Finite Group Databasebeta

← C73×#13043 #32922447

Subgroups — C73×#13043 #32922447

Order 18688.

844 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×B(4,𝔽2)×C73C211yesmaximal, characteristic
2C73×#2375C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C73C211yesmaximal, characteristic, complemented
4C73×#1792C211yesmaximal, characteristic, complemented
5C73×#1790C211yesmaximal, characteristic, complemented
6C73×#1393C211yesmaximal, characteristic, complemented
7C73×#1390C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C73C2211yescharacteristic
9C2×#120×C73—21no—
10C2×#120×C73C2211yescharacteristic
11B(4,𝔽2)×C73—22no—
12B(4,𝔽2)×C73C414yescomplemented
13C2×#104×C73—21no—
14#417×C73—21no—
15C2×#100×C73C2211yescharacteristic
16C2×#99×C73—21no—
17C2×#99×C73—21no—
18C2×#99×C73C2211yescharacteristic
19C2×#99×C73C2211yescharacteristic
20#390×C73—21no—
21#390×C73C2211yescharacteristic
22#388×C73—21no—
23#388×C73—21no—
24#388×C73—21no—
25#386×C73—21no—
26#386×C73—21no—
27#386×C73C2211yescharacteristic
28#379×C73—21no—
29AΣL(1,𝔽16)×C73—22no—
30C25×C73D411yescharacteristic
31H(5,𝔽2)×C73—21no—
32H(5,𝔽2)×C73—21no—
33H(5,𝔽2)×C73—21no—
34H(5,𝔽2)×C73—42no—
35H(5,𝔽2)×C73C2×C412yes—
36C2×#41×C73—21no—
37C2×#41×C73—41no—
38C22×D4×C73—21no—
39C22×D4×C73—21no—
40C22×D4×C73—21no—
41C22×D4×C73—41no—
42C22×D4×C73—41no—
43C22×D4×C73C2311yescharacteristic
44C23×C4×C73D411yescharacteristic, complemented
45C2×M16×C73—21no—
46#120×C73—21no—
47#120×C73—21no—
48#120×C73—24no—
49#120×C73—42no—
50#120×C73C2×C412yes—
51#120×C73D412yes—
52C2×C4⋊C4×C73—21no—
53C2×C4⋊C4×C73D411yescharacteristic, complemented
54C2×C22⋊C4×C73—21no—
55C2×C22⋊C4×C73—21no—
56C2×C22⋊C4×C73—21no—
57C2×C22⋊C4×C73—21no—
58C2×C22⋊C4×C73—21no—
59C2×C22⋊C4×C73—21no—
60C2×C22⋊C4×C73—21no—
61C2×C22⋊C4×C73—21no—
62C2×C22⋊C4×C73—21no—
63C2×C22⋊C4×C73—21no—
64C2×C22⋊C4×C73—41no—
65C2×C22⋊C4×C73—41no—
66C2×C22⋊C4×C73D411yescharacteristic
67C2×C22⋊C4×C73D411yescharacteristic, complemented
68C2×C42×C73—21no—
69C2×C42×C73D411yescharacteristic, complemented
70#104×C73—42no—
71#103×C73—41no—
72#102×C73—41no—
73#100×C73—21no—
74#100×C73—21no—
75#99×C73—21no—
76#99×C73—24no—
77#99×C73—21no—
78#99×C73—21no—
79#99×C73—42no—
80#99×C73C2×C412yes—
81#95×C73—21no—
82#95×C73—21no—
83#95×C73—21no—
84#95×C73—41no—
85C24×C73—21no—
86C24×C73—21no—
87C24×C73—21no—
88C24×C73—21no—
89C24×C73—41no—
90C24×C73—41no—
91C24×C73—81no—
92C24×C73—81no—
93C24×C73C22⋊C412yescomplemented
94C24×C73C2×D411yescharacteristic
95C24×C73C2×D411yescharacteristic
96#41×C73—22no—
97#41×C73—22no—
98#41×C73—42no—
99#41×C73—41no—
100#41×C73—42no—
101#41×C73—42no—
102#41×C73—42no—
103#41×C73—41no—
104C2×Q8×C73—21no—
105C2×D4×C73—21no—
106C2×D4×C73—22no—
107C2×D4×C73—22no—
108C2×D4×C73—22no—
109C2×D4×C73—22no—
110C2×D4×C73—22no—
111C2×D4×C73—22no—
112C2×D4×C73—41no—
113C2×D4×C73—41no—
114C2×D4×C73—42no—
115C2×D4×C73—42no—
116C2×D4×C73—41no—
117C2×D4×C73—41no—
118C2×D4×C73—41no—
119C2×D4×C73—41no—
