Finite Group Databasebeta

← C73×#25801 #32935205

Subgroups — C73×#25801 #32935205

Order 18688.

1444 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C73C211yesmaximal, characteristic, complemented
2C73×#3154C211yesmaximal, characteristic, complemented
3C2×#495×C73C211yesmaximal, characteristic, complemented
4C2×#471×C73C211yesmaximal, characteristic, complemented
5C2×#454×C73C211yesmaximal, characteristic, complemented
6C2×#455×C73C211yesmaximal, characteristic, complemented
7C73×#3011C211yesmaximal, characteristic, complemented
8C73×#3008C211yesmaximal, characteristic, complemented
9C73×#2020C211yesmaximal, characteristic, complemented
10C73×#2018C211yesmaximal, characteristic, complemented
11C73×#2004C211yesmaximal, characteristic, complemented
12C73×#2003C211yesmaximal, characteristic, complemented
13C73×#1977C211yesmaximal, characteristic, complemented
14C73×#1974C211yesmaximal, characteristic, complemented
15C73×#1764C211yesmaximal, 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×AGL(1,ℤ/8)×C73—21no—
25C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C73C2211yescharacteristic, complemented
28C2×#135×C73—21no—
29C2×#135×C73C2211yescharacteristic
30C22×Q16×C73C2211yescharacteristic, complemented
31C22×SD16×C73—21no—
32C22×SD16×C73C2211yescharacteristic
33C22×SD16×C73C2211yescharacteristic, complemented
34C22×D8×C73C2211yescharacteristic
35C2×#131×C73C2211yescharacteristic
36#536×C73C2211yescharacteristic, complemented
37#535×C73C2211yescharacteristic
38C2×#124×C73C2211yescharacteristic
39C2×#124×C73C2211yescharacteristic, complemented
40#497×C73—21no—
41#496×C73—21no—
42#495×C73—21no—
43#495×C73—24no—
44#492×C73—21no—
45#471×C73—24no—
46#455×C73—24no—
47#454×C73—24no—
48#452×C73—22no—
49#451×C73—22no—
50#449×C73—22no—
51#447×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×#100×C73C2211yescharacteristic
62C2×#100×C73C2211yescharacteristic, complemented
63#408×C73C2211yescharacteristic
64#408×C73C2211yescharacteristic, complemented
65#405×C73C2211yescharacteristic, complemented
66C2×C4×C8×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×D4×C73—21no—
90C22×D4×C73—21no—
91C22×D4×C73—41no—
92C22×D4×C73C2311yescharacteristic
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—41no—
101AGL(1,ℤ/8)×C73—28no—
102AGL(1,ℤ/8)×C73—22no—
103AGL(1,ℤ/8)×C73—22no—
104AGL(1,ℤ/8)×C73—22no—
105AGL(1,ℤ/8)×C73—22no—
106AGL(1,ℤ/8)×C73—22no—
107AGL(1,ℤ/8)×C73—41no—
108#135×C73—28no—
109#135×C73—22no—
110#135×C73—22no—
111C2×Q16×C73—21no—
112C2×Q16×C73—21no—
113C2×Q16×C73—22no—
114C2×Q16×C73—21no—
115C2×Q16×C73—22no—
116C2×Q16×C73—41no—
117C2×Q16×C73D411yescharacteristic
118C2×SD16×C73—28no—
119C2×SD16×C73—21no—
120C2×SD16×C73—21no—
121C2×SD16×C73—21no—
122C2×SD16×C73—21no—
123C2×SD16×C73—21no—
124C2×SD16×C73—21no—
125C2×SD16×C73—21no—
126C2×SD16×C73—21no—
127C2×SD16×C73—22no—
128C2×SD16×C73—22no—
129C2×SD16×C73—21no—
130C2×SD16×C73—22no—
131C2×SD16×C73—21no—
132C2×SD16×C73D411yescharacteristic
133C2×SD16×C73D411yescharacteristic
134C2×SD16×C73D414yescomplemented
135C2×D8×C73—21no—
136C2×D8×C73—21no—
