Finite Group Databasebeta

← C73×#23106 #32932510

Subgroups — C73×#23106 #32932510

Order 18688.

946 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C73C211yesmaximal, characteristic
2C73×#2366C211yesmaximal, characteristic
3C73×#2356C211yesmaximal, characteristic, complemented
4C73×#1973C211yesmaximal, characteristic, complemented
5C73×#1968C211yesmaximal, characteristic, complemented
6C73×#1961C211yesmaximal, characteristic
7C73×#1949C211yesmaximal, characteristic, complemented
8C73×#1926C211yesmaximal, characteristic, complemented
9C73×#1925C211yesmaximal, characteristic, complemented
10C73×#1877C211yesmaximal, characteristic, complemented
11C73×#1877C211yesmaximal, characteristic, complemented
12C73×#1771C211yesmaximal, characteristic, complemented
13C73×#1763C211yesmaximal, characteristic, complemented
14C73×#1762C211yesmaximal, characteristic, complemented
15C4×#102×C73C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C2×#127×C73C2211yescharacteristic
19C2×C4×Q8×C73C2211yescharacteristic
20C2×C4×D4×C73—21no—
21C2×C4×D4×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23#460×C73C418yescomplemented
24C2×#107×C73C2211yescharacteristic
25C2×#106×C73C2211yescharacteristic
26C2×C4⋊C8×C73C2211yescharacteristic
27C2×#103×C73C2211yescharacteristic
28C2×#103×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#391×C73C2211yescharacteristic
39#391×C73C2211yescharacteristic
40#390×C73—21no—
41#390×C73C2211yescharacteristic
42#390×C73C2211yescharacteristic
43#387×C73—21no—
44#387×C73—21no—
45#386×C73—21no—
46#386×C73—21no—
47#383×C73—21no—
48#382×C73C2211yescharacteristic
49C4×C4⋊C4×C73C2211yescharacteristic
50C4×C4⋊C4×C73C2211yescharacteristic
51C4×C4⋊C4×C73C2211yescharacteristic
52C4×C4⋊C4×C73C2211yescharacteristic
53#376×C73—21no—
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C22×Q8×C73C2311yescharacteristic
61C22×D4×C73—21no—
62C22×D4×C73—21no—
63C22×D4×C73C2311yescharacteristic
64C22×D4×C73C2311yescharacteristic
65C23×C4×C73—21no—
66C23×C4×C73—21no—
67C2×SD16×C73—41no—
68C2×SD16×C73—41no—
69C2×SD16×C73—41no—
70C2×SD16×C73—41no—
71C2×SD16×C73C2×C414yescomplemented
72C2×SD16×C73C2×C414yescomplemented
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77#127×C73—22no—
78#127×C73C2×C414yes—
79C4×Q8×C73—22no—
80C4×Q8×C73C2×C414yescomplemented
81C4×D4×C73—22no—
82C4×D4×C73—22no—
83C4×D4×C73—41no—
84C4×D4×C73—41no—
85C4×D4×C73—44no—
86C2×C4⋊C4×C73—21no—
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×C42×C73—21no—
101C2×C42×C73—21no—
102C2×C42×C73—21no—
103C2×C42×C73—21no—
104C2×C42×C73C2311yescharacteristic
105C2×C42×C73C2311yescharacteristic
106C2×C42×C73C2311yescharacteristic
107#107×C73—41no—
108#106×C73—41no—
109C4⋊C8×C73C2×C414yescomplemented
110#103×C73—22no—
111#103×C73—22no—
112#102×C73—22no—
113#102×C73—22no—
114#102×C73—41no—
115#102×C73—41no—
116#102×C73C2×C414yescomplemented
117#102×C73C2×C414yescomplemented
118#97×C73—22no—
119#97×C73—41no—
120C4×C8×C73—41no—
121#95×C73—21no—
122#95×C73—21no—
123#95×C73—21no—
124#95×C73—21no—
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—
134C2×Q8×C73—21no—
135C2×Q8×C73—21no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73C22×C412yes—
140C2×D4×C73—24no—
141C2×D4×C73—24no—
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—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—42no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—42no—
168C22×C4×C73—81no—
