Finite Group Databasebeta

← C73×#23108 #32932512

Subgroups — C73×#23108 #32932512

Order 18688.

994 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C73C211yesmaximal, characteristic
2C73×#2366C211yesmaximal, characteristic, complemented
3C73×#2357C211yesmaximal, characteristic, complemented
4C73×#1972C211yesmaximal, characteristic, complemented
5C73×#1970C211yesmaximal, characteristic, complemented
6C73×#1961C211yesmaximal, characteristic, complemented
7C73×#1949C211yesmaximal, characteristic, complemented
8C73×#1926C211yesmaximal, characteristic, complemented
9C73×#1925C211yesmaximal, characteristic, complemented
10C73×#1879C211yesmaximal, characteristic, complemented
11C73×#1879C211yesmaximal, characteristic, complemented
12C73×#1771C211yesmaximal, characteristic, complemented
13C73×#1762C211yesmaximal, characteristic, complemented
14C73×#1762C211yesmaximal, characteristic, complemented
15C4×#102×C73C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C2×#127×C73C2211yescharacteristic
19C2×C4×D4×C73—21no—
20C2×C4×D4×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23#459×C73C418yescomplemented
24C2×#107×C73C2211yescharacteristic
25C2×#106×C73C2211yescharacteristic
26C2×C4⋊C8×C73C2211yescharacteristic
27C2×#102×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#97×C73C2211yescharacteristic
36C2×#97×C73C2211yescharacteristic
37C2×C4×C8×C73C2211yescharacteristic
38#390×C73—21no—
39#390×C73C2211yescharacteristic
40#390×C73C2211yescharacteristic
41#390×C73C2211yescharacteristic
42#390×C73C2211yescharacteristic
43#388×C73—21no—
44#388×C73—21no—
45#386×C73—21no—
46#386×C73—21no—
47#382×C73C2211yescharacteristic
48#381×C73—21no—
49C4×C4⋊C4×C73C2211yescharacteristic
50C4×C4⋊C4×C73C2211yescharacteristic
51C4×C4⋊C4×C73C2211yescharacteristic
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C22⋊C4×C73—21no—
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C22×D4×C73—21no—
61C22×D4×C73—21no—
62C22×D4×C73C2311yescharacteristic
63C22×D4×C73C2311yescharacteristic
64C22×D4×C73C2311yescharacteristic
65C23×C4×C73—21no—
66C23×C4×C73—21no—
67C23×C4×C73—21no—
68C2×D8×C73—41no—
69C2×D8×C73—41no—
70C2×D8×C73—41no—
71C2×D8×C73—41no—
72C2×D8×C73C2×C414yescomplemented
73C2×D8×C73C2×C414yescomplemented
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78#127×C73—22no—
79#127×C73C2×C414yes—
80C4×D4×C73—22no—
81C4×D4×C73—22no—
82C4×D4×C73—22no—
83C4×D4×C73—41no—
84C4×D4×C73—41no—
85C4×D4×C73—44no—
86C4×D4×C73C2×C414yescomplemented
87C2×C4⋊C4×C73D411yescharacteristic
88C2×C4⋊C4×C73D411yescharacteristic
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C42×C73—21no—
106C2×C42×C73—21no—
107C2×C42×C73—21no—
108C2×C42×C73C2311yescharacteristic
109C2×C42×C73C2311yescharacteristic
110C2×C42×C73C2311yescharacteristic
111#107×C73—41no—
112#106×C73—41no—
113C4⋊C8×C73C2×C414yescomplemented
114#102×C73—22no—
115#102×C73—22no—
116#102×C73—22no—
117#102×C73—22no—
118#102×C73—41no—
119#102×C73—41no—
120#102×C73C2×C414yescomplemented
121#102×C73C2×C414yescomplemented
122#97×C73—22no—
123#97×C73—41no—
124C4×C8×C73—41no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73D411yescharacteristic
131#95×C73D411yescharacteristic
132C24×C73—21no—
133C24×C73—21no—
134C24×C73—21no—
135C2×D4×C73—24no—
136C2×D4×C73—24no—
137C2×D4×C73—21no—
138C2×D4×C73—21no—
139C2×D4×C73—21no—
140C2×D4×C73—21no—
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×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—42no—
153C2×D4×C73—42no—
154C2×D4×C73—81no—
155C2×D4×C73—81no—
156C2×D4×C73C22×C412yes—
157C2×D4×C73C22×C412yes—
