Finite Group Databasebeta

← C73×#25396 #32934800

Subgroups — C73×#25396 #32934800

Order 18688.

1184 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C73C211yesmaximal, characteristic, complemented
2C2×#466×C73C211yesmaximal, characteristic, complemented
3C2×#459×C73C211yesmaximal, characteristic, complemented
4C2×#435×C73C211yesmaximal, characteristic, complemented
5C73×#2541C211yesmaximal, characteristic, complemented
6C73×#2535C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#1999C211yesmaximal, characteristic, complemented
10C73×#1999C211yesmaximal, characteristic, complemented
11C73×#1961C211yesmaximal, characteristic, complemented
12C73×#1949C211yesmaximal, characteristic, complemented
13C73×#1895C211yesmaximal, characteristic, complemented
14C73×#1893C211yesmaximal, characteristic, complemented
15C73×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C23×C8×C73C2211yescharacteristic
20C2×#127×C73—21no—
21C2×#127×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×#121×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×C4×D4×C73C2211yescharacteristic
29C2×C4×D4×C73C2211yescharacteristic
30#469×C73—24no—
31#466×C73—24no—
32#459×C73—24no—
33#435×C73—24no—
34C2×#107×C73C2211yescharacteristic
35C2×#106×C73C2211yescharacteristic
36C2×C4⋊C8×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×#97×C73C2211yescharacteristic
48#397×C73—21no—
49#392×C73—21no—
50#392×C73—21no—
51#392×C73—21no—
52#390×C73—21no—
53#386×C73—21no—
54#386×C73—21no—
55#382×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73—21no—
71C22×D4×C73D411yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C22×D4×C73C2311yescharacteristic
74C22×D4×C73C2311yescharacteristic
75C23×C4×C73—21no—
76C23×C4×C73C2311yescharacteristic
77C23×C4×C73C2311yescharacteristic
78C2×D8×C73—22no—
79C2×D8×C73—22no—
80C2×D8×C73—22no—
81C2×D8×C73—22no—
82C2×D8×C73—41no—
83C2×D8×C73—41no—
84C2×M16×C73—22no—
85C2×M16×C73—22no—
86C2×M16×C73—41no—
87C22×C8×C73—22no—
88C22×C8×C73—22no—
89C22×C8×C73—41no—
90C22×C8×C73C2311yescharacteristic
91C22×C8×C73C2311yescharacteristic
92C22×C8×C73C2311yescharacteristic
93C22×C8×C73C2311yescharacteristic
94#127×C73—22no—
95#127×C73—22no—
96#127×C73—44no—
97#121×C73—22no—
98#121×C73—22no—
99#121×C73—22no—
100#121×C73—22no—
101#121×C73—22no—
102#121×C73—22no—
103#121×C73—41no—
104#121×C73—41no—
105#121×C73—41no—
106#121×C73—41no—
107#121×C73—41no—
108#121×C73—41no—
109C4×D4×C73—22no—
110C4×D4×C73—22no—
111C4×D4×C73—22no—
112C4×D4×C73—22no—
113C2×C4⋊C4×C73D411yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C22⋊C4×C73—21no—
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73D411yescharacteristic
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#107×C73—22no—
133#106×C73—22no—
134C4⋊C8×C73D414yescomplemented
135#102×C73—22no—
136#102×C73—22no—
137#102×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—41no—
141#102×C73—41no—
142#102×C73D414yescomplemented
143C22⋊C8×C73—22no—
144C22⋊C8×C73—22no—
145#97×C73—22no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73—21no—
150#95×C73—21no—
151C24×C73—21no—
152C24×C73—21no—
153C24×C73—21no—
154C24×C73C2×D411yescharacteristic
155C24×C73C2×D411yescharacteristic
156C2×D4×C73—22no—
157C2×D4×C73—22no—
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—21no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—41no—
176C2×D4×C73—42no—
177C2×D4×C73—42no—
178C2×D4×C73—42no—
179C2×D4×C73—42no—
180C2×D4×C73—42no—
181C2×D4×C73—42no—
182C2×D4×C73—42no—
183C2×D4×C73—42no—
184C2×D4×C73—42no—
