Finite Group Databasebeta

← C73×#24402 #32933806

Subgroups — C73×#24402 #32933806

Order 18688.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C73C211yesmaximal, characteristic, complemented
2C2×#472×C73C211yesmaximal, characteristic, complemented
3C2×#471×C73C211yesmaximal, characteristic, complemented
4C73×#3006C211yesmaximal, characteristic, complemented
5C2×#449×C73C211yesmaximal, characteristic, complemented
6C73×#2880C211yesmaximal, characteristic, complemented
7C73×#2052C211yesmaximal, characteristic, complemented
8C73×#2051C211yesmaximal, characteristic, complemented
9C73×#2019C211yesmaximal, characteristic, complemented
10C73×#2018C211yesmaximal, characteristic, complemented
11C73×#1908C211yesmaximal, characteristic, complemented
12C73×#1907C211yesmaximal, characteristic, complemented
13C73×#1900C211yesmaximal, characteristic, complemented
14C73×#1855C211yesmaximal, characteristic, complemented
15C73×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×#41×C73C2211yescharacteristic
18#575×C73—24no—
19#575×C73—24no—
20C2×#137×C73—21no—
21C2×#137×C73C2211yescharacteristic
22C2×#137×C73C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C73—21no—
24C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
28C2×#135×C73—21no—
29C2×#135×C73—21no—
30C22×SD16×C73C2211yescharacteristic, complemented
31C22×D8×C73C2211yescharacteristic, complemented
32C2×#131×C73C2211yescharacteristic
33C2×#131×C73C2211yescharacteristic
34C22×M16×C73C2211yescharacteristic
35C2×#121×C73C2211yescharacteristic
36#472×C73—24no—
37#471×C73—24no—
38#449×C73—21no—
39#449×C73—21no—
40#449×C73—21no—
41#449×C73—21no—
42#449×C73—21no—
43#449×C73—21no—
44#448×C73—21no—
45#447×C73—21no—
46C2×#108×C73C2211yescharacteristic, complemented
47C2×#108×C73C2211yescharacteristic, complemented
48#417×C73C2211yescharacteristic
49#417×C73C2211yescharacteristic
50C2×#103×C73C2211yescharacteristic, complemented
51C2×#102×C73C2211yescharacteristic, complemented
52C2×#101×C73C2211yescharacteristic, complemented
53C2×#101×C73C2211yescharacteristic, complemented
54C2×#100×C73C2211yescharacteristic, complemented
55C2×#100×C73C2211yescharacteristic, complemented
56C2×#100×C73C2211yescharacteristic, complemented
57C2×#100×C73C2211yescharacteristic, complemented
58#408×C73—21no—
59#408×C73—21no—
60#408×C73C2211yescharacteristic
61#408×C73C2211yescharacteristic
62#407×C73—21no—
63#407×C73C2211yescharacteristic
64#407×C73C2211yescharacteristic
65C2×C22⋊C8×C73—21no—
66C2×C22⋊C8×C73C2211yescharacteristic
67#343×C73C2211yescharacteristic, complemented
68#343×C73C2211yescharacteristic, complemented
69#341×C73C2211yescharacteristic, complemented
70#341×C73C2211yescharacteristic, complemented
71C2×#41×C73—21no—
72C2×#41×C73—21no—
73C2×#41×C73—22no—
74C2×#41×C73—22no—
75C2×#41×C73—22no—
76C2×#41×C73—22no—
77C2×#41×C73—21no—
78C2×#41×C73—21no—
79C2×#41×C73—21no—
80C2×#41×C73—21no—
81C2×#41×C73—41no—
82C2×#41×C73—41no—
83C2×#41×C73—41no—
84C2×#41×C73—41no—
