Finite Group Databasebeta

← C73×#28950 #32938354

Subgroups — C73×#28950 #32938354

Order 18688.

682 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2509C211yesmaximal, characteristic, complemented
2C73×#2454C211yesmaximal, characteristic
3C73×#2092C211yesmaximal, characteristic
4C73×#2088C211yesmaximal, characteristic, complemented
5C73×#2065C211yesmaximal, characteristic
6C73×#2059C211yesmaximal, characteristic, complemented
7C73×#1991C211yesmaximal, characteristic, complemented
8C73×#1942C211yesmaximal, characteristic, complemented
9C73×#1941C211yesmaximal, characteristic, complemented
10C73×#1934C211yesmaximal, characteristic
11C73×#1934C211yesmaximal, characteristic
12C73×#1921C211yesmaximal, characteristic, complemented
13C73×#1862C211yesmaximal, characteristic
14C8×C4⋊C4×C73C211yesmaximal, characteristic, complemented
15C4×#102×C73C211yesmaximal, characteristic
16C2×#125×C73C2211yescharacteristic
17C2×C4×D4×C73C2211yescharacteristic
18C2×#107×C73C2211yescharacteristic
19C2×#107×C73C2211yescharacteristic
20C2×#106×C73C2211yescharacteristic
21C2×#106×C73C2211yescharacteristic
22C2×C4⋊C8×C73C2211yescharacteristic
23C2×#102×C73C2211yescharacteristic
24C2×#102×C73C2211yescharacteristic
25C2×#102×C73C2211yescharacteristic
26C2×#102×C73C2211yescharacteristic
27C2×C4×C8×C73C2211yescharacteristic
28C2×C4×C8×C73C2211yescharacteristic
29C2×C4×C8×C73C2211yescharacteristic
30#400×C73—21no—
31#400×C73—21no—
32#399×C73—21no—
33#396×C73—21no—
34#390×C73C2211yescharacteristic
35#390×C73C2211yescharacteristic
36#389×C73—21no—
37#389×C73C2211yescharacteristic
38#389×C73C2211yescharacteristic
39#389×C73C2211yescharacteristic
40#389×C73C2211yescharacteristic
41#389×C73C2211yescharacteristic
42#389×C73C2211yescharacteristic
43#387×C73—21no—
44#385×C73—21no—
45#382×C73C2211yescharacteristic
46#380×C73—21no—
47C4×C4⋊C4×C73C2211yescharacteristic
48C4×C4⋊C4×C73C2211yescharacteristic
49#340×C73C2211yescharacteristic
50#340×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×D4×C73C2311yescharacteristic
60C23×C4×C73—21no—
61C22×C8×C73C2311yescharacteristic
62C22×C8×C73C2311yescharacteristic
63C22×C8×C73C2311yescharacteristic
64C22×C8×C73C2311yescharacteristic
65#125×C73—22no—
66#125×C73—41no—
67C4×D4×C73—22no—
68C4×D4×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×C73—21no—
76C2×C4⋊C4×C73—21no—
77C2×C4⋊C4×C73D411yescharacteristic
78C2×C4⋊C4×C73D411yescharacteristic
79C2×C4⋊C4×C73C2311yescharacteristic
80C2×C4⋊C4×C73C2311yescharacteristic
81C2×C4⋊C4×C73C2311yescharacteristic
82C2×C4⋊C4×C73C2311yescharacteristic
83C2×C4⋊C4×C73C2311yescharacteristic
84C2×C4⋊C4×C73C2311yescharacteristic
85C2×C4⋊C4×C73C2311yescharacteristic
86C2×C22⋊C4×C73—21no—
87C2×C22⋊C4×C73—21no—
88C2×C22⋊C4×C73—21no—
89C2×C22⋊C4×C73—21no—
90C2×C22⋊C4×C73—21no—
91C2×C42×C73—21no—
92C2×C42×C73C2311yescharacteristic
93C2×C42×C73C2311yescharacteristic
94C2×C42×C73C2311yescharacteristic
95#107×C73—22no—
96#107×C73—22no—
97#106×C73—22no—
98#106×C73—41no—
99C4⋊C8×C73—22no—
100#102×C73—22no—
101#102×C73—22no—
102#102×C73—41no—
103#102×C73Q814yes—
