Finite Group Databasebeta

← C73×#26603 #32936007

Subgroups — C73×#26603 #32936007

Order 18688.

966 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×#461×C73C211yesmaximal, characteristic, complemented
2C2×#440×C73C211yesmaximal, characteristic, complemented
3C73×#2446C211yesmaximal, characteristic, complemented
4C73×#2366C211yesmaximal, characteristic
5C73×#2067C211yesmaximal, characteristic, complemented
6C73×#2014C211yesmaximal, characteristic
7C73×#2014C211yesmaximal, characteristic
8C73×#2013C211yesmaximal, characteristic, complemented
9C73×#1973C211yesmaximal, characteristic, complemented
10C73×#1928C211yesmaximal, characteristic, complemented
11C73×#1928C211yesmaximal, characteristic, complemented
12C73×#1917C211yesmaximal, characteristic, complemented
13C73×#1880C211yesmaximal, characteristic, complemented
14C73×#1877C211yesmaximal, characteristic, complemented
15C73×#1862C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×SD16×C73C2211yescharacteristic
20C2×C4⋊Q8×C73C2211yescharacteristic
21C2×#127×C73C2211yescharacteristic
22C2×C4×Q8×C73C2211yescharacteristic
23C2×C4×D4×C73—21no—
24C2×C4×D4×C73C2211yescharacteristic
25C2×C4×D4×C73C2211yescharacteristic
26#461×C73—24no—
27#440×C73—24no—
28C2×#107×C73C2211yescharacteristic
29C2×#107×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40#400×C73—21no—
41#398×C73—21no—
42#391×C73C2211yescharacteristic
43#391×C73C2211yescharacteristic
44#391×C73C2211yescharacteristic
45#390×C73—21no—
46#390×C73C2211yescharacteristic
47#390×C73C2211yescharacteristic
48#389×C73C2211yescharacteristic
49#387×C73—21no—
50#387×C73—21no—
51#386×C73—21no—
52#386×C73—21no—
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73C2311yescharacteristic
66C22×D4×C73C2311yescharacteristic
67C23×C4×C73—21no—
68C23×C4×C73—21no—
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×SD16×C73—22no—
72C2×SD16×C73—22no—
73C2×SD16×C73—22no—
74C2×SD16×C73—22no—
75C2×SD16×C73—22no—
76C2×SD16×C73—22no—
77C2×SD16×C73—41no—
78C2×SD16×C73—41no—
79C2×SD16×C73—41no—
80C2×SD16×C73—41no—
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C4⋊Q8×C73—22no—
86C4⋊Q8×C73—41no—
87#127×C73—22no—
88#127×C73—22no—
89C4×Q8×C73—22no—
90C4×Q8×C73—41no—
91C4×D4×C73—22no—
92C4×D4×C73—22no—
93C4×D4×C73—41no—
94C4×D4×C73—41no—
95C4×D4×C73—44no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73D411yescharacteristic
101C2×C4⋊C4×C73D411yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C42×C73—21no—
113C2×C42×C73—21no—
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116C2×C42×C73C2311yescharacteristic
117#107×C73—22no—
118#107×C73—41no—
119C4⋊C8×C73—22no—
120#103×C73—22no—
121#103×C73—22no—
122#103×C73—41no—
123#103×C73D414yescomplemented
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—41no—
127#102×C73—41no—
128#97×C73—22no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73D411yescharacteristic
138#95×C73D411yescharacteristic
139C24×C73—21no—
140C24×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—21no—
152C2×Q8×C73C2×D412yes—
153C2×D4×C73—24no—
154C2×D4×C73—24no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73—81no—
168C2×D4×C73—81no—
169C2×D4×C73#4112yes—
170C2×D4×C73#4112yes—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—42no—
178C22×C4×C73—42no—
179C22×C4×C73—42no—
180C22×C4×C73—42no—
181C22×C4×C73—81no—
182C22×C4×C73—81no—
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2411yescharacteristic
190SD16×C73—28no—
191SD16×C73—44no—
192SD16×C73—44no—
193SD16×C73—44no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73C2×D412yes—
205C2×C8×C73#4112yes—
206C4⋊C4×C73—22no—
207C4⋊C4×C73—22no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73—42no—
217C4⋊C4×C73—42no—
218C4⋊C4×C73—42no—
219C4⋊C4×C73C2×D412yes—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—42no—
224C22⋊C4×C73—81no—
225C22⋊C4×C73—81no—
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73—42no—
233C42×C73—42no—
234C23×C73—22no—
235C23×C73—22no—
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×C73—41no—
248C23×C73C22×D411yescharacteristic
249Q8×C73—22no—
250Q8×C73—22no—
251Q8×C73—41no—
252Q8×C73—41no—
253Q8×C73—41no—
254Q8×C73—41no—
255Q8×C73—41no—
256Q8×C73—41no—
257D4×C73—22no—
258D4×C73—22no—
259D4×C73—22no—
260D4×C73—22no—
261D4×C73—48no—
262D4×C73—41no—
