Finite Group Databasebeta

← C73×#25533 #32934937

Subgroups — C73×#25533 #32934937

Order 18688.

1444 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C73C211yesmaximal, characteristic, complemented
2C2×#480×C73C211yesmaximal, characteristic, complemented
3C2×#466×C73C211yesmaximal, characteristic, complemented
4C73×#2416C211yesmaximal, characteristic, complemented
5C73×#2057C211yesmaximal, characteristic, complemented
6C73×#2033C211yesmaximal, characteristic, complemented
7C73×#2023C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic, complemented
9C73×#1879C211yesmaximal, characteristic, complemented
10C73×#1874C211yesmaximal, characteristic, complemented
11C73×#1874C211yesmaximal, characteristic, complemented
12C73×#1869C211yesmaximal, characteristic, complemented
13C73×#1862C211yesmaximal, characteristic, complemented
14C73×#1852C211yesmaximal, characteristic, complemented
15C2×#340×C73C211yesmaximal, characteristic, complemented
16C22×#41×C73—21no—
17C22×D8×C73C2211yescharacteristic
18C23×C8×C73C2211yescharacteristic
19#547×C73—24no—
20#547×C73—24no—
21C2×C4⋊Q8×C73C2211yescharacteristic
22C2×#123×C73—21no—
23C2×#123×C73—21no—
24C2×C22⋊Q8×C73—21no—
25C2×#121×C73—21no—
26C2×#121×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×#121×C73C2211yescharacteristic
29C2×#121×C73C2211yescharacteristic
30C2×C4×D4×C73C2211yescharacteristic
31C2×C4×D4×C73C2211yescharacteristic
32C22×C4⋊C4×C73C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34C22×C4⋊C4×C73C2211yescharacteristic
35#480×C73—24no—
36#466×C73—24no—
37C2×#107×C73C2211yescharacteristic
38C2×#107×C73C2211yescharacteristic
39C2×#107×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
63C2×#41×C73—28no—
64C2×#41×C73—44no—
65C2×#41×C73—44no—
66C22×Q8×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73—21no—
71C22×D4×C73D411yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C22×D4×C73C2311yescharacteristic
74C23×C4×C73—21no—
75C23×C4×C73—21no—
76C23×C4×C73—21no—
77C23×C4×C73—21no—
78C23×C4×C73C2311yescharacteristic
79C23×C4×C73C2311yescharacteristic
80C2×D8×C73—22no—
81C2×D8×C73—22no—
82C2×D8×C73—41no—
83C22×C8×C73—22no—
84C22×C8×C73—22no—
85C22×C8×C73—41no—
86C22×C8×C73C2311yescharacteristic
87C22×C8×C73C2311yescharacteristic
88C22×C8×C73C2311yescharacteristic
89C22×C8×C73C2311yescharacteristic
90C4⋊Q8×C73—22no—
91C4⋊Q8×C73—22no—
92#123×C73—28no—
93#123×C73—28no—
94C22⋊Q8×C73—28no—
95#121×C73—22no—
96#121×C73—22no—
97#121×C73—22no—
98#121×C73—22no—
99#121×C73—22no—
100#121×C73—22no—
101#121×C73—41no—
102#121×C73—44no—
103#121×C73D414yescomplemented
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×C73—22no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—22no—
113C2×C4⋊C4×C73—22no—
114C2×C4⋊C4×C73—22no—
115C2×C4⋊C4×C73—21no—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73—41no—
118C2×C4⋊C4×C73D411yescharacteristic
119C2×C4⋊C4×C73D414yescomplemented
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73D411yescharacteristic
135C2×C22⋊C4×C73D411yescharacteristic
136C2×C42×C73C2311yescharacteristic
137#107×C73—22no—
138#107×C73—22no—
139#107×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—22no—
143#102×C73—22no—
144#102×C73—22no—
145#102×C73—41no—
146C22⋊C8×C73—22no—
147C22⋊C8×C73—22no—
148C22⋊C8×C73—41no—
149#95×C73—21no—
150#95×C73—21no—
151C24×C73—21no—
152C24×C73—21no—
153C24×C73C2×D411yescharacteristic
154C24×C73C2×D411yescharacteristic
155#41×C73—432no—
156C2×Q8×C73—24no—
157C2×Q8×C73—42no—
158C2×Q8×C73—42no—
159C2×D4×C73—22no—
160C2×D4×C73—22no—
161C2×D4×C73—24no—
162C2×D4×C73—24no—
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—42no—
183C2×D4×C73—81no—
184C2×D4×C73D814yescomplemented
