Finite Group Databasebeta

← C73×#25808 #32935212

Subgroups — C73×#25808 #32935212

Order 18688.

1424 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C73C211yesmaximal, characteristic
2C73×#3156C211yesmaximal, characteristic, complemented
3C2×#497×C73C211yesmaximal, characteristic, complemented
4C2×#473×C73C211yesmaximal, characteristic, complemented
5C2×#456×C73C211yesmaximal, characteristic, complemented
6C2×#455×C73C211yesmaximal, characteristic, complemented
7C73×#3011C211yesmaximal, characteristic, complemented
8C73×#3009C211yesmaximal, characteristic, complemented
9C73×#2020C211yesmaximal, characteristic, complemented
10C73×#2019C211yesmaximal, characteristic, complemented
11C73×#2005C211yesmaximal, characteristic, complemented
12C73×#2003C211yesmaximal, characteristic, complemented
13C73×#1977C211yesmaximal, characteristic, complemented
14C73×#1975C211yesmaximal, characteristic, complemented
15C73×#1765C211yesmaximal, characteristic, complemented
16C2×2−1+4×C73C2211yescharacteristic
17C2×H(5,𝔽2)×C73C2211yescharacteristic
18#577×C73—24no—
19#577×C73—24no—
20C2×#137×C73—21no—
21C2×#137×C73C2211yescharacteristic
22C2×#137×C73C2211yescharacteristic
23C2×#137×C73C2211yescharacteristic
24C2×#137×C73C2211yescharacteristic
25C2×#137×C73C2211yescharacteristic, complemented
26C2×AGL(1,ℤ/8)×C73—21no—
27C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
28C2×#135×C73—21no—
29C2×#135×C73C2211yescharacteristic
30C22×Q16×C73C2211yescharacteristic, complemented
31C22×Q16×C73C2211yescharacteristic, complemented
32C22×SD16×C73—21no—
33C22×SD16×C73C2211yescharacteristic
34C22×SD16×C73C2211yescharacteristic
35C2×#131×C73C2211yescharacteristic
36#536×C73C2211yescharacteristic
37#536×C73C2211yescharacteristic, complemented
38C2×C4⋊Q8×C73C2211yescharacteristic, complemented
39C2×#124×C73C2211yescharacteristic
40#497×C73—24no—
41#497×C73—21no—
42#497×C73—21no—
43#495×C73—21no—
44#494×C73—21no—
45#473×C73—24no—
46#456×C73—24no—
47#455×C73—24no—
48#452×C73—22no—
49#452×C73—22no—
50#451×C73—22no—
51#450×C73—22no—
52C2×#108×C73C2211yescharacteristic, complemented
53C2×#104×C73C2211yescharacteristic
54C2×#104×C73C2211yescharacteristic
55C2×#104×C73C2211yescharacteristic, complemented
56#419×C73C2211yescharacteristic, complemented
57#418×C73C2211yescharacteristic
58#416×C73C2211yescharacteristic
59C2×#101×C73C2211yescharacteristic, complemented
60C2×#101×C73C2211yescharacteristic, complemented
61C2×#101×C73C2211yescharacteristic, complemented
62C2×#100×C73C2211yescharacteristic
63#408×C73C2211yescharacteristic
64#408×C73C2211yescharacteristic, complemented
65#405×C73C2211yescharacteristic, complemented
66C2×#97×C73C2211yescharacteristic, complemented
67#341×C73C2211yescharacteristic, complemented
68#339×C73C2211yescharacteristic, complemented
692−1+4×C73—22no—
702−1+4×C73—22no—
712−1+4×C73—22no—
722−1+4×C73—41no—
73H(5,𝔽2)×C73—22no—
74H(5,𝔽2)×C73—22no—
75H(5,𝔽2)×C73—22no—
