Finite Group Databasebeta

← C73×#29037 #32938441

Subgroups — C73×#29037 #32938441

Order 18688.

660 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2508C211yesmaximal, characteristic, complemented
2C73×#2448C211yesmaximal, characteristic
3C73×#2101C211yesmaximal, characteristic, complemented
4C73×#2066C211yesmaximal, characteristic, complemented
5C73×#2065C211yesmaximal, characteristic
6C73×#2042C211yesmaximal, characteristic
7C73×#1958C211yesmaximal, characteristic
8C73×#1941C211yesmaximal, characteristic, complemented
9C73×#1936C211yesmaximal, characteristic
10C73×#1936C211yesmaximal, characteristic
11C73×#1935C211yesmaximal, characteristic, complemented
12C73×#1926C211yesmaximal, characteristic
13C73×#1865C211yesmaximal, characteristic, complemented
14C73×#1771C211yesmaximal, characteristic, complemented
15C73×#1763C211yesmaximal, characteristic, complemented
16C2×#124×C73C2211yescharacteristic
17C2×C4×Q8×C73C2211yescharacteristic
18C2×#106×C73C2211yescharacteristic
19C2×#106×C73C2211yescharacteristic
20C2×C4⋊C8×C73C2211yescharacteristic
21C2×#103×C73C2211yescharacteristic
22C2×#103×C73C2211yescharacteristic
23C2×#103×C73C2211yescharacteristic
24C2×#103×C73C2211yescharacteristic
25C2×#102×C73C2211yescharacteristic
26C2×#102×C73C2211yescharacteristic
27C2×#102×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×#97×C73C2211yescharacteristic
30C2×#97×C73C2211yescharacteristic
31C2×C4×C8×C73C2211yescharacteristic
32#400×C73—21no—
33#399×C73—21no—
34#398×C73—21no—
35#397×C73—21no—
36#391×C73C2211yescharacteristic
37#390×C73C2211yescharacteristic
38#390×C73C2211yescharacteristic
39#389×C73C2211yescharacteristic
40#389×C73C2211yescharacteristic
41#389×C73C2211yescharacteristic
42#389×C73C2211yescharacteristic
43#389×C73C2211yescharacteristic
44#388×C73—21no—
45#388×C73—21no—
46#387×C73—21no—
47#382×C73—21no—
48#382×C73C2211yescharacteristic
49C4×C4⋊C4×C73C2211yescharacteristic
50C4×C4⋊C4×C73C2211yescharacteristic
51#340×C73C2211yescharacteristic
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×Q8×C73C2311yescharacteristic
60C22×D4×C73C2311yescharacteristic
61C22×C8×C73C2311yescharacteristic
62C22×C8×C73C2311yescharacteristic
63C22×C8×C73C2311yescharacteristic
64C22×C8×C73C2311yescharacteristic
65#124×C73—22no—
66#124×C73—41no—
67C4×Q8×C73—22no—
68C4×Q8×C73—41no—
69C2×C4⋊C4×C73—21no—
70C2×C4⋊C4×C73—21no—
71C2×C4⋊C4×C73—21no—
72C2×C4⋊C4×C73—21no—
73C2×C4⋊C4×C73—21no—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73D411yescharacteristic
76C2×C4⋊C4×C73D411yescharacteristic
77C2×C4⋊C4×C73C2311yescharacteristic
78C2×C4⋊C4×C73C2311yescharacteristic
79C2×C4⋊C4×C73C2311yescharacteristic
80C2×C4⋊C4×C73C2311yescharacteristic
81C2×C4⋊C4×C73C2311yescharacteristic
82C2×C4⋊C4×C73C2311yescharacteristic
83C2×C22⋊C4×C73—21no—
84C2×C22⋊C4×C73—21no—
85C2×C22⋊C4×C73—21no—
86C2×C22⋊C4×C73—21no—
87C2×C22⋊C4×C73—21no—
88C2×C22⋊C4×C73—21no—
89C2×C42×C73—21no—
90C2×C42×C73—21no—
91C2×C42×C73C2311yescharacteristic
92C2×C42×C73C2311yescharacteristic
93C2×C42×C73C2311yescharacteristic
94#106×C73—22no—
95#106×C73—41no—
96C4⋊C8×C73—22no—
97#103×C73—22no—