104C4×C8×C73—22no—
105C4×C8×C73—41no—
106C4×C8×C73—41no—
107#95×C73—21no—
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×C73D411yescharacteristic
117#95×C73D411yescharacteristic
118C24×C73—21no—
119C2×D4×C73—21no—
120C2×D4×C73—21no—
121C2×D4×C73—21no—
122C2×D4×C73—21no—
123C2×D4×C73—21no—
124C2×D4×C73C2×Q812yes—
125C22×C4×C73—21no—
126C22×C4×C73—21no—
127C22×C4×C73—21no—
128C22×C4×C73—21no—
129C22×C4×C73—21no—
130C22×C4×C73—21no—
131C22×C4×C73—21no—
132C22×C4×C73—42no—
133C22×C4×C73—42no—
134C22×C4×C73—81no—
135C22×C4×C73C2×D411yescharacteristic
136C22×C4×C73C2×D411yescharacteristic
137C22×C4×C73C2×D411yescharacteristic
138C22×C4×C73C2×D411yescharacteristic
139C22×C4×C73C2×D411yescharacteristic
140C22×C4×C73C2×D411yescharacteristic
141C22×C4×C73C2411yescharacteristic
142C2×C8×C73—21no—
143C2×C8×C73—21no—
144C2×C8×C73—21no—
145C2×C8×C73—21no—
146C2×C8×C73—21no—
147C2×C8×C73—21no—
148C2×C8×C73—21no—
149C2×C8×C73—21no—
150C2×C8×C73—21no—
151C2×C8×C73C2×Q812yes—
152C2×C8×C73#4112yes—
153C2×C8×C73#4112yes—
154C4⋊C4×C73—22no—
155C4⋊C4×C73—22no—
156C4⋊C4×C73—21no—
157C4⋊C4×C73—21no—
158C4⋊C4×C73—21no—
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—42no—
169C4⋊C4×C73—42no—
170C4⋊C4×C73—42no—
171C4⋊C4×C73—42no—
172C4⋊C4×C73—81no—
173C4⋊C4×C73—81no—
174C4⋊C4×C73—81no—
175C4⋊C4×C73—81no—
176C4⋊C4×C73C2×Q812yes—
177C4⋊C4×C73#4112yes—
178C22⋊C4×C73—42no—
179C22⋊C4×C73—42no—
180C22⋊C4×C73—81no—
181C22⋊C4×C73—81no—
182C22⋊C4×C73—81no—
183C42×C73—21no—
184C42×C73—21no—
185C42×C73—21no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—81no—
190C23×C73—22no—
191C23×C73—41no—
192C23×C73—41no—
193C23×C73—41no—
194C23×C73—41no—
195C23×C73—41no—
196C23×C73—41no—
197C23×C73C22×D411yescharacteristic
198D4×C73—22no—
199D4×C73—22no—
200D4×C73—41no—
201D4×C73—41no—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—22no—
211C2×C4×C73—22no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
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—84no—
240C2×C4×C73#13512yes—
241C2×C4×C73#13512yes—
242C2×C4×C73C22×Q811yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C2×C4×C73C2×#4111yescharacteristic
246C2×C4×C73H(5,𝔽2)11yescharacteristic
247C2×C4×C732−1+411yescharacteristic
248C8×C73—22no—
249C8×C73—22no—
250C8×C73—22no—
251C8×C73—41no—
252C22×C73—42no—
253C22×C73—42no—
254C22×C73—42no—
255C22×C73—81no—
256C22×C73—81no—
257C22×C73—81no—
258C22×C73—81no—
259C22×C73#53211yescharacteristic
260C22×C73#54611yescharacteristic
261C22×C73D4×Q811yescharacteristic
262C22×C73C2×#13511yescharacteristic
263C22×C73C2×#13511yescharacteristic
264C22×C73#57611yescharacteristic
265C22×C73#57711yescharacteristic
266C4×C73—22no—
267C4×C73—22no—
268C4×C73—42no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73—42no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—81no—
275C4×C73—81no—
276C4×C73—81no—
277C4×C73—81no—
278C4×C73—81no—
279C4×C73#53311yescharacteristic
280C4×C73#53911yescharacteristic
281C4×C73#55211yescharacteristic
282C4×C73#55411yescharacteristic
283#28950C7311yesmaximal, characteristic, direct product factor, Sylow
