Finite Group Databasebeta

← C73×#24978 #32934382

Subgroups — C73×#24978 #32934382

Order 18688.

820 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2535C211yesmaximal, characteristic
2C73×#2354C211yesmaximal, characteristic, complemented
3C73×#2077C211yesmaximal, characteristic, complemented
4C73×#2075C211yesmaximal, characteristic, complemented
5C73×#2034C211yesmaximal, characteristic, complemented
6C73×#2033C211yesmaximal, characteristic, complemented
7C73×#1955C211yesmaximal, characteristic, complemented
8C73×#1949C211yesmaximal, characteristic, complemented
9C73×#1875C211yesmaximal, characteristic, complemented
10C73×#1875C211yesmaximal, characteristic, complemented
11C73×#1836C211yesmaximal, characteristic, complemented
12C73×#1825C211yesmaximal, characteristic, complemented
13C73×#1825C211yesmaximal, characteristic, complemented
14C73×#1802C211yesmaximal, characteristic, complemented
15C73×#1762C211yesmaximal, characteristic, complemented
16C2×#121×C73C2211yescharacteristic
17C2×#121×C73C2211yescharacteristic
18C2×C4×D4×C73C2211yescharacteristic
19C2×C4×D4×C73C2211yescharacteristic
20C2×#117×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22C2×#107×C73C2211yescharacteristic
23C2×#106×C73C2211yescharacteristic
24C2×C4⋊C8×C73C2211yescharacteristic
25C2×#102×C73C2211yescharacteristic
26C2×#102×C73C2211yescharacteristic
27C2×#102×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×C22⋊C8×C73C2211yescharacteristic
30C2×C22⋊C8×C73C2211yescharacteristic
31C2×C22⋊C8×C73C2211yescharacteristic
32C2×C22⋊C8×C73C2211yescharacteristic
33C2×#97×C73C2211yescharacteristic
34#397×C73—21no—
35#392×C73—21no—
36#390×C73—21no—
37#388×C73—21no—
38#388×C73—21no—
39#386×C73—21no—
40#386×C73—21no—
41#384×C73C2211yescharacteristic
42#382×C73C2211yescharacteristic
43#380×C73C2211yescharacteristic
44#380×C73C2211yescharacteristic
45#380×C73C2211yescharacteristic
46#380×C73C2211yescharacteristic
47C4×C4⋊C4×C73—21no—
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#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59C22×D4×C73—21no—
60C22×D4×C73—21no—
61C22×D4×C73D411yescharacteristic
62C22×D4×C73C2311yescharacteristic
63C23×C4×C73—21no—
64C23×C4×C73C2311yescharacteristic
65C23×C4×C73C2311yescharacteristic
66C22×C8×C73C2311yescharacteristic
67C22×C8×C73C2311yescharacteristic
68C22×C8×C73C2311yescharacteristic
69C22×C8×C73C2311yescharacteristic
70#121×C73—22no—
71#121×C73—22no—
72#121×C73—41no—
73#121×C73—41no—
74C4×D4×C73—22no—
75C4×D4×C73—22no—
76C4×D4×C73—22no—
77C4×D4×C73—22no—
78#117×C73—22no—
79#117×C73—22no—
80#117×C73—41no—
81#117×C73—41no—
82C2×C4⋊C4×C73—21no—
83C2×C4⋊C4×C73—21no—
84C2×C4⋊C4×C73D411yescharacteristic
85C2×C4⋊C4×C73C2311yescharacteristic
86C2×C4⋊C4×C73C2311yescharacteristic
87C2×C4⋊C4×C73C2311yescharacteristic
88C2×C4⋊C4×C73C2311yescharacteristic
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C22⋊C4×C73—21no—
93C2×C22⋊C4×C73—21no—
94C2×C22⋊C4×C73—21no—
95C2×C22⋊C4×C73—21no—
96C2×C22⋊C4×C73—21no—
97C2×C22⋊C4×C73—21no—
98C2×C22⋊C4×C73—21no—
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73D411yescharacteristic
102C2×C22⋊C4×C73D411yescharacteristic
103C2×C42×C73—21no—
104C2×C42×C73—21no—
105C2×C42×C73—21no—
106C2×C42×C73C2311yescharacteristic
107#107×C73—41no—
108#106×C73—41no—
109C4⋊C8×C73—22no—
