Finite Group Databasebeta

← C73×#25388 #32934792

Subgroups — C73×#25388 #32934792

Order 18688.

1116 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×#466×C73C211yesmaximal, characteristic, complemented
2C2×#465×C73C211yesmaximal, characteristic, complemented
3C2×#463×C73C211yesmaximal, characteristic, complemented
4C2×C8×D4×C73C211yesmaximal, characteristic, complemented
5C73×#2540C211yesmaximal, characteristic, complemented
6C73×#2535C211yesmaximal, characteristic, complemented
7C73×#2036C211yesmaximal, characteristic, complemented
8C73×#2034C211yesmaximal, characteristic, complemented
9C73×#2000C211yesmaximal, characteristic, complemented
10C73×#1999C211yesmaximal, characteristic, complemented
11C73×#1958C211yesmaximal, characteristic, complemented
12C73×#1949C211yesmaximal, characteristic, complemented
13C73×#1893C211yesmaximal, characteristic, complemented
14C73×#1892C211yesmaximal, characteristic, complemented
15C4×#102×C73C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C23×C8×C73C2211yescharacteristic
19C23×C8×C73C2211yescharacteristic
20C2×#124×C73C2211yescharacteristic
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×C22⋊Q8×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×#121×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×C4×D4×C73C2211yescharacteristic
28C2×C4×D4×C73C2211yescharacteristic
29#466×C73—24no—
30#465×C73—24no—
31#463×C73—24no—
32C8×D4×C73—24no—
33C2×#107×C73C2211yescharacteristic
34C2×#106×C73C2211yescharacteristic
35C2×C4⋊C8×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×C4×C8×C73C2211yescharacteristic
47#399×C73—21no—
48#397×C73—21no—
49#392×C73—21no—
50#392×C73—21no—
51#390×C73—21no—
52#390×C73—21no—
53#386×C73—21no—
54#386×C73—21no—
55#382×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×Q8×C73C2311yescharacteristic
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×C73C2311yescharacteristic
73C23×C4×C73C2311yescharacteristic
74C2×SD16×C73—22no—
75C2×SD16×C73—22no—
76C2×SD16×C73—41no—
77C2×D8×C73—22no—
78C2×D8×C73—22no—
79C2×D8×C73—41no—
80C22×C8×C73—22no—
81C22×C8×C73—22no—
82C22×C8×C73—22no—
83C22×C8×C73—22no—
84C22×C8×C73—41no—
85C22×C8×C73—41no—
86C22×C8×C73C2311yescharacteristic
87C22×C8×C73C2311yescharacteristic
88C22×C8×C73C2311yescharacteristic
89C22×C8×C73C2311yescharacteristic
90#124×C73—22no—
91#124×C73—22no—
92C22⋊Q8×C73—22no—
93C22⋊Q8×C73—22no—
94C22⋊Q8×C73—41no—
95C22⋊Q8×C73—41no—
96#121×C73—22no—
97#121×C73—22no—
98#121×C73—22no—
99#121×C73—22no—
100#121×C73—41no—
101#121×C73—41no—
102#121×C73—41no—
103#121×C73—41no—
104C4×D4×C73—22no—
105C4×D4×C73—22no—
106C4×D4×C73—22no—
107C4×D4×C73—22no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73D411yescharacteristic
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
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×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×C73D411yescharacteristic
128C2×C22⋊C4×C73D411yescharacteristic
129C2×C42×C73—21no—
130C2×C42×C73C2311yescharacteristic
131#107×C73—22no—
132#106×C73—22no—
133C4⋊C8×C73D414yescomplemented
134#103×C73—22no—
135#103×C73—22no—
136#103×C73—41no—
137#102×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—41no—
141#102×C73D414yescomplemented
142C22⋊C8×C73—22no—
143C22⋊C8×C73—22no—
144C4×C8×C73—22no—
145#95×C73—21no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73—21no—
150C24×C73—21no—
151C24×C73—21no—
152C24×C73C2×D411yescharacteristic
153C24×C73C2×D411yescharacteristic
154C2×Q8×C73—21no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—21no—
158C2×Q8×C73—21no—
159C2×Q8×C73—21no—
160C2×D4×C73—22no—
161C2×D4×C73—22no—
162C2×D4×C73—22no—