76H(5,𝔽2)×C73—41no—
77C2×#41×C73—21no—
78C2×#41×C73—21no—
79C2×#41×C73—21no—
80C2×#41×C73—21no—
81C2×#41×C73—41no—
82C2×#41×C73C2311yescharacteristic
83C2×#41×C73C2311yescharacteristic
84C2×#41×C73C2311yescharacteristic
85C22×Q8×C73—21no—
86C22×Q8×C73—21no—
87C22×Q8×C73C2311yescharacteristic
88C22×Q8×C73C2311yescharacteristic
89C22×Q8×C73C2311yescharacteristic
90C22×D4×C73—21no—
91C22×D4×C73—21no—
92C22×D4×C73—41no—
93C22×D4×C73C2311yescharacteristic
94#137×C73—28no—
95#137×C73—22no—
96#137×C73—22no—
97#137×C73—22no—
98#137×C73—22no—
99#137×C73—22no—
100#137×C73—22no—
101#137×C73—22no—
102#137×C73—22no—
103#137×C73—41no—
104#137×C73—41no—
105AGL(1,ℤ/8)×C73—28no—
106AGL(1,ℤ/8)×C73—22no—
107AGL(1,ℤ/8)×C73—22no—
108#135×C73—28no—
109#135×C73—22no—
110#135×C73—22no—
111C2×Q16×C73—21no—
112C2×Q16×C73—21no—
113C2×Q16×C73—21no—
114C2×Q16×C73—21no—
115C2×Q16×C73—21no—
116C2×Q16×C73—22no—
117C2×Q16×C73—22no—
118C2×Q16×C73—22no—
119C2×Q16×C73—21no—
120C2×Q16×C73—21no—
121C2×Q16×C73—22no—
122C2×Q16×C73—41no—
123C2×Q16×C73D411yescharacteristic
124C2×SD16×C73—28no—
125C2×SD16×C73—21no—
126C2×SD16×C73—21no—
127C2×SD16×C73—21no—
128C2×SD16×C73—21no—
129C2×SD16×C73—21no—
130C2×SD16×C73—21no—
131C2×SD16×C73—22no—
132C2×SD16×C73—21no—
133C2×SD16×C73—21no—
134C2×SD16×C73—22no—
135C2×SD16×C73—22no—
136C2×SD16×C73—41no—
137C2×SD16×C73D411yescharacteristic
138C2×SD16×C73D414yes—
139C2×SD16×C73D411yescharacteristic
140C2×D8×C73—21no—
141C2×D8×C73D411yescharacteristic
142#131×C73—22no—
143#131×C73D414yes—
144C2×M16×C73—21no—
145C2×M16×C73C2311yescharacteristic
146C2×M16×C73C2311yescharacteristic
147C2×M16×C73C2311yescharacteristic
148C2×M16×C73C2311yescharacteristic
149C22×C8×C73—21no—
150C22×C8×C73C2311yescharacteristic
151C22×C8×C73C2311yescharacteristic
152C4⋊Q8×C73—21no—
153C4⋊Q8×C73—21no—
154C4⋊Q8×C73—22no—
155C4⋊Q8×C73—22no—
156#124×C73—21no—
157#124×C73—21no—
158#124×C73—22no—
159#124×C73—22no—
160#123×C73—41no—
161#123×C73—41no—
162C22⋊Q8×C73—22no—
163C22⋊Q8×C73—22no—
164#117×C73C2311yescharacteristic
165C2×C4⋊C4×C73—41no—
166C2×C22⋊C4×C73—41no—
167C2×C42×C73C2311yescharacteristic
168#108×C73—22no—
169#104×C73—22no—
170#104×C73—22no—
171#104×C73D414yes—
172#103×C73—22no—
173#103×C73D412yes—
174#102×C73—22no—
175#102×C73D412yes—
176#101×C73—22no—
177#101×C73—22no—
178#101×C73—22no—
179#100×C73—22no—
180C22⋊C8×C73—22no—
181C22⋊C8×C73—22no—
182#97×C73—22no—
183#97×C73—21no—
184C4×C8×C73—21no—
185C24×C73—21no—
186C24×C73—41no—
187#41×C73—21no—
188#41×C73—21no—
189#41×C73—24no—
190#41×C73—24no—
191#41×C73—21no—
192#41×C73—21no—
193#41×C73—21no—
194#41×C73—21no—
195#41×C73—21no—
196#41×C73—21no—
197#41×C73—21no—
198#41×C73—21no—
199#41×C73—42no—
200#41×C73—44no—
201#41×C73—42no—
202#41×C73—42no—
203#41×C73—42no—
204#41×C73—44no—
205#41×C73—42no—
206#41×C73—42no—
207#41×C73C2×D412yes—
208#41×C73C2×D412yes—
209C2×Q8×C73—21no—
210C2×Q8×C73—24no—
211C2×Q8×C73—21no—
212C2×Q8×C73—21no—
213C2×Q8×C73—21no—