110#102×C73—22no—
111#102×C73—22no—
112#102×C73—41no—
113#102×C73—41no—
114C22⋊C8×C73—41no—
115C22⋊C8×C73—41no—
116C22⋊C8×C73—41no—
117C22⋊C8×C73—41no—
118#97×C73—22no—
119#95×C73—21no—
120#95×C73—21no—
121#95×C73—21no—
122#95×C73—21no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126C24×C73—21no—
127C24×C73C2×D411yescharacteristic
128C24×C73C2×D411yescharacteristic
129C2×D4×C73—22no—
130C2×D4×C73—21no—
131C2×D4×C73—21no—
132C2×D4×C73—21no—
133C2×D4×C73—21no—
134C2×D4×C73—21no—
135C2×D4×C73—41no—
136C2×D4×C73—41no—
137C2×D4×C73—42no—
138C2×D4×C73—42no—
139C2×D4×C73—42no—
140C2×D4×C73—42no—
141C2×D4×C73—81no—
142C2×D4×C73—81no—
143C2×D4×C73#4112yes—
144C22×C4×C73—21no—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—42no—
164C22×C4×C73—81no—
165C22×C4×C73—81no—
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2411yescharacteristic
171C2×C8×C73—21no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C4⋊C4×C73—22no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—42no—
198C4⋊C4×C73—81no—
199C4⋊C4×C73#4112yes—
200C22⋊C4×C73—22no—
201C22⋊C4×C73—22no—
202C22⋊C4×C73—42no—
203C22⋊C4×C73—42no—
204C22⋊C4×C73—42no—
205C22⋊C4×C73—42no—
206C22⋊C4×C73—42no—
207C22⋊C4×C73—81no—
208C22⋊C4×C73—81no—
209C22⋊C4×C73—81no—
210C22⋊C4×C73—81no—
211C42×C73—42no—
212C42×C73—42no—
213C42×C73—42no—
214C42×C73#4112yes—
215C42×C73#4112yes—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—22no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73C22×D411yescharacteristic
238D4×C73—22no—
239D4×C73—22no—
240D4×C73—44no—
241D4×C73—41no—
242D4×C73—41no—
243D4×C73—84no—
244D4×C73—84no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—22no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—84no—
285C2×C4×C73#12312yes—
286C2×C4×C73#12312yes—
287C2×C4×C73C2×#4111yescharacteristic
288C2×C4×C73C2×#4111yescharacteristic
289C2×C4×C73C2×#4111yescharacteristic
290C2×C4×C73C2×#4111yescharacteristic
291C2×C4×C73H(5,𝔽2)11yescharacteristic
292C2×C4×C73H(5,𝔽2)11yescharacteristic
293C8×C73—41no—
294C8×C73—41no—
295C8×C73—41no—
296C8×C73—41no—
297C22×C73—41no—
298C22×C73—41no—
299C22×C73—41no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73—42no—
304C22×C73—41no—
305C22×C73—41no—
306C22×C73—41no—
307C22×C73—41no—
308C22×C73—41no—
309C22×C73—42no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73—42no—
313C22×C73—41no—
314C22×C73—81no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73C2×#12311yescharacteristic
319C22×C73#54611yescharacteristic
320C22×C73#54611yescharacteristic
321C22×C73#57511yescharacteristic
322C22×C73#57511yescharacteristic
323C22×C73#57611yescharacteristic
324C22×C73#57711yescharacteristic
325C4×C73—22no—
326C4×C73—22no—
327C4×C73—41no—
328C4×C73—41no—
329C4×C73—42no—
330C4×C73—81no—
331C4×C73—81no—
332C4×C73—81no—
333C4×C73—81no—
334C4×C73—81no—
335C4×C73—81no—
336C4×C73#52911yescharacteristic
337C4×C73#54011yescharacteristic
338C4×C73#55311yescharacteristic
339C4×C73#55511yescharacteristic
340#24978C7311yesmaximal, characteristic, direct product factor, Sylow
341C2×C73—81no—
342C2×C73—81no—
343C2×C73—82no—
344C2×C73#242011yescharacteristic
345C2×C73#309311yescharacteristic
346C2×C73#309611yescharacteristic
347C2×C73#330711yescharacteristic
348C2×C73#330911yescharacteristic
349C2×C73#331111yescharacteristic
