Finite Group Databasebeta

← C73×#25554 #32934958

Subgroups — C73×#25554 #32934958

Order 18688.

1236 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C73C211yesmaximal, characteristic, complemented
2C2×#482×C73C211yesmaximal, characteristic, complemented
3C2×#469×C73C211yesmaximal, characteristic, complemented
4C73×#2416C211yesmaximal, characteristic, complemented
5C73×#2058C211yesmaximal, characteristic, complemented
6C73×#2034C211yesmaximal, characteristic, complemented
7C73×#2023C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic, complemented
9C73×#1879C211yesmaximal, characteristic, complemented
10C73×#1875C211yesmaximal, characteristic, complemented
11C73×#1874C211yesmaximal, characteristic, complemented
12C73×#1870C211yesmaximal, characteristic, complemented
13C73×#1862C211yesmaximal, characteristic, complemented
14C73×#1854C211yesmaximal, characteristic, complemented
15C73×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18#555×C73—24no—
19#555×C73—24no—
20C2×C4⋊Q8×C73C2211yescharacteristic
21C2×#124×C73—21no—
22C2×#124×C73—21no—
23C2×#121×C73—21no—
24C2×#121×C73—21no—
25C2×#121×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×#121×C73C2211yescharacteristic
29C2×C4×D4×C73C2211yescharacteristic
30C2×C4×D4×C73C2211yescharacteristic
31C2×#117×C73—21no—
32C2×#117×C73C2211yescharacteristic
33C2×#117×C73C2211yescharacteristic
34C22×C4⋊C4×C73C2211yescharacteristic
35#482×C73—24no—
36#469×C73—24no—
37C2×#107×C73C2211yescharacteristic
38C2×#106×C73C2211yescharacteristic
39C2×#106×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×#102×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48C2×C22⋊C8×C73C2211yescharacteristic
49#396×C73—21no—
50#394×C73—21no—
51#390×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#386×C73—21no—
54#380×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C22×Q8×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73D411yescharacteristic
69C22×D4×C73C2311yescharacteristic
70C22×D4×C73C2311yescharacteristic
71C23×C4×C73—21no—
72C23×C4×C73—21no—
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C2×D8×C73—22no—
76C2×D8×C73—22no—
77C2×D8×C73—41no—
78C2×M16×C73—22no—
79C2×M16×C73—22no—
80C2×M16×C73—41no—
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C4⋊Q8×C73—22no—
86C4⋊Q8×C73—22no—
87#124×C73—28no—
88#124×C73—28no—
89#121×C73—28no—
90#121×C73—22no—
91#121×C73—22no—
92#121×C73—22no—
93#121×C73—22no—
94#121×C73—22no—
95#121×C73—22no—
96#121×C73—41no—
97#121×C73—44no—
98#121×C73D414yescomplemented
99C4×D4×C73—22no—
100C4×D4×C73—22no—
101C4×D4×C73—22no—
102C4×D4×C73—22no—
103#117×C73—28no—
104#117×C73—22no—
105#117×C73—22no—
106#117×C73—22no—
107#117×C73D414yescomplemented
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—22no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—41no—
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×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73D411yescharacteristic
131C2×C22⋊C4×C73D411yescharacteristic
132C2×C42×C73—21no—
133C2×C42×C73—21no—
134C2×C42×C73C2311yescharacteristic
135#107×C73—22no—
136#106×C73—22no—
137#106×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—22no—
143#102×C73—41no—
144C22⋊C8×C73—22no—
145C22⋊C8×C73—22no—
146C22⋊C8×C73—41no—
147#95×C73—21no—
148#95×C73—21no—
149C24×C73—21no—
150C24×C73—21no—
151C24×C73C2×D411yescharacteristic
152C24×C73C2×D411yescharacteristic
153C2×Q8×C73—24no—
154C2×Q8×C73—81no—
155C2×Q8×C73—81no—
156C2×D4×C73—22no—
157C2×D4×C73—24no—
158C2×D4×C73—24no—
159C2×D4×C73—22no—
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—41no—
172C2×D4×C73—42no—
173C2×D4×C73—42no—
174C2×D4×C73—42no—
175C2×D4×C73—42no—
176C2×D4×C73—42no—
