Finite Group Databasebeta

← C73×#24886 #32934290

Subgroups — C73×#24886 #32934290

Order 18688.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C73C211yesmaximal, characteristic, complemented
2C2×#418×C73C211yesmaximal, characteristic, complemented
3C73×#2408C211yesmaximal, characteristic
4C73×#2354C211yesmaximal, characteristic, complemented
5C73×#2094C211yesmaximal, characteristic, complemented
6C73×#2071C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#1925C211yesmaximal, characteristic, complemented
10C73×#1925C211yesmaximal, characteristic, complemented
11C73×#1875C211yesmaximal, characteristic, complemented
12C73×#1870C211yesmaximal, characteristic, complemented
13C73×#1854C211yesmaximal, characteristic, complemented
14C73×#1809C211yesmaximal, characteristic, complemented
15C73×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×#121×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×#120×C73—21no—
21C2×C4×D4×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23C2×#117×C73C2211yescharacteristic, complemented
24#482×C73—24no—
25C2×#107×C73C2211yescharacteristic, complemented
26C2×#107×C73C2211yescharacteristic, complemented
27C2×#106×C73C2211yescharacteristic, complemented
28C2×#106×C73C2211yescharacteristic, complemented
29#418×C73—24no—
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic, complemented
40C2×C22⋊C8×C73C2211yescharacteristic, complemented
41#394×C73—21no—
42#392×C73—21no—
43#390×C73—21no—
44#390×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic
46#388×C73—21no—
47#388×C73—21no—
48#384×C73C2211yescharacteristic, complemented
49#380×C73C2211yescharacteristic
50#380×C73C2211yescharacteristic
51#380×C73C2211yescharacteristic, complemented
52#379×C73—21no—
53C4×C4⋊C4×C73—21no—
54C4×C4⋊C4×C73C2211yescharacteristic, complemented
55#340×C73C2211yescharacteristic, complemented
56#340×C73C2211yescharacteristic, complemented
57#340×C73C2211yescharacteristic, complemented
58#340×C73C2211yescharacteristic, complemented
59#336×C73C2211yescharacteristic, complemented
60#336×C73C2211yescharacteristic, complemented
61C25×C73—21no—
62C22×D4×C73—22no—
63C22×D4×C73—22no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—22no—
68C22×D4×C73—22no—
69C22×D4×C73—41no—
70C22×D4×C73—41no—
71C22×D4×C73D411yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C22×D4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C23×C4×C73C2311yescharacteristic
76C2×M16×C73—22no—
77C2×M16×C73—22no—
78C2×M16×C73—41no—
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83#121×C73—22no—
84#121×C73—22no—
85#121×C73—41no—
86#121×C73—41no—
87#120×C73—44no—
88C4×D4×C73—22no—
89C4×D4×C73—22no—
90#117×C73—22no—
91#117×C73—22no—
92#117×C73—41no—
93#117×C73—41no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73D411yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
114C2×C22⋊C4×C73D411yescharacteristic
115C2×C22⋊C4×C73D411yescharacteristic
116C2×C42×C73—21no—
117C2×C42×C73—21no—
118C2×C42×C73—21no—
119C2×C42×C73C2311yescharacteristic
120#107×C73—22no—
121#107×C73—41no—
122#106×C73—22no—
123#106×C73—41no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—22no—
128#102×C73—22no—
129#102×C73—41no—
130#102×C73—41no—
131#102×C73D414yescomplemented
132C22⋊C8×C73—22no—
133C22⋊C8×C73—22no—
134C22⋊C8×C73—41no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73—21no—
138#95×C73—21no—
139C24×C73—21no—
140C24×C73—21no—
141C24×C73—42no—
142C24×C73—42no—
143C24×C73—42no—
144C24×C73—42no—
145C24×C73—42no—
146C24×C73—81no—
147C24×C73—81no—
148C24×C73C2×D411yescharacteristic
149C24×C73C2×D411yescharacteristic
150C2×D4×C73—28no—
151C2×D4×C73—22no—
152C2×D4×C73—22no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
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—44no—