137C2×D8×C73—22no—
138C2×D8×C73—21no—
139C2×D8×C73—22no—
140C2×D8×C73—41no—
141C2×D8×C73D411yescharacteristic
142#131×C73—22no—
143#131×C73D414yescomplemented
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—
153#127×C73—21no—
154#124×C73—22no—
155#124×C73—21no—
156#124×C73—22no—
157#124×C73—21no—
158#124×C73—22no—
159#124×C73—22no—
160#123×C73—41no—
161C22⋊Q8×C73—22no—
162#121×C73—22no—
163#120×C73—41no—
164#117×C73C2311yescharacteristic
165C2×C22⋊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×C73D414yescomplemented
172#103×C73—22no—
173#103×C73D412yes—
174#102×C73—22no—
175#102×C73D412yes—
176#101×C73—22no—
177#101×C73—22no—
178#100×C73—22no—
179#100×C73—22no—
180C22⋊C8×C73—22no—
181C22⋊C8×C73—22no—
182#97×C73—21no—
183C4×C8×C73—22no—
184C4×C8×C73—21no—
185C24×C73—21no—
186C24×C73—21no—
187C24×C73—41no—
188#41×C73—21no—
189#41×C73—21no—
190#41×C73—24no—
191#41×C73—24no—
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—21no—
200#41×C73—42no—
201#41×C73—44no—
202#41×C73—42no—
203#41×C73—42no—
204#41×C73—42no—
205#41×C73—44no—
206#41×C73—42no—
207#41×C73—42no—
208#41×C73C2×D412yes—
209#41×C73C2×D412yes—
210C2×Q8×C73—21no—
211C2×Q8×C73—24no—
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—41no—
223C2×Q8×C73—42no—
224C2×Q8×C73—42no—
225C2×Q8×C73—42no—
226C2×Q8×C73C2×D411yescharacteristic
227C2×Q8×C73C2×D412yes—
228C2×Q8×C73C2×D411yescharacteristic
229C2×Q8×C73C2×D411yescharacteristic
230C2×D4×C73—21no—
231C2×D4×C73—24no—
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—42no—
246C2×D4×C73—41no—
247C2×D4×C73—41no—
248C2×D4×C73—42no—
249C2×D4×C73—42no—
250C2×D4×C73—44no—
251C2×D4×C73—44no—
252C2×D4×C73—41no—
253C2×D4×C73—42no—
254C2×D4×C73C2×D411yescharacteristic
255C2×D4×C73C2×D412yes—
256C2×D4×C73C2×D411yescharacteristic
257C2×D4×C73C2×D411yescharacteristic
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—41no—
265C22×C4×C73—41no—
266C22×C4×C73—41no—
267C22×C4×C73C2411yescharacteristic
268Q16×C73—24no—
269Q16×C73—22no—
270Q16×C73—44no—
271Q16×C73—42no—
272Q16×C73—42no—
273SD16×C73—24no—
274SD16×C73—24no—
275SD16×C73—22no—
276SD16×C73—24no—
277SD16×C73—24no—
278SD16×C73—22no—
279SD16×C73—42no—
280SD16×C73—42no—
281SD16×C73—42no—
282SD16×C73—42no—
283SD16×C73—42no—
284SD16×C73—42no—
285D8×C73—24no—
286D8×C73—22no—
287D8×C73—44no—
288D8×C73—42no—
289D8×C73—42no—
290M16×C73—21no—
291M16×C73—21no—
292M16×C73—24no—
293M16×C73—21no—
294M16×C73—21no—
295M16×C73—21no—
296M16×C73—21no—
297M16×C73C2×D412yes—
298M16×C73C2×D412yes—
299C2×C8×C73—21no—
300C2×C8×C73—21no—
301C2×C8×C73—21no—
302C2×C8×C73—21no—
303C2×C8×C73—24no—
304C2×C8×C73—21no—
305C2×C8×C73—21no—
306C2×C8×C73C2×D412yes—
307C2×C8×C73C2×D411yescharacteristic
308C2×C8×C73C2×D412yes—
309C2×C8×C73C2×D411yescharacteristic
310C2×C8×C73C2×D412yes—
311C4⋊C4×C73—42no—
312C4⋊C4×C73C2×D412yes—
313C22⋊C4×C73—21no—
314C22⋊C4×C73—44no—
315C22⋊C4×C73—42no—
316C22⋊C4×C73—44no—
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—41no—
329C23×C73—41no—
330C23×C73—41no—
331C23×C73—82no—
332C23×C73—82no—
333C23×C73—162no—
334C23×C73H(5,𝔽2)11yescharacteristic