214C2×Q8×C73—21no—
215C2×Q8×C73—21no—
216C2×Q8×C73—21no—
217C2×Q8×C73—21no—
218C2×Q8×C73—21no—
219C2×Q8×C73—21no—
220C2×Q8×C73—21no—
221C2×Q8×C73—21no—
222C2×Q8×C73—21no—
223C2×Q8×C73—21no—
224C2×Q8×C73—21no—
225C2×Q8×C73—21no—
226C2×Q8×C73—21no—
227C2×Q8×C73—41no—
228C2×Q8×C73—42no—
229C2×Q8×C73—42no—
230C2×Q8×C73—42no—
231C2×Q8×C73C2×D411yescharacteristic
232C2×Q8×C73C2×D412yes—
233C2×Q8×C73C2×D411yescharacteristic
234C2×Q8×C73C2×D411yescharacteristic
235C2×D4×C73—21no—
236C2×D4×C73—24no—
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—42no—
245C2×D4×C73—41no—
246C2×D4×C73—41no—
247C2×D4×C73—42no—
248C2×D4×C73—44no—
249C2×D4×C73—44no—
250C2×D4×C73—41no—
251C2×D4×C73—42no—
252C2×D4×C73C2×D411yescharacteristic
253C2×D4×C73C2×D411yescharacteristic
254C2×D4×C73C2×D412yes—
255C2×D4×C73C2×D411yescharacteristic
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—41no—
264C22×C4×C73—41no—
265C22×C4×C73—41no—
266C22×C4×C73C2411yescharacteristic
267Q16×C73—24no—
268Q16×C73—22no—
269Q16×C73—44no—
270Q16×C73—42no—
271Q16×C73—42no—
272Q16×C73—42no—
273Q16×C73—42no—
274Q16×C73—42no—
275Q16×C73—42no—
276SD16×C73—24no—
277SD16×C73—24no—
278SD16×C73—22no—
279SD16×C73—24no—
280SD16×C73—24no—
281SD16×C73—22no—
282SD16×C73—44no—
283SD16×C73—42no—
284SD16×C73—42no—
285SD16×C73—42no—
286SD16×C73—42no—
287D8×C73—24no—
288D8×C73—22no—
289M16×C73—21no—
290M16×C73—21no—
291M16×C73—24no—
292M16×C73—21no—
293M16×C73—21no—
294M16×C73—21no—
295M16×C73—21no—
296M16×C73C2×D412yes—
297M16×C73C2×D412yes—
298C2×C8×C73—21no—
299C2×C8×C73—21no—
300C2×C8×C73—21no—
301C2×C8×C73—21no—
302C2×C8×C73—24no—
303C2×C8×C73—21no—
304C2×C8×C73—21no—
305C2×C8×C73C2×D412yes—
306C2×C8×C73C2×D411yescharacteristic
307C2×C8×C73C2×D411yescharacteristic
308C2×C8×C73C2×D412yes—
309C2×C8×C73C2×D412yes—
310C4⋊C4×C73—44no—
311C4⋊C4×C73—42no—
312C4⋊C4×C73—42no—
313C4⋊C4×C73C2×D412yes—
314C22⋊C4×C73—21no—
315C22⋊C4×C73—44no—
316C22⋊C4×C73—42no—
317C22⋊C4×C73—42no—
318C42×C73—21no—
319C42×C73—21no—
320C42×C73C2×D412yes—
321C23×C73—21no—
322C23×C73—21no—
323C23×C73—21no—
324C23×C73—22no—
325C23×C73—44no—
326C23×C73—41no—
327C23×C73—41no—
328C23×C73—82no—
329C23×C73—162no—
330C23×C73H(5,𝔽2)11yescharacteristic
331Q8×C73—21no—
332Q8×C73—21no—
333Q8×C73—22no—
334Q8×C73—21no—
335Q8×C73—22no—
336Q8×C73—21no—
337Q8×C73—21no—
338Q8×C73—44no—
339Q8×C73—41no—
340Q8×C73—41no—
341Q8×C73—41no—
342Q8×C73—41no—
343Q8×C73—41no—
344Q8×C73—41no—
345Q8×C73—41no—
346Q8×C73—41no—
347Q8×C73—41no—
348Q8×C73—41no—
349Q8×C73#12712yes—
350D4×C73—22no—
351D4×C73—22no—
352D4×C73—21no—
353D4×C73—22no—
354D4×C73—21no—
355D4×C73—21no—
356D4×C73—22no—
357D4×C73—21no—
358D4×C73—21no—
359D4×C73—44no—
360D4×C73—44no—
361D4×C73—44no—
362D4×C73—41no—
363D4×C73—41no—
364D4×C73—41no—
365D4×C73—41no—
366D4×C73—41no—
367D4×C73—41no—
368D4×C73#12712yes—
369C2×C4×C73—21no—
370C2×C4×C73—22no—
371C2×C4×C73—22no—
372C2×C4×C73—22no—
373C2×C4×C73—22no—
374C2×C4×C73—22no—
