Finite Group Databasebeta

← C73×#25807 #32935211

Subgroups — C73×#25807 #32935211

Order 18688.

1488 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C73C211yesmaximal, characteristic, complemented
2C73×#3155C211yesmaximal, characteristic, complemented
3C2×#496×C73C211yesmaximal, characteristic, complemented
4C2×#472×C73C211yesmaximal, characteristic, complemented
5C2×#454×C73C211yesmaximal, characteristic, complemented
6C2×#453×C73C211yesmaximal, characteristic, complemented
7C73×#3010C211yesmaximal, characteristic, complemented
8C73×#3008C211yesmaximal, characteristic, complemented
9C73×#2019C211yesmaximal, characteristic, complemented
10C73×#2018C211yesmaximal, characteristic, complemented
11C73×#2004C211yesmaximal, characteristic, complemented
12C73×#2002C211yesmaximal, 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×AGL(1,ℤ/8)×C73—21no—
23C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
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×SD16×C73—21no—
31C22×SD16×C73C2211yescharacteristic
32C22×SD16×C73C2211yescharacteristic, complemented
33C22×D8×C73C2211yescharacteristic
34C22×D8×C73C2211yescharacteristic, complemented
35C2×#131×C73C2211yescharacteristic
36#535×C73C2211yescharacteristic
37#535×C73C2211yescharacteristic, complemented
38C2×#127×C73C2211yescharacteristic
39C2×#124×C73C2211yescharacteristic, complemented
40#496×C73—24no—
41#496×C73—21no—
42#496×C73—21no—
43#495×C73—21no—
44#493×C73—21no—
45#472×C73—24no—
46#454×C73—24no—
47#453×C73—24no—
48#449×C73—22no—
49#449×C73—22no—
50#448×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×#100×C73C2211yescharacteristic
61C2×#100×C73C2211yescharacteristic, complemented
62C2×#100×C73C2211yescharacteristic, complemented
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×D4×C73—21no—
89C22×D4×C73—21no—
90C22×D4×C73—41no—
91C22×D4×C73—41no—
92C22×D4×C73C2311yescharacteristic
93C22×D4×C73C2311yescharacteristic
94C22×D4×C73C2311yescharacteristic
95#137×C73—28no—
96#137×C73—22no—
97#137×C73—22no—
98AGL(1,ℤ/8)×C73—28no—
99AGL(1,ℤ/8)×C73—22no—
100AGL(1,ℤ/8)×C73—22no—
101AGL(1,ℤ/8)×C73—22no—
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—
108AGL(1,ℤ/8)×C73—41no—
109#135×C73—28no—
110#135×C73—22no—
111#135×C73—22no—
112C2×Q16×C73—21no—
113C2×Q16×C73D411yescharacteristic, complemented
114C2×SD16×C73—28no—
115C2×SD16×C73—21no—
116C2×SD16×C73—21no—
117C2×SD16×C73—21no—
118C2×SD16×C73—21no—
119C2×SD16×C73—21no—
120C2×SD16×C73—21no—
121C2×SD16×C73—22no—
122C2×SD16×C73—21no—
123C2×SD16×C73—21no—
124C2×SD16×C73—22no—
125C2×SD16×C73—22no—
126C2×SD16×C73—41no—
127C2×SD16×C73D411yescharacteristic, complemented
128C2×SD16×C73D414yescomplemented
129C2×SD16×C73D411yescharacteristic, complemented
130C2×D8×C73—21no—
131C2×D8×C73—21no—
132C2×D8×C73—21no—
133C2×D8×C73—21no—
134C2×D8×C73—21no—
135C2×D8×C73—22no—
136C2×D8×C73—22no—
137C2×D8×C73—22no—
138C2×D8×C73—21no—
139C2×D8×C73—21no—
140C2×D8×C73—22no—
141C2×D8×C73—41no—
142C2×D8×C73D411yescharacteristic, complemented
143#131×C73—22no—
144#131×C73D414yescomplemented
145C2×M16×C73—21no—
146C2×M16×C73C2311yescharacteristic
147C2×M16×C73C2311yescharacteristic
148C2×M16×C73C2311yescharacteristic
149C2×M16×C73C2311yescharacteristic
150C22×C8×C73—21no—