335Q8×C73—21no—
336Q8×C73—21no—
337Q8×C73—22no—
338Q8×C73—21no—
339Q8×C73—21no—
340Q8×C73—22no—
341Q8×C73—21no—
342Q8×C73—44no—
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—41no—
369D4×C73—41no—
370D4×C73—41no—
371D4×C73—41no—
372D4×C73—162no—
373D4×C73#12712yes—
374C2×C4×C73—21no—
375C2×C4×C73—22no—
376C2×C4×C73—22no—
377C2×C4×C73—22no—
378C2×C4×C73—22no—
379C2×C4×C73—22no—
380C2×C4×C73—21no—
381C2×C4×C73—21no—
382C2×C4×C73—44no—
383C2×C4×C73—44no—
384C2×C4×C73—42no—
385C2×C4×C73—44no—
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×C73—41no—
394C2×C4×C73—41no—
395C2×C4×C73C22×D411yescharacteristic
396C2×C4×C73C22×D411yescharacteristic
397C2×C4×C73C22×D411yescharacteristic
398C2×C4×C73C22×D411yescharacteristic
399C2×C4×C73C22×D411yescharacteristic
400C2×C4×C73H(5,𝔽2)11yescharacteristic
401C8×C73—22no—
402C8×C73—22no—
403C8×C73—22no—
404C8×C73—41no—
405C8×C73—41no—
406C8×C73#12012yes—
407C8×C73#12012yes—
408C22×C73—22no—
409C22×C73—22no—
410C22×C73—42no—
411C22×C73—41no—
412C22×C73—41no—
413C22×C73—42no—
414C22×C73—42no—
415C22×C73—42no—
416C22×C73—82no—
417C22×C73—82no—
418C22×C73—82no—
419C22×C73—81no—
420C22×C73—82no—
421C22×C73—161no—
422C22×C73—161no—
423C22×C73—164no—
424C22×C73#53511yescharacteristic
425C22×C73D4211yescharacteristic
426C22×C73D4211yescharacteristic
427C4×C73—22no—
428C4×C73—42no—
429C4×C73—41no—
430C4×C73—42no—
431C4×C73—41no—
432C4×C73—42no—
433C4×C73—81no—
434C4×C73C2×#12011yescharacteristic
435C4×C73C2×#12711yescharacteristic
436C4×C73D4211yescharacteristic
437C4×C73D4211yescharacteristic
438#25801C7311yesmaximal, characteristic, direct product factor, Sylow
439C2×C73—21no—
440C2×C73—21no—
441C2×C73—42no—
442C2×C73—81no—
443C2×C73—81no—
444C2×C73—82no—
445C2×C73—161no—
446C2×C73#243311yescharacteristic
447C2×C73#329012yes—
448C2×#577C2×C7311yescharacteristic, complemented
449#3154C2×C7311yescharacteristic, complemented
450C2×#495C2×C7311yescharacteristic, complemented
451C2×#471C2×C7311yescharacteristic, complemented
452C2×#454C2×C7311yescharacteristic, complemented
453C2×#455C2×C7311yescharacteristic, complemented
454#3011C2×C7311yescharacteristic, complemented
455#3008C2×C7311yescharacteristic, complemented
456#2020C2×C7311yescharacteristic, complemented
457#2018C2×C7311yescharacteristic, complemented
458#2004C2×C7311yescharacteristic, complemented
459#2003C2×C7311yescharacteristic, complemented
460#1977C2×C7311yescharacteristic, complemented
461#1974C2×C7311yescharacteristic, complemented
462#1764C2×C7311yescharacteristic, complemented
463C73#2580111yescharacteristic, direct product factor, Sylow
464C2×2−1+4C22×C7311yescharacteristic
465C2×H(5,𝔽2)C22×C7311yescharacteristic
466#577—24no—
467#577—24no—
468C2×#137—21no—
469C2×#137C22×C7311yescharacteristic
470C2×#137C22×C7311yescharacteristic
471C2×#137C22×C7311yescharacteristic
472C2×AGL(1,ℤ/8)—21no—
473C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
474C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
475C2×AGL(1,ℤ/8)C22×C7311yescharacteristic, complemented
476C2×#135—21no—
477C2×#135C22×C7311yescharacteristic