120C2×D4×C73—42no—
121C2×D4×C73—42no—
122C2×D4×C73—41no—
123C2×D4×C73—41no—
124C2×D4×C73—41no—
125C2×D4×C73—44no—
126C2×D4×C73—81no—
127C2×D4×C73—81no—
128C2×D4×C73—82no—
129C2×D4×C73—82no—
130C2×D4×C73C22×C411yescharacteristic
131C2×D4×C73C2×D411yescharacteristic
132C2×D4×C73#4111yescharacteristic
133C2×D4×C73#4111yescharacteristic
134C22×C4×C73—21no—
135C22×C4×C73—21no—
136C22×C4×C73—21no—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
139C22×C4×C73—21no—
140C22×C4×C73—21no—
141C22×C4×C73—41no—
142C22×C4×C73—41no—
143C22×C4×C73—41no—
144C22×C4×C73—41no—
145C22×C4×C73—81no—
146C22×C4×C73C2×D411yescharacteristic
147M16×C73—41no—
148M16×C73—41no—
149C2×C8×C73—41no—
150C4⋊C4×C73—41no—
151C4⋊C4×C73—81no—
152C22⋊C4×C73—21no—
153C22⋊C4×C73—22no—
154C22⋊C4×C73—22no—
155C22⋊C4×C73—22no—
156C22⋊C4×C73—44no—
157C22⋊C4×C73—41no—
158C22⋊C4×C73—41no—
159C22⋊C4×C73—41no—
160C22⋊C4×C73—41no—
161C22⋊C4×C73—81no—
162C22⋊C4×C73—81no—
163C22⋊C4×C73—81no—
164C22⋊C4×C73—81no—
165C22⋊C4×C73—81no—
166C22⋊C4×C73—81no—
167C22⋊C4×C73—81no—
168C22⋊C4×C73—82no—
169C22⋊C4×C73C22⋊C412yescomplemented
170C42×C73—41no—
171C42×C73—81no—
172C23×C73—21no—
173C23×C73—21no—
174C23×C73—21no—
175C23×C73—21no—
176C23×C73—22no—
177C23×C73—22no—
178C23×C73—22no—
179C23×C73—42no—
180C23×C73—41no—
181C23×C73—41no—
182C23×C73—41no—
183C23×C73—41no—
184C23×C73—41no—
185C23×C73—41no—
186C23×C73—41no—
187C23×C73—41no—
188C23×C73—41no—
189C23×C73—41no—
190C23×C73—42no—
191C23×C73—42no—
192C23×C73—41no—
193C23×C73—41no—
194C23×C73—41no—
195C23×C73—81no—
196C23×C73—82no—
197C23×C73—82no—
198C23×C73—81no—
199C23×C73—81no—
200C23×C73—84no—
201C23×C73—81no—
202C23×C73—81no—
203C23×C73—81no—
204C23×C73—81no—
205C23×C73C2×C22⋊C411yescharacteristic
206C23×C73C4×D411yescharacteristic
207C23×C73#12011yescharacteristic
208C23×C73#12111yescharacteristic
209C23×C73#12311yescharacteristic
210Q8×C73—22no—
211Q8×C73—41no—
212D4×C73—22no—
213D4×C73—41no—
214D4×C73—41no—
215D4×C73—41no—
216D4×C73—41no—
217D4×C73—41no—
218D4×C73—42no—
219D4×C73—42no—
220D4×C73—42no—
221D4×C73—42no—
222D4×C73—42no—
223D4×C73—42no—
224D4×C73—82no—
225D4×C73—82no—
226D4×C73—88no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—22no—
230C2×C4×C73—22no—
231C2×C4×C73—22no—
232C2×C4×C73—42no—
233C2×C4×C73—42no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—42no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—42no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—81no—
254C2×C4×C73—81no—
255C2×C4×C73—81no—
256C2×C4×C73—81no—
257C2×C4×C73—81no—
258C2×C4×C73—81no—
259C2×C4×C73C4×D411yescharacteristic
260C2×C4×C73#12111yescharacteristic
261C8×C73—81no—
262C22×C73—21no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73—21no—
266C22×C73—21no—
267C22×C73—21no—
268C22×C73—41no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—42no—
273C22×C73—42no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73—44no—
279C22×C73—42no—
280C22×C73—42no—