85C2×#41×C73D411yescharacteristic
86C2×#41×C73D411yescharacteristic
87C2×#41×C73C2311yescharacteristic
88C2×#41×C73C2311yescharacteristic
89C22×Q8×C73D411yescharacteristic
90C22×Q8×C73C2311yescharacteristic
91C22×D4×C73—21no—
92C22×D4×C73—21no—
93C22×D4×C73—21no—
94C22×D4×C73D411yescharacteristic
95C22×D4×C73C2311yescharacteristic
96C22×D4×C73C2311yescharacteristic
97C23×C4×C73—21no—
98C23×C4×C73—21no—
99C23×C4×C73C2311yescharacteristic
100#137×C73—28no—
101#137×C73—22no—
102#137×C73—22no—
103#137×C73—22no—
104#137×C73D414yescomplemented
105AGL(1,ℤ/8)×C73—28no—
106AGL(1,ℤ/8)×C73—22no—
107AGL(1,ℤ/8)×C73—22no—
108AGL(1,ℤ/8)×C73—22no—
109AGL(1,ℤ/8)×C73—22no—
110AGL(1,ℤ/8)×C73—22no—
111AGL(1,ℤ/8)×C73—41no—
112AGL(1,ℤ/8)×C73—41no—
113AGL(1,ℤ/8)×C73D414yescomplemented
114#135×C73—28no—
115#135×C73—28no—
116C2×Q16×C73—21no—
117C2×Q16×C73—21no—
118C2×SD16×C73—21no—
119C2×SD16×C73—21no—
120C2×SD16×C73—21no—
121C2×SD16×C73—21no—
122C2×SD16×C73—21no—
123C2×SD16×C73—21no—
124C2×SD16×C73—22no—
125C2×SD16×C73—21no—
126C2×SD16×C73—21no—
127C2×SD16×C73—41no—
128C2×D8×C73—21no—
129C2×D8×C73—21no—
130C2×D8×C73—21no—
131C2×D8×C73—21no—
132C2×D8×C73—22no—
133C2×D8×C73—21no—
134C2×D8×C73—21no—
135C2×D8×C73—41no—
136#131×C73—22no—
137#131×C73—22no—
138#131×C73—41no—
139#131×C73—41no—
140C2×M16×C73—21no—
141C2×M16×C73—22no—
142C2×M16×C73—22no—
143C2×M16×C73—21no—
144C2×M16×C73—21no—
145C2×M16×C73C2311yescharacteristic
146C2×M16×C73C2311yescharacteristic
147C2×M16×C73C2311yescharacteristic
148C2×M16×C73C2311yescharacteristic
149C2×M16×C73C2311yescharacteristic
150C2×M16×C73C2311yescharacteristic
151C22×C8×C73—21no—
152C22×C8×C73—21no—
153C22×C8×C73—21no—
154C22×C8×C73C2311yescharacteristic
155C22×C8×C73C2311yescharacteristic
156#121×C73—21no—
157#121×C73—21no—
158#121×C73—21no—
159#121×C73—21no—
160C2×C4⋊C4×C73C2311yescharacteristic
161C2×C22⋊C4×C73—21no—
162#108×C73—22no—
163#108×C73—22no—
164#103×C73—21no—
165#103×C73—21no—
166#103×C73—21no—
167#103×C73—21no—
168#102×C73—21no—
169#102×C73—21no—
170#102×C73—21no—
171#102×C73—21no—
172#101×C73—22no—
173#101×C73—41no—
174#100×C73—22no—
175#100×C73—22no—
176#100×C73—22no—
177#100×C73—41no—
178C22⋊C8×C73—21no—
179C22⋊C8×C73—21no—
180C22⋊C8×C73—21no—
181C22⋊C8×C73—21no—
182C22⋊C8×C73—21no—
183C22⋊C8×C73—21no—
184C22⋊C8×C73—21no—
185C22⋊C8×C73—21no—
186C22⋊C8×C73D411yescharacteristic
187C22⋊C8×C73D411yescharacteristic
188C22⋊C8×C73D411yescharacteristic
189C22⋊C8×C73D411yescharacteristic
190C24×C73—21no—
191C24×C73—21no—
192C24×C73—21no—
193C24×C73#4111yescharacteristic
194#41×C73—21no—
195#41×C73—21no—
196#41×C73—24no—
197#41×C73—24no—
198#41×C73—22no—
199#41×C73—22no—
200#41×C73—21no—
201#41×C73—21no—
202#41×C73—21no—
203#41×C73—21no—
204#41×C73—42no—
205#41×C73—42no—
206#41×C73—41no—
207#41×C73—41no—
208#41×C73—42no—
209#41×C73—42no—
210#41×C73—42no—
211#41×C73—42no—
212#41×C73—42no—
213#41×C73—42no—
214#41×C73—42no—
215#41×C73—42no—
216#41×C73C2×D412yes—
217#41×C73C2×D412yes—
