Finite Group Databasebeta

← C73×#26188 #32935592

Subgroups — C73×#26188 #32935592

Order 18688.

924 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C73C211yesmaximal, characteristic
2C2×#440×C73C211yesmaximal, characteristic, complemented
3C73×#2448C211yesmaximal, characteristic, complemented
4D4×C4⋊C4×C73C211yesmaximal, characteristic, complemented
5C73×#2093C211yesmaximal, characteristic, complemented
6C73×#2087C211yesmaximal, characteristic, complemented
7C73×#2072C211yesmaximal, characteristic, complemented
8C73×#2042C211yesmaximal, characteristic, complemented
9C73×#1936C211yesmaximal, characteristic, complemented
10C73×#1917C211yesmaximal, characteristic, complemented
11C73×#1879C211yesmaximal, characteristic
12C73×#1879C211yesmaximal, characteristic
13C73×#1877C211yesmaximal, characteristic, complemented
14C73×#1863C211yesmaximal, characteristic, complemented
15C73×#1862C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C2×#124×C73C2211yescharacteristic
19C2×C4×Q8×C73C2211yescharacteristic
20C2×C4×D4×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23C22×C4⋊C4×C73—21no—
24#463×C73—24no—
25#440×C73—24no—
26C2×#107×C73C2211yescharacteristic
27C2×#107×C73C2211yescharacteristic
28C2×C4⋊C8×C73C2211yescharacteristic
29C2×#103×C73C2211yescharacteristic
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#97×C73C2211yescharacteristic
38#399×C73—21no—
39#397×C73—21no—
40#391×C73C2211yescharacteristic
41#390×C73C2211yescharacteristic
42#390×C73C2211yescharacteristic
43#389×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#389×C73C2211yescharacteristic
46#388×C73—21no—
47#388×C73—21no—
48#385×C73—21no—
49#385×C73—21no—
50#384×C73C2211yescharacteristic
51#380×C73—21no—
52C4×C4⋊C4×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×D4×C73C2311yescharacteristic
63C22×D4×C73C2311yescharacteristic
64C23×C4×C73—21no—
65C23×C4×C73—21no—
66C23×C4×C73—21no—
67C2×SD16×C73—22no—
68C2×SD16×C73—22no—
69C2×SD16×C73D414yes—
70C2×D8×C73—22no—
71C2×D8×C73—22no—
72C2×D8×C73—22no—
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77#124×C73—22no—
78#124×C73—41no—
79C4×Q8×C73—22no—
80C4×Q8×C73—41no—
81C4×D4×C73—22no—
82C4×D4×C73—22no—
83C4×D4×C73—22no—
84C4×D4×C73—22no—
85C4×D4×C73—41no—
86C4×D4×C73—41no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—44no—
94C2×C4⋊C4×C73D411yescharacteristic
95C2×C4⋊C4×C73D411yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114#107×C73—22no—
115#107×C73—41no—
116C4⋊C8×C73—22no—
117#103×C73—22no—
118#103×C73—22no—
119#103×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—22no—
123#102×C73—22no—
124#102×C73—41no—
125#97×C73—22no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73D411yescharacteristic
132#95×C73D411yescharacteristic
133C24×C73—21no—
134C24×C73—21no—
135C2×Q8×C73—21no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73C2×D412yes—
141C2×D4×C73—21no—
142C2×D4×C73—21no—
143C2×D4×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73C2×D412yes—
151C2×D4×C73#4112yes—
152C2×D4×C73#4112yes—
153C22×C4×C73—24no—
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—42no—
161C22×C4×C73—42no—
162C22×C4×C73—42no—
163C22×C4×C73—42no—
164C22×C4×C73—42no—
165C22×C4×C73—42no—
166C22×C4×C73—81no—
167C22×C4×C73—81no—
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2411yescharacteristic
175SD16×C73—28no—
176D8×C73—44no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73C2×D412yes—
189C4⋊C4×C73—22no—
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—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—41no—
200C4⋊C4×C73—42no—
201C4⋊C4×C73—42no—
202C4⋊C4×C73—42no—
203C4⋊C4×C73—42no—
204C4⋊C4×C73—81no—
205C4⋊C4×C73—81no—
206C4⋊C4×C73#4112yes—
207C22⋊C4×C73—24no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—81no—
215C22⋊C4×C73—81no—
216C42×C73—21no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—42no—
223C23×C73—22no—
224C23×C73—22no—
225C23×C73—22no—
226C23×C73—41no—
227C23×C73—41no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73C22×D411yescharacteristic
238Q8×C73—22no—
239Q8×C73—22no—
240Q8×C73—41no—
241Q8×C73—41no—
242D4×C73—22no—
243D4×C73—22no—
244D4×C73—22no—
245D4×C73—41no—
246D4×C73—41no—
247D4×C73—41no—
248D4×C73—41no—