151C22×C8×C73C2311yescharacteristic
152C22×C8×C73C2311yescharacteristic
153#127×C73—21no—
154#127×C73—21no—
155#127×C73—22no—
156#127×C73—22no—
157#124×C73—21no—
158#124×C73—21no—
159#124×C73—22no—
160#124×C73—22no—
161#121×C73—22no—
162#121×C73—22no—
163#120×C73—41no—
164#120×C73—41no—
165#117×C73C2311yescharacteristic
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×C73D412yescomplemented
174#102×C73—22no—
175#102×C73D412yescomplemented
176#101×C73—22no—
177#100×C73—22no—
178#100×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—21no—
187C24×C73—21no—
188C24×C73—41no—
189#41×C73—21no—
190#41×C73—21no—
191#41×C73—24no—
192#41×C73—24no—
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—21no—
201#41×C73—42no—
202#41×C73—44no—
203#41×C73—42no—
204#41×C73—42no—
205#41×C73—42no—
206#41×C73—44no—
207#41×C73—42no—
208#41×C73—42no—
209#41×C73C2×D412yes—
210#41×C73C2×D412yes—
211C2×Q8×C73—21no—
212C2×Q8×C73—24no—
213C2×Q8×C73—21no—
214C2×Q8×C73—21no—
215C2×Q8×C73—21no—
216C2×Q8×C73—21no—
217C2×Q8×C73—41no—
218C2×Q8×C73—42no—
219C2×Q8×C73—42no—
220C2×Q8×C73—42no—
221C2×Q8×C73C2×D411yescharacteristic
222C2×Q8×C73C2×D412yes—
223C2×Q8×C73C2×D411yescharacteristic
224C2×Q8×C73C2×D411yescharacteristic
225C2×D4×C73—21no—
226C2×D4×C73—24no—
227C2×D4×C73—21no—
228C2×D4×C73—21no—
229C2×D4×C73—21no—
230C2×D4×C73—21no—
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—42no—
247C2×D4×C73—41no—
248C2×D4×C73—41no—
249C2×D4×C73—44no—
250C2×D4×C73—42no—
251C2×D4×C73—42no—
252C2×D4×C73—42no—
253C2×D4×C73—44no—
254C2×D4×C73—44no—
255C2×D4×C73—41no—
256C2×D4×C73—42no—
257C2×D4×C73—84no—
258C2×D4×C73C2×D411yescharacteristic
259C2×D4×C73C2×D411yescharacteristic
260C2×D4×C73C2×D412yes—
261C2×D4×C73C2×D411yescharacteristic
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—41no—
268C22×C4×C73—41no—
269C22×C4×C73—41no—
270C22×C4×C73C2411yescharacteristic
271Q16×C73—24no—
272Q16×C73—22no—
273SD16×C73—24no—
274SD16×C73—24no—
275SD16×C73—22no—
276SD16×C73—24no—
277SD16×C73—24no—
278SD16×C73—22no—
279SD16×C73—44no—
280SD16×C73—42no—
281SD16×C73—42no—
282SD16×C73—42no—
283SD16×C73—42no—
284D8×C73—24no—
285D8×C73—22no—
286D8×C73—44no—
287D8×C73—42no—
288D8×C73—42no—
289D8×C73—42no—
290D8×C73—42no—
291D8×C73—42no—
292D8×C73—42no—
293M16×C73—21no—
294M16×C73—21no—
295M16×C73—24no—
296M16×C73—21no—
297M16×C73—21no—
298M16×C73—21no—
299M16×C73—21no—
300M16×C73C2×D412yes—
301M16×C73C2×D412yes—
302C2×C8×C73—21no—
303C2×C8×C73—21no—
304C2×C8×C73—21no—
305C2×C8×C73—21no—
306C2×C8×C73—24no—
307C2×C8×C73—21no—
308C2×C8×C73—21no—
309C2×C8×C73C2×D412yes—
310C2×C8×C73C2×D411yescharacteristic
311C2×C8×C73C2×D411yescharacteristic
312C2×C8×C73C2×D412yes—
313C2×C8×C73C2×D412yes—
314C4⋊C4×C73C2×D412yes—
315C22⋊C4×C73—21no—
316C22⋊C4×C73—44no—
317C22⋊C4×C73—42no—
318C22⋊C4×C73—42no—
319C42×C73—21no—
320C42×C73—21no—
321C42×C73C2×D412yes—
322C23×C73—21no—
323C23×C73—21no—
324C23×C73—21no—
325C23×C73—22no—
326C23×C73—44no—
327C23×C73—41no—
328C23×C73—41no—
329C23×C73—41no—
330C23×C73—41no—
331C23×C73—41no—
332C23×C73—41no—
333C23×C73—41no—
334C23×C73—41no—
335C23×C73—82no—
336C23×C73—82no—
337C23×C73—82no—
338C23×C73—162no—
339C23×C73H(5,𝔽2)11yescharacteristic
340Q8×C73—21no—
341Q8×C73—21no—
342Q8×C73—22no—
343Q8×C73—21no—
