Finite Group Databasebeta

← C73×#26982 #32936386

Subgroups — C73×#26982 #32936386

Order 18688.

922 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C73C211yesmaximal, characteristic
2C2×#440×C73C211yesmaximal, characteristic, complemented
3C73×#2426C211yesmaximal, characteristic, complemented
4C73×#2420C211yesmaximal, characteristic, complemented
5C73×#2085C211yesmaximal, characteristic, complemented
6C73×#2033C211yesmaximal, characteristic, complemented
7C73×#2012C211yesmaximal, characteristic, complemented
8C73×#2000C211yesmaximal, characteristic, complemented
9C73×#1958C211yesmaximal, characteristic, complemented
10C73×#1936C211yesmaximal, characteristic, complemented
11C73×#1934C211yesmaximal, characteristic, complemented
12C73×#1894C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1865C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C2×#124×C73C2211yescharacteristic
20C2×C22⋊Q8×C73C2211yescharacteristic
21C2×#121×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×C4×Q8×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25#469×C73—24no—
26#440×C73—24no—
27C2×#107×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#103×C73C2211yescharacteristic
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×#97×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic
40#397×C73—21no—
41#396×C73—21no—
42#394×C73—21no—
43#394×C73—21no—
44#390×C73—21no—
45#390×C73C2211yescharacteristic
46#390×C73C2211yescharacteristic
47#389×C73C2211yescharacteristic
48#389×C73C2211yescharacteristic
49#388×C73—21no—
50#386×C73—21no—
51#382×C73C2211yescharacteristic
52#381×C73—21no—
53#380×C73C2211yescharacteristic
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C22×D4×C73C2311yescharacteristic
66C23×C4×C73—21no—
67C23×C4×C73C2311yescharacteristic
68C2×SD16×C73—22no—
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×D8×C73—22no—
72C2×D8×C73—22no—
73C2×D8×C73—41no—
74C2×M16×C73—22no—
75C2×M16×C73—22no—
76C2×M16×C73—41no—
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81#124×C73—22no—
82#124×C73—41no—
83C22⋊Q8×C73—22no—
84C22⋊Q8×C73—41no—
85#121×C73—22no—
86#121×C73—22no—
87#121×C73—41no—
88#121×C73—41no—
89C4×Q8×C73—22no—
90C4×Q8×C73—41no—
91C4×D4×C73—22no—
92C4×D4×C73—41no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
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×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73D411yescharacteristic
114C2×C22⋊C4×C73D411yescharacteristic
115C2×C42×C73—21no—
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
118#107×C73—22no—
119#106×C73—22no—
120#103×C73—22no—
121#103×C73—22no—
122#103×C73—41no—
123#102×C73—22no—
124#102×C73—22no—
125#102×C73—41no—
126#102×C73—41no—
127#102×C73D414yes—
128C22⋊C8×C73—22no—
129#97×C73—22no—
130C4×C8×C73—41no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73D411yescharacteristic
137#95×C73D411yescharacteristic
138C24×C73—21no—
139C24×C73—21no—
140C24×C73C2×D411yescharacteristic
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73#4112yes—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—42no—
159C2×D4×C73—42no—
160C2×D4×C73—42no—
161C2×D4×C73—42no—
162C2×D4×C73—81no—
163C2×D4×C73—81no—
164C2×D4×C73C2×D412yes—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
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—81no—
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2411yescharacteristic
186SD16×C73—28no—
187D8×C73—44no—
188M16×C73—44no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73C2×D412yes—
199C2×C8×C73#4112yes—
200C2×C8×C73#4112yes—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—42no—
211C4⋊C4×C73—42no—
212C4⋊C4×C73—81no—
213C4⋊C4×C73—81no—
214C4⋊C4×C73C2×D412yes—
215C22⋊C4×C73—41no—
216C22⋊C4×C73—41no—
217C22⋊C4×C73—42no—
218C22⋊C4×C73—42no—
219C22⋊C4×C73—42no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—42no—
224C22⋊C4×C73—81no—
225C22⋊C4×C73—81no—
226C22⋊C4×C73—81no—
227C22⋊C4×C73—81no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73—42no—
233C23×C73—21no—
234C23×C73—22no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73C22×D411yescharacteristic
255Q8×C73—22no—
256Q8×C73—22no—
257Q8×C73—41no—
258Q8×C73—41no—
259D4×C73—22no—
260D4×C73—22no—
261D4×C73—41no—
262D4×C73—41no—
263D4×C73—41no—
264D4×C73—41no—
265D4×C73—41no—
266D4×C73—41no—
267D4×C73—84no—
268D4×C73—84no—
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—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—21no—