375C2×C4×C73—21no—
376C2×C4×C73—21no—
377C2×C4×C73—44no—
378C2×C4×C73—44no—
379C2×C4×C73—42no—
380C2×C4×C73—44no—
381C2×C4×C73—41no—
382C2×C4×C73—41no—
383C2×C4×C73—41no—
384C2×C4×C73—41no—
385C2×C4×C73—41no—
386C2×C4×C73—41no—
387C2×C4×C73—41no—
388C2×C4×C73—41no—
389C2×C4×C73—41no—
390C2×C4×C73—41no—
391C2×C4×C73—41no—
392C2×C4×C73—41no—
393C2×C4×C73C22×D411yescharacteristic
394C2×C4×C73C22×D411yescharacteristic
395C2×C4×C73C22×D411yescharacteristic
396C2×C4×C73C22×D411yescharacteristic
397C2×C4×C73C22×D411yescharacteristic
398C2×C4×C73H(5,𝔽2)11yescharacteristic
399C8×C73—22no—
400C8×C73—22no—
401C8×C73—22no—
402C8×C73—41no—
403C8×C73—41no—
404C8×C73#12012yes—
405C8×C73#12012yes—
406C22×C73—22no—
407C22×C73—22no—
408C22×C73—42no—
409C22×C73—41no—
410C22×C73—41no—
411C22×C73—42no—
412C22×C73—42no—
413C22×C73—42no—
414C22×C73—82no—
415C22×C73—82no—
416C22×C73—161no—
417C22×C73—164no—
418C22×C73#53511yescharacteristic
419C22×C73D4211yescharacteristic
420C22×C73D4211yescharacteristic
421C4×C73—22no—
422C4×C73—42no—
423C4×C73—41no—
424C4×C73—42no—
425C4×C73—41no—
426C4×C73—42no—
427C4×C73—81no—
428C4×C73—81no—
429C4×C73C2×#12011yescharacteristic
430C4×C73C2×#12711yescharacteristic
431C4×C73D4211yescharacteristic
432C4×C73D4211yescharacteristic
433#25808C7311yesmaximal, characteristic, direct product factor, Sylow
434C2×C73—21no—
435C2×C73—21no—
436C2×C73—42no—
437C2×C73—81no—
438C2×C73—81no—
439C2×C73—82no—
440C2×C73#243311yescharacteristic
441C2×C73#328912yes—
442C2×#577C2×C7311yescharacteristic
443#3156C2×C7311yescharacteristic, complemented
444C2×#497C2×C7311yescharacteristic, complemented
445C2×#473C2×C7311yescharacteristic, complemented
446C2×#456C2×C7311yescharacteristic, complemented
447C2×#455C2×C7311yescharacteristic, complemented
448#3011C2×C7311yescharacteristic, complemented
449#3009C2×C7311yescharacteristic, complemented
450#2020C2×C7311yescharacteristic, complemented
451#2019C2×C7311yescharacteristic, complemented
452#2005C2×C7311yescharacteristic, complemented
453#2003C2×C7311yescharacteristic, complemented
454#1977C2×C7311yescharacteristic, complemented
455#1975C2×C7311yescharacteristic, complemented
456#1765C2×C7311yescharacteristic, complemented
457C73#2580811yescharacteristic, direct product factor, Sylow
458C2×2−1+4C22×C7311yescharacteristic
459C2×H(5,𝔽2)C22×C7311yescharacteristic
460#577—24no—
461#577—24no—
462C2×#137—21no—
463C2×#137C22×C7311yescharacteristic
464C2×#137C22×C7311yescharacteristic
465C2×#137C22×C7311yescharacteristic
466C2×#137C22×C7311yescharacteristic
467C2×#137C22×C7311yescharacteristic, complemented
468C2×AGL(1,ℤ/8)—21no—
469C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
470C2×#135—21no—
471C2×#135C22×C7311yescharacteristic
472C22×Q16C22×C7311yescharacteristic, complemented
473C22×Q16C22×C7311yescharacteristic, complemented
474C22×SD16—21no—
475C22×SD16C22×C7311yescharacteristic
476C22×SD16C22×C7311yescharacteristic