164C2×D4×C73—44no—
165C2×D4×C73—41no—
166C2×D4×C73—42no—
167C2×D4×C73—42no—
168C2×D4×C73—44no—
169C2×D4×C73—42no—
170C2×D4×C73—42no—
171C2×D4×C73—42no—
172C2×D4×C73—42no—
173C2×D4×C73—42no—
174C2×D4×C73—81no—
175C2×D4×C73—81no—
176C2×D4×C73C2×D412yes—
177C2×D4×C73#4112yes—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
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—21no—
193C22×C4×C73—21no—
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73#4112yes—
199C22×C4×C73#4112yes—
200C22×C4×C73C2411yescharacteristic
201M16×C73—44no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73C2×D412yes—
214C4⋊C4×C73—22no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—42no—
227C4⋊C4×C73—81no—
228C4⋊C4×C73C2×D412yes—
229C22⋊C4×C73—22no—
230C22⋊C4×C73—22no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—42no—
233C22⋊C4×C73—42no—
234C22⋊C4×C73—42no—
235C22⋊C4×C73—42no—
236C22⋊C4×C73—42no—
237C22⋊C4×C73—42no—
238C22⋊C4×C73—81no—
239C22⋊C4×C73—81no—
240C22⋊C4×C73—81no—
241C22⋊C4×C73—81no—
242C42×C73—21no—
243C42×C73—21no—
244C42×C73—42no—
245C42×C73—42no—
246C42×C73—42no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—22no—
256C23×C73—22no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—48no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—84no—
276C23×C73—84no—
277C23×C73—84no—
278C23×C73—84no—
279C23×C73—84no—
280C23×C73—84no—
281C23×C73#12312yes—
282C23×C73C22×D411yescharacteristic
283D4×C73—22no—
284D4×C73—22no—
285D4×C73—22no—
286D4×C73—22no—
287D4×C73—44no—
288D4×C73—48no—
289D4×C73—41no—
290D4×C73—41no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—84no—
294D4×C73—84no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—22no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
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#12312yes—
332C2×C4×C73AGL(1,ℤ/8)12yes—
333C2×C4×C73C22×D411yescharacteristic
334C2×C4×C73C2×#4111yescharacteristic
335C2×C4×C73C2×#4111yescharacteristic
336C2×C4×C73C2×#4111yescharacteristic
337C2×C4×C73H(5,𝔽2)11yescharacteristic
338C2×C4×C73H(5,𝔽2)11yescharacteristic
339C8×C73—22no—
340C8×C73—41no—
341C8×C73—41no—
342C8×C73—41no—
343C22×C73—22no—
344C22×C73—22no—
345C22×C73—22no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—42no—
354C22×C73—42no—
355C22×C73—41no—
356C22×C73—42no—
357C22×C73—41no—
358C22×C73—42no—
359C22×C73—41no—
360C22×C73—42no—
361C22×C73—41no—
362C22×C73—42no—
363C22×C73—816no—
364C22×C73—81no—
365C22×C73—81no—
366C22×C73—81no—
367C22×C73—81no—
368C22×C73—81no—
369C22×C73—81no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73C2×#12311yescharacteristic
373C22×C73D4211yescharacteristic
374C22×C73#54611yescharacteristic
375C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C73#57511yescharacteristic
377C22×C73#57611yescharacteristic
378C22×C73#57711yescharacteristic
379C4×C73—22no—
380C4×C73—22no—
381C4×C73—41no—
382C4×C73—41no—
383C4×C73—42no—
384C4×C73—81no—
385C4×C73—81no—
386C4×C73—81no—
387C4×C73—81no—
388C4×C73—81no—
389C4×C73#52511yescharacteristic
390C4×C73#53811yescharacteristic
391C4×C73#54611yescharacteristic
392C4×C73#55111yescharacteristic
393#24886C7311yesmaximal, characteristic, direct product factor, Sylow
394C2×C73—42no—
395C2×C73—81no—
396C2×C73—82no—
397C2×C73—82no—
398C2×C73#241811yescharacteristic
399C2×C73#309411yescharacteristic
400C2×C73#309611yescharacteristic
401C2×C73#326811yescharacteristic
402C2×C73#327211yescharacteristic
403C2×C73#331111yescharacteristic
404C2×C73#332511yescharacteristic
405C2×#482C2×C7311yescharacteristic, complemented
406C2×#418C2×C7311yescharacteristic, complemented
407#2408C2×C7311yescharacteristic
408#2354C2×C7311yescharacteristic, complemented
409#2094C2×C7311yescharacteristic, complemented