263D4×C73—41no—
264D4×C73—41no—
265D4×C73—41no—
266D4×C73—84no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
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—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—84no—
302C2×C4×C73—84no—
303C2×C4×C73AGL(1,ℤ/8)12yes—
304C2×C4×C73#13712yes—
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C2×#4111yescharacteristic
307C2×C4×C73C2×#4111yescharacteristic
308C2×C4×C73C2×#4111yescharacteristic
309C2×C4×C73H(5,𝔽2)11yescharacteristic
310C2×C4×C73H(5,𝔽2)11yescharacteristic
311C8×C73—22no—
312C8×C73—22no—
313C8×C73—41no—
314C8×C73—41no—
315C22×C73—42no—
316C22×C73—42no—
317C22×C73—42no—
318C22×C73—42no—
319C22×C73—42no—
320C22×C73—42no—
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×C73#52511yescharacteristic
330C22×C73D4211yescharacteristic
331C22×C73#55011yescharacteristic
332C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C73C2×#13711yescharacteristic
334C22×C73#57711yescharacteristic
335C22×C73#57711yescharacteristic
336C4×C73—22no—
337C4×C73—22no—
338C4×C73—41no—
339C4×C73—42no—
340C4×C73—41no—
341C4×C73—42no—
342C4×C73—41no—
343C4×C73—41no—
344C4×C73—81no—
345C4×C73—81no—
346C4×C73—81no—
347C4×C73—81no—
348C4×C73#52511yescharacteristic
349C4×C73#53811yescharacteristic
350C4×C73#54611yescharacteristic
351C4×C73#55311yescharacteristic
352#26603C7311yesmaximal, characteristic, direct product factor, Sylow
353C2×C73—82no—
354C2×C73—82no—
355C2×C73#245611yescharacteristic
356C2×C73#311011yescharacteristic
357C2×C73#312311yescharacteristic
358C2×C73#326511yescharacteristic
359C2×C73#327811yescharacteristic
360C2×C73#339711yescharacteristic
361C2×C73#340011yescharacteristic
362C2×#461C2×C7311yescharacteristic, complemented
363C2×#440C2×C7311yescharacteristic, complemented
364#2446C2×C7311yescharacteristic, complemented
365#2366C2×C7311yescharacteristic
366#2067C2×C7311yescharacteristic, complemented
367#2014C2×C7311yescharacteristic
368#2014C2×C7311yescharacteristic
369#2013C2×C7311yescharacteristic, complemented
370#1973C2×C7311yescharacteristic, complemented
371#1928C2×C7311yescharacteristic, complemented
372#1928C2×C7311yescharacteristic, complemented
373#1917C2×C7311yescharacteristic, complemented
374#1880C2×C7311yescharacteristic, complemented
375#1877C2×C7311yescharacteristic, complemented
376#1862C2×C7311yescharacteristic, complemented
377C73#2660311yescharacteristic, direct product factor, Sylow
378C22×SD16C22×C7311yescharacteristic
379C22×SD16C22×C7311yescharacteristic
380C22×SD16C22×C7311yescharacteristic
381C22×SD16C22×C7311yescharacteristic
382C2×C4⋊Q8C22×C7311yescharacteristic
383C2×#127C22×C7311yescharacteristic
384C2×C4×Q8C22×C7311yescharacteristic
385C2×C4×D4—21no—
386C2×C4×D4C22×C7311yescharacteristic
387C2×C4×D4C22×C7311yescharacteristic
388#461—24no—
389#440—24no—
390C2×#107C22×C7311yescharacteristic
391C2×#107C22×C7311yescharacteristic
392C2×C4⋊C8C22×C7311yescharacteristic
393C2×#103C22×C7311yescharacteristic
394C2×#103C22×C7311yescharacteristic
395C2×#103C22×C7311yescharacteristic
396C2×#103C22×C7311yescharacteristic
397C2×#102C22×C7311yescharacteristic
398C2×#102C22×C7311yescharacteristic
399C2×#102C22×C7311yescharacteristic
400C2×#102C22×C7311yescharacteristic
401C2×#97C22×C7311yescharacteristic
402#400—21no—
403#398—21no—
404#391C22×C7311yescharacteristic
405#391C22×C7311yescharacteristic
406#391C22×C7311yescharacteristic
407#390—21no—
408#390C22×C7311yescharacteristic
409#390C22×C7311yescharacteristic
410#389C22×C7311yescharacteristic
411#387—21no—
412#387—21no—
413#386—21no—
414#386—21no—
415C4×C4⋊C4C22×C7311yescharacteristic
416C4×C4⋊C4C22×C7311yescharacteristic
417#340C22×C7311yescharacteristic
418#340C22×C7311yescharacteristic
419#336C22×C7311yescharacteristic
420#336C22×C7311yescharacteristic
421#336C22×C7311yescharacteristic
422#336C22×C7311yescharacteristic
423C22×Q8C23×C7311yescharacteristic
424C22×Q8C23×C7311yescharacteristic
425C22×D4—21no—
426C22×D4—21no—
427C22×D4C23×C7311yescharacteristic
428C22×D4C23×C7311yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C2×SD16—22no—
432C2×SD16—22no—
433C2×SD16—22no—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×SD16—22no—
437C2×SD16—22no—
438C2×SD16—22no—
439C2×SD16—41no—
440C2×SD16—41no—
441C2×SD16—41no—
442C2×SD16—41no—