177C2×D4×C73—81no—
178C2×D4×C73—81no—
179C2×D4×C73—81no—
180C2×D4×C73—81no—
181C2×D4×C73—81no—
182C2×D4×C73C2×D412yes—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—24no—
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×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—42no—
201C22×C4×C73—42no—
202C22×C4×C73—42no—
203C22×C4×C73—42no—
204C22×C4×C73—81no—
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D412yes—
209C22×C4×C73C2×D412yes—
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2411yescharacteristic
212D8×C73—44no—
213M16×C73—44no—
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×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73#4112yes—
226C4⋊C4×C73—24no—
227C4⋊C4×C73—22no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—42no—
237C4⋊C4×C73—42no—
238C4⋊C4×C73C2×D412yes—
239C4⋊C4×C73C2×D412yes—
240C4⋊C4×C73C2×D412yes—
241C4⋊C4×C73#4112yes—
242C22⋊C4×C73—24no—
243C22⋊C4×C73—24no—
244C22⋊C4×C73—24no—
245C22⋊C4×C73—24no—
246C22⋊C4×C73—22no—
247C22⋊C4×C73—24no—
248C22⋊C4×C73—22no—
249C22⋊C4×C73—42no—
250C22⋊C4×C73—42no—
251C22⋊C4×C73—42no—
252C22⋊C4×C73—42no—
253C22⋊C4×C73—81no—
254C42×C73—24no—
255C42×C73—24no—
256C42×C73—21no—
257C42×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—22no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
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—41no—
285C23×C73#12012yes—
286C23×C73C22×D411yescharacteristic
287Q8×C73—84no—
288D4×C73—22no—
289D4×C73—22no—
290D4×C73—44no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—41no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—84no—
298D4×C73—84no—
299D4×C73—84no—
300D4×C73—84no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—21no—
310C2×C4×C73—22no—
311C2×C4×C73—21no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—21no—
315C2×C4×C73—22no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—48no—
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—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—84no—
339C2×C4×C73#12012yes—
340C2×C4×C73AGL(1,ℤ/8)12yes—
341C2×C4×C73C22×D411yescharacteristic
342C2×C4×C73C22×D411yescharacteristic
343C2×C4×C73C2×#4111yescharacteristic
344C2×C4×C73C2×#4111yescharacteristic
345C2×C4×C73H(5,𝔽2)11yescharacteristic
346C2×C4×C732−1+411yescharacteristic
347C8×C73—22no—
348C8×C73—41no—
349C8×C73—41no—
350C8×C73—41no—
351C22×C73—22no—
352C22×C73—22no—
353C22×C73—22no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—42no—
362C22×C73—42no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—42no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—81no—
369C22×C73—81no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73—81no—
378C22×C73—81no—
379C22×C73C2×#12011yescharacteristic
380C22×C73#54611yescharacteristic
381C22×C73#54711yescharacteristic
382C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C73#57511yescharacteristic
384C22×C73#57611yescharacteristic
385C22×C73#57711yescharacteristic
386C4×C73—22no—
387C4×C73—22no—
388C4×C73—41no—
389C4×C73—42no—
390C4×C73—41no—
391C4×C73—42no—
392C4×C73—42no—
393C4×C73—42no—
394C4×C73—81no—
395C4×C73—81no—
396C4×C73#53211yescharacteristic
397C4×C73#53711yescharacteristic
398C4×C73#54611yescharacteristic
399C4×C73#54711yescharacteristic
400#25554C7311yesmaximal, characteristic, direct product factor, Sylow
401C2×C73—42no—
402C2×C73—81no—
403C2×C73—82no—
404C2×C73—161no—
405C2×C73#243011yescharacteristic
406C2×C73#300611yescharacteristic
407C2×C73#301211yescharacteristic
408C2×C73#332111yescharacteristic
409C2×C73#332511yescharacteristic
410C2×C73#334711yescharacteristic
411C2×C73#335411yescharacteristic
412C2×#555C2×C7311yescharacteristic, complemented