350C2×C73#331911yescharacteristic
351#2535C2×C7311yescharacteristic
352#2354C2×C7311yescharacteristic, complemented
353#2077C2×C7311yescharacteristic, complemented
354#2075C2×C7311yescharacteristic, complemented
355#2034C2×C7311yescharacteristic, complemented
356#2033C2×C7311yescharacteristic, complemented
357#1955C2×C7311yescharacteristic, complemented
358#1949C2×C7311yescharacteristic, complemented
359#1875C2×C7311yescharacteristic, complemented
360#1875C2×C7311yescharacteristic, complemented
361#1836C2×C7311yescharacteristic, complemented
362#1825C2×C7311yescharacteristic, complemented
363#1825C2×C7311yescharacteristic, complemented
364#1802C2×C7311yescharacteristic, complemented
365#1762C2×C7311yescharacteristic, complemented
366C73#2497811yescharacteristic, direct product factor, Sylow
367C2×#121C22×C7311yescharacteristic
368C2×#121C22×C7311yescharacteristic
369C2×C4×D4C22×C7311yescharacteristic
370C2×C4×D4C22×C7311yescharacteristic
371C2×#117C22×C7311yescharacteristic
372C2×#117C22×C7311yescharacteristic
373C2×#107C22×C7311yescharacteristic
374C2×#106C22×C7311yescharacteristic
375C2×C4⋊C8C22×C7311yescharacteristic
376C2×#102C22×C7311yescharacteristic
377C2×#102C22×C7311yescharacteristic
378C2×#102C22×C7311yescharacteristic
379C2×#102C22×C7311yescharacteristic
380C2×C22⋊C8C22×C7311yescharacteristic
381C2×C22⋊C8C22×C7311yescharacteristic
382C2×C22⋊C8C22×C7311yescharacteristic
383C2×C22⋊C8C22×C7311yescharacteristic
384C2×#97C22×C7311yescharacteristic
385#397—21no—
386#392—21no—
387#390—21no—
388#388—21no—
389#388—21no—
390#386—21no—
391#386—21no—
392#384C22×C7311yescharacteristic
393#382C22×C7311yescharacteristic
394#380C22×C7311yescharacteristic
395#380C22×C7311yescharacteristic
396#380C22×C7311yescharacteristic
397#380C22×C7311yescharacteristic
398C4×C4⋊C4—21no—
399C4×C4⋊C4C22×C7311yescharacteristic
400#340C22×C7311yescharacteristic
401#340C22×C7311yescharacteristic
402#340C22×C7311yescharacteristic
403#340C22×C7311yescharacteristic
404#340C22×C7311yescharacteristic
405#340C22×C7311yescharacteristic
406#340C22×C7311yescharacteristic
407#340C22×C7311yescharacteristic
408#340C22×C7311yescharacteristic
409#340C22×C7311yescharacteristic
410C22×D4—21no—
411C22×D4—21no—
412C22×D4D4×C7311yescharacteristic
413C22×D4C23×C7311yescharacteristic
414C23×C4—21no—
415C23×C4C23×C7311yescharacteristic
416C23×C4C23×C7311yescharacteristic
417C22×C8C23×C7311yescharacteristic
418C22×C8C23×C7311yescharacteristic
419C22×C8C23×C7311yescharacteristic
420C22×C8C23×C7311yescharacteristic
421#121—22no—
422#121—22no—
423#121—41no—
424#121—41no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—22no—
429#117—22no—
430#117—22no—
431#117—41no—
432#117—41no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4D4×C7311yescharacteristic
436C2×C4⋊C4C23×C7311yescharacteristic
437C2×C4⋊C4C23×C7311yescharacteristic
438C2×C4⋊C4C23×C7311yescharacteristic
439C2×C4⋊C4C23×C7311yescharacteristic
440C2×C4⋊C4C23×C7311yescharacteristic
441C2×C4⋊C4C23×C7311yescharacteristic
442C2×C4⋊C4C23×C7311yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4D4×C7311yescharacteristic
453C2×C22⋊C4D4×C7311yescharacteristic
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42C23×C7311yescharacteristic
458#107—41no—
459#106—41no—
460C4⋊C8—22no—
461#102—22no—
462#102—22no—
463#102—41no—