218C2×Q8×C73—21no—
219C2×Q8×C73—21no—
220C2×Q8×C73—22no—
221C2×Q8×C73—21no—
222C2×Q8×C73—21no—
223C2×Q8×C73—21no—
224C2×Q8×C73—21no—
225C2×Q8×C73—41no—
226C2×Q8×C73C2×D412yes—
227C2×Q8×C73C2×D411yescharacteristic
228C2×Q8×C73C2×D411yescharacteristic
229C2×D4×C73—21no—
230C2×D4×C73—22no—
231C2×D4×C73—21no—
232C2×D4×C73—21no—
233C2×D4×C73—21no—
234C2×D4×C73—21no—
235C2×D4×C73—21no—
236C2×D4×C73—21no—
237C2×D4×C73—21no—
238C2×D4×C73—21no—
239C2×D4×C73—21no—
240C2×D4×C73—21no—
241C2×D4×C73—21no—
242C2×D4×C73—21no—
243C2×D4×C73—21no—
244C2×D4×C73—21no—
245C2×D4×C73—21no—
246C2×D4×C73—41no—
247C2×D4×C73—42no—
248C2×D4×C73—42no—
249C2×D4×C73—42no—
250C2×D4×C73—42no—
251C2×D4×C73—41no—
252C2×D4×C73—41no—
253C2×D4×C73—41no—
254C2×D4×C73—41no—
255C2×D4×C73—82no—
256C2×D4×C73C2×D412yes—
257C2×D4×C73C2×D411yescharacteristic
258C2×D4×C73C2×D411yescharacteristic
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—42no—
271C22×C4×C73—42no—
272C22×C4×C73—42no—
273C22×C4×C73—42no—
274C22×C4×C73—41no—
275C22×C4×C73—41no—
276C22×C4×C73C2×D411yescharacteristic
277C22×C4×C73C2×D411yescharacteristic
278C22×C4×C73C2×D411yescharacteristic
279C22×C4×C73C2×D411yescharacteristic
280C22×C4×C73#4111yescharacteristic
281C22×C4×C73C2411yescharacteristic
282Q16×C73—24no—
283Q16×C73—24no—
284SD16×C73—24no—
285SD16×C73—24no—
286SD16×C73—24no—
287SD16×C73—24no—
288SD16×C73—42no—
289SD16×C73—42no—
290SD16×C73—42no—
291SD16×C73—42no—
292D8×C73—24no—
293D8×C73—24no—
294D8×C73—42no—
295D8×C73—42no—
296D8×C73—42no—
297D8×C73—42no—
298M16×C73—24no—
299M16×C73—21no—
300M16×C73—21no—
301M16×C73—21no—
302M16×C73—21no—
303M16×C73—21no—
304M16×C73—21no—
305M16×C73—21no—
306M16×C73—21no—
307M16×C73—21no—
308M16×C73—21no—
309M16×C73—42no—
310M16×C73—42no—
311M16×C73C2×D412yes—
312M16×C73C2×D412yes—
313C2×C8×C73—24no—
314C2×C8×C73—21no—
315C2×C8×C73—21no—
316C2×C8×C73—21no—
317C2×C8×C73—21no—
318C2×C8×C73—21no—
319C2×C8×C73—21no—
320C2×C8×C73—21no—
321C2×C8×C73—21no—
322C2×C8×C73—21no—
323C2×C8×C73—21no—
324C2×C8×C73—42no—
325C2×C8×C73—42no—
326C2×C8×C73C2×D411yescharacteristic
327C2×C8×C73C2×D411yescharacteristic
328C2×C8×C73C2×D411yescharacteristic
329C2×C8×C73C2×D411yescharacteristic
330C4⋊C4×C73—21no—
331C4⋊C4×C73—21no—
332C22⋊C4×C73—41no—
333C22⋊C4×C73—41no—
334C23×C73—21no—
335C23×C73—21no—
336C23×C73—21no—
337C23×C73—21no—
338C23×C73—22no—
339C23×C73—41no—
340C23×C73—41no—
341C23×C73—42no—
342C23×C73—42no—
343C23×C73—41no—
344C23×C73—41no—
345C23×C73—41no—
346C23×C73—41no—
347C23×C73—41no—
348C23×C73—81no—
349C23×C73—81no—
350C23×C73—81no—
351C23×C73—81no—
352C23×C73—81no—
353C23×C73#12111yescharacteristic
354C23×C73#12111yescharacteristic
355C23×C73C2×#4111yescharacteristic
356Q8×C73—21no—
357Q8×C73—21no—
358Q8×C73—22no—
359Q8×C73—21no—
360Q8×C73—22no—
361Q8×C73—42no—
362Q8×C73—41no—
363Q8×C73—41no—
364Q8×C73#12012yes—
365D4×C73—22no—
366D4×C73—22no—
367D4×C73—21no—
368D4×C73—22no—
369D4×C73—21no—
370D4×C73—21no—
371D4×C73—22no—
372D4×C73—42no—
