Finite Group Databasebeta

← C73×#22868 #32932272

Subgroups — C73×#22868 #32932272

Order 18688.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C73C211yesmaximal, characteristic
2C2×#442×C73C211yesmaximal, characteristic, complemented
3C2×#418×C73C211yesmaximal, characteristic, complemented
4C73×#2363C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C73C211yesmaximal, characteristic, complemented
6C73×#1970C211yesmaximal, characteristic, complemented
7C73×#1936C211yesmaximal, characteristic, complemented
8C73×#1926C211yesmaximal, characteristic, complemented
9C73×#1895C211yesmaximal, characteristic, complemented
10C73×#1879C211yesmaximal, characteristic, complemented
11C73×#1879C211yesmaximal, characteristic, complemented
12C73×#1862C211yesmaximal, characteristic, complemented
13C73×#1854C211yesmaximal, characteristic, complemented
14C4×#102×C73C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic
20C2×#121×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23C2×C4×D4×C73C2211yescharacteristic, complemented
24C2×#117×C73C2211yescharacteristic
25C22×C22⋊C4×C73—21no—
26#447×C73C418yescomplemented
27#442×C73—24no—
28C2×#107×C73C2211yescharacteristic, complemented
29C2×#106×C73C2211yescharacteristic, complemented
30#418×C73—24no—
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic, complemented
38C2×#102×C73C2211yescharacteristic, complemented
39C2×C22⋊C8×C73C2211yescharacteristic
40C2×#97×C73C2211yescharacteristic, complemented
41C2×C4×C8×C73C2211yescharacteristic, complemented
42#390×C73—21no—
43#390×C73C2211yescharacteristic
44#390×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic, complemented
46#389×C73C2211yescharacteristic, complemented
47#388×C73—21no—
48#386×C73—21no—
49#386×C73—21no—
50#386×C73—21no—
51#380×C73C2211yescharacteristic
52#379×C73—21no—
53C4×C4⋊C4×C73C2211yescharacteristic, complemented
54C4×C22⋊C4×C73—21no—
55C4×C22⋊C4×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic, complemented
57#340×C73C2211yescharacteristic, complemented
58#340×C73C2211yescharacteristic, complemented
59#340×C73C2211yescharacteristic, complemented
60#336×C73C2211yescharacteristic, complemented
61#336×C73C2211yescharacteristic, complemented
62C25×C73—21no—
63C22×D4×C73—22no—
64C22×D4×C73—22no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—22no—
68C22×D4×C73—41no—
69C22×D4×C73—41no—
70C22×D4×C73C2×C414yescomplemented
71C22×D4×C73C2311yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C22×D4×C73C2311yescharacteristic
74C23×C4×C73—21no—
75C23×C4×C73—21no—
76C23×C4×C73—21no—
77C23×C4×C73C2311yescharacteristic
78C2×D8×C73—22no—
79C2×D8×C73—22no—
80C2×D8×C73—41no—
81C2×D8×C73—41no—
82C2×D8×C73C2×C414yes—
83C2×D8×C73C2×C414yescomplemented
84C2×M16×C73—22no—
85C2×M16×C73—22no—
86C2×M16×C73—41no—
87C22×C8×C73C2311yescharacteristic
88C22×C8×C73C2311yescharacteristic
89C22×C8×C73C2311yescharacteristic
90C22×C8×C73C2311yescharacteristic
91#121×C73—22no—
92#121×C73C2×C414yescomplemented
93C4×D4×C73—22no—
94C4×D4×C73—22no—
95C4×D4×C73—22no—
96C4×D4×C73—41no—
97C4×D4×C73—41no—
98C4×D4×C73—41no—
99#117×C73—22no—
100#117×C73—41no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73—21no—
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—44no—
120C2×C22⋊C4×C73D411yescharacteristic
121C2×C22⋊C4×C73D411yescharacteristic