344Q8×C73—22no—
345Q8×C73—21no—
346Q8×C73—21no—
347Q8×C73—44no—
348Q8×C73—41no—
349Q8×C73—41no—
350Q8×C73#12712yes—
351D4×C73—22no—
352D4×C73—22no—
353D4×C73—21no—
354D4×C73—22no—
355D4×C73—21no—
356D4×C73—21no—
357D4×C73—22no—
358D4×C73—21no—
359D4×C73—21no—
360D4×C73—44no—
361D4×C73—44no—
362D4×C73—44no—
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—41no—
373D4×C73—41no—
374D4×C73—41no—
375D4×C73—41no—
376D4×C73—41no—
377D4×C73—88no—
378D4×C73—162no—
379D4×C73—162no—
380D4×C73#12712yes—
381C2×C4×C73—21no—
382C2×C4×C73—22no—
383C2×C4×C73—22no—
384C2×C4×C73—22no—
385C2×C4×C73—22no—
386C2×C4×C73—22no—
387C2×C4×C73—21no—
388C2×C4×C73—21no—
389C2×C4×C73—44no—
390C2×C4×C73—44no—
391C2×C4×C73—42no—
392C2×C4×C73—44no—
393C2×C4×C73—41no—
394C2×C4×C73—41no—
395C2×C4×C73—41no—
396C2×C4×C73—41no—
397C2×C4×C73—41no—
398C2×C4×C73—41no—
399C2×C4×C73C22×D411yescharacteristic
400C2×C4×C73C22×D411yescharacteristic
401C2×C4×C73C22×D411yescharacteristic
402C2×C4×C73C22×D411yescharacteristic
403C2×C4×C73C22×D411yescharacteristic
404C2×C4×C73H(5,𝔽2)11yescharacteristic
405C8×C73—22no—
406C8×C73—22no—
407C8×C73—22no—
408C8×C73—41no—
409C8×C73—41no—
410C8×C73#12012yes—
411C8×C73#12012yes—
412C22×C73—22no—
413C22×C73—22no—
414C22×C73—42no—
415C22×C73—41no—
416C22×C73—41no—
417C22×C73—42no—
418C22×C73—42no—
419C22×C73—42no—
420C22×C73—82no—
421C22×C73—82no—
422C22×C73—82no—
423C22×C73—82no—
424C22×C73—81no—
425C22×C73—81no—
426C22×C73—82no—
427C22×C73—82no—
428C22×C73—161no—
429C22×C73—161no—
430C22×C73—161no—
431C22×C73—164no—
432C22×C73#53511yescharacteristic
433C22×C73D4211yescharacteristic
434C22×C73D4211yescharacteristic
435C4×C73—22no—
436C4×C73—42no—
437C4×C73—41no—
438C4×C73—42no—
439C4×C73—41no—
440C4×C73—42no—
441C4×C73C2×#12011yescharacteristic
442C4×C73C2×#12711yescharacteristic
443C4×C73D4211yescharacteristic
444C4×C73D4211yescharacteristic
445#25807C7311yesmaximal, characteristic, direct product factor, Sylow
446C2×C73—21no—
447C2×C73—21no—
448C2×C73—42no—
449C2×C73—81no—
450C2×C73—81no—
451C2×C73—82no—
452C2×C73—161no—
453C2×C73—161no—
454C2×C73#243311yescharacteristic
455C2×C73#328812yes—
456C2×#577C2×C7311yescharacteristic, complemented
457#3155C2×C7311yescharacteristic, complemented
458C2×#496C2×C7311yescharacteristic, complemented
459C2×#472C2×C7311yescharacteristic, complemented
460C2×#454C2×C7311yescharacteristic, complemented
461C2×#453C2×C7311yescharacteristic, complemented
462#3010C2×C7311yescharacteristic, complemented
463#3008C2×C7311yescharacteristic, complemented
464#2019C2×C7311yescharacteristic, complemented
465#2018C2×C7311yescharacteristic, complemented
466#2004C2×C7311yescharacteristic, complemented
467#2002C2×C7311yescharacteristic, complemented
468#1977C2×C7311yescharacteristic, complemented
469#1975C2×C7311yescharacteristic, complemented
470#1765C2×C7311yescharacteristic, complemented
471C73#2580711yescharacteristic, direct product factor, Sylow
472C2×2−1+4C22×C7311yescharacteristic
473C2×H(5,𝔽2)C22×C7311yescharacteristic
474#577—24no—
475#577—24no—
476C2×#137—21no—
477C2×#137C22×C7311yescharacteristic
478C2×AGL(1,ℤ/8)—21no—
479C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
480C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