169C22×C4×C73—81no—
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2411yescharacteristic
177SD16×C73—44no—
178SD16×C73—44no—
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×C73C22×C412yes—
189C2×C8×C73C22×C412yes—
190C2×C8×C73#4112yes—
191C4⋊C4×C73—24no—
192C4⋊C4×C73—22no—
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—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—41no—
202C4⋊C4×C73C22×C412yes—
203C4⋊C4×C73#4112yes—
204C22⋊C4×C73—42no—
205C22⋊C4×C73—42no—
206C22⋊C4×C73—42no—
207C22⋊C4×C73—42no—
208C22⋊C4×C73—81no—
209C22⋊C4×C73—81no—
210C42×C73—24no—
211C42×C73—21no—
212C42×C73—21no—
213C42×C73—21no—
214C42×C73—21no—
215C42×C73—42no—
216C42×C73—42no—
217C42×C73—42no—
218C42×C73C22×C412yes—
219C42×C73#4112yes—
220C23×C73—22no—
221C23×C73—22no—
222C23×C73—41no—
223C23×C73—41no—
224C23×C73—41no—
225C23×C73—41no—
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×C73C22×D411yescharacteristic
235Q8×C73—22no—
236Q8×C73—22no—
237Q8×C73—41no—
238Q8×C73—41no—
239D4×C73—22no—
240D4×C73—22no—
241D4×C73—22no—
242D4×C73—22no—
243D4×C73—48no—
244D4×C73—41no—
245D4×C73—41no—
246D4×C73—41no—
247D4×C73—41no—
248D4×C73—84no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—22no—
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—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—84no—
283C2×C4×C73—84no—
284C2×C4×C73C4×D412yes—
285C2×C4×C73C4×D412yes—
286C2×C4×C73AGL(1,ℤ/8)12yes—
287C2×C4×C73C23×C411yescharacteristic
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—22no—
294C8×C73—22no—
295C8×C73—22no—
296C8×C73—41no—
297C22×C73—42no—
298C22×C73—42no—
299C22×C73—42no—
300C22×C73—42no—
301C22×C73—42no—
302C22×C73—42no—
303C22×C73—81no—
304C22×C73—81no—
305C22×C73—81no—
306C22×C73—81no—
307C22×C73—81no—
308C22×C73—81no—
309C22×C73—81no—
310C22×C73—81no—
311C22×C73C2×C4×D411yescharacteristic
312C22×C73#54611yescharacteristic
313C22×C73#55011yescharacteristic
314C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C73#57511yescharacteristic
316C22×C73#57711yescharacteristic
317C22×C73#57711yescharacteristic
318C4×C73—22no—
319C4×C73—22no—
320C4×C73—22no—
321C4×C73—42no—
322C4×C73—42no—
323C4×C73—41no—
324C4×C73—42no—
325C4×C73—41no—
326C4×C73—41no—
327C4×C73—81no—
328C4×C73—81no—
329C4×C73—81no—
330C4×C73C4×#4111yescharacteristic
331C4×C73#51811yescharacteristic
332C4×C73#55311yescharacteristic
333C4×C73#55511yescharacteristic
334#23106C7311yesmaximal, characteristic, direct product factor, Sylow
335C2×C73—82no—
336C2×C73—82no—
337C2×C73#236311yescharacteristic
338C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
339C2×C73#294911yescharacteristic
340C2×C73#331011yescharacteristic
341C2×C73#331711yescharacteristic
342C2×C73#339711yescharacteristic
343C2×C73#340111yescharacteristic
344C2×#460C2×C7311yescharacteristic
345#2366C2×C7311yescharacteristic
346#2356C2×C7311yescharacteristic, complemented
347#1973C2×C7311yescharacteristic, complemented
348#1968C2×C7311yescharacteristic, complemented
349#1961C2×C7311yescharacteristic
350#1949C2×C7311yescharacteristic, complemented
351#1926C2×C7311yescharacteristic, complemented
352#1925C2×C7311yescharacteristic, complemented
353#1877C2×C7311yescharacteristic, complemented
354#1877C2×C7311yescharacteristic, complemented
355#1771C2×C7311yescharacteristic, complemented
356#1763C2×C7311yescharacteristic, complemented
357#1762C2×C7311yescharacteristic, complemented
