Finite Group Databasebeta

← C73×#23145 #32932549

Subgroups — C73×#23145 #32932549

Order 18688.

926 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C73C211yesmaximal, characteristic
2C73×#2363C211yesmaximal, characteristic
3C73×#2360C211yesmaximal, characteristic, complemented
4C73×#1936C211yesmaximal, characteristic, complemented
5C73×#1933C211yesmaximal, characteristic, complemented
6C73×#1921C211yesmaximal, characteristic, complemented
7C73×#1918C211yesmaximal, characteristic, complemented
8C73×#1880C211yesmaximal, characteristic, complemented
9C73×#1877C211yesmaximal, characteristic, complemented
10C73×#1874C211yesmaximal, characteristic
11C73×#1873C211yesmaximal, characteristic, complemented
12C73×#1763C211yesmaximal, characteristic, complemented
13C4×#102×C73C211yesmaximal, characteristic, complemented
14C73×#1753C211yesmaximal, characteristic, complemented
15C73×#1736C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×C22⋊Q8×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×C4×Q8×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24#468×C73C418yescomplemented
25C2×#107×C73C2211yescharacteristic
26C2×#103×C73C2211yescharacteristic
27C2×#103×C73C2211yescharacteristic
28C2×#103×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×C22⋊C8×C73C2211yescharacteristic
33C2×#97×C73C2211yescharacteristic
34C2×C4×C8×C73C2211yescharacteristic
35#391×C73C2211yescharacteristic
36#390×C73—21no—
37#390×C73C2211yescharacteristic
38#389×C73—21no—
39#389×C73C2211yescharacteristic
40#389×C73C2211yescharacteristic
41#388×C73—21no—
42#387×C73—21no—
43#386×C73—21no—
44#385×C73—21no—
45C4×C4⋊C4×C73C2211yescharacteristic
46C4×C4⋊C4×C73C2211yescharacteristic
47C4×C22⋊C4×C73—21no—
48C4×C22⋊C4×C73—21no—
49C4×C22⋊C4×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#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C22×Q8×C73C2311yescharacteristic
61C22×D4×C73—21no—
62C22×D4×C73C2311yescharacteristic
63C23×C4×C73—21no—
64C23×C4×C73—21no—
65C23×C4×C73C2311yescharacteristic
66C2×SD16×C73—41no—
67C2×SD16×C73—41no—
68C2×SD16×C73C2×C414yescomplemented
69C2×M16×C73—41no—
70C2×M16×C73—41no—
71C2×M16×C73C2×C414yescomplemented
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22⋊Q8×C73—22no—
77C22⋊Q8×C73C2×C414yescomplemented
78#121×C73—22no—
79#121×C73C2×C414yes—
80C4×Q8×C73—22no—
81C4×Q8×C73—41no—
82C4×D4×C73—22no—
83C4×D4×C73—41no—
84#117×C73—22no—
85#117×C73—41no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—41no—
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73D411yescharacteristic
106C2×C22⋊C4×C73D411yescharacteristic
107C2×C42×C73—21no—
108C2×C42×C73—21no—
109C2×C42×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113#107×C73C2×C414yescomplemented
114#103×C73—22no—
115#103×C73—41no—
116#103×C73C2×C414yescomplemented
117#102×C73—22no—
118#102×C73—41no—
119#102×C73C2×C414yescomplemented
120C22⋊C8×C73—22no—
121#97×C73—41no—
122C4×C8×C73—41no—
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×C73C2×D411yescharacteristic
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—24no—
140C2×D4×C73—21no—
141C2×D4×C73—21no—
142C2×D4×C73—21no—
143C2×D4×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—81no—
146C2×D4×C73—81no—
147C2×D4×C73C22×C412yes—
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—42no—
160C22×C4×C73—42no—
161C22×C4×C73—42no—
162C22×C4×C73—42no—
163C22×C4×C73—81no—
164C22×C4×C73—81no—
165C22×C4×C73C22×C412yes—