158C2×D4×C73C22×C412yes—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—24no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—42no—
168C22×C4×C73—42no—
169C22×C4×C73—81no—
170C22×C4×C73—81no—
171C22×C4×C73—81no—
172C22×C4×C73—81no—
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2411yescharacteristic
180D8×C73—44no—
181D8×C73—44no—
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×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73C22×C412yes—
192C2×C8×C73C22×C412yes—
193C2×C8×C73#4112yes—
194C4⋊C4×C73—22no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—41no—
204C4⋊C4×C73C22×C412yes—
205C4⋊C4×C73#4112yes—
206C22⋊C4×C73—24no—
207C22⋊C4×C73—42no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—81no—
214C22⋊C4×C73—81no—
215C22⋊C4×C73—81no—
216C22⋊C4×C73—81no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—42no—
222C42×C73—81no—
223C42×C73—81no—
224C42×C73C22×C412yes—
225C42×C73#4112yes—
226C23×C73—22no—
227C23×C73—22no—
228C23×C73—22no—
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×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73C22×D411yescharacteristic
248D4×C73—22no—
249D4×C73—22no—
250D4×C73—22no—
251D4×C73—22no—
252D4×C73—22no—
253D4×C73—22no—
254D4×C73—48no—
255D4×C73—41no—
256D4×C73—41no—
257D4×C73—41no—
258D4×C73—41no—
259D4×C73—41no—
260D4×C73—41no—
261D4×C73—84no—
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—22no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—22no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
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—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—84no—
293C2×C4×C73—84no—
294C2×C4×C73—84no—
295C2×C4×C73C4×D412yes—
296C2×C4×C73C4×D412yes—
297C2×C4×C73AGL(1,ℤ/8)12yes—
298C2×C4×C73C23×C411yescharacteristic
299C2×C4×C73C2×#4111yescharacteristic
300C2×C4×C73C2×#4111yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C8×C73—22no—
305C8×C73—22no—
306C8×C73—22no—
307C8×C73—41no—
308C22×C73—42no—
309C22×C73—42no—
310C22×C73—42no—
311C22×C73—42no—
312C22×C73—42no—
313C22×C73—42no—
314C22×C73—42no—
315C22×C73—42no—
316C22×C73—42no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73—81no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73—81no—
326C22×C73—81no—
327C22×C73—81no—
328C22×C73—81no—
329C22×C73C2×C4×D411yescharacteristic
330C22×C73#54611yescharacteristic
331C22×C73#55011yescharacteristic
332C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C73#57511yescharacteristic
334C22×C73#57611yescharacteristic
335C22×C73#57611yescharacteristic
336C4×C73—22no—
337C4×C73—22no—
338C4×C73—22no—
339C4×C73—42no—
340C4×C73—41no—
341C4×C73—41no—
342C4×C73—41no—
343C4×C73—42no—
344C4×C73—81no—
345C4×C73—81no—
346C4×C73—81no—
347C4×C73C4×#4111yescharacteristic
348C4×C73#51811yescharacteristic
349C4×C73#55311yescharacteristic
350C4×C73#55511yescharacteristic
351#23108C7311yesmaximal, characteristic, direct product factor, Sylow
352C2×C73—82no—
353C2×C73—82no—
354C2×C73—82no—
355C2×C73#236311yescharacteristic
356C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
357C2×C73#294811yescharacteristic
358C2×C73#330911yescharacteristic
359C2×C73#331811yescharacteristic
360C2×C73#339911yescharacteristic
361C2×C73#340311yescharacteristic
362C2×#459C2×C7311yescharacteristic
363#2366C2×C7311yescharacteristic, complemented
364#2357C2×C7311yescharacteristic, complemented
365#1972C2×C7311yescharacteristic, complemented
366#1970C2×C7311yescharacteristic, complemented
367#1961C2×C7311yescharacteristic, complemented
368#1949C2×C7311yescharacteristic, complemented