477C2×#131C22×C7311yescharacteristic
478#536C22×C7311yescharacteristic
479#536C22×C7311yescharacteristic, complemented
480C2×C4⋊Q8C22×C7311yescharacteristic, complemented
481C2×#124C22×C7311yescharacteristic
482#497—24no—
483#497—21no—
484#497—21no—
485#495—21no—
486#494—21no—
487#473—24no—
488#456—24no—
489#455—24no—
490#452—22no—
491#452—22no—
492#451—22no—
493#450—22no—
494C2×#108C22×C7311yescharacteristic, complemented
495C2×#104C22×C7311yescharacteristic
496C2×#104C22×C7311yescharacteristic
497C2×#104C22×C7311yescharacteristic, complemented
498#419C22×C7311yescharacteristic, complemented
499#418C22×C7311yescharacteristic
500#416C22×C7311yescharacteristic
501C2×#101C22×C7311yescharacteristic, complemented
502C2×#101C22×C7311yescharacteristic, complemented
503C2×#101C22×C7311yescharacteristic, complemented
504C2×#100C22×C7311yescharacteristic
505#408C22×C7311yescharacteristic
506#408C22×C7311yescharacteristic, complemented
507#405C22×C7311yescharacteristic, complemented
508C2×#97C22×C7311yescharacteristic, complemented
509#341C22×C7311yescharacteristic, complemented
510#339C22×C7311yescharacteristic, complemented
5112−1+4—22no—
5122−1+4—22no—
5132−1+4—22no—
5142−1+4—41no—
515H(5,𝔽2)—22no—
516H(5,𝔽2)—22no—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—41no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—21no—
523C2×#41—41no—
524C2×#41C23×C7311yescharacteristic
525C2×#41C23×C7311yescharacteristic
526C2×#41C23×C7311yescharacteristic
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8C23×C7311yescharacteristic
530C22×Q8C23×C7311yescharacteristic
531C22×Q8C23×C7311yescharacteristic
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—41no—
535C22×D4C23×C7311yescharacteristic
536#137—28no—
537#137—22no—
538#137—22no—
539#137—22no—
540#137—22no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—22no—
545#137—41no—
546#137—41no—
547AGL(1,ℤ/8)—28no—
548AGL(1,ℤ/8)—22no—
549AGL(1,ℤ/8)—22no—
550#135—28no—
551#135—22no—
552#135—22no—
553C2×Q16—21no—
554C2×Q16—22no—
555C2×Q16—21no—
556C2×Q16—21no—
557C2×Q16—21no—
558C2×Q16—21no—
559C2×Q16—22no—
560C2×Q16—22no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16—22no—
564C2×Q16—41no—
565C2×Q16D4×C7311yescharacteristic
566C2×SD16—28no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16—22no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—21no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×SD16D4×C7311yescharacteristic
580C2×SD16D4×C7314yes—
581C2×SD16D4×C7311yescharacteristic
582C2×D8—21no—
583C2×D8D4×C7311yescharacteristic
584#131—22no—
585#131D4×C7314yes—
586C2×M16—21no—
587C2×M16C23×C7311yescharacteristic
588C2×M16C23×C7311yescharacteristic
589C2×M16C23×C7311yescharacteristic
590C2×M16C23×C7311yescharacteristic
591C22×C8—21no—
592C22×C8C23×C7311yescharacteristic
593C22×C8C23×C7311yescharacteristic
594C4⋊Q8—22no—
595C4⋊Q8—21no—
596C4⋊Q8—21no—
597C4⋊Q8—22no—
598#124—22no—
599#124—21no—
600#124—21no—
