Finite Group Databasebeta

← C73×#26985 #32936389

Subgroups — C73×#26985 #32936389

Order 18688.

936 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C73C211yesmaximal, characteristic, complemented
2C2×#442×C73C211yesmaximal, characteristic, complemented
3C73×#2427C211yesmaximal, characteristic, complemented
4C73×#2420C211yesmaximal, characteristic, complemented
5C73×#2085C211yesmaximal, characteristic, complemented
6C73×#2035C211yesmaximal, characteristic, complemented
7C73×#2012C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic
9C73×#1958C211yesmaximal, characteristic, complemented
10C73×#1935C211yesmaximal, characteristic, complemented
11C73×#1934C211yesmaximal, characteristic, complemented
12C73×#1895C211yesmaximal, characteristic, complemented
13C73×#1877C211yesmaximal, characteristic, complemented
14C73×#1862C211yesmaximal, 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×D4×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25#468×C73—24no—
26#442×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#397×C73—21no—
42#394×C73—21no—
43#394×C73—21no—
44#391×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic
46#389×C73C2211yescharacteristic
47#389×C73C2211yescharacteristic
48#386×C73—21no—
49#386×C73—21no—
50#382×C73C2211yescharacteristic
51#381×C73—21no—
52#380×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×C73—21no—
68C23×C4×C73C2311yescharacteristic
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×SD16×C73—41no—
72C2×D8×C73—22no—
73C2×D8×C73—22no—
74C2×D8×C73—22no—
75C2×M16×C73—22no—
76C2×M16×C73—22no—
77C2×M16×C73—41no—
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82#124×C73—22no—
83#124×C73—41no—
84C22⋊Q8×C73—22no—
85C22⋊Q8×C73—41no—
86#121×C73—22no—
87#121×C73—22no—
88#121×C73—41no—
89#121×C73—41no—
90C4×D4×C73—22no—
91C4×D4×C73—22no—
92C4×D4×C73—41no—
93C4×D4×C73—41no—
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×C73D411yescharacteristic
113C2×C22⋊C4×C73D411yescharacteristic
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116#107×C73—22no—
117#106×C73—22no—
118#103×C73—22no—
119#103×C73—22no—
120#103×C73—41no—
121#102×C73—22no—
122#102×C73—22no—
123#102×C73—41no—
124#102×C73—41no—
125#102×C73D414yescomplemented
126C22⋊C8×C73—22no—
127#97×C73—22no—
128C4×C8×C73—41no—
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×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—21no—
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—42no—
158C2×D4×C73—42no—
159C2×D4×C73—42no—
160C2×D4×C73—42no—
161C2×D4×C73—81no—
162C2×D4×C73—81no—
163C2×D4×C73C2×D412yes—
164C2×D4×C73#4112yes—
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—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×C73C2411yescharacteristic
189SD16×C73—44no—
190D8×C73—28no—
191M16×C73—44no—
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×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73C2×D412yes—
202C2×C8×C73#4112yes—
203C2×C8×C73#4112yes—
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—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—42no—
214C4⋊C4×C73—81no—
215C4⋊C4×C73—81no—
216C4⋊C4×C73C2×D412yes—
217C22⋊C4×C73—41no—
218C22⋊C4×C73—41no—
219C22⋊C4×C73—42no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—42no—
224C22⋊C4×C73—42no—
225C22⋊C4×C73—42no—
226C22⋊C4×C73—81no—
227C22⋊C4×C73—81no—
228C22⋊C4×C73—81no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—22no—
236C23×C73—22no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
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—41no—
256Q8×C73—41no—
257Q8×C73—41no—
258Q8×C73—41no—
259D4×C73—22no—
260D4×C73—22no—
261D4×C73—22no—
262D4×C73—22no—
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—21no—
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—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—84no—
307C2×C4×C73—84no—
308C2×C4×C73C22×D411yescharacteristic
309C2×C4×C73C2×#4111yescharacteristic
310C2×C4×C73C2×#4111yescharacteristic
311C2×C4×C73C2×#4111yescharacteristic
312C2×C4×C73H(5,𝔽2)11yescharacteristic
313C2×C4×C73H(5,𝔽2)11yescharacteristic
314C8×C73—22no—
315C8×C73—22no—
316C8×C73—22no—