358C4×#102C2×C7311yescharacteristic, complemented
359C73#2310611yescharacteristic, direct product factor, Sylow
360C22×SD16C22×C7311yescharacteristic
361C22×SD16C22×C7311yescharacteristic
362C2×#127C22×C7311yescharacteristic
363C2×C4×Q8C22×C7311yescharacteristic
364C2×C4×D4—21no—
365C2×C4×D4C22×C7311yescharacteristic
366C2×C4×D4C22×C7311yescharacteristic
367#460C4×C7318yescomplemented
368C2×#107C22×C7311yescharacteristic
369C2×#106C22×C7311yescharacteristic
370C2×C4⋊C8C22×C7311yescharacteristic
371C2×#103C22×C7311yescharacteristic
372C2×#103C22×C7311yescharacteristic
373C2×#102C22×C7311yescharacteristic
374C2×#102C22×C7311yescharacteristic
375C2×#102C22×C7311yescharacteristic
376C2×#102C22×C7311yescharacteristic
377C2×#102C22×C7311yescharacteristic
378C2×#102C22×C7311yescharacteristic
379C2×#97C22×C7311yescharacteristic
380C2×#97C22×C7311yescharacteristic
381C2×C4×C8C22×C7311yescharacteristic
382#391C22×C7311yescharacteristic
383#391C22×C7311yescharacteristic
384#390—21no—
385#390C22×C7311yescharacteristic
386#390C22×C7311yescharacteristic
387#387—21no—
388#387—21no—
389#386—21no—
390#386—21no—
391#383—21no—
392#382C22×C7311yescharacteristic
393C4×C4⋊C4C22×C7311yescharacteristic
394C4×C4⋊C4C22×C7311yescharacteristic
395C4×C4⋊C4C22×C7311yescharacteristic
396C4×C4⋊C4C22×C7311yescharacteristic
397#376—21no—
398#340C22×C7311yescharacteristic
399#340C22×C7311yescharacteristic
400#340C22×C7311yescharacteristic
401#340C22×C7311yescharacteristic
402#336C22×C7311yescharacteristic
403#336C22×C7311yescharacteristic
404C22×Q8C23×C7311yescharacteristic
405C22×D4—21no—
406C22×D4—21no—
407C22×D4C23×C7311yescharacteristic
408C22×D4C23×C7311yescharacteristic
409C23×C4—21no—
410C23×C4—21no—
411C2×SD16—41no—
412C2×SD16—41no—
413C2×SD16—41no—
414C2×SD16—41no—
415C2×SD16C2×C4×C7314yescomplemented
416C2×SD16C2×C4×C7314yescomplemented
417C22×C8C23×C7311yescharacteristic
418C22×C8C23×C7311yescharacteristic
419C22×C8C23×C7311yescharacteristic
420C22×C8C23×C7311yescharacteristic
421#127—22no—
422#127C2×C4×C7314yes—
423C4×Q8—22no—
424C4×Q8C2×C4×C7314yescomplemented
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—41no—
428C4×D4—41no—
429C4×D4—44no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4D4×C7311yescharacteristic
432C2×C4⋊C4D4×C7311yescharacteristic
433C2×C4⋊C4C23×C7311yescharacteristic
434C2×C4⋊C4C23×C7311yescharacteristic
435C2×C4⋊C4C23×C7311yescharacteristic
436C2×C4⋊C4C23×C7311yescharacteristic
437C2×C4⋊C4C23×C7311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42C23×C7311yescharacteristic
449C2×C42C23×C7311yescharacteristic
450C2×C42C23×C7311yescharacteristic
451#107—41no—
452#106—41no—
453C4⋊C8C2×C4×C7314yescomplemented
454#103—22no—
455#103—22no—
456#102—22no—
457#102—22no—
458#102—41no—
459#102—41no—
460#102C2×C4×C7314yescomplemented
461#102C2×C4×C7314yescomplemented
462#97—22no—
463#97—41no—
464C4×C8—41no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95D4×C7311yescharacteristic
475#95D4×C7311yescharacteristic
476C24—21no—
477C24—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8C22×C4×C7312yes—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—21no—
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×D4—42no—
497C2×D4—42no—
498C2×D4—81no—
499C2×D4—81no—
500C2×D4C22×C4×C7312yes—
501C2×D4C22×C4×C7312yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
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—44no—