185C2×D4×C73—42no—
186C2×D4×C73—42no—
187C2×D4×C73—42no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—42no—
191C2×D4×C73—42no—
192C2×D4×C73—81no—
193C2×D4×C73—81no—
194C2×D4×C73—81no—
195C2×D4×C73—81no—
196C2×D4×C73—81no—
197C2×D4×C73—81no—
198C2×D4×C73—81no—
199C2×D4×C73—81no—
200C2×D4×C73C2×D412yes—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—42no—
219C22×C4×C73—81no—
220C22×C4×C73—81no—
221C22×C4×C73C2×D411yescharacteristic
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2411yescharacteristic
226D8×C73—44no—
227D8×C73—44no—
228M16×C73—44no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—44no—
239C2×C8×C73C2×D412yes—
240C2×C8×C73C2×D412yes—
241C2×C8×C73C2×D412yes—
242C4⋊C4×C73—22no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73C2×D412yes—
252C4⋊C4×C73#4112yes—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—42no—
258C22⋊C4×C73—42no—
259C22⋊C4×C73—42no—
260C22⋊C4×C73—42no—
261C22⋊C4×C73—42no—
262C22⋊C4×C73—81no—
263C22⋊C4×C73—81no—
264C42×C73—42no—
265C42×C73C2×D412yes—
266C42×C73#4112yes—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—22no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—41no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73—41no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73AGL(1,ℤ/8)12yes—
302C23×C73C22×D411yescharacteristic
303D4×C73—22no—
304D4×C73—22no—
305D4×C73—44no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—41no—
310D4×C73—41no—
311D4×C73—41no—
312D4×C73—41no—
313D4×C73—41no—
314D4×C73—41no—
315D4×C73—41no—
316D4×C73—84no—
317D4×C73—84no—
318D4×C73—84no—
319D4×C73—84no—
320D4×C73—84no—
321D4×C73—84no—
322D4×C73—84no—
323D4×C73—84no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73—84no—
358C2×C4×C73#12112yes—
359C2×C4×C73#12112yes—
360C2×C4×C73C22×D411yescharacteristic
361C2×C4×C73C22×D411yescharacteristic
362C2×C4×C73C2×#4111yescharacteristic
363C2×C4×C73C2×#4111yescharacteristic
364C2×C4×C73H(5,𝔽2)11yescharacteristic
365C2×C4×C73H(5,𝔽2)11yescharacteristic
366C8×C73—22no—
367C8×C73—22no—
368C8×C73—22no—
369C8×C73—41no—
370C22×C73—22no—
371C22×C73—22no—
372C22×C73—22no—
373C22×C73—41no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—41no—
377C22×C73—41no—
378C22×C73—42no—
379C22×C73—41no—
380C22×C73—42no—
381C22×C73—41no—
382C22×C73—42no—
383C22×C73—41no—
384C22×C73—41no—
385C22×C73—41no—
386C22×C73—41no—
387C22×C73—81no—
388C22×C73—81no—
389C22×C73—81no—
390C22×C73—81no—
391C22×C73—81no—
392C22×C73—81no—
393C22×C73—81no—
394C22×C73—81no—
395C22×C73—81no—
396C22×C73—81no—
397C22×C73—81no—
398C22×C73—81no—
399C22×C73—81no—
400C22×C73—81no—
401C22×C73—81no—
402C22×C73—81no—
403C22×C73—81no—
404C22×C73—81no—
405C22×C73C2×#12111yescharacteristic
406C22×C73D4211yescharacteristic
407C22×C73#54611yescharacteristic
408C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C73#57511yescharacteristic
410C22×C73#57611yescharacteristic
411C22×C73#57611yescharacteristic
412C4×C73—22no—
413C4×C73—22no—
414C4×C73—41no—
415C4×C73—41no—
416C4×C73—42no—
417C4×C73—42no—
418C4×C73—81no—
419C4×C73—81no—
420C4×C73—81no—
421C4×C73#53211yescharacteristic
422C4×C73#54011yescharacteristic
423C4×C73D4211yescharacteristic
424C4×C73#55011yescharacteristic
425#25396C7311yesmaximal, characteristic, direct product factor, Sylow
426C2×C73—42no—
427C2×C73—81no—
428C2×C73—82no—
429C2×C73—161no—
430C2×C73—161no—
431C2×C73#242811yescharacteristic
432C2×C73#305511yescharacteristic
433C2×C73#305811yescharacteristic
434C2×C73#326411yescharacteristic
435C2×C73#326811yescharacteristic