281C22×C73—81no—
282C22×C73—81no—
283C22×C73—81no—
284C22×C73—81no—
285C22×C73—82no—
286C22×C73—82no—
287C22×C73—82no—
288C22×C73—82no—
289C22×C73—82no—
290C22×C73—81no—
291C22×C73—81no—
292C22×C73—81no—
293C22×C73—81no—
294C22×C73—161no—
295C22×C73—161no—
296C22×C73#38611yescharacteristic
297C22×C73B(4,𝔽2)11yescharacteristic
298C22×C73B(4,𝔽2)11yescharacteristic
299C4×C73—21no—
300C4×C73—21no—
301C4×C73—42no—
302C4×C73—42no—
303C4×C73—81no—
304C4×C73—81no—
305C4×C73—82no—
306C4×C73—81no—
307C4×C73—81no—
308C4×C73—161no—
309#13043C7311yesmaximal, characteristic, direct product factor, Sylow
310C2×C73—21no—
311C2×C73—21no—
312C2×C73—41no—
313C2×C73—41no—
314C2×C73—41no—
315C2×C73—41no—
316C2×C73—82no—
317C2×C73—82no—
318C2×C73#188911yescharacteristic
319C2×C73#219911yescharacteristic
320C2×C73#220011yescharacteristic
321C2×B(4,𝔽2)C2×C7311yescharacteristic
322#2375C2×C7311yescharacteristic, complemented
323C2×AΣL(1,𝔽16)C2×C7311yescharacteristic, complemented
324#1792C2×C7311yescharacteristic, complemented
325#1790C2×C7311yescharacteristic, complemented
326#1393C2×C7311yescharacteristic, complemented
327#1390C2×C7311yescharacteristic, complemented
328C73#1304311yescharacteristic, direct product factor, Sylow
329C2×H(5,𝔽2)C22×C7311yescharacteristic
330C2×#120—21no—
331C2×#120C22×C7311yescharacteristic
332B(4,𝔽2)—22no—
333B(4,𝔽2)C4×C7314yescomplemented
334C2×#104—21no—
335#417—21no—
336C2×#100C22×C7311yescharacteristic
337C2×#99—21no—
338C2×#99—21no—
339C2×#99C22×C7311yescharacteristic
340C2×#99C22×C7311yescharacteristic
341#390—21no—
342#390C22×C7311yescharacteristic
343#388—21no—
344#388—21no—
345#388—21no—
346#386—21no—
347#386—21no—
348#386C22×C7311yescharacteristic
349#379—21no—
350AΣL(1,𝔽16)—22no—
351C25D4×C7311yescharacteristic
352H(5,𝔽2)—21no—
353H(5,𝔽2)—21no—
354H(5,𝔽2)—21no—
355H(5,𝔽2)—42no—
356H(5,𝔽2)C2×C4×C7312yes—
357C2×#41—21no—
358C2×#41—41no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4C23×C7311yescharacteristic
365C23×C4D4×C7311yescharacteristic, complemented
366C2×M16—21no—
367#120—21no—
368#120—21no—
369#120—24no—
370#120—42no—
371#120C2×C4×C7312yes—
372#120D4×C7312yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C7311yescharacteristic, complemented
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4D4×C7311yescharacteristic
388C2×C22⋊C4D4×C7311yescharacteristic, complemented
389C2×C42—21no—
390C2×C42D4×C7311yescharacteristic, complemented
391#104—42no—
392#103—41no—
393#102—41no—
394#100—21no—
395#100—21no—
396#99—21no—
397#99—24no—
398#99—21no—
399#99—21no—
400#99—42no—
401#99C2×C4×C7312yes—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—41no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—41no—
411C24—41no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C7312yescomplemented
415C24C2×D4×C7311yescharacteristic
416C24C2×D4×C7311yescharacteristic
417#41—22no—
418#41—22no—
419#41—42no—
420#41—41no—
421#41—42no—
422#41—42no—
423#41—42no—
424#41—41no—