185C2×D4×C73C2×D412yes—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—24no—
191C22×C4×C73—24no—
192C22×C4×C73—24no—
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—42no—
207C22×C4×C73—42no—
208C22×C4×C73—42no—
209C22×C4×C73—42no—
210C22×C4×C73—42no—
211C22×C4×C73—42no—
212C22×C4×C73—42no—
213C22×C4×C73—81no—
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D412yes—
218C22×C4×C73C2×D412yes—
219C22×C4×C73C2×D411yescharacteristic
220C22×C4×C73C2411yescharacteristic
221D8×C73—44no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—44no—
234C2×C8×C73#4112yescomplemented
235C4⋊C4×C73—24no—
236C4⋊C4×C73—24no—
237C4⋊C4×C73—24no—
238C4⋊C4×C73—22no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—42no—
248C4⋊C4×C73—42no—
249C4⋊C4×C73C2×D412yes—
250C4⋊C4×C73C2×D412yes—
251C4⋊C4×C73C2×D412yes—
252C4⋊C4×C73#4112yescomplemented
253C22⋊C4×C73—24no—
254C22⋊C4×C73—24no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—24no—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—42no—
259C22⋊C4×C73—42no—
260C22⋊C4×C73—42no—
261C22⋊C4×C73—42no—
262C22⋊C4×C73—81no—
263C42×C73—21no—
264C42×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—22no—
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—41no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73—41no—
289C23×C73#12012yes—
290C23×C73C2×D812yes—
291C23×C73C2×D812yes—
292C23×C73AGL(1,ℤ/8)12yes—
293C23×C73C22×D411yescharacteristic
294Q8×C73—48no—
295D4×C73—28no—
296D4×C73—22no—
297D4×C73—22no—
298D4×C73—48no—
299D4×C73—48no—
300D4×C73—41no—
301D4×C73—41no—
302D4×C73—41no—
303D4×C73—41no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—84no—
307D4×C73—84no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—21no—
322C2×C4×C73—22no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—48no—
327C2×C4×C73—48no—
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—48no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—84no—
348C2×C4×C73#12012yes—
349C2×C4×C73C2×D812yes—
350C2×C4×C73C22×D411yescharacteristic
351C2×C4×C73C22×D411yescharacteristic
352C2×C4×C73C2×#4111yescharacteristic
353C2×C4×C73C2×#4111yescharacteristic
354C2×C4×C73H(5,𝔽2)11yescharacteristic
355C2×C4×C732−1+411yescharacteristic
356C8×C73—22no—
357C8×C73—41no—
358C8×C73—41no—
359C8×C73—41no—
360C22×C73—22no—
361C22×C73—22no—
362C22×C73—22no—
363C22×C73—22no—
364C22×C73—22no—
365C22×C73—22no—
366C22×C73—22no—
367C22×C73—22no—
368C22×C73—22no—
369C22×C73—41no—
370C22×C73—41no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73—42no—
374C22×C73—42no—
375C22×C73—42no—
376C22×C73—81no—
377C22×C73—81no—
378C22×C73—81no—
379C22×C73—81no—
380C22×C73—81no—
381C22×C73—81no—
382C22×C73—81no—
383C22×C73—81no—
384C22×C73—81no—
385C22×C73—81no—
386C22×C73—81no—
387C22×C73#44714yes—
388C22×C73C2×#12011yescharacteristic
389C22×C73#54611yescharacteristic
390C22×C73#54711yescharacteristic
391C22×C73C22×D811yescharacteristic
392C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C73#57711yescharacteristic
394C22×C73#57811yescharacteristic
395C4×C73—22no—
396C4×C73—22no—
397C4×C73—41no—
398C4×C73—42no—
399C4×C73—42no—
400C4×C73—42no—
401C4×C73—41no—
402C4×C73—42no—
403C4×C73—81no—
404C4×C73—81no—
405C4×C73#53211yescharacteristic
406C4×C73#53711yescharacteristic
407C4×C73#54611yescharacteristic
408C4×C73#54711yescharacteristic
409#25533C7311yesmaximal, characteristic, direct product factor, Sylow
410C2×C73—24no—
411C2×C73—42no—
412C2×C73—82no—
413C2×C73—161no—
414C2×C73#243011yescharacteristic
415C2×C73C2×#44711yescharacteristic
416C2×C73#301311yescharacteristic
417C2×C73#329411yescharacteristic
418C2×C73#330811yescharacteristic
419C2×C73#333411yescharacteristic
420C2×C73#334511yescharacteristic