373D4×C73—42no—
374D4×C73—42no—
375D4×C73—44no—
376D4×C73—44no—
377D4×C73—41no—
378D4×C73—41no—
379D4×C73—41no—
380D4×C73—41no—
381D4×C73—41no—
382D4×C73—41no—
383D4×C73—41no—
384D4×C73—41no—
385D4×C73—82no—
386D4×C73—82no—
387D4×C73#12012yes—
388C2×C4×C73—21no—
389C2×C4×C73—21no—
390C2×C4×C73—21no—
391C2×C4×C73—21no—
392C2×C4×C73—21no—
393C2×C4×C73—21no—
394C2×C4×C73—21no—
395C2×C4×C73—22no—
396C2×C4×C73—22no—
397C2×C4×C73—21no—
398C2×C4×C73—21no—
399C2×C4×C73—21no—
400C2×C4×C73—21no—
401C2×C4×C73—21no—
402C2×C4×C73—22no—
403C2×C4×C73—42no—
404C2×C4×C73—42no—
405C2×C4×C73—42no—
406C2×C4×C73—44no—
407C2×C4×C73—44no—
408C2×C4×C73—41no—
409C2×C4×C73—41no—
410C2×C4×C73—41no—
411C2×C4×C73—41no—
412C2×C4×C73—41no—
413C2×C4×C73—81no—
414C2×C4×C73#12111yescharacteristic
415C2×C4×C73#12111yescharacteristic
416C2×C4×C73C22×D411yescharacteristic
417C2×C4×C73C22×D411yescharacteristic
418C2×C4×C73C22×D411yescharacteristic
419C2×C4×C73C22×D411yescharacteristic
420C2×C4×C73H(5,𝔽2)11yescharacteristic
421C2×C4×C73H(5,𝔽2)11yescharacteristic
422C8×C73—22no—
423C8×C73—22no—
424C8×C73—21no—
425C8×C73—21no—
426C8×C73—21no—
427C8×C73—21no—
428C8×C73—41no—
429C8×C73—41no—
430C8×C73—41no—
431C8×C73—41no—
432C22×C73—21no—
433C22×C73—21no—
434C22×C73—21no—
435C22×C73—21no—
436C22×C73—22no—
437C22×C73—21no—
438C22×C73—21no—
439C22×C73—21no—
440C22×C73—21no—
441C22×C73—41no—
442C22×C73—41no—
443C22×C73—41no—
444C22×C73—42no—
445C22×C73—41no—
446C22×C73—41no—
447C22×C73—81no—
448C22×C73—81no—
449C22×C73—82no—
450C22×C73—82no—
451C22×C73—84no—
452C22×C73—81no—
453C22×C73—81no—
454C22×C73—81no—
455C22×C73—81no—
456C22×C73—81no—
457C22×C73—161no—
458C22×C73—161no—
459C22×C73C2×#12111yescharacteristic
460C22×C73#54611yescharacteristic
461C22×C73#54611yescharacteristic
462C4×C73—21no—
463C4×C73—21no—
464C4×C73—22no—
465C4×C73—41no—
466C4×C73—42no—
467C4×C73—81no—
468C4×C73C2×#12011yescharacteristic
469C4×C73#53411yescharacteristic
470C4×C73D4211yescharacteristic
471C4×C73D4211yescharacteristic
472#24402C7311yesmaximal, characteristic, direct product factor, Sylow
473C2×C73—21no—
474C2×C73—21no—
475C2×C73—41no—
476C2×C73—41no—
477C2×C73—42no—
478C2×C73—81no—
479C2×C73—82no—
480C2×C73—161no—
481C2×C73#241011yescharacteristic
482C2×C73#306711yescharacteristic
483C2×C73#306811yescharacteristic
484C2×#575C2×C7311yescharacteristic, complemented
485C2×#472C2×C7311yescharacteristic, complemented
486C2×#471C2×C7311yescharacteristic, complemented
487#3006C2×C7311yescharacteristic, complemented
488C2×#449C2×C7311yescharacteristic, complemented
489#2880C2×C7311yescharacteristic, complemented
490#2052C2×C7311yescharacteristic, complemented
491#2051C2×C7311yescharacteristic, complemented
492#2019C2×C7311yescharacteristic, complemented
493#2018C2×C7311yescharacteristic, complemented
494#1908C2×C7311yescharacteristic, complemented
495#1907C2×C7311yescharacteristic, complemented
496#1900C2×C7311yescharacteristic, complemented
