C22×C73—81no—
292C22×C73—81no—
293C22×C73—81no—
294C22×C73C2×#12011yescharacteristic
295C4×C73—21no—
296C4×C73—21no—
297C4×C73—21no—
298C4×C73—21no—
299C4×C73—21no—
300C4×C73—21no—
301C4×C73—42no—
302C4×C73—42no—
303C4×C73—41no—
304C4×C73—41no—
305C4×C73—42no—
306C4×C73—41no—
307C4×C73—81no—
308#19088C7311yesmaximal, characteristic, direct product factor, Sylow
309C2×C73—41no—
310C2×C73—82no—
311C2×C73—81no—
312C2×C73—161no—
313C2×C73#301911yescharacteristic
314C2×C73#302011yescharacteristic
315C2×C73#302111yescharacteristic
316#3559C2×C7311yescharacteristic, complemented
317#3234C2×C7311yescharacteristic, complemented
318#3219C2×C7311yescharacteristic, complemented
319#3214C2×C7311yescharacteristic, complemented
320#1664C2×C7312yescomplemented
321#1661C2×C7312yescomplemented
322#1657C2×C7312yescomplemented
323#1656C2×C7312yescomplemented
324#1536C2×C7311yescharacteristic, complemented
325#1535C2×C7311yescharacteristic, complemented
326#1534C2×C7311yescharacteristic, complemented
327C73#1908811yescharacteristic, direct product factor, Sylow
328#563C22×C7312yes—
329#562C22×C7312yes—
330#554—21no—
331#553—21no—
332#553—21no—
333#547—22no—
334#547—21no—
335#544—21no—
336#540—21no—
337#539—22no—
338#539—21no—
339#537—21no—
340#532C22×C7311yescharacteristic
341#532C22×C7311yescharacteristic
342#529C22×C7311yescharacteristic
343C2×#125C22×C7311yescharacteristic
344#501C22×C7312yes—
345#497C22×C7311yescharacteristic
346#496C22×C7311yescharacteristic
347#496C22×C7312yes—
348#491C22×C7311yescharacteristic
349#490C22×C7312yes—
350#490C22×C7311yescharacteristic
351#489C22×C7312yes—
352#481—21no—
353#480—21no—
354#478—22no—
355#464—21no—
356#463—21no—
357#461—21no—
358#459—21no—
359#452—21no—
360#449—22no—
361#449—21no—
362#432C22×C7311yescharacteristic
363#432C22×C7311yescharacteristic
364#432C22×C7311yescharacteristic
365#330C22×C7312yes—
366#330C22×C7312yes—
367#330C22×C7312yes—
368#329C22×C7312yes—
369#329C22×C7312yes—
370#329C22×C7312yes—
371C2×#41—22no—
372C2×#41—21no—
373C2×#41D4×C7312yes—
374C2×Q16—21no—
375C2×SD16—22no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×D8—22no—
379C2×D8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—22no—
382C4⋊Q8D4×C7311yescharacteristic
383C4⋊Q8C23×C7311yescharacteristic
384#127D4×C7311yescharacteristic
385#127C23×C7311yescharacteristic
386#126—22no—
387#126—22no—
388#126—21no—
389#125—22no—
390#125—21no—
391#125—21no—
392#125—21no—
393#125D4×C7312yes—
394#125C23×C7312yes—
395#125C23×C7311yescharacteristic
396#124—21no—
397#124C23×C7311yescharacteristic
398#124C23×C7312yes—
399#123—22no—
400#123—22no—
401#123—22no—
402#123—22no—
403#123—21no—
404#123—22no—
405#123—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8D4×C7311yescharacteristic
413#121—22no—
414#121—22no—
415#121—21no—
416#121—21no—
417#121—22no—
418#121—22no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121—21no—
423#121D4×C7311yescharacteristic
424C4×Q8D4×C7311yescharacteristic
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4D4×C7311yescharacteristic
435#117—21no—
436#117—21no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4D4×C7311yescharacteristic
442C2×C4⋊C4D4×C7311yescharacteristic
443C2×C42C23×C7311yescharacteristic
444#107—22no—