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—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—42no—
175C2×D4×C73—42no—
176C2×D4×C73—42no—
177C2×D4×C73—42no—
178C2×D4×C73—42no—
179C2×D4×C73—42no—
180C2×D4×C73—42no—
181C2×D4×C73—42no—
182C2×D4×C73—81no—
183C2×D4×C73—81no—
184C2×D4×C73—81no—
185C2×D4×C73—81no—
186C2×D4×C73C2×D412yes—
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×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—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—42no—
206C22×C4×C73—81no—
207C22×C4×C73—81no—
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2411yescharacteristic
213SD16×C73—44no—
214D8×C73—44no—
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—44no—
225C2×C8×C73—44no—
226C2×C8×C73C2×D412yes—
227C2×C8×C73C2×D412yes—
228C2×C8×C73C2×D412yes—
229C4⋊C4×C73—22no—
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—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—42no—
239C4⋊C4×C73—42no—
240C4⋊C4×C73C2×D412yes—
241C4⋊C4×C73#4112yes—
242C22⋊C4×C73—22no—
243C22⋊C4×C73—22no—
244C22⋊C4×C73—42no—
245C22⋊C4×C73—42no—
246C22⋊C4×C73—42no—
247C22⋊C4×C73—42no—
248C22⋊C4×C73—42no—
249C22⋊C4×C73—42no—
250C22⋊C4×C73—42no—
251C22⋊C4×C73—42no—
252C22⋊C4×C73—42no—
253C22⋊C4×C73—81no—
254C22⋊C4×C73—81no—
255C42×C73—81no—
256C42×C73C2×D412yes—
257C42×C73#4112yes—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—22no—
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#13512yes—
285C23×C73#13512yes—
286C23×C73C22×D411yescharacteristic
287Q8×C73—41no—
288Q8×C73—41no—
289Q8×C73—41no—
290Q8×C73—41no—
291D4×C73—28no—
292D4×C73—22no—
293D4×C73—22no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—41no—
298D4×C73—41no—
299D4×C73—41no—
300D4×C73—84no—
301D4×C73—84no—
302D4×C73—84no—
303D4×C73—84no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—22no—
312C2×C4×C73—21no—
313C2×C4×C73—22no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
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—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—41no—
339C2×C4×C73—41no—
340C2×C4×C73—84no—
341C2×C4×C73#12112yes—
342C2×C4×C73#12112yes—
343C2×C4×C73C22×D411yescharacteristic
344C2×C4×C73C22×D411yescharacteristic
345C2×C4×C73C2×#4111yescharacteristic
346C2×C4×C73C2×#4111yescharacteristic
347C2×C4×C73H(5,𝔽2)11yescharacteristic
348C2×C4×C73H(5,𝔽2)11yescharacteristic
349C8×C73—22no—
350C8×C73—22no—
351C8×C73—22no—
352C8×C73—41no—
353C22×C73—22no—
354C22×C73—22no—
355C22×C73—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—42no—
368C22×C73—42no—
369C22×C73—42no—
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×C73—81no—
380C22×C73—81no—
381C22×C73C2×#12111yescharacteristic
382C22×C73D4211yescharacteristic
383C22×C73#54611yescharacteristic
384C22×C73C2×#13511yescharacteristic
385C22×C73C2×#13511yescharacteristic
386C22×C73#57611yescharacteristic
387C22×C73#57711yescharacteristic
388C4×C73—22no—
389C4×C73—22no—
390C4×C73—41no—
391C4×C73—41no—
392C4×C73—42no—
393C4×C73—42no—
394C4×C73—81no—
395C4×C73—81no—
396C4×C73—81no—
397C4×C73—81no—
398C4×C73#53211yescharacteristic
399C4×C73#54011yescharacteristic
400C4×C73D4211yescharacteristic
401C4×C73#55011yescharacteristic
402#25388C7311yesmaximal, characteristic, direct product factor, Sylow
403C2×C73—42no—
404C2×C73—42no—
405C2×C73—82no—
406C2×C73—161no—
407C2×C73#242811yescharacteristic
408C2×C73#305011yescharacteristic
409C2×C73#306211yescharacteristic
410C2×C73#328011yescharacteristic
411C2×C73#328211yescharacteristic
412C2×C73#329711yescharacteristic
413C2×C73#330111yescharacteristic
414C2×#466C2×C7311yescharacteristic, complemented
415C2×#465C2×C7311yescharacteristic, complemented