369#1926C2×C7311yescharacteristic, complemented
370#1925C2×C7311yescharacteristic, complemented
371#1879C2×C7311yescharacteristic, complemented
372#1879C2×C7311yescharacteristic, complemented
373#1771C2×C7311yescharacteristic, complemented
374#1762C2×C7311yescharacteristic, complemented
375#1762C2×C7311yescharacteristic, complemented
376C4×#102C2×C7311yescharacteristic, complemented
377C73#2310811yescharacteristic, direct product factor, Sylow
378C22×D8C22×C7311yescharacteristic
379C22×D8C22×C7311yescharacteristic
380C2×#127C22×C7311yescharacteristic
381C2×C4×D4—21no—
382C2×C4×D4C22×C7311yescharacteristic
383C2×C4×D4C22×C7311yescharacteristic
384C2×C4×D4C22×C7311yescharacteristic
385#459C4×C7318yescomplemented
386C2×#107C22×C7311yescharacteristic
387C2×#106C22×C7311yescharacteristic
388C2×C4⋊C8C22×C7311yescharacteristic
389C2×#102C22×C7311yescharacteristic
390C2×#102C22×C7311yescharacteristic
391C2×#102C22×C7311yescharacteristic
392C2×#102C22×C7311yescharacteristic
393C2×#102C22×C7311yescharacteristic
394C2×#102C22×C7311yescharacteristic
395C2×#102C22×C7311yescharacteristic
396C2×#102C22×C7311yescharacteristic
397C2×#97C22×C7311yescharacteristic
398C2×#97C22×C7311yescharacteristic
399C2×C4×C8C22×C7311yescharacteristic
400#390—21no—
401#390C22×C7311yescharacteristic
402#390C22×C7311yescharacteristic
403#390C22×C7311yescharacteristic
404#390C22×C7311yescharacteristic
405#388—21no—
406#388—21no—
407#386—21no—
408#386—21no—
409#382C22×C7311yescharacteristic
410#381—21no—
411C4×C4⋊C4C22×C7311yescharacteristic
412C4×C4⋊C4C22×C7311yescharacteristic
413C4×C4⋊C4C22×C7311yescharacteristic
414C4×C4⋊C4C22×C7311yescharacteristic
415C4×C22⋊C4—21no—
416#340C22×C7311yescharacteristic
417#340C22×C7311yescharacteristic
418#340C22×C7311yescharacteristic
419#340C22×C7311yescharacteristic
420#336C22×C7311yescharacteristic
421#336C22×C7311yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C23×C7311yescharacteristic
425C22×D4C23×C7311yescharacteristic
426C22×D4C23×C7311yescharacteristic
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—21no—
430C2×D8—41no—
431C2×D8—41no—
432C2×D8—41no—
433C2×D8—41no—
434C2×D8C2×C4×C7314yescomplemented
435C2×D8C2×C4×C7314yescomplemented
436C22×C8C23×C7311yescharacteristic
437C22×C8C23×C7311yescharacteristic
438C22×C8C23×C7311yescharacteristic
439C22×C8C23×C7311yescharacteristic
440#127—22no—
441#127C2×C4×C7314yes—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—44no—
448C4×D4C2×C4×C7314yescomplemented
449C2×C4⋊C4D4×C7311yescharacteristic
450C2×C4⋊C4D4×C7311yescharacteristic
451C2×C4⋊C4C23×C7311yescharacteristic
452C2×C4⋊C4C23×C7311yescharacteristic
453C2×C4⋊C4C23×C7311yescharacteristic
454C2×C4⋊C4C23×C7311yescharacteristic
455C2×C4⋊C4C23×C7311yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42C23×C7311yescharacteristic
471C2×C42C23×C7311yescharacteristic
472C2×C42C23×C7311yescharacteristic
473#107—41no—
474#106—41no—
475C4⋊C8C2×C4×C7314yescomplemented
476#102—22no—
477#102—22no—
478#102—22no—
479#102—22no—
480#102—41no—
481#102—41no—
482#102C2×C4×C7314yescomplemented
483#102C2×C4×C7314yescomplemented
484#97—22no—
485#97—41no—
486C4×C8—41no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95D4×C7311yescharacteristic
493#95D4×C7311yescharacteristic
494C24—21no—
495C24—21no—
496C24—21no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C22×C4×C7312yes—
519C2×D4C22×C4×C7312yes—
520C2×D4C22×C4×C7312yes—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4C2×D4×C7311yescharacteristic
536C22×C4C2×D4×C7311yescharacteristic