436C2×C73#330911yescharacteristic
437C2×C73#331811yescharacteristic
438C2×#469C2×C7311yescharacteristic, complemented
439C2×#466C2×C7311yescharacteristic, complemented
440C2×#459C2×C7311yescharacteristic, complemented
441C2×#435C2×C7311yescharacteristic, complemented
442#2541C2×C7311yescharacteristic, complemented
443#2535C2×C7311yescharacteristic, complemented
444#2034C2×C7311yescharacteristic, complemented
445#2033C2×C7311yescharacteristic, complemented
446#1999C2×C7311yescharacteristic, complemented
447#1999C2×C7311yescharacteristic, complemented
448#1961C2×C7311yescharacteristic, complemented
449#1949C2×C7311yescharacteristic, complemented
450#1895C2×C7311yescharacteristic, complemented
451#1893C2×C7311yescharacteristic, complemented
452#1762C2×C7311yescharacteristic, complemented
453C73#2539611yescharacteristic, direct product factor, Sylow
454C22×D8C22×C7311yescharacteristic
455C22×D8C22×C7311yescharacteristic
456C22×M16C22×C7311yescharacteristic
457C23×C8C22×C7311yescharacteristic
458C2×#127—21no—
459C2×#127C22×C7311yescharacteristic
460C2×#121C22×C7311yescharacteristic
461C2×#121C22×C7311yescharacteristic
462C2×#121C22×C7311yescharacteristic
463C2×#121C22×C7311yescharacteristic
464C2×#121C22×C7311yescharacteristic
465C2×#121C22×C7311yescharacteristic
466C2×C4×D4C22×C7311yescharacteristic
467C2×C4×D4C22×C7311yescharacteristic
468#469—24no—
469#466—24no—
470#459—24no—
471#435—24no—
472C2×#107C22×C7311yescharacteristic
473C2×#106C22×C7311yescharacteristic
474C2×C4⋊C8C22×C7311yescharacteristic
475C2×#102C22×C7311yescharacteristic
476C2×#102C22×C7311yescharacteristic
477C2×#102C22×C7311yescharacteristic
478C2×#102C22×C7311yescharacteristic
479C2×#102C22×C7311yescharacteristic
480C2×#102C22×C7311yescharacteristic
481C2×#102C22×C7311yescharacteristic
482C2×#102C22×C7311yescharacteristic
483C2×C22⋊C8C22×C7311yescharacteristic
484C2×C22⋊C8C22×C7311yescharacteristic
485C2×#97C22×C7311yescharacteristic
486#397—21no—
487#392—21no—
488#392—21no—
489#392—21no—
490#390—21no—
491#386—21no—
492#386—21no—
493#382C22×C7311yescharacteristic
494#380C22×C7311yescharacteristic
495#380C22×C7311yescharacteristic
496C4×C4⋊C4C22×C7311yescharacteristic
497#340C22×C7311yescharacteristic
498#340C22×C7311yescharacteristic
499#340C22×C7311yescharacteristic
500#340C22×C7311yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4D4×C7311yescharacteristic
510C22×D4C23×C7311yescharacteristic
511C22×D4C23×C7311yescharacteristic
512C22×D4C23×C7311yescharacteristic
513C23×C4—21no—
514C23×C4C23×C7311yescharacteristic
515C23×C4C23×C7311yescharacteristic
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—41no—
521C2×D8—41no—
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—41no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8C23×C7311yescharacteristic
529C22×C8C23×C7311yescharacteristic
530C22×C8C23×C7311yescharacteristic
531C22×C8C23×C7311yescharacteristic
532#127—22no—
533#127—22no—
534#127—44no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—41no—
542#121—41no—
543#121—41no—
544#121—41no—
545#121—41no—
546#121—41no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—22no—
551C2×C4⋊C4D4×C7311yescharacteristic
552C2×C4⋊C4C23×C7311yescharacteristic
553C2×C4⋊C4C23×C7311yescharacteristic
554C2×C4⋊C4C23×C7311yescharacteristic
555C2×C4⋊C4C23×C7311yescharacteristic
556C2×C4⋊C4C23×C7311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4D4×C7311yescharacteristic
567C2×C22⋊C4D4×C7311yescharacteristic
568C2×C42—21no—
569C2×C42C23×C7311yescharacteristic