478C22×Q16C22×C7311yescharacteristic, complemented
479C22×SD16—21no—
480C22×SD16C22×C7311yescharacteristic
481C22×SD16C22×C7311yescharacteristic, complemented
482C22×D8C22×C7311yescharacteristic
483C2×#131C22×C7311yescharacteristic
484#536C22×C7311yescharacteristic, complemented
485#535C22×C7311yescharacteristic
486C2×#124C22×C7311yescharacteristic
487C2×#124C22×C7311yescharacteristic, complemented
488#497—21no—
489#496—21no—
490#495—21no—
491#495—24no—
492#492—21no—
493#471—24no—
494#455—24no—
495#454—24no—
496#452—22no—
497#451—22no—
498#449—22no—
499#447—22no—
500C2×#108C22×C7311yescharacteristic, complemented
501C2×#104C22×C7311yescharacteristic
502C2×#104C22×C7311yescharacteristic
503C2×#104C22×C7311yescharacteristic, complemented
504#419C22×C7311yescharacteristic, complemented
505#418C22×C7311yescharacteristic
506#416C22×C7311yescharacteristic
507C2×#101C22×C7311yescharacteristic, complemented
508C2×#101C22×C7311yescharacteristic, complemented
509C2×#100C22×C7311yescharacteristic
510C2×#100C22×C7311yescharacteristic, complemented
511#408C22×C7311yescharacteristic
512#408C22×C7311yescharacteristic, complemented
513#405C22×C7311yescharacteristic, complemented
514C2×C4×C8C22×C7311yescharacteristic, complemented
515#341C22×C7311yescharacteristic, complemented
516#339C22×C7311yescharacteristic, complemented
5172−1+4—22no—
5182−1+4—22no—
5192−1+4—22no—
5202−1+4—41no—
521H(5,𝔽2)—22no—
522H(5,𝔽2)—22no—
523H(5,𝔽2)—22no—
524H(5,𝔽2)—41no—
525C2×#41—21no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C7311yescharacteristic
531C2×#41C23×C7311yescharacteristic
532C2×#41C23×C7311yescharacteristic
533C22×Q8—21no—
534C22×Q8—21no—
535C22×Q8C23×C7311yescharacteristic
536C22×Q8C23×C7311yescharacteristic
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—41no—
540C22×D4C23×C7311yescharacteristic
541C22×D4C23×C7311yescharacteristic
542#137—28no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—41no—
549AGL(1,ℤ/8)—28no—
550AGL(1,ℤ/8)—22no—
551AGL(1,ℤ/8)—22no—
552AGL(1,ℤ/8)—22no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—41no—
556#135—28no—
557#135—22no—
558#135—22no—
559C2×Q16—21no—
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—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—21no—
574C2×SD16—21no—
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—21no—
578C2×SD16—22no—
579C2×SD16—21no—
580C2×SD16D4×C7311yescharacteristic
581C2×SD16D4×C7311yescharacteristic
582C2×SD16D4×C7314yescomplemented
583C2×D8—21no—
584C2×D8—22no—
585C2×D8—21no—
586C2×D8—21no—
587C2×D8—22no—
588C2×D8—41no—
589C2×D8D4×C7311yescharacteristic
590#131—22no—
591#131D4×C7314yescomplemented
592C2×M16—21no—
593C2×M16C23×C7311yescharacteristic
594C2×M16C23×C7311yescharacteristic
595C2×M16C23×C7311yescharacteristic
596C2×M16C23×C7311yescharacteristic
597C22×C8—21no—
598C22×C8C23×C7311yescharacteristic
599C22×C8C23×C7311yescharacteristic
600C4⋊Q8—21no—
601#127—21no—
602#124—22no—
603#124—21no—
604#124—22no—
605#124—21no—
606#124—22no—
607#124—22no—
608#123—41no—
609C22⋊Q8—22no—
610#121—22no—
611#120—41no—
612#117C23×C7311yescharacteristic