425C2×Q8—21no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—44no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4—82no—
450C2×D4—82no—
451C2×D4C22×C4×C7311yescharacteristic
452C2×D4C2×D4×C7311yescharacteristic
453C2×D4#41×C7311yescharacteristic
454C2×D4#41×C7311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—81no—
467C22×C4C2×D4×C7311yescharacteristic
468M16—41no—
469M16—41no—
470C2×C8—41no—
471C4⋊C4—41no—
472C4⋊C4—81no—
473C22⋊C4—21no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—44no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—82no—
490C22⋊C4C22⋊C4×C7312yescomplemented
491C42—41no—
492C42—81no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—81no—
517C23—82no—
518C23—82no—
519C23—81no—
520C23—81no—
521C23—84no—
522C23—81no—
523C23—81no—
524C23—81no—
525C23—81no—
526C23C2×C22⋊C4×C7311yescharacteristic
527C23C4×D4×C7311yescharacteristic
528C23#120×C7311yescharacteristic
529C23#121×C7311yescharacteristic
530C23#123×C7311yescharacteristic
531Q8—22no—
532Q8—41no—
533D4—22no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—82no—
546D4—82no—
547D4—88no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4C4×D4×C7311yescharacteristic
581C2×C4#121×C7311yescharacteristic
582C8—81no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—44no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—161no—
616C22—161no—
617C22#386×C7311yescharacteristic
618C22B(4,𝔽2)×C7311yescharacteristic
619C22B(4,𝔽2)×C7311yescharacteristic
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—82no—
627C4—81no—
628C4—81no—
629C4—161no—
630C2—21no—
631C2—21no—
632C2—41no—
633C2—41no—
634C2—41no—
635C2—41no—
636C2—82no—
637C2—82no—
638C2C73×#188911yescharacteristic
639C2C73×#219911yescharacteristic
640C2C73×#220011yescharacteristic
subgroupG/H
center, socleC22×C73B(4,𝔽2)
commutatorC2×D4C22×C4×C73
Frattini, cosocleC22×D4C23×C73
prime radicalC2×B(4,𝔽2)×C73C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C73 ◁ C22×D4×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C73×#2375C2semidirect
3. C2×AΣL(1,𝔽16)×C73C2semidirect
4. C73×#1792C2semidirect
5. C73×#1790C2semidirect
6. C73×#1393C2semidirect
7. C73×#1390C2semidirect
12. B(4,𝔽2)×C73C4semidirect
44. C23×C4×C73D4semidirect
53. C2×C4⋊C4×C73D4semidirect
67. C2×C22⋊C4×C73D4semidirect
69. C2×C42×C73D4semidirect
93. C24×C73C22⋊C4semidirect
169. C22⋊C4×C73C22⋊C4semidirect
309. #13043C73direct (N × H)
322. #2375C2×C73semidirect
323. C2×AΣL(1,𝔽16)C2×C73semidirect
324. #1792C2×C73semidirect
325. #1790C2×C73semidirect
326. #1393C2×C73semidirect
327. #1390C2×C73semidirect
328. C73#13043direct (N × H)
333. B(4,𝔽2)C4×C73semidirect
365. C23×C4D4×C73semidirect
374. C2×C4⋊C4D4×C73semidirect
388. C2×C22⋊C4D4×C73semidirect
390. C2×C42D4×C73semidirect
414. C24C22⋊C4×C73semidirect
490. C22⋊C4C22⋊C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×B(4,𝔽2)×C732
C73×#23752
C2×AΣL(1,𝔽16)×C732
C73×#17922
C73×#17902
C73×#13932
C73×#13902
#1304373