249D4×C73#12314yes—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—22no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—22no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—48no—
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—41no—
285C2×C4×C73—41no—
286C2×C4×C73—84no—
287C2×C4×C73—84no—
288C2×C4×C73AGL(1,ℤ/8)12yes—
289C2×C4×C73C22×D411yescharacteristic
290C2×C4×C73C2×#4111yescharacteristic
291C2×C4×C73C2×#4111yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73H(5,𝔽2)11yescharacteristic
294C2×C4×C732−1+411yescharacteristic
295C8×C73—22no—
296C8×C73—41no—
297C8×C73—41no—
298C8×C73—41no—
299C22×C73—24no—
300C22×C73—42no—
301C22×C73—42no—
302C22×C73—42no—
303C22×C73—42no—
304C22×C73—42no—
305C22×C73—42no—
306C22×C73—81no—
307C22×C73—81no—
308C22×C73—81no—
309C22×C73—81no—
310C22×C73—81no—
311C22×C73—81no—
312C22×C73—81no—
313C22×C73#52511yescharacteristic
314C22×C73D4211yescharacteristic
315C22×C73#54811yescharacteristic
316C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
317C22×C73#57511yescharacteristic
318C22×C73#57611yescharacteristic
319C22×C73#57811yescharacteristic
320C4×C73—22no—
321C4×C73—42no—
322C4×C73—41no—
323C4×C73—42no—
324C4×C73—41no—
325C4×C73—41no—
326C4×C73—41no—
327C4×C73—41no—
328C4×C73—81no—
329C4×C73—81no—
330C4×C73—81no—
331C4×C73—81no—
332C4×C73C2×#12311yescharacteristic
333C4×C73#53911yescharacteristic
334C4×C73#54711yescharacteristic
335C4×C73#55311yescharacteristic
336#26188C7311yesmaximal, characteristic, direct product factor, Sylow
337C2×C73—44no—
338C2×C73—161no—
339C2×C73#244311yescharacteristic
340C2×C73#311411yescharacteristic
341C2×C73#312411yescharacteristic
342C2×C73#326911yescharacteristic
343C2×C73#327411yescharacteristic
344C2×C73#336711yescharacteristic
345C2×C73#337011yescharacteristic
346C2×#463C2×C7311yescharacteristic
347C2×#440C2×C7311yescharacteristic, complemented
348#2448C2×C7311yescharacteristic, complemented
349D4×C4⋊C4C2×C7311yescharacteristic, complemented
350#2093C2×C7311yescharacteristic, complemented
351#2087C2×C7311yescharacteristic, complemented
352#2072C2×C7311yescharacteristic, complemented
353#2042C2×C7311yescharacteristic, complemented
354#1936C2×C7311yescharacteristic, complemented
355#1917C2×C7311yescharacteristic, complemented
356#1879C2×C7311yescharacteristic
357#1879C2×C7311yescharacteristic
358#1877C2×C7311yescharacteristic, complemented
359#1863C2×C7311yescharacteristic, complemented
360#1862C2×C7311yescharacteristic, complemented
361C73#2618811yescharacteristic, direct product factor, Sylow
362C22×SD16C22×C7311yescharacteristic
363C22×D8C22×C7311yescharacteristic
364C2×#124C22×C7311yescharacteristic
365C2×C4×Q8C22×C7311yescharacteristic
366C2×C4×D4C22×C7311yescharacteristic
367C2×C4×D4C22×C7311yescharacteristic
368C2×C4×D4C22×C7311yescharacteristic
369C22×C4⋊C4—21no—
370#463—24no—
371#440—24no—
372C2×#107C22×C7311yescharacteristic
373C2×#107C22×C7311yescharacteristic
374C2×C4⋊C8C22×C7311yescharacteristic
375C2×#103C22×C7311yescharacteristic
376C2×#103C22×C7311yescharacteristic
377C2×#103C22×C7311yescharacteristic
378C2×#102C22×C7311yescharacteristic
379C2×#102C22×C7311yescharacteristic
380C2×#102C22×C7311yescharacteristic
381C2×#102C22×C7311yescharacteristic
382C2×#102C22×C7311yescharacteristic
383C2×#97C22×C7311yescharacteristic
384#399—21no—
385#397—21no—
386#391C22×C7311yescharacteristic
387#390C22×C7311yescharacteristic
388#390C22×C7311yescharacteristic
389#389C22×C7311yescharacteristic
390#389C22×C7311yescharacteristic
391#389C22×C7311yescharacteristic
392#388—21no—
393#388—21no—
394#385—21no—
395#385—21no—
396#384C22×C7311yescharacteristic
397#380—21no—
398C4×C4⋊C4C22×C7311yescharacteristic
399#340C22×C7311yescharacteristic
400#340C22×C7311yescharacteristic
401#340C22×C7311yescharacteristic
402#340C22×C7311yescharacteristic
403#336C22×C7311yescharacteristic
404#336C22×C7311yescharacteristic
405#336C22×C7311yescharacteristic
406#336C22×C7311yescharacteristic
407C22×Q8C23×C7311yescharacteristic
408C22×D4C23×C7311yescharacteristic
409C22×D4C23×C7311yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—21no—
413C2×SD16—22no—
414C2×SD16—22no—
415C2×SD16D4×C7314yes—
416C2×D8—22no—
417C2×D8—22no—
418C2×D8—22no—
419C22×C8C23×C7311yescharacteristic
420C22×C8C23×C7311yescharacteristic
421C22×C8C23×C7311yescharacteristic
422C22×C8C23×C7311yescharacteristic
423#124—22no—