497#1855C2×C7311yescharacteristic, complemented
498#1785C2×C7311yescharacteristic, complemented
499C73#2440211yescharacteristic, direct product factor, Sylow
500C22×#41C22×C7311yescharacteristic
501C22×#41C22×C7311yescharacteristic
502#575—24no—
503#575—24no—
504C2×#137—21no—
505C2×#137C22×C7311yescharacteristic
506C2×#137C22×C7311yescharacteristic
507C2×AGL(1,ℤ/8)—21no—
508C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
509C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
510C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
511C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
512C2×#135—21no—
513C2×#135—21no—
514C22×SD16C22×C7311yescharacteristic, complemented
515C22×D8C22×C7311yescharacteristic, complemented
516C2×#131C22×C7311yescharacteristic
517C2×#131C22×C7311yescharacteristic
518C22×M16C22×C7311yescharacteristic
519C2×#121C22×C7311yescharacteristic
520#472—24no—
521#471—24no—
522#449—21no—
523#449—21no—
524#449—21no—
525#449—21no—
526#449—21no—
527#449—21no—
528#448—21no—
529#447—21no—
530C2×#108C22×C7311yescharacteristic, complemented
531C2×#108C22×C7311yescharacteristic, complemented
532#417C22×C7311yescharacteristic
533#417C22×C7311yescharacteristic
534C2×#103C22×C7311yescharacteristic, complemented
535C2×#102C22×C7311yescharacteristic, complemented
536C2×#101C22×C7311yescharacteristic, complemented
537C2×#101C22×C7311yescharacteristic, complemented
538C2×#100C22×C7311yescharacteristic, complemented
539C2×#100C22×C7311yescharacteristic, complemented
540C2×#100C22×C7311yescharacteristic, complemented
541C2×#100C22×C7311yescharacteristic, complemented
542#408—21no—
543#408—21no—
544#408C22×C7311yescharacteristic
545#408C22×C7311yescharacteristic
546#407—21no—
547#407C22×C7311yescharacteristic
548#407C22×C7311yescharacteristic
549C2×C22⋊C8—21no—
550C2×C22⋊C8C22×C7311yescharacteristic
551#343C22×C7311yescharacteristic, complemented
552#343C22×C7311yescharacteristic, complemented
553#341C22×C7311yescharacteristic, complemented
554#341C22×C7311yescharacteristic, complemented
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C7311yescharacteristic
570C2×#41D4×C7311yescharacteristic
571C2×#41C23×C7311yescharacteristic
572C2×#41C23×C7311yescharacteristic
573C22×Q8D4×C7311yescharacteristic
574C22×Q8C23×C7311yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C7311yescharacteristic
579C22×D4C23×C7311yescharacteristic
580C22×D4C23×C7311yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C23×C7311yescharacteristic
584#137—28no—
585#137—22no—
586#137—22no—
587#137—22no—
588#137D4×C7314yescomplemented
589AGL(1,ℤ/8)—28no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—22no—
595AGL(1,ℤ/8)—41no—
596AGL(1,ℤ/8)—41no—
597AGL(1,ℤ/8)D4×C7314yescomplemented
598#135—28no—
599#135—28no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—22no—
607C2×SD16—21no—
608C2×SD16—21no—
609C2×SD16—21no—
610C2×SD16—21no—
611C2×SD16—41no—
612C2×D8—21no—
613C2×D8—21no—
614C2×D8—22no—
615C2×D8—21no—
616C2×D8—21no—