537C22×C4C2×D4×C7311yescharacteristic
538C22×C4C2×D4×C7311yescharacteristic
539C22×C4C2×D4×C7311yescharacteristic
540C22×C4C2×D4×C7311yescharacteristic
541C22×C4C24×C7311yescharacteristic
542D8—44no—
543D8—44no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8C22×C4×C7312yes—
554C2×C8C22×C4×C7312yes—
555C2×C8#41×C7312yes—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—41no—
566C4⋊C4C22×C4×C7312yes—
567C4⋊C4#41×C7312yes—
568C22⋊C4—24no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—42no—
584C42—81no—
585C42—81no—
586C42C22×C4×C7312yes—
587C42#41×C7312yes—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23C22×D4×C7311yescharacteristic
610D4—22no—
611D4—22no—
612D4—22no—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—48no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—84no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—84no—
656C2×C4—84no—
657C2×C4C4×D4×C7312yes—
658C2×C4C4×D4×C7312yes—
659C2×C4AGL(1,ℤ/8)×C7312yes—
660C2×C4C23×C4×C7311yescharacteristic
661C2×C4C2×#41×C7311yescharacteristic
662C2×C4C2×#41×C7311yescharacteristic
663C2×C4C2×#41×C7311yescharacteristic
664C2×C4H(5,𝔽2)×C7311yescharacteristic
665C2×C4H(5,𝔽2)×C7311yescharacteristic
666C8—22no—
667C8—22no—
668C8—22no—
669C8—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×C4×D4×C7311yescharacteristic
692C22#546×C7311yescharacteristic
693C22#550×C7311yescharacteristic
694C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
695C22#575×C7311yescharacteristic
696C22#576×C7311yescharacteristic
697C22#576×C7311yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—42no—
705C4—42no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4C4×#41×C7311yescharacteristic
710C4#518×C7311yescharacteristic
711C4#553×C7311yescharacteristic
712C4#555×C7311yescharacteristic
713C2—82no—
714C2—82no—
715C2—82no—
716C2C73×#236311yescharacteristic
717C2C4×AGL(1,ℤ/8)×C7311yescharacteristic
718C2C73×#294811yescharacteristic
719C2C73×#330911yescharacteristic
720C2C73×#331811yescharacteristic
721C2C73×#339911yescharacteristic
722C2C73×#340311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC2×#459×C73C2
LCSG ▷ C2×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. C73×#2366C2semidirect
3. C73×#2357C2semidirect
4. C73×#1972C2semidirect
5. C73×#1970C2semidirect
6. C73×#1961C2semidirect
7. C73×#1949C2semidirect
8. C73×#1926C2semidirect
9. C73×#1925C2semidirect
10. C73×#1879C2semidirect
11. C73×#1879C2semidirect
12. C73×#1771C2semidirect
13. C73×#1762C2semidirect
14. C73×#1762C2semidirect
15. C4×#102×C73C2semidirect
23. #459×C73C4semidirect
72. C2×D8×C73C2×C4semidirect
73. C2×D8×C73C2×C4semidirect
86. C4×D4×C73C2×C4semidirect
113. C4⋊C8×C73C2×C4semidirect
120. #102×C73C2×C4semidirect
121. #102×C73C2×C4semidirect
351. #23108C73direct (N × H)
363. #2366C2×C73semidirect
364. #2357C2×C73semidirect
365. #1972C2×C73semidirect
366. #1970C2×C73semidirect
367. #1961C2×C73semidirect
368. #1949C2×C73semidirect
369. #1926C2×C73semidirect
370. #1925C2×C73semidirect
371. #1879C2×C73semidirect
372. #1879C2×C73semidirect
373. #1771C2×C73semidirect
374. #1762C2×C73semidirect
375. #1762C2×C73semidirect
376. C4×#102C2×C73semidirect
377. C73#23108direct (N × H)
385. #459C4×C73semidirect
434. C2×D8C2×C4×C73semidirect
435. C2×D8C2×C4×C73semidirect
448. C4×D4C2×C4×C73semidirect
475. C4⋊C8C2×C4×C73semidirect
482. #102C2×C4×C73semidirect
483. #102C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C732
C73×#23662
C73×#23572
C73×#19722
C73×#19702
C73×#19612
C73×#19492
C73×#19262
C73×#19252
C73×#18792
C73×#17712
C73×#17622
C4×#102×C732
#2310873