Finite Group Databasebeta

← C73×#24792 #32934196

Subgroups — C73×#24792 #32934196

Order 18688.

1076 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C73C211yesmaximal, characteristic, complemented
2C2×#469×C73C211yesmaximal, characteristic, complemented
3C2×#436×C73C211yesmaximal, characteristic, complemented
4C2×#428×C73C211yesmaximal, characteristic, complemented
5C73×#2416C211yesmaximal, characteristic, complemented
6C73×#2414C211yesmaximal, characteristic, complemented
7C73×#2067C211yesmaximal, characteristic, complemented
8C73×#2065C211yesmaximal, characteristic, complemented
9C73×#2034C211yesmaximal, characteristic, complemented
10C73×#2033C211yesmaximal, characteristic, complemented
11C73×#1970C211yesmaximal, characteristic, complemented
12C73×#1941C211yesmaximal, characteristic, complemented
13C73×#1875C211yesmaximal, characteristic, complemented
14C73×#1874C211yesmaximal, characteristic, complemented
15C73×#1809C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C2×#121×C73—21no—
20C2×#121×C73C2211yescharacteristic
21C2×#121×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25C2×#117×C73C2211yescharacteristic
26C22×C4⋊C4×C73C2211yescharacteristic
27#469×C73—24no—
28#469×C73—24no—
29#436×C73—24no—
30#428×C73—24no—
31C2×#107×C73C2211yescharacteristic
32C2×#107×C73C2211yescharacteristic
33C2×#106×C73C2211yescharacteristic
34C2×#106×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×C22⋊C8×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic
45C2×C4×C8×C73C2211yescharacteristic
46#396×C73—21no—
47#394×C73—21no—
48#394×C73—21no—
49#392×C73—21no—
50#390×C73—21no—
51#390×C73C2211yescharacteristic
52#390×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#389×C73C2211yescharacteristic
55#388×C73—21no—
56#386×C73—21no—
57#380×C73C2211yescharacteristic
58#380×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×C73D411yescharacteristic
68C22×D4×C73C2311yescharacteristic
69C22×D4×C73C2311yescharacteristic
70C23×C4×C73—21no—
71C23×C4×C73C2311yescharacteristic
72C23×C4×C73C2311yescharacteristic
73C2×D8×C73—22no—
74C2×D8×C73—22no—
75C2×D8×C73—22no—
76C2×M16×C73—22no—
77C2×M16×C73—22no—
78C2×M16×C73—22no—
79C2×M16×C73—22no—
80C2×M16×C73—22no—
81C2×M16×C73D414yescomplemented
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86#121×C73—22no—
87#121×C73—22no—
88#121×C73—22no—
89#121×C73—22no—
90#121×C73—22no—
91#121×C73—22no—
92#121×C73—41no—
93#121×C73—41no—
94#121×C73—44no—
95C4×D4×C73—22no—
96C4×D4×C73—22no—
97#117×C73—22no—
98#117×C73—41no—
99C2×C4⋊C4×C73—22no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—21no—
103C2×C4⋊C4×C73—41no—
104C2×C4⋊C4×C73D411yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C4⋊C4×C73C2311yescharacteristic
110C2×C4⋊C4×C73C2311yescharacteristic
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—21no—
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73D411yescharacteristic
123C2×C22⋊C4×C73D411yescharacteristic
124C2×C42×C73—21no—
125C2×C42×C73C2311yescharacteristic
126#107×C73—22no—
127#107×C73—22no—
128#106×C73—22no—
129#106×C73—22no—
130#106×C73D414yescomplemented
131C4⋊C8×C73—22no—
132#102×C73—22no—
133#102×C73—22no—
134#102×C73—22no—
135#102×C73—22no—
136#102×C73—41no—
137#102×C73—41no—
138C22⋊C8×C73—22no—
139C22⋊C8×C73—22no—
140C4×C8×C73—22no—
141#95×C73—21no—
142#95×C73—21no—
143#95×C73—21no—
144#95×C73—21no—
145C24×C73—21no—
146C24×C73—21no—
147C24×C73C2×D411yescharacteristic
148C24×C73C2×D411yescharacteristic
149C2×D4×C73—22no—
150C2×D4×C73—22no—
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—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—41no—