413C2×#482C2×C7311yescharacteristic, complemented
414C2×#469C2×C7311yescharacteristic, complemented
415#2416C2×C7311yescharacteristic, complemented
416#2058C2×C7311yescharacteristic, complemented
417#2034C2×C7311yescharacteristic, complemented
418#2023C2×C7311yescharacteristic, complemented
419#1999C2×C7311yescharacteristic, complemented
420#1879C2×C7311yescharacteristic, complemented
421#1875C2×C7311yescharacteristic, complemented
422#1874C2×C7311yescharacteristic, complemented
423#1870C2×C7311yescharacteristic, complemented
424#1862C2×C7311yescharacteristic, complemented
425#1854C2×C7311yescharacteristic, complemented
426#1736C2×C7311yescharacteristic, complemented
427C73#2555411yescharacteristic, direct product factor, Sylow
428C22×D8C22×C7311yescharacteristic
429C22×M16C22×C7311yescharacteristic
430#555—24no—
431#555—24no—
432C2×C4⋊Q8C22×C7311yescharacteristic
433C2×#124—21no—
434C2×#124—21no—
435C2×#121—21no—
436C2×#121—21no—
437C2×#121C22×C7311yescharacteristic
438C2×#121C22×C7311yescharacteristic
439C2×#121C22×C7311yescharacteristic
440C2×#121C22×C7311yescharacteristic
441C2×C4×D4C22×C7311yescharacteristic
442C2×C4×D4C22×C7311yescharacteristic
443C2×#117—21no—
444C2×#117C22×C7311yescharacteristic
445C2×#117C22×C7311yescharacteristic
446C22×C4⋊C4C22×C7311yescharacteristic
447#482—24no—
448#469—24no—
449C2×#107C22×C7311yescharacteristic
450C2×#106C22×C7311yescharacteristic
451C2×#106C22×C7311yescharacteristic
452C2×#102C22×C7311yescharacteristic
453C2×#102C22×C7311yescharacteristic
454C2×#102C22×C7311yescharacteristic
455C2×#102C22×C7311yescharacteristic
456C2×#102C22×C7311yescharacteristic
457C2×#102C22×C7311yescharacteristic
458C2×C22⋊C8C22×C7311yescharacteristic
459C2×C22⋊C8C22×C7311yescharacteristic
460C2×C22⋊C8C22×C7311yescharacteristic
461#396—21no—
462#394—21no—
463#390C22×C7311yescharacteristic
464#389C22×C7311yescharacteristic
465#386—21no—
466#380C22×C7311yescharacteristic
467#340C22×C7311yescharacteristic
468#340C22×C7311yescharacteristic
469#340C22×C7311yescharacteristic
470#340C22×C7311yescharacteristic
471#340C22×C7311yescharacteristic
472#340C22×C7311yescharacteristic
473#336C22×C7311yescharacteristic
474#336C22×C7311yescharacteristic
475C22×Q8—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4D4×C7311yescharacteristic
481C22×D4C23×C7311yescharacteristic
482C22×D4C23×C7311yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C7311yescharacteristic
486C23×C4C23×C7311yescharacteristic
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—41no—
493C22×C8C23×C7311yescharacteristic
494C22×C8C23×C7311yescharacteristic
495C22×C8C23×C7311yescharacteristic
496C22×C8C23×C7311yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—22no—
499#124—28no—
500#124—28no—
501#121—28no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—41no—
509#121—44no—
510#121D4×C7314yescomplemented
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515#117—28no—
516#117—22no—
517#117—22no—
518#117—22no—
519#117D4×C7314yescomplemented
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4D4×C7311yescharacteristic
526C2×C4⋊C4C23×C7311yescharacteristic
527C2×C4⋊C4C23×C7311yescharacteristic
528C2×C4⋊C4C23×C7311yescharacteristic
529C2×C4⋊C4C23×C7311yescharacteristic
530C2×C4⋊C4C23×C7311yescharacteristic
531C2×C4⋊C4C23×C7311yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4D4×C7311yescharacteristic
543C2×C22⋊C4D4×C7311yescharacteristic
544C2×C42—21no—
545C2×C42—21no—
546C2×C42C23×C7311yescharacteristic
547#107—22no—
548#106—22no—
549#106—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—22no—
555#102—41no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—41no—
559#95—21no—
560#95—21no—
