Finite Group Databasebeta

← C73×#24539 #32933943

Subgroups — C73×#24539 #32933943

Order 18688.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C73C211yesmaximal, characteristic
2C2×#418×C73C211yesmaximal, characteristic, complemented
3C73×#2500C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C73C211yesmaximal, characteristic, complemented
5C73×#2073C211yesmaximal, characteristic, complemented
6C73×#2071C211yesmaximal, characteristic, complemented
7C73×#2054C211yesmaximal, characteristic, complemented
8C73×#2054C211yesmaximal, characteristic, complemented
9C73×#1895C211yesmaximal, characteristic, complemented
10C73×#1879C211yesmaximal, characteristic, complemented
11C73×#1879C211yesmaximal, characteristic, complemented
12C73×#1851C211yesmaximal, characteristic, complemented
13C73×#1825C211yesmaximal, characteristic, complemented
14C73×#1804C211yesmaximal, characteristic, complemented
15C73×#1802C211yesmaximal, 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×#117×C73C2211yescharacteristic
24C22×C22⋊C4×C73—21no—
25#447×C73—24no—
26C2×C4⋊C8×C73C2211yescharacteristic, complemented
27C2×C4⋊C8×C73C2211yescharacteristic, complemented
28#418×C73—24no—
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic, complemented
36C2×#102×C73C2211yescharacteristic, complemented
37C2×C22⋊C8×C73C2211yescharacteristic
38#394×C73—21no—
39#394×C73—21no—
40#390×C73C2211yescharacteristic
41#390×C73C2211yescharacteristic
42#390×C73C2211yescharacteristic, complemented
43#390×C73C2211yescharacteristic, complemented
44#388×C73—21no—
45#388×C73—21no—
46#386×C73—21no—
47#386×C73—21no—
48#384×C73C2211yescharacteristic, complemented
49#382×C73C2211yescharacteristic, complemented
50#380×C73C2211yescharacteristic
51#379×C73—21no—
52C4×C22⋊C4×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic, complemented
54#340×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—22no—
67C22×D4×C73—41no—
68C22×D4×C73—41no—
69C22×D4×C73D414yes—
70C22×D4×C73C2311yescharacteristic
71C22×D4×C73C2311yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C23×C4×C73—21no—
74C23×C4×C73—21no—
75C23×C4×C73C2311yescharacteristic
76C2×D8×C73—22no—
77C2×D8×C73—22no—
78C2×D8×C73—22no—
79C2×D8×C73—22no—
80C2×D8×C73—41no—
81C2×D8×C73—41no—
82C2×M16×C73—22no—
83C2×M16×C73—41no—
84C2×M16×C73—41no—
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87C22×C8×C73C2311yescharacteristic
88C22×C8×C73C2311yescharacteristic
89#121×C73—22no—
90#121×C73—22no—
91C4×D4×C73—22no—
92C4×D4×C73—22no—
93C4×D4×C73—41no—
94C4×D4×C73—41no—
95#117×C73—22no—
96#117×C73—22no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
115C2×C22⋊C4×C73—21no—
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73—44no—
118C2×C22⋊C4×C73D411yescharacteristic
119C2×C22⋊C4×C73D411yescharacteristic
120C2×C42×C73—21no—
121C2×C42×C73C2311yescharacteristic
122C2×C42×C73C2311yescharacteristic
123C4⋊C8×C73—41no—
124C4⋊C8×C73—41no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—22no—
128#102×C73—22no—
129#102×C73—22no—
130#102×C73—22no—
131#102×C73—41no—
132#102×C73—41no—
133C22⋊C8×C73—22no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73D411yescharacteristic
138#95×C73D411yescharacteristic
139C24×C73—21no—
140C24×C73—21no—
141C24×C73—24no—
142C24×C73—21no—
143C24×C73—42no—
144C24×C73—42no—
145C24×C73—42no—
146C24×C73—42no—
147C24×C73—81no—
148C24×C73—81no—
149C24×C73C2×D411yescharacteristic
150C2×D4×C73—28no—
151C2×D4×C73—24no—
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—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—44no—
167C2×D4×C73—44no—
168C2×D4×C73—44no—
169C2×D4×C73—42no—
170C2×D4×C73—42no—
171C2×D4×C73—42no—
172C2×D4×C73—81no—
173C2×D4×C73—81no—
174C2×D4×C73C2×D412yes—
175C2×D4×C73C2×D412yes—
176C2×D4×C73#4112yes—