617C2×D8—21no—
618C2×D8—21no—
619C2×D8—41no—
620#131—22no—
621#131—22no—
622#131—41no—
623#131—41no—
624C2×M16—21no—
625C2×M16—22no—
626C2×M16—22no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16C23×C7311yescharacteristic
630C2×M16C23×C7311yescharacteristic
631C2×M16C23×C7311yescharacteristic
632C2×M16C23×C7311yescharacteristic
633C2×M16C23×C7311yescharacteristic
634C2×M16C23×C7311yescharacteristic
635C22×C8—21no—
636C22×C8—21no—
637C22×C8—21no—
638C22×C8C23×C7311yescharacteristic
639C22×C8C23×C7311yescharacteristic
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644C2×C4⋊C4C23×C7311yescharacteristic
645C2×C22⋊C4—21no—
646#108—22no—
647#108—22no—
648#103—21no—
649#103—21no—
650#103—21no—
651#103—21no—
652#102—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#101—22no—
657#101—41no—
658#100—22no—
659#100—22no—
660#100—22no—
661#100—41no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8D4×C7311yescharacteristic
671C22⋊C8D4×C7311yescharacteristic
672C22⋊C8D4×C7311yescharacteristic
673C22⋊C8D4×C7311yescharacteristic
674C24—21no—
675C24—21no—
676C24—21no—
677C24#41×C7311yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×D4×C7312yes—
701#41C2×D4×C7312yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×D4×C7312yes—
711C2×Q8C2×D4×C7311yescharacteristic
712C2×Q8C2×D4×C7311yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—82no—
740C2×D4C2×D4×C7312yes—
741C2×D4C2×D4×C7311yescharacteristic
742C2×D4C2×D4×C7311yescharacteristic
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4C2×D4×C7311yescharacteristic
761C22×C4C2×D4×C7311yescharacteristic
762C22×C4C2×D4×C7311yescharacteristic
763C22×C4C2×D4×C7311yescharacteristic
764C22×C4#41×C7311yescharacteristic
765C22×C4C24×C7311yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776D8—24no—
777D8—24no—
778D8—42no—
779D8—42no—
780D8—42no—
781D8—42no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—21no—
786M16—21no—
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—42no—
794M16—42no—
795M16C2×D4×C7312yes—
796M16C2×D4×C7312yes—
797C2×C8—24no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—42no—
809C2×C8—42no—
810C2×C8C2×D4×C7311yescharacteristic
811C2×C8C2×D4×C7311yescharacteristic
812C2×C8C2×D4×C7311yescharacteristic
813C2×C8C2×D4×C7311yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—21no—
816C22⋊C4—41no—
817C22⋊C4—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23#121×C7311yescharacteristic
838C23#121×C7311yescharacteristic
839C23C2×#41×C7311yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8#120×C7312yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—22no—
853D4—21no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—41no—
866D4—41no—
867D4—41no—
868D4—41no—
869D4—82no—
870D4—82no—
871D4#120×C7312yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4#121×C7311yescharacteristic
899C2×C4#121×C7311yescharacteristic
900C2×C4C22×D4×C7311yescharacteristic
901C2×C4C22×D4×C7311yescharacteristic
902C2×C4C22×D4×C7311yescharacteristic