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73#4112yes—
172C22×C4×C73C2411yescharacteristic
173SD16×C73—44no—
174M16×C73—44no—
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—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73C22×C412yes—
186C2×C8×C73C22×C412yes—
187C4⋊C4×C73—24no—
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—42no—
197C4⋊C4×C73—42no—
198C4⋊C4×C73—81no—
199C4⋊C4×C73—81no—
200C4⋊C4×C73C22×C412yes—
201C4⋊C4×C73C22×C412yes—
202C4⋊C4×C73#4112yes—
203C4⋊C4×C73#4112yes—
204C22⋊C4×C73—24no—
205C22⋊C4×C73—24no—
206C22⋊C4×C73—22no—
207C22⋊C4×C73—41no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—81no—
212C42×C73—21no—
213C42×C73—21no—
214C42×C73—21no—
215C42×C73—21no—
216C42×C73—42no—
217C42×C73—42no—
218C42×C73—81no—
219C42×C73—81no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—22no—
227C23×C73—41no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73C4×D412yes—
234C23×C73C22×D411yescharacteristic
235Q8×C73—22no—
236Q8×C73—22no—
237Q8×C73—41no—
238Q8×C73—41no—
239D4×C73—22no—
240D4×C73—22no—
241D4×C73—41no—
242D4×C73—41no—
243D4×C73—84no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—22no—
249C2×C4×C73—22no—
250C2×C4×C73—22no—
251C2×C4×C73—22no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—22no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
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—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—84no—
283C2×C4×C73—84no—
284C2×C4×C73C4×D412yes—
285C2×C4×C73#13712yes—
286C2×C4×C73C23×C411yescharacteristic
287C2×C4×C73C2×#4111yescharacteristic
288C2×C4×C73C2×#4111yescharacteristic
289C2×C4×C73C2×#4111yescharacteristic
290C2×C4×C73H(5,𝔽2)11yescharacteristic
291C2×C4×C73H(5,𝔽2)11yescharacteristic
292C8×C73—22no—
293C8×C73—22no—
294C8×C73—41no—
295C8×C73—41no—
296C22×C73—22no—
297C22×C73—22no—
298C22×C73—22no—
299C22×C73—41no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73—42no—
304C22×C73—42no—
305C22×C73—42no—
306C22×C73—81no—
307C22×C73—81no—
308C22×C73—81no—
309C22×C73—81no—
310C22×C73C2×C4×D411yescharacteristic
311C22×C73#54611yescharacteristic
312C22×C73#54611yescharacteristic
313C22×C73C2×#13711yescharacteristic
314C22×C73#57511yescharacteristic
315C22×C73#57611yescharacteristic
316C22×C73#57711yescharacteristic
317C4×C73—22no—
318C4×C73—22no—
319C4×C73—41no—
320C4×C73—42no—
321C4×C73—42no—
322C4×C73—42no—
323C4×C73—42no—
324C4×C73—41no—
325C4×C73—41no—
326C4×C73—42no—
327C4×C73—81no—
328C4×C73—81no—
329C4×C73C4×#4111yescharacteristic
330C4×C73#51811yescharacteristic
331C4×C73#55311yescharacteristic
332C4×C73#55311yescharacteristic
333#23145C7311yesmaximal, characteristic, direct product factor, Sylow
334C2×C73—42no—
335C2×C73—82no—
336C2×C73#236411yescharacteristic
337C2×C73C4×#13711yescharacteristic
338C2×C73#294611yescharacteristic
339C2×C73#331411yescharacteristic
340C2×C73#331711yescharacteristic
341C2×C73#332211yescharacteristic
342C2×C73#332911yescharacteristic
343C2×#468C2×C7311yescharacteristic
344#2363C2×C7311yescharacteristic
345#2360C2×C7311yescharacteristic, complemented
346#1936C2×C7311yescharacteristic, complemented
347#1933C2×C7311yescharacteristic, complemented
348#1921C2×C7311yescharacteristic, complemented
349#1918C2×C7311yescharacteristic, complemented
350#1880C2×C7311yescharacteristic, complemented
351#1877C2×C7311yescharacteristic, complemented
352#1874C2×C7311yescharacteristic
353#1873C2×C7311yescharacteristic, complemented
