Finite Group Databasebeta

← C73×#23098 #32932502

Subgroups — C73×#23098 #32932502

Order 18688.

906 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C73C211yesmaximal, characteristic
2C73×#2367C211yesmaximal, characteristic, complemented
3C73×#2357C211yesmaximal, characteristic, complemented
4C73×#1970C211yesmaximal, characteristic
5C73×#1968C211yesmaximal, characteristic, complemented
6C73×#1958C211yesmaximal, characteristic, complemented
7C73×#1949C211yesmaximal, characteristic, complemented
8C73×#1928C211yesmaximal, characteristic, complemented
9C73×#1926C211yesmaximal, characteristic, complemented
10C73×#1880C211yesmaximal, characteristic, complemented
11C73×#1879C211yesmaximal, characteristic
12C8×C4⋊C4×C73C211yesmaximal, characteristic, complemented
13C4×#103×C73C211yesmaximal, characteristic, complemented
14C4×#102×C73C211yesmaximal, characteristic, complemented
15C4×#102×C73C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C2×#124×C73C2211yescharacteristic
19C2×C4×Q8×C73C2211yescharacteristic
20C2×C4×D4×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22#463×C73C418yescomplemented
23C2×#107×C73C2211yescharacteristic
24C2×#106×C73C2211yescharacteristic
25C2×C4⋊C8×C73C2211yescharacteristic
26C2×#103×C73C2211yescharacteristic
27C2×#103×C73C2211yescharacteristic
28C2×#103×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×C4×C8×C73C2211yescharacteristic
35C2×C4×C8×C73C2211yescharacteristic
36C2×C4×C8×C73C2211yescharacteristic
37#391×C73C2211yescharacteristic
38#390×C73C2211yescharacteristic
39#390×C73C2211yescharacteristic
40#390×C73C2211yescharacteristic
41#388×C73—21no—
42#388×C73—21no—
43#388×C73—21no—
44#388×C73—21no—
45#385×C73—21no—
46#382×C73C2211yescharacteristic
47#381×C73—21no—
48C4×C4⋊C4×C73C2211yescharacteristic
49C4×C4⋊C4×C73C2211yescharacteristic
50C4×C4⋊C4×C73C2211yescharacteristic
51C4×C4⋊C4×C73C2211yescharacteristic
52C4×C22⋊C4×C73—21no—
53C4×C22⋊C4×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×C73C2311yescharacteristic
62C22×D4×C73C2311yescharacteristic
63C23×C4×C73—21no—
64C23×C4×C73—21no—
65C2×SD16×C73—41no—
66C2×SD16×C73—41no—
67C2×SD16×C73C2×C414yescomplemented
68C2×D8×C73—41no—
69C2×D8×C73—41no—
70C2×D8×C73C2×C414yes—
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75#124×C73—22no—
76#124×C73C2×C414yes—
77C4×Q8×C73—22no—
78C4×Q8×C73—41no—
79C4×D4×C73—22no—
80C4×D4×C73—22no—
81C4×D4×C73—41no—
82C4×D4×C73C2×C414yescomplemented
83C2×C4⋊C4×C73—21no—
84C2×C4⋊C4×C73D411yescharacteristic
85C2×C4⋊C4×C73D411yescharacteristic
86C2×C4⋊C4×C73C2311yescharacteristic
87C2×C4⋊C4×C73C2311yescharacteristic
88C2×C4⋊C4×C73C2311yescharacteristic
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C22⋊C4×C73—21no—
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×C42×C73—21no—
102C2×C42×C73—21no—
103C2×C42×C73—21no—
104C2×C42×C73—21no—
105C2×C42×C73C2311yescharacteristic
106C2×C42×C73C2311yescharacteristic
107C2×C42×C73C2311yescharacteristic
108#107×C73—41no—
109#106×C73—41no—
110C4⋊C8×C73C2×C414yescomplemented
111#103×C73—22no—
112#103×C73—41no—
113#103×C73C2×C414yescomplemented
114#102×C73—22no—
115#102×C73—22no—
116#102×C73—22no—
117#102×C73—41no—
118#102×C73C2×C414yes—
119C4×C8×C73—22no—
120C4×C8×C73—41no—
121C4×C8×C73—41no—
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×C73D411yescharacteristic
130#95×C73D411yescharacteristic
131C24×C73—21no—
132C24×C73—21no—
133C2×Q8×C73—21no—
134C2×Q8×C73—21no—
135C2×Q8×C73—21no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73C22×C412yes—