122C2×C42×C73—21no—
123C2×C42×C73—21no—
124C2×C42×C73C2311yescharacteristic
125C2×C42×C73C2311yescharacteristic
126#107×C73—41no—
127#106×C73—22no—
128#102×C73—22no—
129#102×C73—22no—
130#102×C73—22no—
131#102×C73—22no—
132#102×C73—41no—
133#102×C73C2×C414yescomplemented
134#102×C73C2×C414yescomplemented
135#102×C73D414yescomplemented
136C22⋊C8×C73C2×C414yescomplemented
137#97×C73—22no—
138C4×C8×C73—41no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73—21no—
142#95×C73D411yescharacteristic
143#95×C73D411yescharacteristic
144C24×C73—21no—
145C24×C73—21no—
146C24×C73—21no—
147C24×C73—24no—
148C24×C73—42no—
149C24×C73—42no—
150C24×C73—42no—
151C24×C73—42no—
152C24×C73—81no—
153C24×C73—81no—
154C24×C73C2×D411yescharacteristic
155C2×D4×C73—28no—
156C2×D4×C73—24no—
157C2×D4×C73—24no—
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—44no—
172C2×D4×C73—44no—
173C2×D4×C73—44no—
174C2×D4×C73—42no—
175C2×D4×C73—42no—
176C2×D4×C73—81no—
177C2×D4×C73—81no—
178C2×D4×C73C22×C412yes—
179C2×D4×C73C22×C412yes—
180C2×D4×C73C22×C412yes—
181C2×D4×C73C2×D412yes—
182C2×D4×C73#4112yes—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—42no—
193C22×C4×C73—42no—
194C22×C4×C73—42no—
195C22×C4×C73—42no—
196C22×C4×C73—42no—
197C22×C4×C73—42no—
198C22×C4×C73—81no—
199C22×C4×C73—81no—
200C22×C4×C73—81no—
201C22×C4×C73C22×C412yes—
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73#4112yes—
208C22×C4×C73C2411yescharacteristic
209D8×C73—28no—
210D8×C73—44no—
211M16×C73—44no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73C22×C412yes—
222C2×C8×C73C22×C412yes—
223C2×C8×C73C2×D412yes—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—81no—
233C4⋊C4×C73C22×C412yes—
234C4⋊C4×C73C2×D412yes—
235C22⋊C4×C73—24no—
236C22⋊C4×C73—22no—
237C22⋊C4×C73—41no—
238C22⋊C4×C73—42no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—42no—
241C22⋊C4×C73—42no—
242C22⋊C4×C73—42no—
243C22⋊C4×C73—42no—
244C22⋊C4×C73—42no—
245C22⋊C4×C73—42no—
246C22⋊C4×C73—81no—
247C22⋊C4×C73—81no—
248C22⋊C4×C73—81no—
249C42×C73—21no—
250C42×C73—21no—
251C42×C73—21no—
252C42×C73—21no—
253C42×C73—42no—
254C42×C73—81no—
255C23×C73—22no—
256C23×C73—21no—
257C23×C73—22no—
258C23×C73—22no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—22no—
265C23×C73—22no—
266C23×C73—48no—
267C23×C73—48no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—84no—
285C23×C73—84no—
286C23×C73—84no—
287C23×C73—84no—
288C23×C73—84no—
289C23×C73C4×D412yes—
290C23×C73C22×D411yescharacteristic
291D4×C73—22no—
292D4×C73—22no—
293D4×C73—22no—
294D4×C73—22no—
295D4×C73—22no—
296D4×C73—22no—
297D4×C73—22no—
298D4×C73—48no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—41no—
302D4×C73—41no—
303D4×C73—84no—
304D4×C73C4×D414yes—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—22no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—84no—
338C2×C4×C73—84no—
339C2×C4×C73—84no—
340C2×C4×C73C4×D412yes—
341C2×C4×C73AGL(1,ℤ/8)12yes—
342C2×C4×C73C23×C411yescharacteristic
343C2×C4×C73C22×D411yescharacteristic
344C2×C4×C73C2×#4111yescharacteristic
345C2×C4×C73C2×#4111yescharacteristic
346C2×C4×C73H(5,𝔽2)11yescharacteristic
347C2×C4×C73H(5,𝔽2)11yescharacteristic
348C8×C73—22no—
349C8×C73—22no—
350C8×C73—22no—
351C8×C73—41no—
352C22×C73—22no—
353C22×C73—24no—
354C22×C73—22no—
355C22×C73—22no—
356C22×C73—42no—