570#107—22no—
571#106—22no—
572C4⋊C8D4×C7314yescomplemented
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580#102D4×C7314yescomplemented
581C22⋊C8—22no—
582C22⋊C8—22no—
583#97—22no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24C2×D4×C7311yescharacteristic
593C24C2×D4×C7311yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4C2×D4×C7312yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4C2×D4×C7311yescharacteristic
660C22×C4C2×D4×C7311yescharacteristic
661C22×C4C2×D4×C7311yescharacteristic
662C22×C4C2×D4×C7311yescharacteristic
663C22×C4C24×C7311yescharacteristic
664D8—44no—
665D8—44no—
666M16—44no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—44no—
677C2×C8C2×D4×C7312yes—
678C2×C8C2×D4×C7312yes—
679C2×C8C2×D4×C7312yes—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4C2×D4×C7312yes—
690C4⋊C4#41×C7312yes—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C42—42no—
703C42C2×D4×C7312yes—
704C42#41×C7312yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23AGL(1,ℤ/8)×C7312yes—
740C23C22×D4×C7311yescharacteristic
741D4—22no—
742D4—22no—
743D4—44no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760D4—84no—
761D4—84no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4#121×C7312yes—
797C2×C4#121×C7312yes—
798C2×C4C22×D4×C7311yescharacteristic
799C2×C4C22×D4×C7311yescharacteristic
800C2×C4C2×#41×C7311yescharacteristic
801C2×C4C2×#41×C7311yescharacteristic
802C2×C4H(5,𝔽2)×C7311yescharacteristic
803C2×C4H(5,𝔽2)×C7311yescharacteristic
804C8—22no—
805C8—22no—
806C8—22no—
807C8—41no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#121×C7311yescharacteristic
844C22D42×C7311yescharacteristic
845C22#546×C7311yescharacteristic
846C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
847C22#575×C7311yescharacteristic
848C22#576×C7311yescharacteristic
849C22#576×C7311yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4#532×C7311yescharacteristic
860C4#540×C7311yescharacteristic
861C4D42×C7311yescharacteristic
862C4#550×C7311yescharacteristic
863C2—42no—
864C2—81no—
865C2—82no—
866C2—161no—
867C2—161no—
868C2C73×#242811yescharacteristic
869C2C73×#305511yescharacteristic
870C2C73×#305811yescharacteristic
871C2C73×#326411yescharacteristic
872C2C73×#326811yescharacteristic
873C2C73×#330911yescharacteristic
874C2C73×#331811yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#469×C73C2semidirect
2. C2×#466×C73C2semidirect
3. C2×#459×C73C2semidirect
4. C2×#435×C73C2semidirect
5. C73×#2541C2semidirect
6. C73×#2535C2semidirect
7. C73×#2034C2semidirect
8. C73×#2033C2semidirect
9. C73×#1999C2semidirect
10. C73×#1999C2semidirect
11. C73×#1961C2semidirect
12. C73×#1949C2semidirect
13. C73×#1895C2semidirect
14. C73×#1893C2semidirect
15. C73×#1762C2semidirect
134. C4⋊C8×C73D4semidirect
142. #102×C73D4semidirect
425. #25396C73direct (N × H)
438. C2×#469C2×C73semidirect
439. C2×#466C2×C73semidirect
440. C2×#459C2×C73semidirect
441. C2×#435C2×C73semidirect
442. #2541C2×C73semidirect
443. #2535C2×C73semidirect
444. #2034C2×C73semidirect
445. #2033C2×C73semidirect
446. #1999C2×C73semidirect
447. #1999C2×C73semidirect
448. #1961C2×C73semidirect
449. #1949C2×C73semidirect
450. #1895C2×C73semidirect
451. #1893C2×C73semidirect
452. #1762C2×C73semidirect
453. C73#25396direct (N × H)
572. C4⋊C8D4×C73semidirect
580. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C732
C2×#466×C732
C2×#459×C732
C2×#435×C732
C73×#25412
C73×#25352
C73×#20342
C73×#20332
C73×#19992
C73×#19612
C73×#19492
C73×#18952
C73×#18932
C73×#17622
#2539673