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×C73C22×C412yes—
150C2×D4×C73C22×C412yes—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—24no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—42no—
159C22×C4×C73—42no—
160C22×C4×C73—81no—
161C22×C4×C73—81no—
162C22×C4×C73—81no—
163C22×C4×C73C2×D411yescharacteristic
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2411yescharacteristic
170SD16×C73—44no—
171D8×C73—44no—
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×C73C22×C412yes—
182C2×C8×C73C22×C412yes—
183C2×C8×C73#4112yes—
184C4⋊C4×C73—22no—
185C4⋊C4×C73—22no—
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—42no—
195C4⋊C4×C73C22×C412yes—
196C4⋊C4×C73#4112yes—
197C22⋊C4×C73—24no—
198C22⋊C4×C73—24no—
199C22⋊C4×C73—24no—
200C22⋊C4×C73—42no—
201C22⋊C4×C73—42no—
202C22⋊C4×C73—42no—
203C22⋊C4×C73—42no—
204C22⋊C4×C73—81no—
205C22⋊C4×C73—81no—
206C22⋊C4×C73—81no—
207C42×C73—21no—
208C42×C73—21no—
209C42×C73—21no—
210C42×C73—21no—
211C42×C73—42no—
212C42×C73—81no—
213C42×C73—81no—
214C42×C73—81no—
215C42×C73C22×C412yes—
216C42×C73#4112yes—
217C23×C73—22no—
218C23×C73—22no—
219C23×C73—41no—
220C23×C73—41no—
221C23×C73—41no—
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×C73C22×D411yescharacteristic
232Q8×C73—22no—
233Q8×C73—22no—
234Q8×C73—41no—
235Q8×C73—41no—
236D4×C73—22no—
237D4×C73—22no—
238D4×C73—22no—
239D4×C73—22no—
240D4×C73—41no—
241D4×C73—41no—
242D4×C73—41no—
243D4×C73—41no—
244C2×C4×C73—21no—
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—21no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—22no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
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—84no—
277C2×C4×C73—84no—
278C2×C4×C73C4×D412yes—
279C2×C4×C73C4×D412yes—
280C2×C4×C73#13512yes—
281C2×C4×C73#13512yes—
282C2×C4×C73C23×C411yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×C4×C73C2×#4111yescharacteristic
285C2×C4×C73C2×#4111yescharacteristic
286C2×C4×C73H(5,𝔽2)11yescharacteristic
287C2×C4×C73H(5,𝔽2)11yescharacteristic
288C8×C73—22no—
289C8×C73—22no—
290C8×C73—22no—
291C8×C73—41no—
292C22×C73—42no—
293C22×C73—42no—
294C22×C73—42no—
295C22×C73—42no—
296C22×C73—42no—
297C22×C73—42no—
298C22×C73—81no—
299C22×C73—81no—
300C22×C73—81no—
301C22×C73—81no—
302C22×C73—81no—
303C22×C73—81no—
304C22×C73—81no—
305C22×C73—81no—
306C22×C73C2×C4×D411yescharacteristic
307C22×C73#54611yescharacteristic
308C22×C73#55011yescharacteristic
309C22×C73C2×#13511yescharacteristic
310C22×C73C2×#13511yescharacteristic
311C22×C73#57611yescharacteristic
312C22×C73#57711yescharacteristic
313C4×C73—22no—
314C4×C73—22no—
315C4×C73—22no—
316C4×C73—22no—
317C4×C73—42no—
318C4×C73—42no—
319C4×C73—41no—
320C4×C73—42no—
321C4×C73—41no—
322C4×C73—81no—
323C4×C73—81no—
324C4×C73—81no—
325C4×C73C4×#4111yescharacteristic
326C4×C73#51811yescharacteristic
327C4×C73#55311yescharacteristic
328C4×C73#55511yescharacteristic
329#23098C7311yesmaximal, characteristic, direct product factor, Sylow
330C2×C73—82no—
331C2×C73—82no—
332C2×C73#236311yescharacteristic
333C2×C73C4×#13511yescharacteristic
334C2×C73#294611yescharacteristic
335C2×C73#329711yescharacteristic
336C2×C73#330111yescharacteristic
337C2×C73#339411yescharacteristic
338C2×C73#339611yescharacteristic
339C2×#463C2×C7311yescharacteristic
340#2367C2×C7311yescharacteristic, complemented
341#2357C2×C7311yescharacteristic, complemented
342#1970C2×C7311yescharacteristic
343#1968C2×C7311yescharacteristic, complemented
344#1958C2×C7311yescharacteristic, complemented