481C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
482C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
483C2×AGL(1,ℤ/8)C22×C7311yescharacteristic, complemented
484C2×#135—21no—
485C2×#135C22×C7311yescharacteristic
486C22×SD16—21no—
487C22×SD16C22×C7311yescharacteristic
488C22×SD16C22×C7311yescharacteristic, complemented
489C22×D8C22×C7311yescharacteristic
490C22×D8C22×C7311yescharacteristic, complemented
491C2×#131C22×C7311yescharacteristic
492#535C22×C7311yescharacteristic
493#535C22×C7311yescharacteristic, complemented
494C2×#127C22×C7311yescharacteristic
495C2×#124C22×C7311yescharacteristic, complemented
496#496—24no—
497#496—21no—
498#496—21no—
499#495—21no—
500#493—21no—
501#472—24no—
502#454—24no—
503#453—24no—
504#449—22no—
505#449—22no—
506#448—22no—
507#447—22no—
508C2×#108C22×C7311yescharacteristic, complemented
509C2×#104C22×C7311yescharacteristic
510C2×#104C22×C7311yescharacteristic
511C2×#104C22×C7311yescharacteristic, complemented
512#419C22×C7311yescharacteristic, complemented
513#418C22×C7311yescharacteristic
514#416C22×C7311yescharacteristic
515C2×#101C22×C7311yescharacteristic, complemented
516C2×#100C22×C7311yescharacteristic
517C2×#100C22×C7311yescharacteristic, complemented
518C2×#100C22×C7311yescharacteristic, complemented
519#408C22×C7311yescharacteristic
520#408C22×C7311yescharacteristic, complemented
521#405C22×C7311yescharacteristic, complemented
522C2×#97C22×C7311yescharacteristic, complemented
523#341C22×C7311yescharacteristic, complemented
524#339C22×C7311yescharacteristic, complemented
5252−1+4—22no—
5262−1+4—22no—
5272−1+4—22no—
5282−1+4—41no—
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—22no—
532H(5,𝔽2)—41no—
533C2×#41—21no—
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—41no—
538C2×#41C23×C7311yescharacteristic
539C2×#41C23×C7311yescharacteristic
540C2×#41C23×C7311yescharacteristic
541C22×Q8—21no—
542C22×Q8—21no—
543C22×Q8C23×C7311yescharacteristic
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—41no—
547C22×D4—41no—
548C22×D4C23×C7311yescharacteristic
549C22×D4C23×C7311yescharacteristic
550C22×D4C23×C7311yescharacteristic
551#137—28no—
552#137—22no—
553#137—22no—
554AGL(1,ℤ/8)—28no—
555AGL(1,ℤ/8)—22no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—41no—
564AGL(1,ℤ/8)—41no—
565#135—28no—
566#135—22no—
567#135—22no—
568C2×Q16—21no—
569C2×Q16D4×C7311yescharacteristic, complemented
570C2×SD16—28no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—41no—
583C2×SD16D4×C7311yescharacteristic, complemented
584C2×SD16D4×C7314yescomplemented
585C2×SD16D4×C7311yescharacteristic, complemented
586C2×D8—21no—
587C2×D8—22no—
588C2×D8—21no—
589C2×D8—21no—
590C2×D8—21no—
591C2×D8—21no—
592C2×D8—22no—
593C2×D8—22no—
594C2×D8—21no—
595C2×D8—21no—
596C2×D8—22no—
597C2×D8—41no—
598C2×D8D4×C7311yescharacteristic, complemented
599#131—22no—
600#131D4×C7314yescomplemented
601C2×M16—21no—
602C2×M16C23×C7311yescharacteristic
603C2×M16C23×C7311yescharacteristic
604C2×M16C23×C7311yescharacteristic
605C2×M16C23×C7311yescharacteristic
606C22×C8—21no—
607C22×C8C23×C7311yescharacteristic
608C22×C8C23×C7311yescharacteristic
609#127—22no—
610#127—21no—
611#127—21no—
612#127—22no—
613#124—22no—
614#124—21no—
615#124—21no—
616#124—22no—
617#121—22no—