445#106—22no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449#103—22no—
450#103—21no—
451#103—21no—
452#102—22no—
453#102—21no—
454#102—21no—
455#102—22no—
456#102—22no—
457C22⋊C8—21no—
458C22⋊C8—21no—
459C22⋊C8—21no—
460#97C23×C7312yes—
461#97C23×C7311yescharacteristic
462#97C23×C7311yescharacteristic
463#97C23×C7312yes—
464#41—84no—
465#41—81no—
466#41—81no—
467#41—82no—
468C2×Q8—22no—
469C2×Q8—21no—
470C2×Q8C2×D4×C7312yes—
471C2×Q8C2×D4×C7311yescharacteristic
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—41no—
482C2×D4C2×D4×C7312yes—
483C2×D4C2×D4×C7311yescharacteristic
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—41no—
492C22×C4C2×D4×C7311yescharacteristic
493C22×C4C2×D4×C7311yescharacteristic
494C22×C4C2×D4×C7311yescharacteristic
495Q16—81no—
496SD16—82no—
497SD16—81no—
498SD16—81no—
499D8—81no—
500D8—82no—
501C2×C8—22no—
502C2×C8—21no—
503C2×C8—22no—
504C2×C8—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4C2×D4×C7311yescharacteristic
524C4⋊C4C2×D4×C7311yescharacteristic
525C4⋊C4C2×D4×C7312yes—
526C4⋊C4C2×D4×C7312yes—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C42—22no—
542C42—21no—
543C42C2×D4×C7311yescharacteristic
544C42C2×D4×C7311yescharacteristic
545C42C2×D4×C7311yescharacteristic
546C42C24×C7311yescharacteristic
547C23—22no—
548C23—21no—
549C23—41no—
550C23#120×C7311yescharacteristic
551Q8—41no—
552Q8—42no—
553Q8—41no—
554Q8—41no—
555Q8—82no—
556D4—41no—
557D4—42no—
558D4—42no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—42no—
564D4—44no—
565D4—42no—
566D4—81no—
567D4—82no—
568D4—82no—
569D4—82no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4—81no—
585C2×C4—82no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4#120×C7311yescharacteristic
589C2×C4#120×C7311yescharacteristic
590C2×C4#120×C7311yescharacteristic
591C2×C4C22×D4×C7311yescharacteristic
592C2×C4C22×D4×C7311yescharacteristic
593C2×C4C22×D4×C7311yescharacteristic
594C8—42no—
595C8—41no—
596C8—41no—
597C8—42no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—41no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22C2×#120×C7311yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—42no—
622C4—41no—
623C4—81no—
624C2—41no—
625C2—82no—
626C2—81no—
627C2—161no—
628C2C73×#301911yescharacteristic
629C2C73×#302011yescharacteristic
630C2C73×#302111yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
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×#3559C2semidirect
2. C73×#3234C2semidirect
3. C73×#3219C2semidirect
4. C73×#3214C2semidirect
5. C73×#1664C2semidirect
6. C73×#1661C2semidirect
7. C73×#1657C2semidirect
8. C73×#1656C2semidirect
9. C73×#1536C2semidirect
10. C73×#1535C2semidirect
11. C73×#1534C2semidirect
308. #19088C73direct (N × H)
316. #3559C2×C73semidirect
317. #3234C2×C73semidirect
318. #3219C2×C73semidirect
319. #3214C2×C73semidirect
320. #1664C2×C73semidirect
321. #1661C2×C73semidirect
322. #1657C2×C73semidirect
323. #1656C2×C73semidirect
324. #1536C2×C73semidirect
325. #1535C2×C73semidirect
326. #1534C2×C73semidirect
327. C73#19088direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35592
C73×#32342
C73×#32192
C73×#32142
C73×#16642
C73×#16612
C73×#16572
C73×#16562
C73×#15362
C73×#15352
C73×#15342
#1908873