357C22×C73—42no—
358C22×C73—41no—
359C22×C73—42no—
360C22×C73—42no—
361C22×C73—41no—
362C22×C73—42no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—42no—
366C22×C73—42no—
367C22×C73—42no—
368C22×C73—42no—
369C22×C73—42no—
370C22×C73—42no—
371C22×C73—42no—
372C22×C73—816no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73—81no—
378C22×C73—81no—
379C22×C73—81no—
380C22×C73—81no—
381C22×C73C2×C4×D411yescharacteristic
382C22×C73D4211yescharacteristic
383C22×C73#54611yescharacteristic
384C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C73#57511yescharacteristic
386C22×C73#57611yescharacteristic
387C22×C73#57611yescharacteristic
388C4×C73—22no—
389C4×C73—22no—
390C4×C73—42no—
391C4×C73—41no—
392C4×C73—42no—
393C4×C73—41no—
394C4×C73—41no—
395C4×C73—81no—
396C4×C73—81no—
397C4×C73—81no—
398C4×C73C2×C4×D411yescharacteristic
399C4×C73#51811yescharacteristic
400C4×C73#54611yescharacteristic
401C4×C73#55111yescharacteristic
402#22868C7311yesmaximal, characteristic, direct product factor, Sylow
403C2×C73—42no—
404C2×C73—44no—
405C2×C73—82no—
406C2×C73—82no—
407C2×C73#235811yescharacteristic
408C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
409C2×C73#294811yescharacteristic
410C2×C73#327311yescharacteristic
411C2×C73#327411yescharacteristic
412C2×C73#331811yescharacteristic
413C2×C73#331911yescharacteristic
414C2×#447C2×C7311yescharacteristic
415C2×#442C2×C7311yescharacteristic, complemented
416C2×#418C2×C7311yescharacteristic, complemented
417#2363C2×C7311yescharacteristic, complemented
418D4×C22⋊C4C2×C7311yescharacteristic, complemented
419#1970C2×C7311yescharacteristic, complemented
420#1936C2×C7311yescharacteristic, complemented
421#1926C2×C7311yescharacteristic, complemented
422#1895C2×C7311yescharacteristic, complemented
423#1879C2×C7311yescharacteristic, complemented
424#1879C2×C7311yescharacteristic, complemented
425#1862C2×C7311yescharacteristic, complemented
426#1854C2×C7311yescharacteristic, complemented
427C4×#102C2×C7311yescharacteristic, complemented
428#1753C2×C7311yescharacteristic, complemented
429C73#2286811yescharacteristic, direct product factor, Sylow
430C23×D4C22×C7311yescharacteristic
431C22×D8C22×C7311yescharacteristic
432C22×D8C22×C7311yescharacteristic
433C22×M16C22×C7311yescharacteristic
434C2×#121C22×C7311yescharacteristic
435C2×C4×D4C22×C7311yescharacteristic
436C2×C4×D4C22×C7311yescharacteristic
437C2×C4×D4C22×C7311yescharacteristic, complemented
438C2×#117C22×C7311yescharacteristic
439C22×C22⋊C4—21no—
440#447C4×C7318yescomplemented
441#442—24no—
442C2×#107C22×C7311yescharacteristic, complemented
443C2×#106C22×C7311yescharacteristic, complemented
444#418—24no—
445C2×#102C22×C7311yescharacteristic
446C2×#102C22×C7311yescharacteristic
447C2×#102C22×C7311yescharacteristic
448C2×#102C22×C7311yescharacteristic
449C2×#102C22×C7311yescharacteristic
450C2×#102C22×C7311yescharacteristic
451C2×#102C22×C7311yescharacteristic, complemented
452C2×#102C22×C7311yescharacteristic, complemented
453C2×C22⋊C8C22×C7311yescharacteristic
454C2×#97C22×C7311yescharacteristic, complemented
455C2×C4×C8C22×C7311yescharacteristic, complemented
456#390—21no—
457#390C22×C7311yescharacteristic
458#390C22×C7311yescharacteristic
459#390C22×C7311yescharacteristic, complemented
460#389C22×C7311yescharacteristic, complemented
461#388—21no—