618#121—22no—
619#120—41no—
620#120—41no—
621#117C23×C7311yescharacteristic
622C2×C22⋊C4—41no—
623C2×C42C23×C7311yescharacteristic
624#108—22no—
625#104—22no—
626#104—22no—
627#104D4×C7314yescomplemented
628#103—22no—
629#103D4×C7312yescomplemented
630#102—22no—
631#102D4×C7312yescomplemented
632#101—22no—
633#100—22no—
634#100—22no—
635#100—22no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638#97—22no—
639#97—21no—
640C4×C8—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—41no—
645#41—21no—
646#41—21no—
647#41—24no—
648#41—24no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—21no—
657#41—42no—
658#41—44no—
659#41—42no—
660#41—42no—
661#41—42no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C7312yes—
666#41C2×D4×C7312yes—
667C2×Q8—21no—
668C2×Q8—24no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—41no—
674C2×Q8—42no—
675C2×Q8—42no—
676C2×Q8—42no—
677C2×Q8C2×D4×C7311yescharacteristic
678C2×Q8C2×D4×C7312yes—
679C2×Q8C2×D4×C7311yescharacteristic
680C2×Q8C2×D4×C7311yescharacteristic
681C2×D4—21no—
682C2×D4—24no—
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—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—44no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—84no—
714C2×D4C2×D4×C7311yescharacteristic
715C2×D4C2×D4×C7311yescharacteristic
716C2×D4C2×D4×C7312yes—
717C2×D4C2×D4×C7311yescharacteristic
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—41no—
724C22×C4—41no—
725C22×C4—41no—
726C22×C4C24×C7311yescharacteristic
727Q16—24no—
728Q16—22no—
729SD16—24no—
730SD16—24no—
731SD16—22no—
732SD16—24no—
733SD16—24no—
734SD16—22no—
735SD16—44no—
736SD16—42no—
737SD16—42no—
738SD16—42no—
739SD16—42no—
740D8—24no—
741D8—22no—
742D8—44no—
743D8—42no—
744D8—42no—
745D8—42no—
746D8—42no—
747D8—42no—
748D8—42no—
749M16—21no—
750M16—21no—
751M16—24no—
752M16—21no—
753M16—21no—
754M16—21no—
755M16—21no—
756M16C2×D4×C7312yes—
757M16C2×D4×C7312yes—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—24no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8C2×D4×C7312yes—
766C2×C8C2×D4×C7311yescharacteristic
767C2×C8C2×D4×C7311yescharacteristic
768C2×C8C2×D4×C7312yes—
769C2×C8C2×D4×C7312yes—
770C4⋊C4C2×D4×C7312yes—
771C22⋊C4—21no—
772C22⋊C4—44no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C42—21no—
776C42—21no—
777C42C2×D4×C7312yes—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—22no—
782C23—44no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—82no—
792C23—82no—
793C23—82no—
794C23—162no—
795C23H(5,𝔽2)×C7311yescharacteristic
796Q8—21no—
797Q8—21no—
798Q8—22no—
799Q8—21no—
800Q8—22no—
801Q8—21no—
802Q8—21no—
803Q8—44no—
804Q8—41no—
805Q8—41no—
806Q8#127×C7312yes—
807D4—22no—
808D4—22no—
809D4—21no—
810D4—22no—
811D4—21no—
812D4—21no—
813D4—22no—
814D4—21no—
815D4—21no—
816D4—44no—
817D4—44no—
818D4—44no—
819D4—41no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—88no—
834D4—162no—
835D4—162no—
836D4#127×C7312yes—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4C22×D4×C7311yescharacteristic
856C2×C4C22×D4×C7311yescharacteristic
857C2×C4C22×D4×C7311yescharacteristic
858C2×C4C22×D4×C7311yescharacteristic
859C2×C4C22×D4×C7311yescharacteristic
860C2×C4H(5,𝔽2)×C7311yescharacteristic
861C8—22no—
862C8—22no—
863C8—22no—