354#1763C2×C7311yescharacteristic, complemented
355C4×#102C2×C7311yescharacteristic, complemented
356#1753C2×C7311yescharacteristic, complemented
357#1736C2×C7311yescharacteristic, complemented
358C73#2314511yescharacteristic, direct product factor, Sylow
359C22×SD16C22×C7311yescharacteristic
360C22×M16C22×C7311yescharacteristic
361C2×C22⋊Q8C22×C7311yescharacteristic
362C2×#121C22×C7311yescharacteristic
363C2×C4×Q8C22×C7311yescharacteristic
364C2×C4×D4C22×C7311yescharacteristic
365C2×#117C22×C7311yescharacteristic
366C22×C4⋊C4C22×C7311yescharacteristic
367#468C4×C7318yescomplemented
368C2×#107C22×C7311yescharacteristic
369C2×#103C22×C7311yescharacteristic
370C2×#103C22×C7311yescharacteristic
371C2×#103C22×C7311yescharacteristic
372C2×#102C22×C7311yescharacteristic
373C2×#102C22×C7311yescharacteristic
374C2×#102C22×C7311yescharacteristic
375C2×C22⋊C8C22×C7311yescharacteristic
376C2×#97C22×C7311yescharacteristic
377C2×C4×C8C22×C7311yescharacteristic
378#391C22×C7311yescharacteristic
379#390—21no—
380#390C22×C7311yescharacteristic
381#389—21no—
382#389C22×C7311yescharacteristic
383#389C22×C7311yescharacteristic
384#388—21no—
385#387—21no—
386#386—21no—
387#385—21no—
388C4×C4⋊C4C22×C7311yescharacteristic
389C4×C4⋊C4C22×C7311yescharacteristic
390C4×C22⋊C4—21no—
391C4×C22⋊C4—21no—
392C4×C22⋊C4C22×C7311yescharacteristic
393#340C22×C7311yescharacteristic
394#340C22×C7311yescharacteristic
395#340C22×C7311yescharacteristic
396#340C22×C7311yescharacteristic
397#340C22×C7311yescharacteristic
398#340C22×C7311yescharacteristic
399#340C22×C7311yescharacteristic
400#340C22×C7311yescharacteristic
401#336C22×C7311yescharacteristic
402#336C22×C7311yescharacteristic
403C22×Q8C23×C7311yescharacteristic
404C22×D4—21no—
405C22×D4C23×C7311yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4C23×C7311yescharacteristic
409C2×SD16—41no—
410C2×SD16—41no—
411C2×SD16C2×C4×C7314yescomplemented
412C2×M16—41no—
413C2×M16—41no—
414C2×M16C2×C4×C7314yescomplemented
415C22×C8C23×C7311yescharacteristic
416C22×C8C23×C7311yescharacteristic
417C22×C8C23×C7311yescharacteristic
418C22×C8C23×C7311yescharacteristic
419C22⋊Q8—22no—
420C22⋊Q8C2×C4×C7314yescomplemented
421#121—22no—
422#121C2×C4×C7314yes—
423C4×Q8—22no—
424C4×Q8—41no—
425C4×D4—22no—
426C4×D4—41no—
427#117—22no—
428#117—41no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—41no—
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×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C7311yescharacteristic
449C2×C22⋊C4D4×C7311yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42C23×C7311yescharacteristic
455C2×C42C23×C7311yescharacteristic
456#107C2×C4×C7314yescomplemented
457#103—22no—
458#103—41no—
459#103C2×C4×C7314yescomplemented
460#102—22no—
461#102—41no—
462#102C2×C4×C7314yescomplemented
463C22⋊C8—22no—
464#97—41no—
465C4×C8—41no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95D4×C7311yescharacteristic
473#95D4×C7311yescharacteristic
474C24—21no—
475C24C2×D4×C7311yescharacteristic
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8C22×C4×C7312yes—
482C2×D4—24no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—81no—
489C2×D4—81no—
490C2×D4C22×C4×C7312yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4C22×C4×C7312yes—
509C22×C4C2×D4×C7311yescharacteristic
510C22×C4C2×D4×C7311yescharacteristic
511C22×C4C2×D4×C7311yescharacteristic
512C22×C4C2×D4×C7311yescharacteristic
513C22×C4C2×D4×C7311yescharacteristic