421C2×#547C2×C7311yescharacteristic, complemented
422C2×#480C2×C7311yescharacteristic, complemented
423C2×#466C2×C7311yescharacteristic, complemented
424#2416C2×C7311yescharacteristic, complemented
425#2057C2×C7311yescharacteristic, complemented
426#2033C2×C7311yescharacteristic, complemented
427#2023C2×C7311yescharacteristic, complemented
428#1999C2×C7311yescharacteristic, complemented
429#1879C2×C7311yescharacteristic, complemented
430#1874C2×C7311yescharacteristic, complemented
431#1874C2×C7311yescharacteristic, complemented
432#1869C2×C7311yescharacteristic, complemented
433#1862C2×C7311yescharacteristic, complemented
434#1852C2×C7311yescharacteristic, complemented
435C2×#340C2×C7311yescharacteristic, complemented
436C73#2553311yescharacteristic, direct product factor, Sylow
437C22×#41—21no—
438C22×D8C22×C7311yescharacteristic
439C23×C8C22×C7311yescharacteristic
440#547—24no—
441#547—24no—
442C2×C4⋊Q8C22×C7311yescharacteristic
443C2×#123—21no—
444C2×#123—21no—
445C2×C22⋊Q8—21no—
446C2×#121—21no—
447C2×#121C22×C7311yescharacteristic
448C2×#121C22×C7311yescharacteristic
449C2×#121C22×C7311yescharacteristic
450C2×#121C22×C7311yescharacteristic
451C2×C4×D4C22×C7311yescharacteristic
452C2×C4×D4C22×C7311yescharacteristic
453C22×C4⋊C4C22×C7311yescharacteristic
454C22×C4⋊C4C22×C7311yescharacteristic
455C22×C4⋊C4C22×C7311yescharacteristic
456#480—24no—
457#466—24no—
458C2×#107C22×C7311yescharacteristic
459C2×#107C22×C7311yescharacteristic
460C2×#107C22×C7311yescharacteristic
461C2×#102C22×C7311yescharacteristic
462C2×#102C22×C7311yescharacteristic
463C2×#102C22×C7311yescharacteristic
464C2×#102C22×C7311yescharacteristic
465C2×#102C22×C7311yescharacteristic
466C2×#102C22×C7311yescharacteristic
467C2×C22⋊C8C22×C7311yescharacteristic
468C2×C22⋊C8C22×C7311yescharacteristic
469C2×C22⋊C8C22×C7311yescharacteristic
470#396—21no—
471#394—21no—
472#390C22×C7311yescharacteristic
473#389C22×C7311yescharacteristic
474#386—21no—
475#380C22×C7311yescharacteristic
476#340C22×C7311yescharacteristic
477#340C22×C7311yescharacteristic
478#340C22×C7311yescharacteristic
479#340C22×C7311yescharacteristic
480#340C22×C7311yescharacteristic
481#340C22×C7311yescharacteristic
482#336C22×C7311yescharacteristic
483#336C22×C7311yescharacteristic
484C2×#41—28no—
485C2×#41—44no—
486C2×#41—44no—
487C22×Q8—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C7311yescharacteristic
493C22×D4C23×C7311yescharacteristic
494C22×D4C23×C7311yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C23×C7311yescharacteristic
500C23×C4C23×C7311yescharacteristic
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C22×C8—22no—
505C22×C8—22no—
506C22×C8—41no—
507C22×C8C23×C7311yescharacteristic
508C22×C8C23×C7311yescharacteristic
509C22×C8C23×C7311yescharacteristic
510C22×C8C23×C7311yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513#123—28no—
514#123—28no—
515C22⋊Q8—28no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—41no—
523#121—44no—
524#121D4×C7314yescomplemented
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4D4×C7311yescharacteristic
540C2×C4⋊C4D4×C7314yescomplemented
541C2×C4⋊C4C23×C7311yescharacteristic
542C2×C4⋊C4C23×C7311yescharacteristic
543C2×C4⋊C4C23×C7311yescharacteristic
544C2×C4⋊C4C23×C7311yescharacteristic
545C2×C4⋊C4C23×C7311yescharacteristic
546C2×C4⋊C4C23×C7311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C7311yescharacteristic
556C2×C22⋊C4D4×C7311yescharacteristic
557C2×C42C23×C7311yescharacteristic
558#107—22no—
559#107—22no—
560#107—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C22⋊C8—41no—
570#95—21no—
571#95—21no—
572C24—21no—
573C24—21no—
574C24C2×D4×C7311yescharacteristic
575C24C2×D4×C7311yescharacteristic