462#386—21no—
463#386—21no—
464#386—21no—
465#380C22×C7311yescharacteristic
466#379—21no—
467C4×C4⋊C4C22×C7311yescharacteristic, complemented
468C4×C22⋊C4—21no—
469C4×C22⋊C4C22×C7311yescharacteristic
470#340C22×C7311yescharacteristic, complemented
471#340C22×C7311yescharacteristic, complemented
472#340C22×C7311yescharacteristic, complemented
473#340C22×C7311yescharacteristic, complemented
474#336C22×C7311yescharacteristic, complemented
475#336C22×C7311yescharacteristic, complemented
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—22no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×C4×C7314yescomplemented
485C22×D4C23×C7311yescharacteristic
486C22×D4C23×C7311yescharacteristic
487C22×D4C23×C7311yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C23×C7311yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×C4×C7314yes—
497C2×D8C2×C4×C7314yescomplemented
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8C23×C7311yescharacteristic
502C22×C8C23×C7311yescharacteristic
503C22×C8C23×C7311yescharacteristic
504C22×C8C23×C7311yescharacteristic
505#121—22no—
506#121C2×C4×C7314yescomplemented
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4C23×C7311yescharacteristic
517C2×C4⋊C4C23×C7311yescharacteristic
518C2×C4⋊C4C23×C7311yescharacteristic
519C2×C4⋊C4C23×C7311yescharacteristic
520C2×C4⋊C4C23×C7311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—44no—
534C2×C22⋊C4D4×C7311yescharacteristic
535C2×C22⋊C4D4×C7311yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42C23×C7311yescharacteristic
539C2×C42C23×C7311yescharacteristic
540#107—41no—
541#106—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—41no—
547#102C2×C4×C7314yescomplemented
548#102C2×C4×C7314yescomplemented
549#102D4×C7314yescomplemented
550C22⋊C8C2×C4×C7314yescomplemented
551#97—22no—
552C4×C8—41no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95D4×C7311yescharacteristic
557#95D4×C7311yescharacteristic
558C24—21no—
559C24—21no—
560C24—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24C2×D4×C7311yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C22×C4×C7312yes—
593C2×D4C22×C4×C7312yes—
594C2×D4C22×C4×C7312yes—
595C2×D4C2×D4×C7312yes—
596C2×D4#41×C7312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C22×C4×C7312yes—
616C22×C4C2×D4×C7311yescharacteristic
617C22×C4C2×D4×C7311yescharacteristic
618C22×C4C2×D4×C7311yescharacteristic
619C22×C4C2×D4×C7311yescharacteristic
620C22×C4C2×D4×C7311yescharacteristic
621C22×C4#41×C7312yes—
622C22×C4C24×C7311yescharacteristic
623D8—28no—
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8C22×C4×C7312yes—
636C2×C8C22×C4×C7312yes—
637C2×C8C2×D4×C7312yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C22×C4×C7312yes—
648C4⋊C4C2×D4×C7312yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23C4×D4×C7312yes—
704C23C22×D4×C7311yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4C4×D4×C7314yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4C4×D4×C7312yes—
755C2×C4AGL(1,ℤ/8)×C7312yes—
756C2×C4C23×C4×C7311yescharacteristic
757C2×C4C22×D4×C7311yescharacteristic
758C2×C4C2×#41×C7311yescharacteristic
759C2×C4C2×#41×C7311yescharacteristic
760C2×C4H(5,𝔽2)×C7311yescharacteristic
761C2×C4H(5,𝔽2)×C7311yescharacteristic
762C8—22no—
763C8—22no—
764C8—22no—
765C8—41no—
766C22—22no—