164C2×D4×C73—42no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73—42no—
168C2×D4×C73—42no—
169C2×D4×C73—42no—
170C2×D4×C73—42no—
171C2×D4×C73—42no—
172C2×D4×C73—81no—
173C2×D4×C73—81no—
174C2×D4×C73—81no—
175C2×D4×C73—81no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
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—42no—
193C22×C4×C73—42no—
194C22×C4×C73—81no—
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2×D412yes—
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73#4112yes—
201C22×C4×C73C2411yescharacteristic
202D8×C73—44no—
203M16×C73—28no—
204M16×C73—44no—
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—
214C2×C8×C73C2×D412yes—
215C2×C8×C73C2×D412yes—
216C2×C8×C73#4112yes—
217C4⋊C4×C73—22no—
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—21no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—42no—
229C4⋊C4×C73—42no—
230C4⋊C4×C73—81no—
231C4⋊C4×C73C2×D412yes—
232C4⋊C4×C73C2×D412yes—
233C22⋊C4×C73—22no—
234C22⋊C4×C73—22no—
235C22⋊C4×C73—42no—
236C22⋊C4×C73—42no—
237C22⋊C4×C73—42no—
238C22⋊C4×C73—42no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—42no—
241C22⋊C4×C73—42no—
242C22⋊C4×C73—42no—
243C22⋊C4×C73—81no—
244C22⋊C4×C73—81no—
245C22⋊C4×C73—81no—
246C42×C73—21no—
247C42×C73—21no—
248C42×C73—42no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
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#12112yes—
277C23×C73C22×D411yescharacteristic
278D4×C73—44no—
279D4×C73—41no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—41no—
284D4×C73—41no—
285D4×C73—41no—
286D4×C73—41no—
287D4×C73—84no—
288D4×C73—84no—
289D4×C73—84no—
290D4×C73—84no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—22no—
302C2×C4×C73—21no—
303C2×C4×C73—22no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
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—84no—
328C2×C4×C73#12112yes—
329C2×C4×C73AGL(1,ℤ/8)12yes—
330C2×C4×C73C22×D411yescharacteristic
331C2×C4×C73C22×D411yescharacteristic
332C2×C4×C73C2×#4111yescharacteristic
333C2×C4×C73C2×#4111yescharacteristic
334C2×C4×C73H(5,𝔽2)11yescharacteristic
335C2×C4×C732−1+411yescharacteristic
336C8×C73—22no—
337C8×C73—41no—
338C8×C73—41no—
339C8×C73#12114yescomplemented
340C22×C73—22no—
341C22×C73—22no—
342C22×C73—22no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—81no—
355C22×C73—81no—
356C22×C73—81no—
357C22×C73—81no—
358C22×C73—81no—
359C22×C73—81no—
360C22×C73—81no—
361C22×C73—81no—
362C22×C73—81no—
363C22×C73—81no—
364C22×C73—81no—
365C22×C73—81no—
366C22×C73—81no—
367C22×C73—81no—
368C22×C73C2×#12111yescharacteristic
369C22×C73D4211yescharacteristic
370C22×C73#54711yescharacteristic
371C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C73#57511yescharacteristic
373C22×C73#57611yescharacteristic
374C22×C73#57711yescharacteristic
375C4×C73—22no—
376C4×C73—22no—
377C4×C73—41no—
378C4×C73—42no—
379C4×C73—42no—
380C4×C73—41no—
381C4×C73—81no—
382C4×C73—81no—
383C4×C73—81no—
384C4×C73—81no—
385C4×C73C2×#12111yescharacteristic
386C4×C73#53711yescharacteristic
387C4×C73#54811yescharacteristic
388C4×C73#55311yescharacteristic
389#24792C7311yesmaximal, characteristic, direct product factor, Sylow
390C2×C73—42no—
391C2×C73—81no—
392C2×C73—161no—
393C2×C73—161no—
394C2×C73#241611yescharacteristic
395C2×C73#305511yescharacteristic
396C2×C73#306211yescharacteristic
397C2×C73#327411yescharacteristic
398C2×C73#327511yescharacteristic
399C2×C73#335411yescharacteristic
400C2×C73#335511yescharacteristic
401C2×#469C2×C7311yescharacteristic, complemented
402C2×#469C2×C7311yescharacteristic, complemented