416C2×#463C2×C7311yescharacteristic, complemented
417C2×C8×D4C2×C7311yescharacteristic, complemented
418#2540C2×C7311yescharacteristic, complemented
419#2535C2×C7311yescharacteristic, complemented
420#2036C2×C7311yescharacteristic, complemented
421#2034C2×C7311yescharacteristic, complemented
422#2000C2×C7311yescharacteristic, complemented
423#1999C2×C7311yescharacteristic, complemented
424#1958C2×C7311yescharacteristic, complemented
425#1949C2×C7311yescharacteristic, complemented
426#1893C2×C7311yescharacteristic, complemented
427#1892C2×C7311yescharacteristic, complemented
428C4×#102C2×C7311yescharacteristic, complemented
429C73#2538811yescharacteristic, direct product factor, Sylow
430C22×SD16C22×C7311yescharacteristic
431C22×D8C22×C7311yescharacteristic
432C23×C8C22×C7311yescharacteristic
433C23×C8C22×C7311yescharacteristic
434C2×#124C22×C7311yescharacteristic
435C2×C22⋊Q8C22×C7311yescharacteristic
436C2×C22⋊Q8C22×C7311yescharacteristic
437C2×#121C22×C7311yescharacteristic
438C2×#121C22×C7311yescharacteristic
439C2×#121C22×C7311yescharacteristic
440C2×#121C22×C7311yescharacteristic
441C2×C4×D4C22×C7311yescharacteristic
442C2×C4×D4C22×C7311yescharacteristic
443#466—24no—
444#465—24no—
445#463—24no—
446C8×D4—24no—
447C2×#107C22×C7311yescharacteristic
448C2×#106C22×C7311yescharacteristic
449C2×C4⋊C8C22×C7311yescharacteristic
450C2×#103C22×C7311yescharacteristic
451C2×#103C22×C7311yescharacteristic
452C2×#103C22×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×C4×C8C22×C7311yescharacteristic
461#399—21no—
462#397—21no—
463#392—21no—
464#392—21no—
465#390—21no—
466#390—21no—
467#386—21no—
468#386—21no—
469#382C22×C7311yescharacteristic
470#380C22×C7311yescharacteristic
471#380C22×C7311yescharacteristic
472C4×C4⋊C4C22×C7311yescharacteristic
473#340C22×C7311yescharacteristic
474#340C22×C7311yescharacteristic
475#340C22×C7311yescharacteristic
476#340C22×C7311yescharacteristic
477C22×Q8C23×C7311yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4D4×C7311yescharacteristic
483C22×D4C23×C7311yescharacteristic
484C22×D4C23×C7311yescharacteristic
485C23×C4—21no—
486C23×C4C23×C7311yescharacteristic
487C23×C4C23×C7311yescharacteristic
488C2×SD16—22no—
489C2×SD16—22no—
490C2×SD16—41no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—41no—
494C22×C8—22no—
495C22×C8—22no—
496C22×C8—22no—
497C22×C8—22no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8C23×C7311yescharacteristic
501C22×C8C23×C7311yescharacteristic
502C22×C8C23×C7311yescharacteristic
503C22×C8C23×C7311yescharacteristic
504#124—22no—
505#124—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—41no—
515#121—41no—
516#121—41no—
517#121—41no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4D4×C7311yescharacteristic
525C2×C4⋊C4C23×C7311yescharacteristic
526C2×C4⋊C4C23×C7311yescharacteristic
527C2×C4⋊C4C23×C7311yescharacteristic
528C2×C4⋊C4C23×C7311yescharacteristic
529C2×C4⋊C4C23×C7311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
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⋊C4D4×C7311yescharacteristic
542C2×C22⋊C4D4×C7311yescharacteristic
543C2×C42—21no—
544C2×C42C23×C7311yescharacteristic
545#107—22no—
546#106—22no—
547C4⋊C8D4×C7314yescomplemented
548#103—22no—
549#103—22no—
550#103—41no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—41no—
555#102D4×C7314yescomplemented
556C22⋊C8—22no—
557C22⋊C8—22no—
558C4×C8—22no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564C24—21no—
565C24—21no—
566C24C2×D4×C7311yescharacteristic
567C24C2×D4×C7311yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