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C42C23×C7311yescharacteristic
616#108—22no—
617#104—22no—
618#104—22no—
619#104D4×C7314yescomplemented
620#103—22no—
621#103D4×C7312yes—
622#102—22no—
623#102D4×C7312yes—
624#101—22no—
625#101—22no—
626#100—22no—
627#100—22no—
628C22⋊C8—22no—
629C22⋊C8—22no—
630#97—21no—
631C4×C8—22no—
632C4×C8—21no—
633C24—21no—
634C24—21no—
635C24—41no—
636#41—21no—
637#41—21no—
638#41—24no—
639#41—24no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—21no—
647#41—21no—
648#41—42no—
649#41—44no—
650#41—42no—
651#41—42no—
652#41—42no—
653#41—44no—
654#41—42no—
655#41—42no—
656#41C2×D4×C7312yes—
657#41C2×D4×C7312yes—
658C2×Q8—21no—
659C2×Q8—24no—
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—21no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8C2×D4×C7311yescharacteristic
675C2×Q8C2×D4×C7312yes—
676C2×Q8C2×D4×C7311yescharacteristic
677C2×Q8C2×D4×C7311yescharacteristic
678C2×D4—21no—
679C2×D4—24no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—42no—
694C2×D4—41no—
695C2×D4—41no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4C2×D4×C7311yescharacteristic
703C2×D4C2×D4×C7312yes—
704C2×D4C2×D4×C7311yescharacteristic
705C2×D4C2×D4×C7311yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—41no—
713C22×C4—41no—
714C22×C4—41no—
715C22×C4C24×C7311yescharacteristic
716Q16—24no—
717Q16—22no—
718Q16—44no—
719Q16—42no—
720Q16—42no—
721SD16—24no—
722SD16—24no—
723SD16—22no—
724SD16—24no—
725SD16—24no—
726SD16—22no—
727SD16—42no—
728SD16—42no—
729SD16—42no—
730SD16—42no—
731SD16—42no—
732SD16—42no—
733D8—24no—
734D8—22no—
735D8—44no—
736D8—42no—
737D8—42no—
738M16—21no—
739M16—21no—
740M16—24no—
741M16—21no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16C2×D4×C7312yes—
746M16C2×D4×C7312yes—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—24no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8C2×D4×C7312yes—
755C2×C8C2×D4×C7311yescharacteristic
756C2×C8C2×D4×C7312yes—
757C2×C8C2×D4×C7311yescharacteristic
758C2×C8C2×D4×C7312yes—
759C4⋊C4—42no—
760C4⋊C4C2×D4×C7312yes—
761C22⋊C4—21no—
762C22⋊C4—44no—
763C22⋊C4—42no—
764C22⋊C4—44no—
765C22⋊C4—42no—
766C42—21no—
767C42—21no—
768C42C2×D4×C7312yes—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—44no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—82no—
780C23—82no—
781C23—162no—
782C23H(5,𝔽2)×C7311yescharacteristic
783Q8—21no—
784Q8—21no—
785Q8—22no—
786Q8—21no—
787Q8—21no—
788Q8—22no—
789Q8—21no—
790Q8—44no—
791Q8—41no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796Q8—41no—
797Q8#127×C7312yes—
798D4—22no—
799D4—22no—
800D4—21no—
801D4—22no—
802D4—21no—
803D4—21no—
804D4—22no—
805D4—21no—
806D4—21no—
807D4—44no—
808D4—44no—
809D4—44no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—41no—
816D4—41no—
817D4—41no—
818D4—41no—
819D4—41no—
820D4—162no—
821D4#127×C7312yes—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4C22×D4×C7311yescharacteristic
844C2×C4C22×D4×C7311yescharacteristic
845C2×C4C22×D4×C7311yescharacteristic
846C2×C4C22×D4×C7311yescharacteristic
847C2×C4C22×D4×C7311yescharacteristic