443C22×C8C23×C7311yescharacteristic
444C22×C8C23×C7311yescharacteristic
445C22×C8C23×C7311yescharacteristic
446C22×C8C23×C7311yescharacteristic
447C4⋊Q8—22no—
448C4⋊Q8—41no—
449#127—22no—
450#127—22no—
451C4×Q8—22no—
452C4×Q8—41no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—44no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4D4×C7311yescharacteristic
463C2×C4⋊C4D4×C7311yescharacteristic
464C2×C4⋊C4C23×C7311yescharacteristic
465C2×C4⋊C4C23×C7311yescharacteristic
466C2×C4⋊C4C23×C7311yescharacteristic
467C2×C4⋊C4C23×C7311yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42C23×C7311yescharacteristic
477C2×C42C23×C7311yescharacteristic
478C2×C42C23×C7311yescharacteristic
479#107—22no—
480#107—41no—
481C4⋊C8—22no—
482#103—22no—
483#103—22no—
484#103—41no—
485#103D4×C7314yescomplemented
486#102—22no—
487#102—22no—
488#102—41no—
489#102—41no—
490#97—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95D4×C7311yescharacteristic
500#95D4×C7311yescharacteristic
501C24—21no—
502C24—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8C2×D4×C7312yes—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4#41×C7312yes—
532C2×D4#41×C7312yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4C2×D4×C7311yescharacteristic
546C22×C4C2×D4×C7311yescharacteristic
547C22×C4C2×D4×C7311yescharacteristic
548C22×C4C2×D4×C7311yescharacteristic
549C22×C4C2×D4×C7311yescharacteristic
550C22×C4C2×D4×C7311yescharacteristic
551C22×C4C24×C7311yescharacteristic
552SD16—28no—
553SD16—44no—
554SD16—44no—
555SD16—44no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8C2×D4×C7312yes—
567C2×C8#41×C7312yes—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4C2×D4×C7312yes—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—42no—
595C42—42no—
596C23—22no—
597C23—22no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C22×D4×C7311yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619D4—22no—
620D4—22no—
621D4—22no—
622D4—22no—
623D4—48no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—84no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4AGL(1,ℤ/8)×C7312yes—
666C2×C4#137×C7312yes—
667C2×C4C22×D4×C7311yescharacteristic
668C2×C4C2×#41×C7311yescharacteristic
669C2×C4C2×#41×C7311yescharacteristic
670C2×C4C2×#41×C7311yescharacteristic
671C2×C4H(5,𝔽2)×C7311yescharacteristic
672C2×C4H(5,𝔽2)×C7311yescharacteristic
673C8—22no—
674C8—22no—
675C8—41no—
676C8—41no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22#525×C7311yescharacteristic
692C22D42×C7311yescharacteristic
693C22#550×C7311yescharacteristic
694C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
695C22C2×#137×C7311yescharacteristic
696C22#577×C7311yescharacteristic
697C22#577×C7311yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—41no—
702C4—42no—
703C4—41no—
704C4—41no—
705C4—41no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4#525×C7311yescharacteristic
711C4#538×C7311yescharacteristic
712C4#546×C7311yescharacteristic
713C4#553×C7311yescharacteristic
714C2—82no—
715C2—82no—
716C2C73×#245611yescharacteristic
717C2C73×#311011yescharacteristic
718C2C73×#312311yescharacteristic
719C2C73×#326511yescharacteristic
720C2C73×#327811yescharacteristic
721C2C73×#339711yescharacteristic
722C2C73×#340011yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#127×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
1. C2×#461×C73C2semidirect
2. C2×#440×C73C2semidirect
3. C73×#2446C2semidirect
5. C73×#2067C2semidirect
8. C73×#2013C2semidirect
9. C73×#1973C2semidirect
10. C73×#1928C2semidirect
11. C73×#1928C2semidirect
12. C73×#1917C2semidirect
13. C73×#1880C2semidirect
14. C73×#1877C2semidirect
15. C73×#1862C2semidirect
123. #103×C73D4semidirect
352. #26603C73direct (N × H)
362. C2×#461C2×C73semidirect
363. C2×#440C2×C73semidirect
364. #2446C2×C73semidirect
366. #2067C2×C73semidirect
369. #2013C2×C73semidirect
370. #1973C2×C73semidirect
371. #1928C2×C73semidirect
372. #1928C2×C73semidirect
373. #1917C2×C73semidirect
374. #1880C2×C73semidirect
375. #1877C2×C73semidirect
376. #1862C2×C73semidirect
377. C73#26603direct (N × H)
485. #103D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C732
C2×#440×C732
C73×#24462
C73×#23662
C73×#20672
C73×#20142
C73×#20132
C73×#19732
C73×#19282
C73×#19172
C73×#18802
C73×#18772
C73×#18622
#2660373