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—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—84no—
307C2×C4×C73C22×D411yescharacteristic
308C2×C4×C73C2×#4111yescharacteristic
309C2×C4×C73C2×#4111yescharacteristic
310C2×C4×C73C2×#4111yescharacteristic
311C2×C4×C73H(5,𝔽2)11yescharacteristic
312C2×C4×C73H(5,𝔽2)11yescharacteristic
313C8×C73—22no—
314C8×C73—22no—
315C8×C73—22no—
316C8×C73—41no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—42no—
321C22×C73—42no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—42no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—81no—
328C22×C73—81no—
329C22×C73—81no—
330C22×C73—81no—
331C22×C73—81no—
332C22×C73—81no—
333C22×C73—81no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73—81no—
338C22×C73#53211yescharacteristic
339C22×C73D4211yescharacteristic
340C22×C73#54611yescharacteristic
341C22×C73#57511yescharacteristic
342C22×C73#57511yescharacteristic
343C22×C73#57611yescharacteristic
344C22×C73#57711yescharacteristic
345C4×C73—41no—
346C4×C73—42no—
347C4×C73—41no—
348C4×C73—42no—
349C4×C73—41no—
350C4×C73—41no—
351C4×C73—41no—
352C4×C73—81no—
353C4×C73—81no—
354C4×C73—81no—
355C4×C73—81no—
356C4×C73#52511yescharacteristic
357C4×C73#54011yescharacteristic
358C4×C73#54611yescharacteristic
359C4×C73#55311yescharacteristic
360#26982C7311yesmaximal, characteristic, direct product factor, Sylow
361C2×C73—81no—
362C2×C73—82no—
363C2×C73—161no—
364C2×C73#246411yescharacteristic
365C2×C73#317911yescharacteristic
366C2×C73#318311yescharacteristic
367C2×C73#327311yescharacteristic
368C2×C73#327511yescharacteristic
369C2×C73#330911yescharacteristic
370C2×C73#332111yescharacteristic
371C2×#469C2×C7311yescharacteristic
372C2×#440C2×C7311yescharacteristic, complemented
373#2426C2×C7311yescharacteristic, complemented
374#2420C2×C7311yescharacteristic, complemented
375#2085C2×C7311yescharacteristic, complemented
376#2033C2×C7311yescharacteristic, complemented
377#2012C2×C7311yescharacteristic, complemented
378#2000C2×C7311yescharacteristic, complemented
379#1958C2×C7311yescharacteristic, complemented
380#1936C2×C7311yescharacteristic, complemented
381#1934C2×C7311yescharacteristic, complemented
382#1894C2×C7311yescharacteristic, complemented
383#1879C2×C7311yescharacteristic, complemented
384#1865C2×C7311yescharacteristic, complemented
385#1753C2×C7311yescharacteristic, complemented
386C73#2698211yescharacteristic, direct product factor, Sylow
387C22×SD16C22×C7311yescharacteristic
388C22×D8C22×C7311yescharacteristic
389C22×M16C22×C7311yescharacteristic
390C2×#124C22×C7311yescharacteristic
391C2×C22⋊Q8C22×C7311yescharacteristic
392C2×#121C22×C7311yescharacteristic
393C2×#121C22×C7311yescharacteristic
394C2×C4×Q8C22×C7311yescharacteristic
395C2×C4×D4C22×C7311yescharacteristic
396#469—24no—
397#440—24no—
398C2×#107C22×C7311yescharacteristic
399C2×#106C22×C7311yescharacteristic
400C2×#103C22×C7311yescharacteristic
401C2×#103C22×C7311yescharacteristic
402C2×#103C22×C7311yescharacteristic
403C2×#102C22×C7311yescharacteristic
404C2×#102C22×C7311yescharacteristic
405C2×#102C22×C7311yescharacteristic
406C2×#102C22×C7311yescharacteristic
407C2×#102C22×C7311yescharacteristic
408C2×C22⋊C8C22×C7311yescharacteristic
409C2×#97C22×C7311yescharacteristic
410C2×C4×C8C22×C7311yescharacteristic
411#397—21no—
412#396—21no—
413#394—21no—
414#394—21no—
415#390—21no—
416#390C22×C7311yescharacteristic
417#390C22×C7311yescharacteristic
418#389C22×C7311yescharacteristic
419#389C22×C7311yescharacteristic
420#388—21no—
421#386—21no—
422#382C22×C7311yescharacteristic
423#381—21no—
424#380C22×C7311yescharacteristic
425C4×C22⋊C4C22×C7311yescharacteristic
426#340C22×C7311yescharacteristic
427#340C22×C7311yescharacteristic
428#340C22×C7311yescharacteristic
429#340C22×C7311yescharacteristic
430#336C22×C7311yescharacteristic
431#336C22×C7311yescharacteristic
432C22×Q8C23×C7311yescharacteristic
433C22×D4—21no—
434C22×D4—21no—
435C22×D4C23×C7311yescharacteristic
436C22×D4C23×C7311yescharacteristic
437C23×C4—21no—
438C23×C4C23×C7311yescharacteristic
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×D8—22no—
443C2×D8—22no—
444C2×D8—41no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—41no—
448C22×C8C23×C7311yescharacteristic
449C22×C8C23×C7311yescharacteristic
450C22×C8C23×C7311yescharacteristic