410#2071C2×C7311yescharacteristic, complemented
411#2034C2×C7311yescharacteristic, complemented
412#2033C2×C7311yescharacteristic, complemented
413#1925C2×C7311yescharacteristic, complemented
414#1925C2×C7311yescharacteristic, complemented
415#1875C2×C7311yescharacteristic, complemented
416#1870C2×C7311yescharacteristic, complemented
417#1854C2×C7311yescharacteristic, complemented
418#1809C2×C7311yescharacteristic, complemented
419#1786C2×C7311yescharacteristic, complemented
420C73#2488611yescharacteristic, direct product factor, Sylow
421C23×D4C22×C7311yescharacteristic
422C22×M16C22×C7311yescharacteristic
423C2×#121C22×C7311yescharacteristic
424C2×#121C22×C7311yescharacteristic
425C2×#120—21no—
426C2×C4×D4C22×C7311yescharacteristic
427C2×#117C22×C7311yescharacteristic
428C2×#117C22×C7311yescharacteristic, complemented
429#482—24no—
430C2×#107C22×C7311yescharacteristic, complemented
431C2×#107C22×C7311yescharacteristic, complemented
432C2×#106C22×C7311yescharacteristic, complemented
433C2×#106C22×C7311yescharacteristic, complemented
434#418—24no—
435C2×#102C22×C7311yescharacteristic
436C2×#102C22×C7311yescharacteristic
437C2×#102C22×C7311yescharacteristic
438C2×#102C22×C7311yescharacteristic
439C2×#102C22×C7311yescharacteristic
440C2×#102C22×C7311yescharacteristic
441C2×#102C22×C7311yescharacteristic
442C2×#102C22×C7311yescharacteristic
443C2×C22⋊C8C22×C7311yescharacteristic
444C2×C22⋊C8C22×C7311yescharacteristic, complemented
445C2×C22⋊C8C22×C7311yescharacteristic, complemented
446#394—21no—
447#392—21no—
448#390—21no—
449#390C22×C7311yescharacteristic
450#390C22×C7311yescharacteristic
451#388—21no—
452#388—21no—
453#384C22×C7311yescharacteristic, complemented
454#380C22×C7311yescharacteristic
455#380C22×C7311yescharacteristic
456#380C22×C7311yescharacteristic, complemented
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C22×C7311yescharacteristic, complemented
460#340C22×C7311yescharacteristic, complemented
461#340C22×C7311yescharacteristic, complemented
462#340C22×C7311yescharacteristic, complemented
463#340C22×C7311yescharacteristic, complemented
464#336C22×C7311yescharacteristic, complemented
465#336C22×C7311yescharacteristic, complemented
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4D4×C7311yescharacteristic
477C22×D4C23×C7311yescharacteristic
478C22×D4C23×C7311yescharacteristic
479C23×C4C23×C7311yescharacteristic
480C23×C4C23×C7311yescharacteristic
481C2×M16—22no—
482C2×M16—22no—
483C2×M16—41no—
484C22×C8C23×C7311yescharacteristic
485C22×C8C23×C7311yescharacteristic
486C22×C8C23×C7311yescharacteristic
487C22×C8C23×C7311yescharacteristic
488#121—22no—
489#121—22no—
490#121—41no—
491#121—41no—
492#120—44no—
493C4×D4—22no—
494C4×D4—22no—
495#117—22no—
496#117—22no—
497#117—41no—
498#117—41no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C7311yescharacteristic
502C2×C4⋊C4C23×C7311yescharacteristic
503C2×C4⋊C4C23×C7311yescharacteristic
504C2×C4⋊C4C23×C7311yescharacteristic
505C2×C4⋊C4C23×C7311yescharacteristic
506C2×C4⋊C4C23×C7311yescharacteristic
507C2×C4⋊C4C23×C7311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C7311yescharacteristic
520C2×C22⋊C4D4×C7311yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42C23×C7311yescharacteristic
525#107—22no—
526#107—41no—
527#106—22no—
528#106—41no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—41no—
535#102—41no—
536#102D4×C7314yescomplemented
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—41no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24C2×D4×C7311yescharacteristic
554C24C2×D4×C7311yescharacteristic
555C2×D4—28no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—41no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4C2×D4×C7312yes—