561C24—21no—
562C24—21no—
563C24C2×D4×C7311yescharacteristic
564C24C2×D4×C7311yescharacteristic
565C2×Q8—24no—
566C2×Q8—81no—
567C2×Q8—81no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—22no—
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—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4C2×D4×C7312yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4C2×D4×C7311yescharacteristic
618C22×C4C2×D4×C7311yescharacteristic
619C22×C4C2×D4×C7311yescharacteristic
620C22×C4C2×D4×C7312yes—
621C22×C4C2×D4×C7312yes—
622C22×C4C2×D4×C7311yescharacteristic
623C22×C4C24×C7311yescharacteristic
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×C8—21no—
636C2×C8—21no—
637C2×C8#41×C7312yes—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4C2×D4×C7312yes—
651C4⋊C4C2×D4×C7312yes—
652C4⋊C4C2×D4×C7312yes—
653C4⋊C4#41×C7312yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—22no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C42—24no—
667C42—24no—
668C42—21no—
669C42—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
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#120×C7312yes—
698C23C22×D4×C7311yescharacteristic
699Q8—84no—
700D4—22no—
701D4—22no—
702D4—44no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
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—84no—
751C2×C4#120×C7312yes—
752C2×C4AGL(1,ℤ/8)×C7312yes—
753C2×C4C22×D4×C7311yescharacteristic
754C2×C4C22×D4×C7311yescharacteristic
755C2×C4C2×#41×C7311yescharacteristic
756C2×C4C2×#41×C7311yescharacteristic
757C2×C4H(5,𝔽2)×C7311yescharacteristic
758C2×C42−1+4×C7311yescharacteristic
759C8—22no—
760C8—41no—
761C8—41no—
762C8—41no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#120×C7311yescharacteristic
792C22#546×C7311yescharacteristic
793C22#547×C7311yescharacteristic
794C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
795C22#575×C7311yescharacteristic
796C22#576×C7311yescharacteristic
797C22#577×C7311yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—41no—
806C4—81no—
807C4—81no—
808C4#532×C7311yescharacteristic
809C4#537×C7311yescharacteristic
810C4#546×C7311yescharacteristic
811C4#547×C7311yescharacteristic
812C2—42no—
813C2—81no—
814C2—82no—
815C2—161no—
816C2C73×#243011yescharacteristic
817C2C73×#300611yescharacteristic
818C2C73×#301211yescharacteristic
819C2C73×#332111yescharacteristic
820C2C73×#332511yescharacteristic
821C2C73×#334711yescharacteristic
822C2C73×#335411yescharacteristic
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×#555×C73C2semidirect
2. C2×#482×C73C2semidirect
3. C2×#469×C73C2semidirect
4. C73×#2416C2semidirect
5. C73×#2058C2semidirect
6. C73×#2034C2semidirect
7. C73×#2023C2semidirect
8. C73×#1999C2semidirect
9. C73×#1879C2semidirect
10. C73×#1875C2semidirect
11. C73×#1874C2semidirect
12. C73×#1870C2semidirect
13. C73×#1862C2semidirect
14. C73×#1854C2semidirect
15. C73×#1736C2semidirect
98. #121×C73D4semidirect
107. #117×C73D4semidirect
400. #25554C73direct (N × H)
412. C2×#555C2×C73semidirect
413. C2×#482C2×C73semidirect
414. C2×#469C2×C73semidirect
415. #2416C2×C73semidirect
416. #2058C2×C73semidirect
417. #2034C2×C73semidirect
418. #2023C2×C73semidirect
419. #1999C2×C73semidirect
420. #1879C2×C73semidirect
421. #1875C2×C73semidirect
422. #1874C2×C73semidirect
423. #1870C2×C73semidirect
424. #1862C2×C73semidirect
425. #1854C2×C73semidirect
426. #1736C2×C73semidirect
427. C73#25554direct (N × H)
510. #121D4×C73semidirect
519. #117D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C732
C2×#482×C732
C2×#469×C732
C73×#24162
C73×#20582
C73×#20342
C73×#20232
C73×#19992
C73×#18792
C73×#18752
C73×#18742
C73×#18702
C73×#18622
C73×#18542
C73×#17362
#2555473