601#124—22no—
602#123—41no—
603#123—41no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606#117C23×C7311yescharacteristic
607C2×C4⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C42C23×C7311yescharacteristic
610#108—22no—
611#104—22no—
612#104—22no—
613#104D4×C7314yes—
614#103—22no—
615#103D4×C7312yes—
616#102—22no—
617#102D4×C7312yes—
618#101—22no—
619#101—22no—
620#101—22no—
621#100—22no—
622C22⋊C8—22no—
623C22⋊C8—22no—
624#97—22no—
625#97—21no—
626C4×C8—21no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—24no—
632#41—24no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—42no—
642#41—44no—
643#41—42no—
644#41—42no—
645#41—42no—
646#41—44no—
647#41—42no—
648#41—42no—
649#41C2×D4×C7312yes—
650#41C2×D4×C7312yes—
651C2×Q8—21no—
652C2×Q8—24no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8—42no—
672C2×Q8—42no—
673C2×Q8C2×D4×C7311yescharacteristic
674C2×Q8C2×D4×C7312yes—
675C2×Q8C2×D4×C7311yescharacteristic
676C2×Q8C2×D4×C7311yescharacteristic
677C2×D4—21no—
678C2×D4—24no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—42no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—42no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—41no—
693C2×D4—42no—
694C2×D4C2×D4×C7311yescharacteristic
695C2×D4C2×D4×C7311yescharacteristic
696C2×D4C2×D4×C7312yes—
697C2×D4C2×D4×C7311yescharacteristic
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4C24×C7311yescharacteristic
709Q16—24no—
710Q16—22no—
711Q16—44no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715Q16—42no—
716Q16—42no—
717Q16—42no—
718SD16—24no—
719SD16—24no—
720SD16—22no—
721SD16—24no—
722SD16—24no—
723SD16—22no—
724SD16—44no—
725SD16—42no—
726SD16—42no—
727SD16—42no—
728SD16—42no—
729D8—24no—
730D8—22no—
731M16—21no—
732M16—21no—
733M16—24no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16C2×D4×C7312yes—
739M16C2×D4×C7312yes—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—24no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8C2×D4×C7312yes—
748C2×C8C2×D4×C7311yescharacteristic
749C2×C8C2×D4×C7311yescharacteristic
750C2×C8C2×D4×C7312yes—
751C2×C8C2×D4×C7312yes—
752C4⋊C4—44no—
753C4⋊C4—42no—
754C4⋊C4—42no—
755C4⋊C4C2×D4×C7312yes—
756C22⋊C4—21no—
757C22⋊C4—44no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42C2×D4×C7312yes—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—22no—
767C23—44no—
768C23—41no—
769C23—41no—
770C23—82no—
771C23—162no—
772C23H(5,𝔽2)×C7311yescharacteristic
773Q8—21no—
774Q8—21no—
775Q8—22no—
776Q8—21no—
777Q8—22no—
778Q8—21no—
779Q8—21no—
780Q8—44no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8#127×C7312yes—
792D4—22no—
793D4—22no—
794D4—21no—
795D4—22no—
796D4—21no—
797D4—21no—
798D4—22no—
799D4—21no—
800D4—21no—
801D4—44no—
802D4—44no—
803D4—44no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4#127×C7312yes—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4C22×D4×C7311yescharacteristic
836C2×C4C22×D4×C7311yescharacteristic