903C2×C4C22×D4×C7311yescharacteristic
904C2×C4H(5,𝔽2)×C7311yescharacteristic
905C2×C4H(5,𝔽2)×C7311yescharacteristic
906C8—22no—
907C8—22no—
908C8—21no—
909C8—21no—
910C8—21no—
911C8—21no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—41no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—42no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—161no—
942C22—161no—
943C22C2×#121×C7311yescharacteristic
944C22#546×C7311yescharacteristic
945C22#546×C7311yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—41no—
950C4—42no—
951C4—81no—
952C4C2×#120×C7311yescharacteristic
953C4#534×C7311yescharacteristic
954C4D42×C7311yescharacteristic
955C4D42×C7311yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2C73×#241011yescharacteristic
965C2C73×#306711yescharacteristic
966C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#575×C73C2semidirect
2. C2×#472×C73C2semidirect
3. C2×#471×C73C2semidirect
4. C73×#3006C2semidirect
5. C2×#449×C73C2semidirect
6. C73×#2880C2semidirect
7. C73×#2052C2semidirect
8. C73×#2051C2semidirect
9. C73×#2019C2semidirect
10. C73×#2018C2semidirect
11. C73×#1908C2semidirect
12. C73×#1907C2semidirect
13. C73×#1900C2semidirect
14. C73×#1855C2semidirect
15. C73×#1785C2semidirect
30. C22×SD16×C73C22semidirect
31. C22×D8×C73C22semidirect
46. C2×#108×C73C22semidirect
47. C2×#108×C73C22semidirect
50. C2×#103×C73C22semidirect
51. C2×#102×C73C22semidirect
52. C2×#101×C73C22semidirect
53. C2×#101×C73C22semidirect
54. C2×#100×C73C22semidirect
55. C2×#100×C73C22semidirect
56. C2×#100×C73C22semidirect
57. C2×#100×C73C22semidirect
67. #343×C73C22semidirect
68. #343×C73C22semidirect
69. #341×C73C22semidirect
70. #341×C73C22semidirect
104. #137×C73D4semidirect
113. AGL(1,ℤ/8)×C73D4semidirect
472. #24402C73direct (N × H)
484. C2×#575C2×C73semidirect
485. C2×#472C2×C73semidirect
486. C2×#471C2×C73semidirect
487. #3006C2×C73semidirect
488. C2×#449C2×C73semidirect
489. #2880C2×C73semidirect
490. #2052C2×C73semidirect
491. #2051C2×C73semidirect
492. #2019C2×C73semidirect
493. #2018C2×C73semidirect
494. #1908C2×C73semidirect
495. #1907C2×C73semidirect
496. #1900C2×C73semidirect
497. #1855C2×C73semidirect
498. #1785C2×C73semidirect
499. C73#24402direct (N × H)
514. C22×SD16C22×C73semidirect
515. C22×D8C22×C73semidirect
530. C2×#108C22×C73semidirect
531. C2×#108C22×C73semidirect
534. C2×#103C22×C73semidirect
535. C2×#102C22×C73semidirect
536. C2×#101C22×C73semidirect
537. C2×#101C22×C73semidirect
538. C2×#100C22×C73semidirect
539. C2×#100C22×C73semidirect
540. C2×#100C22×C73semidirect
541. C2×#100C22×C73semidirect
551. #343C22×C73semidirect
552. #343C22×C73semidirect
553. #341C22×C73semidirect
554. #341C22×C73semidirect
588. #137D4×C73semidirect
597. AGL(1,ℤ/8)D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C732
C2×#472×C732
C2×#471×C732
C73×#30062
C2×#449×C732
C73×#28802
C73×#20522
C73×#20512
C73×#20192
C73×#20182
C73×#19082
C73×#19072
C73×#19002
C73×#18552
C73×#17852
#2440273