864C8—41no—
865C8—41no—
866C8#120×C7312yes—
867C8#120×C7312yes—
868C22—22no—
869C22—22no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—42no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—81no—
883C22—81no—
884C22—161no—
885C22—161no—
886C22—161no—
887C22—164no—
888C22#535×C7311yescharacteristic
889C22D42×C7311yescharacteristic
890C22D42×C7311yescharacteristic
891C4—22no—
892C4—42no—
893C4—42no—
894C4—41no—
895C4—41no—
896C4—42no—
897C4C2×#120×C7311yescharacteristic
898C4C2×#127×C7311yescharacteristic
899C4D42×C7311yescharacteristic
900C4D42×C7311yescharacteristic
901C2—21no—
902C2—21no—
903C2—42no—
904C2—81no—
905C2—81no—
906C2—82no—
907C2—161no—
908C2—161no—
909C2C73×#243311yescharacteristic
910C2C73×#328812yes—
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×#3155C2semidirect
3. C2×#496×C73C2semidirect
4. C2×#472×C73C2semidirect
5. C2×#454×C73C2semidirect
6. C2×#453×C73C2semidirect
7. C73×#3010C2semidirect
8. C73×#3008C2semidirect
9. C73×#2019C2semidirect
10. C73×#2018C2semidirect
11. C73×#2004C2semidirect
12. C73×#2002C2semidirect
13. C73×#1977C2semidirect
14. C73×#1975C2semidirect
15. C73×#1765C2semidirect
27. C2×AGL(1,ℤ/8)×C73C22semidirect
32. C22×SD16×C73C22semidirect
34. C22×D8×C73C22semidirect
37. #535×C73C22semidirect
39. C2×#124×C73C22semidirect
52. C2×#108×C73C22semidirect
55. C2×#104×C73C22semidirect
56. #419×C73C22semidirect
59. C2×#101×C73C22semidirect
61. C2×#100×C73C22semidirect
62. C2×#100×C73C22semidirect
64. #408×C73C22semidirect
65. #405×C73C22semidirect
66. C2×#97×C73C22semidirect
67. #341×C73C22semidirect
68. #339×C73C22semidirect
113. C2×Q16×C73D4semidirect
127. C2×SD16×C73D4semidirect
128. C2×SD16×C73D4semidirect
129. C2×SD16×C73D4semidirect
142. C2×D8×C73D4semidirect
144. #131×C73D4semidirect
171. #104×C73D4semidirect
173. #103×C73D4semidirect
175. #102×C73D4semidirect
445. #25807C73direct (N × H)
456. C2×#577C2×C73semidirect
457. #3155C2×C73semidirect
458. C2×#496C2×C73semidirect
459. C2×#472C2×C73semidirect
460. C2×#454C2×C73semidirect
461. C2×#453C2×C73semidirect
462. #3010C2×C73semidirect
463. #3008C2×C73semidirect
464. #2019C2×C73semidirect
465. #2018C2×C73semidirect
466. #2004C2×C73semidirect
467. #2002C2×C73semidirect
468. #1977C2×C73semidirect
469. #1975C2×C73semidirect
470. #1765C2×C73semidirect
471. C73#25807direct (N × H)
483. C2×AGL(1,ℤ/8)C22×C73semidirect
488. C22×SD16C22×C73semidirect
490. C22×D8C22×C73semidirect
493. #535C22×C73semidirect
495. C2×#124C22×C73semidirect
508. C2×#108C22×C73semidirect
511. C2×#104C22×C73semidirect
512. #419C22×C73semidirect
515. C2×#101C22×C73semidirect
517. C2×#100C22×C73semidirect
518. C2×#100C22×C73semidirect
520. #408C22×C73semidirect
521. #405C22×C73semidirect
522. C2×#97C22×C73semidirect
523. #341C22×C73semidirect
524. #339C22×C73semidirect
569. C2×Q16D4×C73semidirect
583. C2×SD16D4×C73semidirect
584. C2×SD16D4×C73semidirect
585. C2×SD16D4×C73semidirect
598. C2×D8D4×C73semidirect
600. #131D4×C73semidirect
627. #104D4×C73semidirect
629. #103D4×C73semidirect
631. #102D4×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×#31552
C2×#496×C732
C2×#472×C732
C2×#454×C732
C2×#453×C732
C73×#30102
C73×#30082
C73×#20192
C73×#20182
C73×#20042
C73×#20022
C73×#19772
C73×#19752
C73×#17652
#2580773