98#103×C73—22no—
99#103×C73—22no—
100#103×C73—22no—
101#102×C73—22no—
102#102×C73—22no—
103#102×C73—22no—
104#102×C73—41no—
105#97×C73—22no—
106#97×C73—41no—
107C4×C8×C73—41no—
108#95×C73—21no—
109#95×C73—21no—
110#95×C73—21no—
111#95×C73—21no—
112#95×C73—21no—
113#95×C73—21no—
114#95×C73—21no—
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73D411yescharacteristic
119#95×C73D411yescharacteristic
120C24×C73—21no—
121C2×Q8×C73—21no—
122C2×Q8×C73—21no—
123C2×Q8×C73—21no—
124C2×Q8×C73—21no—
125C2×Q8×C73—21no—
126C2×Q8×C73#4112yes—
127C2×D4×C73—21no—
128C2×D4×C73—21no—
129C2×D4×C73—21no—
130C2×D4×C73—21no—
131C2×D4×C73—21no—
132C2×D4×C73—21no—
133C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
141C22×C4×C73C2×D411yescharacteristic
142C22×C4×C73C2×D411yescharacteristic
143C22×C4×C73C2×D411yescharacteristic
144C22×C4×C73C2×D411yescharacteristic
145C22×C4×C73C2×D411yescharacteristic
146C22×C4×C73C2411yescharacteristic
147C2×C8×C73—21no—
148C2×C8×C73—21no—
149C2×C8×C73—21no—
150C2×C8×C73—21no—
151C2×C8×C73—21no—
152C2×C8×C73—21no—
153C2×C8×C73—21no—
154C2×C8×C73—21no—
155C2×C8×C73—21no—
156C2×C8×C73—21no—
157C2×C8×C73#4112yes—
158C2×C8×C73#4112yes—
159C4⋊C4×C73—21no—
160C4⋊C4×C73—21no—
161C4⋊C4×C73—21no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73—21no—
165C4⋊C4×C73—21no—
166C4⋊C4×C73—21no—
167C4⋊C4×C73—21no—
168C4⋊C4×C73—21no—
169C4⋊C4×C73—21no—
170C4⋊C4×C73—41no—
171C4⋊C4×C73—41no—
172C4⋊C4×C73—42no—
173C4⋊C4×C73—42no—
174C4⋊C4×C73—81no—
175C4⋊C4×C73—81no—
176C4⋊C4×C73—81no—
177C4⋊C4×C73—81no—
178C4⋊C4×C73#4112yes—
179C22⋊C4×C73—42no—
180C22⋊C4×C73—42no—
181C22⋊C4×C73—42no—
182C22⋊C4×C73—42no—
183C22⋊C4×C73—81no—
184C22⋊C4×C73—81no—
185C42×C73—21no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—42no—
192C42×C73—42no—
193C23×C73—41no—
194C23×C73—41no—
195C23×C73—41no—
196C23×C73—41no—
197C23×C73—41no—
198C23×C73—41no—
199C23×C73—41no—
200C23×C73C22×D411yescharacteristic
201Q8×C73—22no—
202Q8×C73—22no—
203Q8×C73—41no—
204Q8×C73—41no—
205D4×C73—41no—
206D4×C73—41no—
207D4×C73—41no—
208D4×C73—41no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—22no—
216C2×C4×C73—22no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
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—41no—
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×C73C2×#4111yescharacteristic
249C2×C4×C73C2×#4111yescharacteristic
250C2×C4×C73C2×#4111yescharacteristic
251C2×C4×C73C2×#4111yescharacteristic
252C2×C4×C73H(5,𝔽2)11yescharacteristic
253C2×C4×C732−1+411yescharacteristic
254C8×C73—22no—
255C8×C73—22no—
256C8×C73—41no—
257C8×C73—41no—
258C22×C73—81no—
259C22×C73—81no—
260C22×C73—81no—
261C22×C73—81no—
262C22×C73—81no—
263C22×C73—81no—
264C22×C73—81no—
265C22×C73#53211yescharacteristic
266C22×C73#54611yescharacteristic
267C22×C73#54811yescharacteristic
268C22×C73#57511yescharacteristic
269C22×C73#57511yescharacteristic
270C22×C73#57711yescharacteristic
271C22×C73#57711yescharacteristic
272C4×C73—42no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—42no—
280C4×C73—81no—
281C4×C73—81no—
282C4×C73—81no—
283C4×C73—81no—
284C4×C73—81no—
285C4×C73#52911yescharacteristic