317C8×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73—42no—
322C22×C73—42no—
323C22×C73—41no—
324C22×C73—42no—
325C22×C73—42no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—42no—
329C22×C73—41no—
330C22×C73—42no—
331C22×C73—81no—
332C22×C73—81no—
333C22×C73—81no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73—81no—
338C22×C73—81no—
339C22×C73#53211yescharacteristic
340C22×C73D4211yescharacteristic
341C22×C73#54611yescharacteristic
342C22×C73#57511yescharacteristic
343C22×C73#57511yescharacteristic
344C22×C73#57611yescharacteristic
345C22×C73#57711yescharacteristic
346C4×C73—41no—
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—81no—
357C4×C73#52511yescharacteristic
358C4×C73#54011yescharacteristic
359C4×C73#54611yescharacteristic
360C4×C73#55311yescharacteristic
361#26985C7311yesmaximal, characteristic, direct product factor, Sylow
362C2×C73—81no—
363C2×C73—82no—
364C2×C73—82no—
365C2×C73#246411yescharacteristic
366C2×C73#317911yescharacteristic
367C2×C73#318311yescharacteristic
368C2×C73#327311yescharacteristic
369C2×C73#327511yescharacteristic
370C2×C73#330711yescharacteristic
371C2×C73#331911yescharacteristic
372C2×#468C2×C7311yescharacteristic, complemented
373C2×#442C2×C7311yescharacteristic, complemented
374#2427C2×C7311yescharacteristic, complemented
375#2420C2×C7311yescharacteristic, complemented
376#2085C2×C7311yescharacteristic, complemented
377#2035C2×C7311yescharacteristic, complemented
378#2012C2×C7311yescharacteristic, complemented
379#1999C2×C7311yescharacteristic
380#1958C2×C7311yescharacteristic, complemented
381#1935C2×C7311yescharacteristic, complemented
382#1934C2×C7311yescharacteristic, complemented
383#1895C2×C7311yescharacteristic, complemented
384#1877C2×C7311yescharacteristic, complemented
385#1862C2×C7311yescharacteristic, complemented
386#1753C2×C7311yescharacteristic, complemented
387C73#2698511yescharacteristic, direct product factor, Sylow
388C22×SD16C22×C7311yescharacteristic
389C22×D8C22×C7311yescharacteristic
390C22×M16C22×C7311yescharacteristic
391C2×#124C22×C7311yescharacteristic
392C2×C22⋊Q8C22×C7311yescharacteristic
393C2×#121C22×C7311yescharacteristic
394C2×#121C22×C7311yescharacteristic
395C2×C4×D4C22×C7311yescharacteristic
396C2×C4×D4C22×C7311yescharacteristic
397#468—24no—
398#442—24no—
399C2×#107C22×C7311yescharacteristic
400C2×#106C22×C7311yescharacteristic
401C2×#103C22×C7311yescharacteristic
402C2×#103C22×C7311yescharacteristic
403C2×#103C22×C7311yescharacteristic
404C2×#102C22×C7311yescharacteristic
405C2×#102C22×C7311yescharacteristic
406C2×#102C22×C7311yescharacteristic
407C2×#102C22×C7311yescharacteristic
408C2×#102C22×C7311yescharacteristic
409C2×C22⋊C8C22×C7311yescharacteristic
410C2×#97C22×C7311yescharacteristic
411C2×C4×C8C22×C7311yescharacteristic
412#397—21no—
413#397—21no—
414#394—21no—
415#394—21no—
416#391C22×C7311yescharacteristic
417#390C22×C7311yescharacteristic
418#389C22×C7311yescharacteristic
419#389C22×C7311yescharacteristic
420#386—21no—
421#386—21no—
422#382C22×C7311yescharacteristic
423#381—21no—
424#380—21no—
425#380C22×C7311yescharacteristic
426C4×C22⋊C4C22×C7311yescharacteristic
427#340C22×C7311yescharacteristic
428#340C22×C7311yescharacteristic
429#340C22×C7311yescharacteristic
430#340C22×C7311yescharacteristic
431#336C22×C7311yescharacteristic
432#336C22×C7311yescharacteristic
433C22×Q8C23×C7311yescharacteristic
434C22×D4—21no—
435C22×D4—21no—
436C22×D4C23×C7311yescharacteristic
437C22×D4C23×C7311yescharacteristic
438C23×C4—21no—
439C23×C4—21no—
440C23×C4C23×C7311yescharacteristic
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—41no—
444C2×D8—22no—
445C2×D8—22no—
446C2×D8—22no—
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—41no—
450C22×C8C23×C7311yescharacteristic
451C22×C8C23×C7311yescharacteristic
452C22×C8C23×C7311yescharacteristic
453C22×C8C23×C7311yescharacteristic
454#124—22no—
455#124—41no—
456C22⋊Q8—22no—
457C22⋊Q8—41no—
458#121—22no—
459#121—22no—
460#121—41no—
461#121—41no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—41no—
465C4×D4—41no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4C23×C7311yescharacteristic