848C2×C4H(5,𝔽2)×C7311yescharacteristic
849C8—22no—
850C8—22no—
851C8—22no—
852C8—41no—
853C8—41no—
854C8#120×C7312yes—
855C8#120×C7312yes—
856C22—22no—
857C22—22no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—41no—
863C22—42no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—81no—
869C22—161no—
870C22—161no—
871C22—164no—
872C22#535×C7311yescharacteristic
873C22D42×C7311yescharacteristic
874C22D42×C7311yescharacteristic
875C4—22no—
876C4—42no—
877C4—42no—
878C4—41no—
879C4—42no—
880C4—41no—
881C4—81no—
882C4C2×#120×C7311yescharacteristic
883C4C2×#127×C7311yescharacteristic
884C4D42×C7311yescharacteristic
885C4D42×C7311yescharacteristic
886C2—21no—
887C2—21no—
888C2—42no—
889C2—81no—
890C2—81no—
891C2—82no—
892C2—161no—
893C2C73×#243311yescharacteristic
894C2C73×#329012yes—
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC22×C4C24×C73
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
1. C2×#577×C73C2semidirect
2. C73×#3154C2semidirect
3. C2×#495×C73C2semidirect
4. C2×#471×C73C2semidirect
5. C2×#454×C73C2semidirect
6. C2×#455×C73C2semidirect
7. C73×#3011C2semidirect
8. C73×#3008C2semidirect
9. C73×#2020C2semidirect
10. C73×#2018C2semidirect
11. C73×#2004C2semidirect
12. C73×#2003C2semidirect
13. C73×#1977C2semidirect
14. C73×#1974C2semidirect
15. C73×#1764C2semidirect
27. C2×AGL(1,ℤ/8)×C73C22semidirect
30. C22×Q16×C73C22semidirect
33. C22×SD16×C73C22semidirect
36. #536×C73C22semidirect
39. C2×#124×C73C22semidirect
52. C2×#108×C73C22semidirect
55. C2×#104×C73C22semidirect
56. #419×C73C22semidirect
59. C2×#101×C73C22semidirect
60. C2×#101×C73C22semidirect
62. C2×#100×C73C22semidirect
64. #408×C73C22semidirect
65. #405×C73C22semidirect
66. C2×C4×C8×C73C22semidirect
67. #341×C73C22semidirect
68. #339×C73C22semidirect
134. C2×SD16×C73D4semidirect
143. #131×C73D4semidirect
171. #104×C73D4semidirect
438. #25801C73direct (N × H)
448. C2×#577C2×C73semidirect
449. #3154C2×C73semidirect
450. C2×#495C2×C73semidirect
451. C2×#471C2×C73semidirect
452. C2×#454C2×C73semidirect
453. C2×#455C2×C73semidirect
454. #3011C2×C73semidirect
455. #3008C2×C73semidirect
456. #2020C2×C73semidirect
457. #2018C2×C73semidirect
458. #2004C2×C73semidirect
459. #2003C2×C73semidirect
460. #1977C2×C73semidirect
461. #1974C2×C73semidirect
462. #1764C2×C73semidirect
463. C73#25801direct (N × H)
475. C2×AGL(1,ℤ/8)C22×C73semidirect
478. C22×Q16C22×C73semidirect
481. C22×SD16C22×C73semidirect
484. #536C22×C73semidirect
487. C2×#124C22×C73semidirect
500. C2×#108C22×C73semidirect
503. C2×#104C22×C73semidirect
504. #419C22×C73semidirect
507. C2×#101C22×C73semidirect
508. C2×#101C22×C73semidirect
510. C2×#100C22×C73semidirect
512. #408C22×C73semidirect
513. #405C22×C73semidirect
514. C2×C4×C8C22×C73semidirect
515. #341C22×C73semidirect
516. #339C22×C73semidirect
582. C2×SD16D4×C73semidirect
591. #131D4×C73semidirect
619. #104D4×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×#31542
C2×#495×C732
C2×#471×C732
C2×#454×C732
C2×#455×C732
C73×#30112
C73×#30082
C73×#20202
C73×#20182
C73×#20042
C73×#20032
C73×#19772
C73×#19742
C73×#17642
#2580173