286C4×C73#53911yescharacteristic
287C4×C73#55211yescharacteristic
288C4×C73#55311yescharacteristic
289#29037C7311yesmaximal, characteristic, direct product factor, Sylow
290C2×C73—161no—
291C2×C73#255811yescharacteristic
292C2×C73#317311yescharacteristic
293C2×C73#318311yescharacteristic
294C2×C73#331711yescharacteristic
295C2×C73#332111yescharacteristic
296C2×C73#337111yescharacteristic
297C2×C73#337611yescharacteristic
298#2508C2×C7311yescharacteristic, complemented
299#2448C2×C7311yescharacteristic
300#2101C2×C7311yescharacteristic, complemented
301#2066C2×C7311yescharacteristic, complemented
302#2065C2×C7311yescharacteristic
303#2042C2×C7311yescharacteristic
304#1958C2×C7311yescharacteristic
305#1941C2×C7311yescharacteristic, complemented
306#1936C2×C7311yescharacteristic
307#1936C2×C7311yescharacteristic
308#1935C2×C7311yescharacteristic, complemented
309#1926C2×C7311yescharacteristic
310#1865C2×C7311yescharacteristic, complemented
311#1771C2×C7311yescharacteristic, complemented
312#1763C2×C7311yescharacteristic, complemented
313C73#2903711yescharacteristic, direct product factor, Sylow
314C2×#124C22×C7311yescharacteristic
315C2×C4×Q8C22×C7311yescharacteristic
316C2×#106C22×C7311yescharacteristic
317C2×#106C22×C7311yescharacteristic
318C2×C4⋊C8C22×C7311yescharacteristic
319C2×#103C22×C7311yescharacteristic
320C2×#103C22×C7311yescharacteristic
321C2×#103C22×C7311yescharacteristic
322C2×#103C22×C7311yescharacteristic
323C2×#102C22×C7311yescharacteristic
324C2×#102C22×C7311yescharacteristic
325C2×#102C22×C7311yescharacteristic
326C2×#102C22×C7311yescharacteristic
327C2×#97C22×C7311yescharacteristic
328C2×#97C22×C7311yescharacteristic
329C2×C4×C8C22×C7311yescharacteristic
330#400—21no—
331#399—21no—
332#398—21no—
333#397—21no—
334#391C22×C7311yescharacteristic
335#390C22×C7311yescharacteristic
336#390C22×C7311yescharacteristic
337#389C22×C7311yescharacteristic
338#389C22×C7311yescharacteristic
339#389C22×C7311yescharacteristic
340#389C22×C7311yescharacteristic
341#389C22×C7311yescharacteristic
342#388—21no—
343#388—21no—
344#387—21no—
345#382—21no—
346#382C22×C7311yescharacteristic
347C4×C4⋊C4C22×C7311yescharacteristic
348C4×C4⋊C4C22×C7311yescharacteristic
349#340C22×C7311yescharacteristic
350#340C22×C7311yescharacteristic
351#340C22×C7311yescharacteristic
352#340C22×C7311yescharacteristic
353#340C22×C7311yescharacteristic
354#340C22×C7311yescharacteristic
355#336C22×C7311yescharacteristic
356#336C22×C7311yescharacteristic
357C22×Q8C23×C7311yescharacteristic
358C22×D4C23×C7311yescharacteristic
359C22×C8C23×C7311yescharacteristic
360C22×C8C23×C7311yescharacteristic
361C22×C8C23×C7311yescharacteristic
362C22×C8C23×C7311yescharacteristic
363#124—22no—
364#124—41no—
365C4×Q8—22no—
366C4×Q8—41no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4D4×C7311yescharacteristic
374C2×C4⋊C4D4×C7311yescharacteristic
375C2×C4⋊C4C23×C7311yescharacteristic
376C2×C4⋊C4C23×C7311yescharacteristic
377C2×C4⋊C4C23×C7311yescharacteristic
378C2×C4⋊C4C23×C7311yescharacteristic
379C2×C4⋊C4C23×C7311yescharacteristic
380C2×C4⋊C4C23×C7311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C7311yescharacteristic