284C2×C73—82no—
285C2×C73#255611yescharacteristic
286C2×C73#316811yescharacteristic
287C2×C73#317911yescharacteristic
288C2×C73#329711yescharacteristic
289C2×C73#330411yescharacteristic
290C2×C73#338011yescharacteristic
291C2×C73#338111yescharacteristic
292#2509C2×C7311yescharacteristic, complemented
293#2454C2×C7311yescharacteristic
294#2092C2×C7311yescharacteristic
295#2088C2×C7311yescharacteristic, complemented
296#2065C2×C7311yescharacteristic
297#2059C2×C7311yescharacteristic, complemented
298#1991C2×C7311yescharacteristic, complemented
299#1942C2×C7311yescharacteristic, complemented
300#1941C2×C7311yescharacteristic, complemented
301#1934C2×C7311yescharacteristic
302#1934C2×C7311yescharacteristic
303#1921C2×C7311yescharacteristic, complemented
304#1862C2×C7311yescharacteristic
305C8×C4⋊C4C2×C7311yescharacteristic, complemented
306C4×#102C2×C7311yescharacteristic
307C73#2895011yescharacteristic, direct product factor, Sylow
308C2×#125C22×C7311yescharacteristic
309C2×C4×D4C22×C7311yescharacteristic
310C2×#107C22×C7311yescharacteristic
311C2×#107C22×C7311yescharacteristic
312C2×#106C22×C7311yescharacteristic
313C2×#106C22×C7311yescharacteristic
314C2×C4⋊C8C22×C7311yescharacteristic
315C2×#102C22×C7311yescharacteristic
316C2×#102C22×C7311yescharacteristic
317C2×#102C22×C7311yescharacteristic
318C2×#102C22×C7311yescharacteristic
319C2×C4×C8C22×C7311yescharacteristic
320C2×C4×C8C22×C7311yescharacteristic
321C2×C4×C8C22×C7311yescharacteristic
322#400—21no—
323#400—21no—
324#399—21no—
325#396—21no—
326#390C22×C7311yescharacteristic
327#390C22×C7311yescharacteristic
328#389—21no—
329#389C22×C7311yescharacteristic
330#389C22×C7311yescharacteristic
331#389C22×C7311yescharacteristic
332#389C22×C7311yescharacteristic
333#389C22×C7311yescharacteristic
334#389C22×C7311yescharacteristic
335#387—21no—
336#385—21no—
337#382C22×C7311yescharacteristic
338#380—21no—
339C4×C4⋊C4C22×C7311yescharacteristic
340C4×C4⋊C4C22×C7311yescharacteristic
341#340C22×C7311yescharacteristic
342#340C22×C7311yescharacteristic
343#340C22×C7311yescharacteristic
344#340C22×C7311yescharacteristic
345#340C22×C7311yescharacteristic
346#340C22×C7311yescharacteristic
347#340C22×C7311yescharacteristic
348#340C22×C7311yescharacteristic
349#336C22×C7311yescharacteristic
350#336C22×C7311yescharacteristic
351C22×D4C23×C7311yescharacteristic
352C23×C4—21no—
353C22×C8C23×C7311yescharacteristic
354C22×C8C23×C7311yescharacteristic
355C22×C8C23×C7311yescharacteristic
356C22×C8C23×C7311yescharacteristic
357#125—22no—
358#125—41no—
359C4×D4—22no—
360C4×D4—41no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4D4×C7311yescharacteristic
370C2×C4⋊C4D4×C7311yescharacteristic
371C2×C4⋊C4C23×C7311yescharacteristic
372C2×C4⋊C4C23×C7311yescharacteristic
373C2×C4⋊C4C23×C7311yescharacteristic
374C2×C4⋊C4C23×C7311yescharacteristic
375C2×C4⋊C4C23×C7311yescharacteristic
376C2×C4⋊C4C23×C7311yescharacteristic
377C2×C4⋊C4C23×C7311yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C42—21no—
384C2×C42C23×C7311yescharacteristic
385C2×C42C23×C7311yescharacteristic