837C2×C4C22×D4×C7311yescharacteristic
838C2×C4C22×D4×C7311yescharacteristic
839C2×C4C22×D4×C7311yescharacteristic
840C2×C4H(5,𝔽2)×C7311yescharacteristic
841C8—22no—
842C8—22no—
843C8—22no—
844C8—41no—
845C8—41no—
846C8#120×C7312yes—
847C8#120×C7312yes—
848C22—22no—
849C22—22no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—41no—
854C22—41no—
855C22—42no—
856C22—82no—
857C22—82no—
858C22—161no—
859C22—164no—
860C22#535×C7311yescharacteristic
861C22D42×C7311yescharacteristic
862C22D42×C7311yescharacteristic
863C4—22no—
864C4—42no—
865C4—42no—
866C4—41no—
867C4—41no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4C2×#120×C7311yescharacteristic
872C4C2×#127×C7311yescharacteristic
873C4D42×C7311yescharacteristic
874C4D42×C7311yescharacteristic
875C2—21no—
876C2—21no—
877C2—42no—
878C2—81no—
879C2—81no—
880C2—82no—
881C2C73×#243311yescharacteristic
882C2C73×#328912yes—
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#577×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3156C2semidirect
3. C2×#497×C73C2semidirect
4. C2×#473×C73C2semidirect
5. C2×#456×C73C2semidirect
6. C2×#455×C73C2semidirect
7. C73×#3011C2semidirect
8. C73×#3009C2semidirect
9. C73×#2020C2semidirect
10. C73×#2019C2semidirect
11. C73×#2005C2semidirect
12. C73×#2003C2semidirect
13. C73×#1977C2semidirect
14. C73×#1975C2semidirect
15. C73×#1765C2semidirect
25. C2×#137×C73C22semidirect
30. C22×Q16×C73C22semidirect
31. C22×Q16×C73C22semidirect
37. #536×C73C22semidirect
38. C2×C4⋊Q8×C73C22semidirect
52. C2×#108×C73C22semidirect
55. C2×#104×C73C22semidirect
56. #419×C73C22semidirect
59. C2×#101×C73C22semidirect
60. C2×#101×C73C22semidirect
61. C2×#101×C73C22semidirect
64. #408×C73C22semidirect
65. #405×C73C22semidirect
66. C2×#97×C73C22semidirect
67. #341×C73C22semidirect
68. #339×C73C22semidirect
433. #25808C73direct (N × H)
443. #3156C2×C73semidirect
444. C2×#497C2×C73semidirect
445. C2×#473C2×C73semidirect
446. C2×#456C2×C73semidirect
447. C2×#455C2×C73semidirect
448. #3011C2×C73semidirect
449. #3009C2×C73semidirect
450. #2020C2×C73semidirect
451. #2019C2×C73semidirect
452. #2005C2×C73semidirect
453. #2003C2×C73semidirect
454. #1977C2×C73semidirect
455. #1975C2×C73semidirect
456. #1765C2×C73semidirect
457. C73#25808direct (N × H)
467. C2×#137C22×C73semidirect
472. C22×Q16C22×C73semidirect
473. C22×Q16C22×C73semidirect
479. #536C22×C73semidirect
480. C2×C4⋊Q8C22×C73semidirect
494. C2×#108C22×C73semidirect
497. C2×#104C22×C73semidirect
498. #419C22×C73semidirect
501. C2×#101C22×C73semidirect
502. C2×#101C22×C73semidirect
503. C2×#101C22×C73semidirect
506. #408C22×C73semidirect
507. #405C22×C73semidirect
508. C2×#97C22×C73semidirect
509. #341C22×C73semidirect
510. #339C22×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C732
C73×#31562
C2×#497×C732
C2×#473×C732
C2×#456×C732
C2×#455×C732
C73×#30112
C73×#30092
C73×#20202
C73×#20192
C73×#20052
C73×#20032
C73×#19772
C73×#19752
C73×#17652
#2580873