470C2×C4⋊C4C23×C7311yescharacteristic
471C2×C4⋊C4C23×C7311yescharacteristic
472C2×C4⋊C4C23×C7311yescharacteristic
473C2×C4⋊C4C23×C7311yescharacteristic
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×C42C23×C7311yescharacteristic
487C2×C42C23×C7311yescharacteristic
488#107—22no—
489#106—22no—
490#103—22no—
491#103—22no—
492#103—41no—
493#102—22no—
494#102—22no—
495#102—41no—
496#102—41no—
497#102D4×C7314yescomplemented
498C22⋊C8—22no—
499#97—22no—
500C4×C8—41no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95D4×C7311yescharacteristic
509#95D4×C7311yescharacteristic
510C24—21no—
511C24—21no—
512C24C2×D4×C7311yescharacteristic
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—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—
536C2×D4#41×C7312yes—
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—21no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4C2×D4×C7311yescharacteristic
556C22×C4C2×D4×C7311yescharacteristic
557C22×C4C2×D4×C7311yescharacteristic
558C22×C4C2×D4×C7311yescharacteristic
559C22×C4C2×D4×C7311yescharacteristic
560C22×C4C24×C7311yescharacteristic
561SD16—44no—
562D8—28no—
563M16—44no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8C2×D4×C7312yes—
574C2×C8#41×C7312yes—
575C2×C8#41×C7312yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4—81no—
587C4⋊C4—81no—
588C4⋊C4C2×D4×C7312yes—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C23—21no—
606C23—21no—
607C23—22no—
608C23—22no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23C22×D4×C7311yescharacteristic
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—84no—
640D4—84no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
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—41no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4C22×D4×C7311yescharacteristic
681C2×C4C2×#41×C7311yescharacteristic
682C2×C4C2×#41×C7311yescharacteristic
683C2×C4C2×#41×C7311yescharacteristic
684C2×C4H(5,𝔽2)×C7311yescharacteristic
685C2×C4H(5,𝔽2)×C7311yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—41no—
690C22—41no—
691C22—42no—
692C22—42no—
693C22—41no—
694C22—42no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—41no—
702C22—41no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22#532×C7311yescharacteristic
712C22D42×C7311yescharacteristic
713C22#546×C7311yescharacteristic
714C22#575×C7311yescharacteristic
715C22#575×C7311yescharacteristic
716C22#576×C7311yescharacteristic
717C22#577×C7311yescharacteristic
718C4—41no—
719C4—41no—
720C4—42no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4#525×C7311yescharacteristic
730C4#540×C7311yescharacteristic
731C4#546×C7311yescharacteristic
732C4#553×C7311yescharacteristic
733C2—81no—
734C2—82no—
735C2—82no—
736C2C73×#246411yescharacteristic
737C2C73×#317911yescharacteristic
738C2C73×#318311yescharacteristic
739C2C73×#327311yescharacteristic
740C2C73×#327511yescharacteristic
741C2C73×#330711yescharacteristic
742C2C73×#331911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#1999C2
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
1. C2×#468×C73C2semidirect
2. C2×#442×C73C2semidirect
3. C73×#2427C2semidirect
4. C73×#2420C2semidirect
5. C73×#2085C2semidirect
6. C73×#2035C2semidirect
7. C73×#2012C2semidirect
9. C73×#1958C2semidirect
10. C73×#1935C2semidirect
11. C73×#1934C2semidirect
12. C73×#1895C2semidirect
13. C73×#1877C2semidirect
14. C73×#1862C2semidirect
15. C73×#1753C2semidirect
125. #102×C73D4semidirect
361. #26985C73direct (N × H)
372. C2×#468C2×C73semidirect
373. C2×#442C2×C73semidirect
374. #2427C2×C73semidirect
375. #2420C2×C73semidirect
376. #2085C2×C73semidirect
377. #2035C2×C73semidirect
378. #2012C2×C73semidirect
380. #1958C2×C73semidirect
381. #1935C2×C73semidirect
382. #1934C2×C73semidirect
383. #1895C2×C73semidirect
384. #1877C2×C73semidirect
385. #1862C2×C73semidirect
386. #1753C2×C73semidirect
387. C73#26985direct (N × H)
497. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C732
C2×#442×C732
C73×#24272
C73×#24202
C73×#20852
C73×#20352
C73×#20122
C73×#19992
C73×#19582
C73×#19352
C73×#19342
C73×#18952
C73×#18772
C73×#18622
C73×#17532
#2698573