582C2×D4#41×C7312yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4C2×D4×C7311yescharacteristic
600C22×C4C2×D4×C7311yescharacteristic
601C22×C4C2×D4×C7311yescharacteristic
602C22×C4C2×D4×C7311yescharacteristic
603C22×C4#41×C7312yes—
604C22×C4#41×C7312yes—
605C22×C4C24×C7311yescharacteristic
606M16—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8C2×D4×C7312yes—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—81no—
633C4⋊C4C2×D4×C7312yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C42—42no—
651C42—42no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#123×C7312yes—
687C23C22×D4×C7311yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4#123×C7312yes—
737C2×C4AGL(1,ℤ/8)×C7312yes—
738C2×C4C22×D4×C7311yescharacteristic
739C2×C4C2×#41×C7311yescharacteristic
740C2×C4C2×#41×C7311yescharacteristic
741C2×C4C2×#41×C7311yescharacteristic
742C2×C4H(5,𝔽2)×C7311yescharacteristic
743C2×C4H(5,𝔽2)×C7311yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—42no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#123×C7311yescharacteristic
778C22D42×C7311yescharacteristic
779C22#546×C7311yescharacteristic
780C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
781C22#575×C7311yescharacteristic
782C22#576×C7311yescharacteristic
783C22#577×C7311yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4#525×C7311yescharacteristic
795C4#538×C7311yescharacteristic
796C4#546×C7311yescharacteristic
797C4#551×C7311yescharacteristic
798C2—42no—
799C2—81no—
800C2—82no—
801C2—82no—
802C2C73×#241811yescharacteristic
803C2C73×#309411yescharacteristic
804C2C73×#309611yescharacteristic
805C2C73×#326811yescharacteristic
806C2C73×#327211yescharacteristic
807C2C73×#331111yescharacteristic
808C2C73×#332511yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2408C2
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×#482×C73C2semidirect
2. C2×#418×C73C2semidirect
4. C73×#2354C2semidirect
5. C73×#2094C2semidirect
6. C73×#2071C2semidirect
7. C73×#2034C2semidirect
8. C73×#2033C2semidirect
9. C73×#1925C2semidirect
10. C73×#1925C2semidirect
11. C73×#1875C2semidirect
12. C73×#1870C2semidirect
13. C73×#1854C2semidirect
14. C73×#1809C2semidirect
15. C73×#1786C2semidirect
23. C2×#117×C73C22semidirect
25. C2×#107×C73C22semidirect
26. C2×#107×C73C22semidirect
27. C2×#106×C73C22semidirect
28. C2×#106×C73C22semidirect
39. C2×C22⋊C8×C73C22semidirect
40. C2×C22⋊C8×C73C22semidirect
48. #384×C73C22semidirect
51. #380×C73C22semidirect
54. C4×C4⋊C4×C73C22semidirect
55. #340×C73C22semidirect
56. #340×C73C22semidirect
57. #340×C73C22semidirect
58. #340×C73C22semidirect
59. #336×C73C22semidirect
60. #336×C73C22semidirect
131. #102×C73D4semidirect
393. #24886C73direct (N × H)
405. C2×#482C2×C73semidirect
406. C2×#418C2×C73semidirect
408. #2354C2×C73semidirect
409. #2094C2×C73semidirect
410. #2071C2×C73semidirect
411. #2034C2×C73semidirect
412. #2033C2×C73semidirect
413. #1925C2×C73semidirect
414. #1925C2×C73semidirect
415. #1875C2×C73semidirect
416. #1870C2×C73semidirect
417. #1854C2×C73semidirect
418. #1809C2×C73semidirect
419. #1786C2×C73semidirect
420. C73#24886direct (N × H)
428. C2×#117C22×C73semidirect
430. C2×#107C22×C73semidirect
431. C2×#107C22×C73semidirect
432. C2×#106C22×C73semidirect
433. C2×#106C22×C73semidirect
444. C2×C22⋊C8C22×C73semidirect
445. C2×C22⋊C8C22×C73semidirect
453. #384C22×C73semidirect
456. #380C22×C73semidirect
459. C4×C4⋊C4C22×C73semidirect
460. #340C22×C73semidirect
461. #340C22×C73semidirect
462. #340C22×C73semidirect
463. #340C22×C73semidirect
464. #336C22×C73semidirect
465. #336C22×C73semidirect
536. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C732
C2×#418×C732
C73×#24082
C73×#23542
C73×#20942
C73×#20712
C73×#20342
C73×#20332
C73×#19252
C73×#18752
C73×#18702
C73×#18542
C73×#18092
C73×#17862
#2488673