576#41—432no—
577C2×Q8—24no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4D8×C7314yescomplemented
606C2×D4C2×D4×C7312yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—81no—
635C22×C4C2×D4×C7311yescharacteristic
636C22×C4C2×D4×C7311yescharacteristic
637C22×C4C2×D4×C7311yescharacteristic
638C22×C4C2×D4×C7312yes—
639C22×C4C2×D4×C7312yes—
640C22×C4C2×D4×C7311yescharacteristic
641C22×C4C24×C7311yescharacteristic
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8#41×C7312yescomplemented
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C7312yes—
671C4⋊C4C2×D4×C7312yes—
672C4⋊C4C2×D4×C7312yes—
673C4⋊C4#41×C7312yescomplemented
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—22no—
677C22⋊C4—24no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—81no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23#120×C7312yes—
711C23C2×D8×C7312yes—
712C23C2×D8×C7312yes—
713C23AGL(1,ℤ/8)×C7312yes—
714C23C22×D4×C7311yescharacteristic
715Q8—48no—
716D4—28no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—84no—
728D4—84no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—84no—
769C2×C4#120×C7312yes—
770C2×C4C2×D8×C7312yes—
771C2×C4C22×D4×C7311yescharacteristic
772C2×C4C22×D4×C7311yescharacteristic
773C2×C4C2×#41×C7311yescharacteristic
774C2×C4C2×#41×C7311yescharacteristic
775C2×C4H(5,𝔽2)×C7311yescharacteristic
776C2×C42−1+4×C7311yescharacteristic
777C8—22no—
778C8—41no—
779C8—41no—
780C8—41no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22#447×C7314yes—
809C22C2×#120×C7311yescharacteristic
810C22#546×C7311yescharacteristic
811C22#547×C7311yescharacteristic
812C22C22×D8×C7311yescharacteristic
813C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
814C22#577×C7311yescharacteristic
815C22#578×C7311yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—41no—
822C4—42no—
823C4—41no—
824C4—81no—
825C4—81no—
826C4#532×C7311yescharacteristic
827C4#537×C7311yescharacteristic
828C4#546×C7311yescharacteristic
829C4#547×C7311yescharacteristic
830C2—24no—
831C2—42no—
832C2—82no—
833C2—161no—
834C2C73×#243011yescharacteristic
835C2C2×#447×C7311yescharacteristic
836C2C73×#301311yescharacteristic
837C2C73×#329411yescharacteristic
838C2C73×#330811yescharacteristic
839C2C73×#333411yescharacteristic
840C2C73×#334511yescharacteristic
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×#547×C73C2semidirect
2. C2×#480×C73C2semidirect
3. C2×#466×C73C2semidirect
4. C73×#2416C2semidirect
5. C73×#2057C2semidirect
6. C73×#2033C2semidirect
7. C73×#2023C2semidirect
8. C73×#1999C2semidirect
9. C73×#1879C2semidirect
10. C73×#1874C2semidirect
11. C73×#1874C2semidirect
12. C73×#1869C2semidirect
13. C73×#1862C2semidirect
14. C73×#1852C2semidirect
15. C2×#340×C73C2semidirect
103. #121×C73D4semidirect
119. C2×C4⋊C4×C73D4semidirect
184. C2×D4×C73D8semidirect
234. C2×C8×C73#41semidirect
252. C4⋊C4×C73#41semidirect
409. #25533C73direct (N × H)
421. C2×#547C2×C73semidirect
422. C2×#480C2×C73semidirect
423. C2×#466C2×C73semidirect
424. #2416C2×C73semidirect
425. #2057C2×C73semidirect
426. #2033C2×C73semidirect
427. #2023C2×C73semidirect
428. #1999C2×C73semidirect
429. #1879C2×C73semidirect
430. #1874C2×C73semidirect
431. #1874C2×C73semidirect
432. #1869C2×C73semidirect
433. #1862C2×C73semidirect
434. #1852C2×C73semidirect
435. C2×#340C2×C73semidirect
436. C73#25533direct (N × H)
524. #121D4×C73semidirect
540. C2×C4⋊C4D4×C73semidirect
605. C2×D4D8×C73semidirect
655. C2×C8#41×C73semidirect
673. C4⋊C4#41×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C732
C2×#480×C732
C2×#466×C732
C73×#24162
C73×#20572
C73×#20332
C73×#20232
C73×#19992
C73×#18792
C73×#18742
C73×#18692
C73×#18622
C73×#18522
C2×#340×C732
#2553373