403C2×#436C2×C7311yescharacteristic, complemented
404C2×#428C2×C7311yescharacteristic, complemented
405#2416C2×C7311yescharacteristic, complemented
406#2414C2×C7311yescharacteristic, complemented
407#2067C2×C7311yescharacteristic, complemented
408#2065C2×C7311yescharacteristic, complemented
409#2034C2×C7311yescharacteristic, complemented
410#2033C2×C7311yescharacteristic, complemented
411#1970C2×C7311yescharacteristic, complemented
412#1941C2×C7311yescharacteristic, complemented
413#1875C2×C7311yescharacteristic, complemented
414#1874C2×C7311yescharacteristic, complemented
415#1809C2×C7311yescharacteristic, complemented
416C73#2479211yescharacteristic, direct product factor, Sylow
417C22×D8C22×C7311yescharacteristic
418C22×M16C22×C7311yescharacteristic
419C22×M16C22×C7311yescharacteristic
420C2×#121—21no—
421C2×#121C22×C7311yescharacteristic
422C2×#121C22×C7311yescharacteristic
423C2×#121C22×C7311yescharacteristic
424C2×#121C22×C7311yescharacteristic
425C2×C4×D4C22×C7311yescharacteristic
426C2×#117C22×C7311yescharacteristic
427C22×C4⋊C4C22×C7311yescharacteristic
428#469—24no—
429#469—24no—
430#436—24no—
431#428—24no—
432C2×#107C22×C7311yescharacteristic
433C2×#107C22×C7311yescharacteristic
434C2×#106C22×C7311yescharacteristic
435C2×#106C22×C7311yescharacteristic
436C2×#106C22×C7311yescharacteristic
437C2×C4⋊C8C22×C7311yescharacteristic
438C2×#102C22×C7311yescharacteristic
439C2×#102C22×C7311yescharacteristic
440C2×#102C22×C7311yescharacteristic
441C2×#102C22×C7311yescharacteristic
442C2×#102C22×C7311yescharacteristic
443C2×#102C22×C7311yescharacteristic
444C2×C22⋊C8C22×C7311yescharacteristic
445C2×C22⋊C8C22×C7311yescharacteristic
446C2×C4×C8C22×C7311yescharacteristic
447#396—21no—
448#394—21no—
449#394—21no—
450#392—21no—
451#390—21no—
452#390C22×C7311yescharacteristic
453#390C22×C7311yescharacteristic
454#389C22×C7311yescharacteristic
455#389C22×C7311yescharacteristic
456#388—21no—
457#386—21no—
458#380C22×C7311yescharacteristic
459#380C22×C7311yescharacteristic
460#340C22×C7311yescharacteristic
461#340C22×C7311yescharacteristic
462#340C22×C7311yescharacteristic
463#340C22×C7311yescharacteristic
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4D4×C7311yescharacteristic
469C22×D4C23×C7311yescharacteristic
470C22×D4C23×C7311yescharacteristic
471C23×C4—21no—
472C23×C4C23×C7311yescharacteristic
473C23×C4C23×C7311yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16D4×C7314yescomplemented
483C22×C8C23×C7311yescharacteristic
484C22×C8C23×C7311yescharacteristic
485C22×C8C23×C7311yescharacteristic
486C22×C8C23×C7311yescharacteristic
487#121—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495#121—44no—
496C4×D4—22no—
497C4×D4—22no—
498#117—22no—
499#117—41no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4D4×C7311yescharacteristic
506C2×C4⋊C4C23×C7311yescharacteristic
507C2×C4⋊C4C23×C7311yescharacteristic
508C2×C4⋊C4C23×C7311yescharacteristic
509C2×C4⋊C4C23×C7311yescharacteristic
510C2×C4⋊C4C23×C7311yescharacteristic
511C2×C4⋊C4C23×C7311yescharacteristic
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⋊C4D4×C7311yescharacteristic
524C2×C22⋊C4D4×C7311yescharacteristic
525C2×C42—21no—
526C2×C42C23×C7311yescharacteristic
527#107—22no—
528#107—22no—
529#106—22no—
530#106—22no—
531#106D4×C7314yescomplemented
532C4⋊C8—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C4×C8—22no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546C24—21no—
547C24—21no—
548C24C2×D4×C7311yescharacteristic
549C24C2×D4×C7311yescharacteristic