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—42no—
188C22×C4×C73—42no—
189C22×C4×C73—42no—
190C22×C4×C73—42no—
191C22×C4×C73—81no—
192C22×C4×C73—81no—
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73C2×D412yes—
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73#4112yes—
200C22×C4×C73C2411yescharacteristic
201D8×C73—44no—
202D8×C73—44no—
203M16×C73—44no—
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×C73—21no—
214C2×C8×C73—21no—
215C2×C8×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—81no—
227C4⋊C4×C73—81no—
228C22⋊C4×C73—22no—
229C22⋊C4×C73—41no—
230C22⋊C4×C73—42no—
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—42no—
239C22⋊C4×C73—81no—
240C22⋊C4×C73—81no—
241C22⋊C4×C73—81no—
242C22⋊C4×C73—81no—
243C42×C73—21no—
244C42×C73—21no—
245C42×C73—21no—
246C42×C73—21no—
247C42×C73—42no—
248C23×C73—22no—
249C23×C73—22no—
250C23×C73—22no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—22no—
258C23×C73—48no—
259C23×C73—48no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73—41no—
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—41no—
276C23×C73—41no—
277C23×C73—84no—
278C23×C73—84no—
279C23×C73—84no—
280C23×C73—84no—
281C23×C73—84no—
282C23×C73#12112yes—
283C23×C73C22×D411yescharacteristic
284D4×C73—22no—
285D4×C73—22no—
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—22no—
289D4×C73—48no—
290D4×C73—41no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—41no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—84no—
297D4×C73#12314yes—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
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—84no—
331C2×C4×C73—84no—
332C2×C4×C73#12112yes—
333C2×C4×C73AGL(1,ℤ/8)12yes—
334C2×C4×C73C22×D411yescharacteristic
335C2×C4×C73C2×#4111yescharacteristic
336C2×C4×C73C2×#4111yescharacteristic
337C2×C4×C73C2×#4111yescharacteristic
338C2×C4×C73H(5,𝔽2)11yescharacteristic
339C2×C4×C73H(5,𝔽2)11yescharacteristic
340C8×C73—41no—
341C8×C73—41no—
342C8×C73—41no—
343C8×C73—41no—
344C22×C73—22no—
345C22×C73—24no—
346C22×C73—22no—
347C22×C73—22no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—42no—
354C22×C73—41no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—41no—
358C22×C73—42no—
359C22×C73—42no—
360C22×C73—42no—
361C22×C73—816no—
362C22×C73—81no—
363C22×C73—81no—
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×C73—81no—
373C22×C73C2×#12111yescharacteristic
374C22×C73#54611yescharacteristic
375C22×C73#54611yescharacteristic
376C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C73#57511yescharacteristic
378C22×C73#57611yescharacteristic
379C22×C73#57611yescharacteristic
380C4×C73—22no—
381C4×C73—22no—
382C4×C73—41no—
383C4×C73—41no—
384C4×C73—41no—
385C4×C73—81no—
386C4×C73—81no—
387C4×C73—81no—
388C4×C73—81no—
389C4×C73—81no—
390C4×C73C2×#12311yescharacteristic
391C4×C73#53411yescharacteristic
392C4×C73#55111yescharacteristic
393C4×C73#55111yescharacteristic
394#24539C7311yesmaximal, characteristic, direct product factor, Sylow
395C2×C73—42no—
396C2×C73—44no—
397C2×C73—82no—
398C2×C73—161no—
399C2×C73#241211yescharacteristic
400C2×C73#303611yescharacteristic
401C2×C73#304111yescharacteristic
402C2×C73#331811yescharacteristic
403C2×C73#331911yescharacteristic
404C2×C73#332211yescharacteristic
405C2×C73#332511yescharacteristic
406C2×#447C2×C7311yescharacteristic
407C2×#418C2×C7311yescharacteristic, complemented
408#2500C2×C7311yescharacteristic, complemented
409D4×C22⋊C4C2×C7311yescharacteristic, complemented
410#2073C2×C7311yescharacteristic, complemented
411#2071C2×C7311yescharacteristic, complemented
412#2054C2×C7311yescharacteristic, complemented
413#2054C2×C7311yescharacteristic, complemented
414#1895C2×C7311yescharacteristic, complemented
415#1879C2×C7311yescharacteristic, complemented
416#1879C2×C7311yescharacteristic, complemented