522SD16—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×C8C22×C4×C7312yes—
533C2×C8C22×C4×C7312yes—
534C2×C8#41×C7312yes—
535C4⋊C4—24no—
536C4⋊C4—22no—
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⋊C4C22×C4×C7312yes—
547C4⋊C4#41×C7312yes—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C42—24no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—42no—
560C42—42no—
561C42—42no—
562C42C22×C4×C7312yes—
563C42#41×C7312yes—
564C23—22no—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C22×D4×C7311yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4—22no—
587D4—48no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—84no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
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—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—84no—
627C2×C4—84no—
628C2×C4C4×D4×C7312yes—
629C2×C4C4×D4×C7312yes—
630C2×C4AGL(1,ℤ/8)×C7312yes—
631C2×C4C23×C4×C7311yescharacteristic
632C2×C4C2×#41×C7311yescharacteristic
633C2×C4C2×#41×C7311yescharacteristic
634C2×C4C2×#41×C7311yescharacteristic
635C2×C4H(5,𝔽2)×C7311yescharacteristic
636C2×C4H(5,𝔽2)×C7311yescharacteristic
637C8—22no—
638C8—22no—
639C8—22no—
640C8—41no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C2×C4×D4×C7311yescharacteristic
656C22#546×C7311yescharacteristic
657C22#550×C7311yescharacteristic
658C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
659C22#575×C7311yescharacteristic
660C22#577×C7311yescharacteristic
661C22#577×C7311yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—42no—
667C4—41no—
668C4—41no—
669C4—42no—
670C4—42no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4C4×#41×C7311yescharacteristic
675C4#518×C7311yescharacteristic
676C4#553×C7311yescharacteristic
677C4#555×C7311yescharacteristic
678C2—82no—
679C2—82no—
680C2C73×#236311yescharacteristic
681C2C4×AGL(1,ℤ/8)×C7311yescharacteristic
682C2C73×#294911yescharacteristic
683C2C73×#331011yescharacteristic
684C2C73×#331711yescharacteristic
685C2C73×#339711yescharacteristic
686C2C73×#340111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC2×#127×C73C22
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
3. C73×#2356C2semidirect
4. C73×#1973C2semidirect
5. C73×#1968C2semidirect
7. C73×#1949C2semidirect
8. C73×#1926C2semidirect
9. C73×#1925C2semidirect
10. C73×#1877C2semidirect
11. C73×#1877C2semidirect
12. C73×#1771C2semidirect
13. C73×#1763C2semidirect
14. C73×#1762C2semidirect
15. C4×#102×C73C2semidirect
23. #460×C73C4semidirect
71. C2×SD16×C73C2×C4semidirect
72. C2×SD16×C73C2×C4semidirect
80. C4×Q8×C73C2×C4semidirect
109. C4⋊C8×C73C2×C4semidirect
116. #102×C73C2×C4semidirect
117. #102×C73C2×C4semidirect
334. #23106C73direct (N × H)
346. #2356C2×C73semidirect
347. #1973C2×C73semidirect
348. #1968C2×C73semidirect
350. #1949C2×C73semidirect
351. #1926C2×C73semidirect
352. #1925C2×C73semidirect
353. #1877C2×C73semidirect
354. #1877C2×C73semidirect
355. #1771C2×C73semidirect
356. #1763C2×C73semidirect
357. #1762C2×C73semidirect
358. C4×#102C2×C73semidirect
359. C73#23106direct (N × H)
367. #460C4×C73semidirect
415. C2×SD16C2×C4×C73semidirect
416. C2×SD16C2×C4×C73semidirect
424. C4×Q8C2×C4×C73semidirect
453. C4⋊C8C2×C4×C73semidirect
460. #102C2×C4×C73semidirect
461. #102C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C732
C73×#23662
C73×#23562
C73×#19732
C73×#19682
C73×#19612
C73×#19492
C73×#19262
C73×#19252
C73×#18772
C73×#17712
C73×#17632
C73×#17622
C4×#102×C732
#2310673