424#124—41no—
425C4×Q8—22no—
426C4×Q8—41no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—41no—
432C4×D4—41no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—44no—
440C2×C4⋊C4D4×C7311yescharacteristic
441C2×C4⋊C4D4×C7311yescharacteristic
442C2×C4⋊C4C23×C7311yescharacteristic
443C2×C4⋊C4C23×C7311yescharacteristic
444C2×C4⋊C4C23×C7311yescharacteristic
445C2×C4⋊C4C23×C7311yescharacteristic
446C2×C4⋊C4C23×C7311yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C42—21no—
457C2×C42C23×C7311yescharacteristic
458C2×C42C23×C7311yescharacteristic
459C2×C42C23×C7311yescharacteristic
460#107—22no—
461#107—41no—
462C4⋊C8—22no—
463#103—22no—
464#103—22no—
465#103—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—22no—
470#102—41no—
471#97—22no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95D4×C7311yescharacteristic
478#95D4×C7311yescharacteristic
479C24—21no—
480C24—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C2×D4×C7312yes—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4C2×D4×C7312yes—
497C2×D4#41×C7312yes—
498C2×D4#41×C7312yes—
499C22×C4—24no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4C2×D4×C7311yescharacteristic
515C22×C4C2×D4×C7311yescharacteristic
516C22×C4C2×D4×C7311yescharacteristic
517C22×C4C2×D4×C7311yescharacteristic
518C22×C4C2×D4×C7311yescharacteristic
519C22×C4C2×D4×C7311yescharacteristic
520C22×C4C24×C7311yescharacteristic
521SD16—28no—
522D8—44no—
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—
534C2×C8C2×D4×C7312yes—
535C4⋊C4—22no—
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—41no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4#41×C7312yes—
553C22⋊C4—24no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—42no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C22×D4×C7311yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—41no—
587Q8—41no—
588D4—22no—
589D4—22no—
590D4—22no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4#123×C7314yes—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—48no—
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—84no—
633C2×C4—84no—
634C2×C4AGL(1,ℤ/8)×C7312yes—
635C2×C4C22×D4×C7311yescharacteristic
636C2×C4C2×#41×C7311yescharacteristic
637C2×C4C2×#41×C7311yescharacteristic
638C2×C4C2×#41×C7311yescharacteristic
639C2×C4H(5,𝔽2)×C7311yescharacteristic
640C2×C42−1+4×C7311yescharacteristic
641C8—22no—
642C8—41no—
643C8—41no—
644C8—41no—
645C22—24no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22#525×C7311yescharacteristic
660C22D42×C7311yescharacteristic
661C22#548×C7311yescharacteristic
662C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
663C22#575×C7311yescharacteristic
664C22#576×C7311yescharacteristic
665C22#578×C7311yescharacteristic
666C4—22no—
667C4—42no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—42no—
673C4—41no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—81no—
678C4C2×#123×C7311yescharacteristic
679C4#539×C7311yescharacteristic
680C4#547×C7311yescharacteristic
681C4#553×C7311yescharacteristic
682C2—44no—
683C2—161no—
684C2C73×#244311yescharacteristic
685C2C73×#311411yescharacteristic
686C2C73×#312411yescharacteristic
687C2C73×#326911yescharacteristic
688C2C73×#327411yescharacteristic
689C2C73×#336711yescharacteristic
690C2C73×#337011yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D8×C73C22
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
2. C2×#440×C73C2semidirect
3. C73×#2448C2semidirect
4. D4×C4⋊C4×C73C2semidirect
5. C73×#2093C2semidirect
6. C73×#2087C2semidirect
7. C73×#2072C2semidirect
8. C73×#2042C2semidirect
9. C73×#1936C2semidirect
10. C73×#1917C2semidirect
13. C73×#1877C2semidirect
14. C73×#1863C2semidirect
15. C73×#1862C2semidirect
336. #26188C73direct (N × H)
347. C2×#440C2×C73semidirect
348. #2448C2×C73semidirect
349. D4×C4⋊C4C2×C73semidirect
350. #2093C2×C73semidirect
351. #2087C2×C73semidirect
352. #2072C2×C73semidirect
353. #2042C2×C73semidirect
354. #1936C2×C73semidirect
355. #1917C2×C73semidirect
358. #1877C2×C73semidirect
359. #1863C2×C73semidirect
360. #1862C2×C73semidirect
361. C73#26188direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#463×C732
C2×#440×C732
C73×#24482
D4×C4⋊C4×C732
C73×#20932
C73×#20872
C73×#20722
C73×#20422
C73×#19362
C73×#19172
C73×#18792
C73×#18772
C73×#18632
C73×#18622
#2618873