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—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4C2×D4×C7312yes—
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—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C7311yescharacteristic
623C22×C4C2×D4×C7311yescharacteristic
624C22×C4C2×D4×C7311yescharacteristic
625C22×C4C2×D4×C7311yescharacteristic
626C22×C4C24×C7311yescharacteristic
627SD16—44no—
628D8—44no—
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—21no—
638C2×C8—44no—
639C2×C8—44no—
640C2×C8C2×D4×C7312yes—
641C2×C8C2×D4×C7312yes—
642C2×C8C2×D4×C7312yes—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4C2×D4×C7312yes—
655C4⋊C4#41×C7312yes—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C42—81no—
670C42C2×D4×C7312yes—
671C42#41×C7312yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
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#135×C7312yes—
699C23#135×C7312yes—
700C23C22×D4×C7311yescharacteristic
701Q8—41no—
702Q8—41no—
703Q8—41no—
704Q8—41no—
705D4—28no—
706D4—22no—
707D4—22no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717D4—84no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—41no—
731C2×C4—41no—
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—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—84no—
755C2×C4#121×C7312yes—
756C2×C4#121×C7312yes—
757C2×C4C22×D4×C7311yescharacteristic
758C2×C4C22×D4×C7311yescharacteristic
759C2×C4C2×#41×C7311yescharacteristic
760C2×C4C2×#41×C7311yescharacteristic
761C2×C4H(5,𝔽2)×C7311yescharacteristic
762C2×C4H(5,𝔽2)×C7311yescharacteristic
763C8—22no—
764C8—22no—
765C8—22no—
766C8—41no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×#121×C7311yescharacteristic
796C22D42×C7311yescharacteristic
797C22#546×C7311yescharacteristic
798C22C2×#135×C7311yescharacteristic
799C22C2×#135×C7311yescharacteristic
800C22#576×C7311yescharacteristic
801C22#577×C7311yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—41no—
807C4—41no—
808C4—81no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4#532×C7311yescharacteristic
813C4#540×C7311yescharacteristic
814C4D42×C7311yescharacteristic
815C4#550×C7311yescharacteristic
816C2—42no—
817C2—42no—
818C2—82no—
819C2—161no—
820C2C73×#242811yescharacteristic
821C2C73×#305011yescharacteristic
822C2C73×#306211yescharacteristic
823C2C73×#328011yescharacteristic
824C2C73×#328211yescharacteristic
825C2C73×#329711yescharacteristic
826C2C73×#330111yescharacteristic
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×#466×C73C2semidirect
2. C2×#465×C73C2semidirect
3. C2×#463×C73C2semidirect
4. C2×C8×D4×C73C2semidirect
5. C73×#2540C2semidirect
6. C73×#2535C2semidirect
7. C73×#2036C2semidirect
8. C73×#2034C2semidirect
9. C73×#2000C2semidirect
10. C73×#1999C2semidirect
11. C73×#1958C2semidirect
12. C73×#1949C2semidirect
13. C73×#1893C2semidirect
14. C73×#1892C2semidirect
15. C4×#102×C73C2semidirect
133. C4⋊C8×C73D4semidirect
141. #102×C73D4semidirect
402. #25388C73direct (N × H)
414. C2×#466C2×C73semidirect
415. C2×#465C2×C73semidirect
416. C2×#463C2×C73semidirect
417. C2×C8×D4C2×C73semidirect
418. #2540C2×C73semidirect
419. #2535C2×C73semidirect
420. #2036C2×C73semidirect
421. #2034C2×C73semidirect
422. #2000C2×C73semidirect
423. #1999C2×C73semidirect
424. #1958C2×C73semidirect
425. #1949C2×C73semidirect
426. #1893C2×C73semidirect
427. #1892C2×C73semidirect
428. C4×#102C2×C73semidirect
429. C73#25388direct (N × H)
547. C4⋊C8D4×C73semidirect
555. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C732
C2×#465×C732
C2×#463×C732
C2×C8×D4×C732
C73×#25402
C73×#25352
C73×#20362
C73×#20342
C73×#20002
C73×#19992
C73×#19582
C73×#19492
C73×#18932
C73×#18922
C4×#102×C732
#2538873