451C22×C8C23×C7311yescharacteristic
452#124—22no—
453#124—41no—
454C22⋊Q8—22no—
455C22⋊Q8—41no—
456#121—22no—
457#121—22no—
458#121—41no—
459#121—41no—
460C4×Q8—22no—
461C4×Q8—41no—
462C4×D4—22no—
463C4×D4—41no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4C23×C7311yescharacteristic
469C2×C4⋊C4C23×C7311yescharacteristic
470C2×C4⋊C4C23×C7311yescharacteristic
471C2×C4⋊C4C23×C7311yescharacteristic
472C2×C4⋊C4C23×C7311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4D4×C7311yescharacteristic
485C2×C22⋊C4D4×C7311yescharacteristic
486C2×C42—21no—
487C2×C42C23×C7311yescharacteristic
488C2×C42C23×C7311yescharacteristic
489#107—22no—
490#106—22no—
491#103—22no—
492#103—22no—
493#103—41no—
494#102—22no—
495#102—22no—
496#102—41no—
497#102—41no—
498#102D4×C7314yes—
499C22⋊C8—22no—
500#97—22no—
501C4×C8—41no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95D4×C7311yescharacteristic
508#95D4×C7311yescharacteristic
509C24—21no—
510C24—21no—
511C24C2×D4×C7311yescharacteristic
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8#41×C7312yes—
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—21no—
528C2×D4—21no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—81no—
534C2×D4—81no—
535C2×D4C2×D4×C7312yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—81no—
551C22×C4C2×D4×C7311yescharacteristic
552C22×C4C2×D4×C7311yescharacteristic
553C22×C4C2×D4×C7311yescharacteristic
554C22×C4C2×D4×C7311yescharacteristic
555C22×C4C2×D4×C7311yescharacteristic
556C22×C4C24×C7311yescharacteristic
557SD16—28no—
558D8—44no—
559M16—44no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8C2×D4×C7312yes—
570C2×C8#41×C7312yes—
571C2×C8#41×C7312yes—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—81no—
584C4⋊C4—81no—
585C4⋊C4C2×D4×C7312yes—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—42no—
604C23—21no—
605C23—22no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C22×D4×C7311yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—41no—
629Q8—41no—
630D4—22no—
631D4—22no—
632D4—41no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—84no—
639D4—84no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—84no—
678C2×C4C22×D4×C7311yescharacteristic
679C2×C4C2×#41×C7311yescharacteristic
680C2×C4C2×#41×C7311yescharacteristic
681C2×C4C2×#41×C7311yescharacteristic
682C2×C4H(5,𝔽2)×C7311yescharacteristic
683C2×C4H(5,𝔽2)×C7311yescharacteristic
684C8—22no—
685C8—22no—
686C8—22no—
687C8—41no—
688C22—41no—
689C22—42no—
690C22—42no—
691C22—41no—
692C22—41no—
693C22—42no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22#532×C7311yescharacteristic
710C22D42×C7311yescharacteristic
711C22#546×C7311yescharacteristic
712C22#575×C7311yescharacteristic
713C22#575×C7311yescharacteristic
714C22#576×C7311yescharacteristic
715C22#577×C7311yescharacteristic
716C4—41no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4#525×C7311yescharacteristic
728C4#540×C7311yescharacteristic
729C4#546×C7311yescharacteristic
730C4#553×C7311yescharacteristic
731C2—81no—
732C2—82no—
733C2—161no—
734C2C73×#246411yescharacteristic
735C2C73×#317911yescharacteristic
736C2C73×#318311yescharacteristic
737C2C73×#327311yescharacteristic
738C2C73×#327511yescharacteristic
739C2C73×#330911yescharacteristic
740C2C73×#332111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#469×C73C2
LCSG ▷ C22×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
2. C2×#440×C73C2semidirect
3. C73×#2426C2semidirect
4. C73×#2420C2semidirect
5. C73×#2085C2semidirect
6. C73×#2033C2semidirect
7. C73×#2012C2semidirect
8. C73×#2000C2semidirect
9. C73×#1958C2semidirect
10. C73×#1936C2semidirect
11. C73×#1934C2semidirect
12. C73×#1894C2semidirect
13. C73×#1879C2semidirect
14. C73×#1865C2semidirect
15. C73×#1753C2semidirect
360. #26982C73direct (N × H)
372. C2×#440C2×C73semidirect
373. #2426C2×C73semidirect
374. #2420C2×C73semidirect
375. #2085C2×C73semidirect
376. #2033C2×C73semidirect
377. #2012C2×C73semidirect
378. #2000C2×C73semidirect
379. #1958C2×C73semidirect
380. #1936C2×C73semidirect
381. #1934C2×C73semidirect
382. #1894C2×C73semidirect
383. #1879C2×C73semidirect
384. #1865C2×C73semidirect
385. #1753C2×C73semidirect
386. C73#26982direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#469×C732
C2×#440×C732
C73×#24262
C73×#24202
C73×#20852
C73×#20332
C73×#20122
C73×#20002
C73×#19582
C73×#19362
C73×#19342
C73×#18942
C73×#18792
C73×#18652
C73×#17532
#2698273