345#1949C2×C7311yescharacteristic, complemented
346#1928C2×C7311yescharacteristic, complemented
347#1926C2×C7311yescharacteristic, complemented
348#1880C2×C7311yescharacteristic, complemented
349#1879C2×C7311yescharacteristic
350C8×C4⋊C4C2×C7311yescharacteristic, complemented
351C4×#103C2×C7311yescharacteristic, complemented
352C4×#102C2×C7311yescharacteristic, complemented
353C4×#102C2×C7311yescharacteristic, complemented
354C73#2309811yescharacteristic, direct product factor, Sylow
355C22×SD16C22×C7311yescharacteristic
356C22×D8C22×C7311yescharacteristic
357C2×#124C22×C7311yescharacteristic
358C2×C4×Q8C22×C7311yescharacteristic
359C2×C4×D4C22×C7311yescharacteristic
360C2×C4×D4C22×C7311yescharacteristic
361#463C4×C7318yescomplemented
362C2×#107C22×C7311yescharacteristic
363C2×#106C22×C7311yescharacteristic
364C2×C4⋊C8C22×C7311yescharacteristic
365C2×#103C22×C7311yescharacteristic
366C2×#103C22×C7311yescharacteristic
367C2×#103C22×C7311yescharacteristic
368C2×#102C22×C7311yescharacteristic
369C2×#102C22×C7311yescharacteristic
370C2×#102C22×C7311yescharacteristic
371C2×#102C22×C7311yescharacteristic
372C2×#102C22×C7311yescharacteristic
373C2×C4×C8C22×C7311yescharacteristic
374C2×C4×C8C22×C7311yescharacteristic
375C2×C4×C8C22×C7311yescharacteristic
376#391C22×C7311yescharacteristic
377#390C22×C7311yescharacteristic
378#390C22×C7311yescharacteristic
379#390C22×C7311yescharacteristic
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#385—21no—
385#382C22×C7311yescharacteristic
386#381—21no—
387C4×C4⋊C4C22×C7311yescharacteristic
388C4×C4⋊C4C22×C7311yescharacteristic
389C4×C4⋊C4C22×C7311yescharacteristic
390C4×C4⋊C4C22×C7311yescharacteristic
391C4×C22⋊C4—21no—
392C4×C22⋊C4—21no—
393#340C22×C7311yescharacteristic
394#340C22×C7311yescharacteristic
395#340C22×C7311yescharacteristic
396#340C22×C7311yescharacteristic
397#336C22×C7311yescharacteristic
398#336C22×C7311yescharacteristic
399C22×Q8C23×C7311yescharacteristic
400C22×D4C23×C7311yescharacteristic
401C22×D4C23×C7311yescharacteristic
402C23×C4—21no—
403C23×C4—21no—
404C2×SD16—41no—
405C2×SD16—41no—
406C2×SD16C2×C4×C7314yescomplemented
407C2×D8—41no—
408C2×D8—41no—
409C2×D8C2×C4×C7314yes—
410C22×C8C23×C7311yescharacteristic
411C22×C8C23×C7311yescharacteristic
412C22×C8C23×C7311yescharacteristic
413C22×C8C23×C7311yescharacteristic
414#124—22no—
415#124C2×C4×C7314yes—
416C4×Q8—22no—
417C4×Q8—41no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—41no—
421C4×D4C2×C4×C7314yescomplemented
422C2×C4⋊C4—21no—
423C2×C4⋊C4D4×C7311yescharacteristic
424C2×C4⋊C4D4×C7311yescharacteristic
425C2×C4⋊C4C23×C7311yescharacteristic
426C2×C4⋊C4C23×C7311yescharacteristic
427C2×C4⋊C4C23×C7311yescharacteristic
428C2×C4⋊C4C23×C7311yescharacteristic
429C2×C4⋊C4C23×C7311yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C23×C7311yescharacteristic
445C2×C42C23×C7311yescharacteristic
446C2×C42C23×C7311yescharacteristic
447#107—41no—
448#106—41no—
449C4⋊C8C2×C4×C7314yescomplemented
450#103—22no—
451#103—41no—
452#103C2×C4×C7314yescomplemented
453#102—22no—
454#102—22no—
455#102—22no—
456#102—41no—
457#102C2×C4×C7314yes—
458C4×C8—22no—
459C4×C8—41no—
460C4×C8—41no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95D4×C7311yescharacteristic
469#95D4×C7311yescharacteristic
470C24—21no—
471C24—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8C22×C4×C7312yes—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C22×C4×C7312yes—
489C2×D4C22×C4×C7312yes—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4C2×D4×C7311yescharacteristic