464#102—41no—
465C22⋊C8—41no—
466C22⋊C8—41no—
467C22⋊C8—41no—
468C22⋊C8—41no—
469#97—22no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477C24—21no—
478C24C2×D4×C7311yescharacteristic
479C24C2×D4×C7311yescharacteristic
480C2×D4—22no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—81no—
493C2×D4—81no—
494C2×D4#41×C7312yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4C2×D4×C7311yescharacteristic
518C22×C4C2×D4×C7311yescharacteristic
519C22×C4C2×D4×C7311yescharacteristic
520C22×C4C2×D4×C7311yescharacteristic
521C22×C4C24×C7311yescharacteristic
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—81no—
550C4⋊C4#41×C7312yes—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C42—42no—
563C42—42no—
564C42—42no—
565C42#41×C7312yes—
566C42#41×C7312yes—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—22no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C22×D4×C7311yescharacteristic
589D4—22no—
590D4—22no—
591D4—44no—
592D4—41no—
593D4—41no—
594D4—84no—
595D4—84no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4#123×C7312yes—
637C2×C4#123×C7312yes—
638C2×C4C2×#41×C7311yescharacteristic
639C2×C4C2×#41×C7311yescharacteristic
640C2×C4C2×#41×C7311yescharacteristic
641C2×C4C2×#41×C7311yescharacteristic
642C2×C4H(5,𝔽2)×C7311yescharacteristic
643C2×C4H(5,𝔽2)×C7311yescharacteristic
644C8—41no—
645C8—41no—
646C8—41no—
647C8—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—42no—
654C22—41no—
655C22—41no—
656C22—42no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22C2×#123×C7311yescharacteristic
670C22#546×C7311yescharacteristic
671C22#546×C7311yescharacteristic
672C22#575×C7311yescharacteristic
673C22#575×C7311yescharacteristic
674C22#576×C7311yescharacteristic
675C22#577×C7311yescharacteristic
676C4—22no—
677C4—22no—
678C4—42no—
679C4—41no—
680C4—41no—
681C4—81no—
682C4—81no—
683C4—81no—
684C4—81no—
685C4—81no—
686C4—81no—
687C4#529×C7311yescharacteristic
688C4#540×C7311yescharacteristic
689C4#553×C7311yescharacteristic
690C4#555×C7311yescharacteristic
691C2—81no—
692C2—81no—
693C2—82no—
694C2C73×#242011yescharacteristic
695C2C73×#309311yescharacteristic
696C2C73×#309611yescharacteristic
697C2C73×#330711yescharacteristic
698C2C73×#330911yescharacteristic
699C2C73×#331111yescharacteristic
700C2C73×#331911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2354C2semidirect
3. C73×#2077C2semidirect
4. C73×#2075C2semidirect
5. C73×#2034C2semidirect
6. C73×#2033C2semidirect
7. C73×#1955C2semidirect
8. C73×#1949C2semidirect
9. C73×#1875C2semidirect
10. C73×#1875C2semidirect
11. C73×#1836C2semidirect
12. C73×#1825C2semidirect
13. C73×#1825C2semidirect
14. C73×#1802C2semidirect
15. C73×#1762C2semidirect
340. #24978C73direct (N × H)
352. #2354C2×C73semidirect
353. #2077C2×C73semidirect
354. #2075C2×C73semidirect
355. #2034C2×C73semidirect
356. #2033C2×C73semidirect
357. #1955C2×C73semidirect
358. #1949C2×C73semidirect
359. #1875C2×C73semidirect
360. #1875C2×C73semidirect
361. #1836C2×C73semidirect
362. #1825C2×C73semidirect
363. #1825C2×C73semidirect
364. #1802C2×C73semidirect
365. #1762C2×C73semidirect
366. C73#24978direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#25352
C73×#23542
C73×#20772
C73×#20752
C73×#20342
C73×#20332
C73×#19552
C73×#19492
C73×#18752
C73×#18362
C73×#18252
C73×#18022
C73×#17622
#2497873