767C22—24no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C4×D4×C7311yescharacteristic
796C22D42×C7311yescharacteristic
797C22#546×C7311yescharacteristic
798C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
799C22#575×C7311yescharacteristic
800C22#576×C7311yescharacteristic
801C22#576×C7311yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—42no—
806C4—41no—
807C4—41no—
808C4—42no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C2×C4×D4×C7311yescharacteristic
813C4#518×C7311yescharacteristic
814C4#546×C7311yescharacteristic
815C4#551×C7311yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2C73×#235811yescharacteristic
821C2C4×AGL(1,ℤ/8)×C7311yescharacteristic
822C2C73×#294811yescharacteristic
823C2C73×#327311yescharacteristic
824C2C73×#327411yescharacteristic
825C2C73×#331811yescharacteristic
826C2C73×#331911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC2×#447×C73C2
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
2. C2×#442×C73C2semidirect
3. C2×#418×C73C2semidirect
4. C73×#2363C2semidirect
5. D4×C22⋊C4×C73C2semidirect
6. C73×#1970C2semidirect
7. C73×#1936C2semidirect
8. C73×#1926C2semidirect
9. C73×#1895C2semidirect
10. C73×#1879C2semidirect
11. C73×#1879C2semidirect
12. C73×#1862C2semidirect
13. C73×#1854C2semidirect
14. C4×#102×C73C2semidirect
15. C73×#1753C2semidirect
23. C2×C4×D4×C73C22semidirect
26. #447×C73C4semidirect
28. C2×#107×C73C22semidirect
29. C2×#106×C73C22semidirect
37. C2×#102×C73C22semidirect
38. C2×#102×C73C22semidirect
40. C2×#97×C73C22semidirect
41. C2×C4×C8×C73C22semidirect
45. #390×C73C22semidirect
46. #389×C73C22semidirect
53. C4×C4⋊C4×C73C22semidirect
56. #340×C73C22semidirect
57. #340×C73C22semidirect
58. #340×C73C22semidirect
59. #340×C73C22semidirect
60. #336×C73C22semidirect
61. #336×C73C22semidirect
70. C22×D4×C73C2×C4semidirect
83. C2×D8×C73C2×C4semidirect
92. #121×C73C2×C4semidirect
133. #102×C73C2×C4semidirect
134. #102×C73C2×C4semidirect
135. #102×C73D4semidirect
136. C22⋊C8×C73C2×C4semidirect
402. #22868C73direct (N × H)
415. C2×#442C2×C73semidirect
416. C2×#418C2×C73semidirect
417. #2363C2×C73semidirect
418. D4×C22⋊C4C2×C73semidirect
419. #1970C2×C73semidirect
420. #1936C2×C73semidirect
421. #1926C2×C73semidirect
422. #1895C2×C73semidirect
423. #1879C2×C73semidirect
424. #1879C2×C73semidirect
425. #1862C2×C73semidirect
426. #1854C2×C73semidirect
427. C4×#102C2×C73semidirect
428. #1753C2×C73semidirect
429. C73#22868direct (N × H)
437. C2×C4×D4C22×C73semidirect
440. #447C4×C73semidirect
442. C2×#107C22×C73semidirect
443. C2×#106C22×C73semidirect
451. C2×#102C22×C73semidirect
452. C2×#102C22×C73semidirect
454. C2×#97C22×C73semidirect
455. C2×C4×C8C22×C73semidirect
459. #390C22×C73semidirect
460. #389C22×C73semidirect
467. C4×C4⋊C4C22×C73semidirect
470. #340C22×C73semidirect
471. #340C22×C73semidirect
472. #340C22×C73semidirect
473. #340C22×C73semidirect
474. #336C22×C73semidirect
475. #336C22×C73semidirect
484. C22×D4C2×C4×C73semidirect
497. C2×D8C2×C4×C73semidirect
506. #121C2×C4×C73semidirect
547. #102C2×C4×C73semidirect
548. #102C2×C4×C73semidirect
549. #102D4×C73semidirect
550. C22⋊C8C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C732
C2×#442×C732
C2×#418×C732
C73×#23632
D4×C22⋊C4×C732
C73×#19702
C73×#19362
C73×#19262
C73×#18952
C73×#18792
C73×#18622
C73×#18542
C4×#102×C732
C73×#17532
#2286873