514C22×C4#41×C7312yes—
515C22×C4C24×C7311yescharacteristic
516SD16—44no—
517M16—44no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8C22×C4×C7312yes—
529C2×C8C22×C4×C7312yes—
530C4⋊C4—24no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—81no—
542C4⋊C4—81no—
543C4⋊C4C22×C4×C7312yes—
544C4⋊C4C22×C4×C7312yes—
545C4⋊C4#41×C7312yes—
546C4⋊C4#41×C7312yes—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—22no—
550C22⋊C4—41no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—81no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—42no—
560C42—42no—
561C42—81no—
562C42—81no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23C4×D4×C7312yes—
577C23C22×D4×C7311yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—41no—
581Q8—41no—
582D4—22no—
583D4—22no—
584D4—41no—
585D4—41no—
586D4—84no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
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—84no—
626C2×C4—84no—
627C2×C4C4×D4×C7312yes—
628C2×C4#137×C7312yes—
629C2×C4C23×C4×C7311yescharacteristic
630C2×C4C2×#41×C7311yescharacteristic
631C2×C4C2×#41×C7311yescharacteristic
632C2×C4C2×#41×C7311yescharacteristic
633C2×C4H(5,𝔽2)×C7311yescharacteristic
634C2×C4H(5,𝔽2)×C7311yescharacteristic
635C8—22no—
636C8—22no—
637C8—41no—
638C8—41no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C2×C4×D4×C7311yescharacteristic
654C22#546×C7311yescharacteristic
655C22#546×C7311yescharacteristic
656C22C2×#137×C7311yescharacteristic
657C22#575×C7311yescharacteristic
658C22#576×C7311yescharacteristic
659C22#577×C7311yescharacteristic
660C4—22no—
661C4—22no—
662C4—42no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—42no—
668C4—42no—
669C4—42no—
670C4—81no—
671C4—81no—
672C4C4×#41×C7311yescharacteristic
673C4#518×C7311yescharacteristic
674C4#553×C7311yescharacteristic
675C4#553×C7311yescharacteristic
676C2—42no—
677C2—82no—
678C2C73×#236411yescharacteristic
679C2C4×#137×C7311yescharacteristic
680C2C73×#294611yescharacteristic
681C2C73×#331411yescharacteristic
682C2C73×#331711yescharacteristic
683C2C73×#332211yescharacteristic
684C2C73×#332911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
3. C73×#2360C2semidirect
4. C73×#1936C2semidirect
5. C73×#1933C2semidirect
6. C73×#1921C2semidirect
7. C73×#1918C2semidirect
8. C73×#1880C2semidirect
9. C73×#1877C2semidirect
11. C73×#1873C2semidirect
12. C73×#1763C2semidirect
13. C4×#102×C73C2semidirect
14. C73×#1753C2semidirect
15. C73×#1736C2semidirect
24. #468×C73C4semidirect
68. C2×SD16×C73C2×C4semidirect
71. C2×M16×C73C2×C4semidirect
77. C22⋊Q8×C73C2×C4semidirect
113. #107×C73C2×C4semidirect
116. #103×C73C2×C4semidirect
119. #102×C73C2×C4semidirect
333. #23145C73direct (N × H)
345. #2360C2×C73semidirect
346. #1936C2×C73semidirect
347. #1933C2×C73semidirect
348. #1921C2×C73semidirect
349. #1918C2×C73semidirect
350. #1880C2×C73semidirect
351. #1877C2×C73semidirect
353. #1873C2×C73semidirect
354. #1763C2×C73semidirect
355. C4×#102C2×C73semidirect
356. #1753C2×C73semidirect
357. #1736C2×C73semidirect
358. C73#23145direct (N × H)
367. #468C4×C73semidirect
411. C2×SD16C2×C4×C73semidirect
414. C2×M16C2×C4×C73semidirect
420. C22⋊Q8C2×C4×C73semidirect
456. #107C2×C4×C73semidirect
459. #103C2×C4×C73semidirect
462. #102C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C732
C73×#23632
C73×#23602
C73×#19362
C73×#19332
C73×#19212
C73×#19182
C73×#18802
C73×#18772
C73×#18742
C73×#18732
C73×#17632
C4×#102×C732
C73×#17532
C73×#17362
#2314573