417#1851C2×C7311yescharacteristic, complemented
418#1825C2×C7311yescharacteristic, complemented
419#1804C2×C7311yescharacteristic, complemented
420#1802C2×C7311yescharacteristic, complemented
421C73#2453911yescharacteristic, direct product factor, Sylow
422C23×D4C22×C7311yescharacteristic
423C22×D8C22×C7311yescharacteristic
424C22×D8C22×C7311yescharacteristic
425C22×M16C22×C7311yescharacteristic
426C2×#121C22×C7311yescharacteristic
427C2×C4×D4C22×C7311yescharacteristic
428C2×C4×D4C22×C7311yescharacteristic
429C2×#117C22×C7311yescharacteristic
430C22×C22⋊C4—21no—
431#447—24no—
432C2×C4⋊C8C22×C7311yescharacteristic, complemented
433C2×C4⋊C8C22×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, complemented
442C2×#102C22×C7311yescharacteristic, complemented
443C2×C22⋊C8C22×C7311yescharacteristic
444#394—21no—
445#394—21no—
446#390C22×C7311yescharacteristic
447#390C22×C7311yescharacteristic
448#390C22×C7311yescharacteristic, complemented
449#390C22×C7311yescharacteristic, complemented
450#388—21no—
451#388—21no—
452#386—21no—
453#386—21no—
454#384C22×C7311yescharacteristic, complemented
455#382C22×C7311yescharacteristic, complemented
456#380C22×C7311yescharacteristic
457#379—21no—
458C4×C22⋊C4C22×C7311yescharacteristic
459#340C22×C7311yescharacteristic, complemented
460#340C22×C7311yescharacteristic, complemented
461#340C22×C7311yescharacteristic, complemented
462#340C22×C7311yescharacteristic, complemented
463#340C22×C7311yescharacteristic, complemented
464#340C22×C7311yescharacteristic, complemented
465#336C22×C7311yescharacteristic, complemented
466#336C22×C7311yescharacteristic, complemented
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4D4×C7314yes—
476C22×D4C23×C7311yescharacteristic
477C22×D4C23×C7311yescharacteristic
478C22×D4C23×C7311yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C7311yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—41no—
487C2×D8—41no—
488C2×M16—22no—
489C2×M16—41no—
490C2×M16—41no—
491C22×C8C23×C7311yescharacteristic
492C22×C8C23×C7311yescharacteristic
493C22×C8C23×C7311yescharacteristic
494C22×C8C23×C7311yescharacteristic
495#121—22no—
496#121—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—41no—
500C4×D4—41no—
501#117—22no—
502#117—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C7311yescharacteristic
506C2×C4⋊C4C23×C7311yescharacteristic
507C2×C4⋊C4C23×C7311yescharacteristic
508C2×C4⋊C4C23×C7311yescharacteristic
509C2×C4⋊C4C23×C7311yescharacteristic
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⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—44no—
524C2×C22⋊C4D4×C7311yescharacteristic
525C2×C22⋊C4D4×C7311yescharacteristic
526C2×C42—21no—
527C2×C42C23×C7311yescharacteristic
528C2×C42C23×C7311yescharacteristic
529C4⋊C8—41no—
530C4⋊C8—41no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539C22⋊C8—22no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C7311yescharacteristic
544#95D4×C7311yescharacteristic
545C24—21no—
546C24—21no—
547C24—24no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C7311yescharacteristic
556C2×D4—28no—
557C2×D4—24no—
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—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C2×D4×C7312yes—
581C2×D4C2×D4×C7312yes—
582C2×D4#41×C7312yes—
583C2×D4#41×C7312yes—
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—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4C2×D4×C7311yescharacteristic
600C22×C4C2×D4×C7311yescharacteristic
601C22×C4C2×D4×C7311yescharacteristic
602C22×C4C2×D4×C7311yescharacteristic
603C22×C4C2×D4×C7312yes—
604C22×C4C2×D4×C7311yescharacteristic
605C22×C4#41×C7312yes—
606C22×C4C24×C7311yescharacteristic
607D8—44no—
608D8—44no—
609M16—44no—