390C2×C42C23×C7311yescharacteristic
391C2×C42C23×C7311yescharacteristic
392#106—22no—
393#106—41no—
394C4⋊C8—22no—
395#103—22no—
396#103—22no—
397#103—22no—
398#103—22no—
399#102—22no—
400#102—22no—
401#102—22no—
402#102—41no—
403#97—22no—
404#97—41no—
405C4×C8—41no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95D4×C7311yescharacteristic
417#95D4×C7311yescharacteristic
418C24—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8#41×C7312yes—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4C2×D4×C7311yescharacteristic
439C22×C4C2×D4×C7311yescharacteristic
440C22×C4C2×D4×C7311yescharacteristic
441C22×C4C2×D4×C7311yescharacteristic
442C22×C4C2×D4×C7311yescharacteristic
443C22×C4C2×D4×C7311yescharacteristic
444C22×C4C24×C7311yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8#41×C7312yes—
456C2×C8#41×C7312yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4#41×C7312yes—
477C22⋊C4—42no—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—81no—
482C22⋊C4—81no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—42no—
490C42—42no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23C22×D4×C7311yescharacteristic
499Q8—22no—
500Q8—22no—
501Q8—41no—
502Q8—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4C2×#41×C7311yescharacteristic
547C2×C4C2×#41×C7311yescharacteristic
548C2×C4C2×#41×C7311yescharacteristic
549C2×C4C2×#41×C7311yescharacteristic
550C2×C4H(5,𝔽2)×C7311yescharacteristic
551C2×C42−1+4×C7311yescharacteristic
552C8—22no—
553C8—22no—
554C8—41no—
555C8—41no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22#532×C7311yescharacteristic
564C22#546×C7311yescharacteristic
565C22#548×C7311yescharacteristic
566C22#575×C7311yescharacteristic
567C22#575×C7311yescharacteristic
568C22#577×C7311yescharacteristic
569C22#577×C7311yescharacteristic
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—42no—
575C4—42no—
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4#529×C7311yescharacteristic
584C4#539×C7311yescharacteristic
585C4#552×C7311yescharacteristic
586C4#553×C7311yescharacteristic
587C2—161no—
588C2C73×#255811yescharacteristic
589C2C73×#317311yescharacteristic
590C2C73×#318311yescharacteristic
591C2C73×#331711yescharacteristic
592C2C73×#332111yescharacteristic
593C2C73×#337111yescharacteristic
594C2C73×#337611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C4⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2508C2semidirect
3. C73×#2101C2semidirect
4. C73×#2066C2semidirect
8. C73×#1941C2semidirect
11. C73×#1935C2semidirect
13. C73×#1865C2semidirect
14. C73×#1771C2semidirect
15. C73×#1763C2semidirect
289. #29037C73direct (N × H)
298. #2508C2×C73semidirect
300. #2101C2×C73semidirect
301. #2066C2×C73semidirect
305. #1941C2×C73semidirect
308. #1935C2×C73semidirect
310. #1865C2×C73semidirect
311. #1771C2×C73semidirect
312. #1763C2×C73semidirect
313. C73#29037direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#25082
C73×#24482
C73×#21012
C73×#20662
C73×#20652
C73×#20422
C73×#19582
C73×#19412
C73×#19362
C73×#19352
C73×#19262
C73×#18652
C73×#17712
C73×#17632
#2903773