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—41no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
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—42no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4C2×D4×C7311yescharacteristic
597C22×C4C2×D4×C7311yescharacteristic
598C22×C4C2×D4×C7311yescharacteristic
599C22×C4C2×D4×C7312yes—
600C22×C4C2×D4×C7311yescharacteristic
601C22×C4#41×C7312yes—
602C22×C4C24×C7311yescharacteristic
603D8—44no—
604M16—28no—
605M16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8C2×D4×C7312yes—
615C2×C8C2×D4×C7312yes—
616C2×C8C2×D4×C7312yes—
617C2×C8#41×C7312yes—
618C4⋊C4—22no—
619C4⋊C4—21no—
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—42no—
630C4⋊C4—42no—
631C4⋊C4—81no—
632C4⋊C4C2×D4×C7312yes—
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—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23#121×C7312yes—
678C23C22×D4×C7311yescharacteristic
679D4—44no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—84no—
689D4—84no—
690D4—84no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
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—84no—
729C2×C4#121×C7312yes—
730C2×C4AGL(1,ℤ/8)×C7312yes—
731C2×C4C22×D4×C7311yescharacteristic
732C2×C4C22×D4×C7311yescharacteristic
733C2×C4C2×#41×C7311yescharacteristic
734C2×C4C2×#41×C7311yescharacteristic
735C2×C4H(5,𝔽2)×C7311yescharacteristic
736C2×C42−1+4×C7311yescharacteristic
737C8—22no—
738C8—41no—
739C8—41no—
740C8#121×C7314yescomplemented
741C22—22no—
742C22—22no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C2×#121×C7311yescharacteristic
770C22D42×C7311yescharacteristic
771C22#547×C7311yescharacteristic
772C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
773C22#575×C7311yescharacteristic
774C22#576×C7311yescharacteristic
775C22#577×C7311yescharacteristic
776C4—22no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—41no—
781C4—41no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4C2×#121×C7311yescharacteristic
787C4#537×C7311yescharacteristic
788C4#548×C7311yescharacteristic
789C4#553×C7311yescharacteristic
790C2—42no—
791C2—81no—
792C2—161no—
793C2—161no—
794C2C73×#241611yescharacteristic
795C2C73×#305511yescharacteristic
796C2C73×#306211yescharacteristic
797C2C73×#327411yescharacteristic
798C2C73×#327511yescharacteristic
799C2C73×#335411yescharacteristic
800C2C73×#335511yescharacteristic
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×#469×C73C2semidirect
3. C2×#436×C73C2semidirect
4. C2×#428×C73C2semidirect
5. C73×#2416C2semidirect
6. C73×#2414C2semidirect
7. C73×#2067C2semidirect
8. C73×#2065C2semidirect
9. C73×#2034C2semidirect
10. C73×#2033C2semidirect
11. C73×#1970C2semidirect
12. C73×#1941C2semidirect
13. C73×#1875C2semidirect
14. C73×#1874C2semidirect
15. C73×#1809C2semidirect
81. C2×M16×C73D4semidirect
130. #106×C73D4semidirect
339. C8×C73#121semidirect
389. #24792C73direct (N × H)
401. C2×#469C2×C73semidirect
402. C2×#469C2×C73semidirect
403. C2×#436C2×C73semidirect
404. C2×#428C2×C73semidirect
405. #2416C2×C73semidirect
406. #2414C2×C73semidirect
407. #2067C2×C73semidirect
408. #2065C2×C73semidirect
409. #2034C2×C73semidirect
410. #2033C2×C73semidirect
411. #1970C2×C73semidirect
412. #1941C2×C73semidirect
413. #1875C2×C73semidirect
414. #1874C2×C73semidirect
415. #1809C2×C73semidirect
416. C73#24792direct (N × H)
482. C2×M16D4×C73semidirect
531. #106D4×C73semidirect
740. C8#121×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×#436×C732
C2×#428×C732
C73×#24162
C73×#24142
C73×#20672
C73×#20652
C73×#20342
C73×#20332
C73×#19702
C73×#19412
C73×#18752
C73×#18742
C73×#18092
#2479273