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×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—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—21no—
632C4⋊C4—81no—
633C4⋊C4—81no—
634C22⋊C4—22no—
635C22⋊C4—41no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—42no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
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—41no—
681C23—41no—
682C23—41no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23#121×C7312yes—
689C23C22×D4×C7311yescharacteristic
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4#123×C7314yes—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
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—84no—
737C2×C4—84no—
738C2×C4#121×C7312yes—
739C2×C4AGL(1,ℤ/8)×C7312yes—
740C2×C4C22×D4×C7311yescharacteristic
741C2×C4C2×#41×C7311yescharacteristic
742C2×C4C2×#41×C7311yescharacteristic
743C2×C4C2×#41×C7311yescharacteristic
744C2×C4H(5,𝔽2)×C7311yescharacteristic
745C2×C4H(5,𝔽2)×C7311yescharacteristic
746C8—41no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—816no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×#121×C7311yescharacteristic
780C22#546×C7311yescharacteristic
781C22#546×C7311yescharacteristic
782C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
783C22#575×C7311yescharacteristic
784C22#576×C7311yescharacteristic
785C22#576×C7311yescharacteristic
786C4—22no—
787C4—22no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C7311yescharacteristic
797C4#534×C7311yescharacteristic
798C4#551×C7311yescharacteristic
799C4#551×C7311yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—161no—
804C2C73×#241211yescharacteristic
805C2C73×#303611yescharacteristic
806C2C73×#304111yescharacteristic
807C2C73×#331811yescharacteristic
808C2C73×#331911yescharacteristic
809C2C73×#332211yescharacteristic
810C2C73×#332511yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#447×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×#418×C73C2semidirect
3. C73×#2500C2semidirect
4. D4×C22⋊C4×C73C2semidirect
5. C73×#2073C2semidirect
6. C73×#2071C2semidirect
7. C73×#2054C2semidirect
8. C73×#2054C2semidirect
9. C73×#1895C2semidirect
10. C73×#1879C2semidirect
11. C73×#1879C2semidirect
12. C73×#1851C2semidirect
13. C73×#1825C2semidirect
14. C73×#1804C2semidirect
15. C73×#1802C2semidirect
26. C2×C4⋊C8×C73C22semidirect
27. C2×C4⋊C8×C73C22semidirect
35. C2×#102×C73C22semidirect
36. C2×#102×C73C22semidirect
42. #390×C73C22semidirect
43. #390×C73C22semidirect
48. #384×C73C22semidirect
49. #382×C73C22semidirect
53. #340×C73C22semidirect
54. #340×C73C22semidirect
55. #340×C73C22semidirect
56. #340×C73C22semidirect
57. #340×C73C22semidirect
58. #340×C73C22semidirect
59. #336×C73C22semidirect
60. #336×C73C22semidirect
394. #24539C73direct (N × H)
407. C2×#418C2×C73semidirect
408. #2500C2×C73semidirect
409. D4×C22⋊C4C2×C73semidirect
410. #2073C2×C73semidirect
411. #2071C2×C73semidirect
412. #2054C2×C73semidirect
413. #2054C2×C73semidirect
414. #1895C2×C73semidirect
415. #1879C2×C73semidirect
416. #1879C2×C73semidirect
417. #1851C2×C73semidirect
418. #1825C2×C73semidirect
419. #1804C2×C73semidirect
420. #1802C2×C73semidirect
421. C73#24539direct (N × H)
432. C2×C4⋊C8C22×C73semidirect
433. C2×C4⋊C8C22×C73semidirect
441. C2×#102C22×C73semidirect
442. C2×#102C22×C73semidirect
448. #390C22×C73semidirect
449. #390C22×C73semidirect
454. #384C22×C73semidirect
455. #382C22×C73semidirect
459. #340C22×C73semidirect
460. #340C22×C73semidirect
461. #340C22×C73semidirect
462. #340C22×C73semidirect
463. #340C22×C73semidirect
464. #340C22×C73semidirect
465. #336C22×C73semidirect
466. #336C22×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×#418×C732
C73×#25002
D4×C22⋊C4×C732
C73×#20732
C73×#20712
C73×#20542
C73×#18952
C73×#18792
C73×#18512
C73×#18252
C73×#18042
C73×#18022
#2453973