386C2×C42C23×C7311yescharacteristic
387#107—22no—
388#107—22no—
389#106—22no—
390#106—41no—
391C4⋊C8—22no—
392#102—22no—
393#102—22no—
394#102—41no—
395#102Q8×C7314yes—
396C4×C8—22no—
397C4×C8—41no—
398C4×C8—41no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95D4×C7311yescharacteristic
409#95D4×C7311yescharacteristic
410C24—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4C2×Q8×C7312yes—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—81no—
427C22×C4C2×D4×C7311yescharacteristic
428C22×C4C2×D4×C7311yescharacteristic
429C22×C4C2×D4×C7311yescharacteristic
430C22×C4C2×D4×C7311yescharacteristic
431C22×C4C2×D4×C7311yescharacteristic
432C22×C4C2×D4×C7311yescharacteristic
433C22×C4C24×C7311yescharacteristic
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8C2×Q8×C7312yes—
444C2×C8#41×C7312yes—
445C2×C8#41×C7312yes—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4C2×Q8×C7312yes—
469C4⋊C4#41×C7312yes—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—81no—
482C23—22no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23C22×D4×C7311yescharacteristic
490D4—22no—
491D4—22no—
492D4—41no—
493D4—41no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—84no—
532C2×C4#135×C7312yes—
533C2×C4#135×C7312yes—
534C2×C4C22×Q8×C7311yescharacteristic
535C2×C4C2×#41×C7311yescharacteristic
536C2×C4C2×#41×C7311yescharacteristic
537C2×C4C2×#41×C7311yescharacteristic
538C2×C4H(5,𝔽2)×C7311yescharacteristic
539C2×C42−1+4×C7311yescharacteristic
540C8—22no—
541C8—22no—
542C8—22no—
543C8—41no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22#532×C7311yescharacteristic
552C22#546×C7311yescharacteristic
553C22D4×Q8×C7311yescharacteristic
554C22C2×#135×C7311yescharacteristic
555C22C2×#135×C7311yescharacteristic
556C22#576×C7311yescharacteristic
557C22#577×C7311yescharacteristic
558C4—22no—
559C4—22no—
560C4—41no—
561C4—42no—
562C4—41no—
563C4—41no—
564C4—42no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4#533×C7311yescharacteristic
572C4#539×C7311yescharacteristic
573C4#552×C7311yescharacteristic
574C4#554×C7311yescharacteristic
575C2—82no—
576C2C73×#255611yescharacteristic
577C2C73×#316811yescharacteristic
578C2C73×#317911yescharacteristic
579C2C73×#329711yescharacteristic
580C2C73×#330411yescharacteristic
581C2C73×#338011yescharacteristic
582C2C73×#338111yescharacteristic
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×#2509C2semidirect
4. C73×#2088C2semidirect
6. C73×#2059C2semidirect
7. C73×#1991C2semidirect
8. C73×#1942C2semidirect
9. C73×#1941C2semidirect
12. C73×#1921C2semidirect
14. C8×C4⋊C4×C73C2semidirect
283. #28950C73direct (N × H)
292. #2509C2×C73semidirect
295. #2088C2×C73semidirect
297. #2059C2×C73semidirect
298. #1991C2×C73semidirect
299. #1942C2×C73semidirect
300. #1941C2×C73semidirect
303. #1921C2×C73semidirect
305. C8×C4⋊C4C2×C73semidirect
307. C73#28950direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#25092
C73×#24542
C73×#20922
C73×#20882
C73×#20652
C73×#20592
C73×#19912
C73×#19422
C73×#19412
C73×#19342
C73×#19212
C73×#18622
C8×C4⋊C4×C732
C4×#102×C732
#2895073