503C22×C4C2×D4×C7311yescharacteristic
504C22×C4C2×D4×C7311yescharacteristic
505C22×C4C2×D4×C7311yescharacteristic
506C22×C4C2×D4×C7311yescharacteristic
507C22×C4C2×D4×C7311yescharacteristic
508C22×C4C24×C7311yescharacteristic
509SD16—44no—
510D8—44no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8C22×C4×C7312yes—
521C2×C8C22×C4×C7312yes—
522C2×C8#41×C7312yes—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4C22×C4×C7312yes—
535C4⋊C4#41×C7312yes—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—24no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C22⋊C4—81no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—81no—
552C42—81no—
553C42—81no—
554C42C22×C4×C7312yes—
555C42#41×C7312yes—
556C23—22no—
557C23—22no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23C22×D4×C7311yescharacteristic
571Q8—22no—
572Q8—22no—
573Q8—41no—
574Q8—41no—
575D4—22no—
576D4—22no—
577D4—22no—
578D4—22no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
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—84no—
616C2×C4—84no—
617C2×C4C4×D4×C7312yes—
618C2×C4C4×D4×C7312yes—
619C2×C4#135×C7312yes—
620C2×C4#135×C7312yes—
621C2×C4C23×C4×C7311yescharacteristic
622C2×C4C2×#41×C7311yescharacteristic
623C2×C4C2×#41×C7311yescharacteristic
624C2×C4C2×#41×C7311yescharacteristic
625C2×C4H(5,𝔽2)×C7311yescharacteristic
626C2×C4H(5,𝔽2)×C7311yescharacteristic
627C8—22no—
628C8—22no—
629C8—22no—
630C8—41no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22C2×C4×D4×C7311yescharacteristic
646C22#546×C7311yescharacteristic
647C22#550×C7311yescharacteristic
648C22C2×#135×C7311yescharacteristic
649C22C2×#135×C7311yescharacteristic
650C22#576×C7311yescharacteristic
651C22#577×C7311yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—42no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4C4×#41×C7311yescharacteristic
665C4#518×C7311yescharacteristic
666C4#553×C7311yescharacteristic
667C4#555×C7311yescharacteristic
668C2—82no—
669C2—82no—
670C2C73×#236311yescharacteristic
671C2C4×#135×C7311yescharacteristic
672C2C73×#294611yescharacteristic
673C2C73×#329711yescharacteristic
674C2C73×#330111yescharacteristic
675C2C73×#339411yescharacteristic
676C2C73×#339611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC22×D8×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
2. C73×#2367C2semidirect
3. C73×#2357C2semidirect
5. C73×#1968C2semidirect
6. C73×#1958C2semidirect
7. C73×#1949C2semidirect
8. C73×#1928C2semidirect
9. C73×#1926C2semidirect
10. C73×#1880C2semidirect
12. C8×C4⋊C4×C73C2semidirect
13. C4×#103×C73C2semidirect
14. C4×#102×C73C2semidirect
15. C4×#102×C73C2semidirect
22. #463×C73C4semidirect
67. C2×SD16×C73C2×C4semidirect
82. C4×D4×C73C2×C4semidirect
110. C4⋊C8×C73C2×C4semidirect
113. #103×C73C2×C4semidirect
329. #23098C73direct (N × H)
340. #2367C2×C73semidirect
341. #2357C2×C73semidirect
343. #1968C2×C73semidirect
344. #1958C2×C73semidirect
345. #1949C2×C73semidirect
346. #1928C2×C73semidirect
347. #1926C2×C73semidirect
348. #1880C2×C73semidirect
350. C8×C4⋊C4C2×C73semidirect
351. C4×#103C2×C73semidirect
352. C4×#102C2×C73semidirect
353. C4×#102C2×C73semidirect
354. C73#23098direct (N × H)
361. #463C4×C73semidirect
406. C2×SD16C2×C4×C73semidirect
421. C4×D4C2×C4×C73semidirect
449. C4⋊C8C2×C4×C73semidirect
452. #103C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C732
C73×#23672
C73×#23572
C73×#19702
C73×#19682
C73×#19582
C73×#19492
C73×#19282
C73×#19262
C73×#18802
C73×#18792
C8×C4⋊C4×C732
C4×#103×C732
C4×#102×C732
#2309873