Finite Group Databasebeta

← C73×#24031 #32933435

Subgroups — C73×#24031 #32933435

Order 18688.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3488C211yesmaximal, characteristic
2C73×#3093C211yesmaximal, characteristic, complemented
3C73×#2896C211yesmaximal, characteristic, complemented
4C73×#2500C211yesmaximal, characteristic, complemented
5C73×#2040C211yesmaximal, characteristic, complemented
6C73×#2039C211yesmaximal, characteristic, complemented
7C73×#2037C211yesmaximal, characteristic, complemented
8C73×#2037C211yesmaximal, characteristic, complemented
9C73×#1900C211yesmaximal, characteristic, complemented
10C73×#1871C211yesmaximal, characteristic, complemented
11C73×#1860C211yesmaximal, characteristic, complemented
12C73×#1859C211yesmaximal, characteristic, complemented
13C73×#1792C211yesmaximal, characteristic, complemented
14C73×#1792C211yesmaximal, characteristic, complemented
15C73×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C73C2211yescharacteristic
17C22×#41×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic, complemented
19#550×C73—21no—
20#548×C73—21no—
21#546×C73—21no—
22#546×C73—22no—
23D42×C73—22no—
24D42×C73—21no—
25#537×C73—21no—
26#537×C73C2211yescharacteristic
27#535×C73—21no—
28#535×C73C2211yescharacteristic
29#525×C73—21no—
30#525×C73C2211yescharacteristic
31C2×#121×C73—21no—
32C2×#121×C73C2211yescharacteristic
33#520×C73C2211yescharacteristic
34C2×#117×C73C2211yescharacteristic, complemented
35#485×C73—21no—
36#485×C73—21no—
37#482×C73—21no—
38#482×C73—21no—
39#428×C73C2211yescharacteristic, complemented
40#428×C73C2211yescharacteristic, complemented
41C2×#104×C73C2211yescharacteristic
42C2×#104×C73C2211yescharacteristic
43C2×#104×C73C2211yescharacteristic, complemented
44C2×#104×C73C2211yescharacteristic, complemented
45C2×#104×C73C2211yescharacteristic, complemented
46C2×#104×C73C2211yescharacteristic, complemented
47#419×C73—21no—
48#418×C73—21no—
49#417×C73C2211yescharacteristic
50#417×C73C2211yescharacteristic
51#417×C73C2211yescharacteristic, complemented
52#417×C73C2211yescharacteristic, complemented
53#417×C73C2211yescharacteristic, complemented
54#417×C73C2211yescharacteristic, complemented
55#416×C73—21no—
56#416×C73—21no—
57C2×#100×C73C2211yescharacteristic, complemented
58C2×#100×C73C2211yescharacteristic, complemented
59#407×C73C2211yescharacteristic, complemented
60#394×C73—22no—
61#390×C73C2211yescharacteristic, complemented
62#390×C73C2211yescharacteristic, complemented
63#388×C73—22no—
64#384×C73C2211yescharacteristic, complemented
65#382×C73C2211yescharacteristic, complemented
66C4×C22⋊C4×C73C2211yescharacteristic, complemented
67#343×C73C2211yescharacteristic, complemented
68#343×C73C2211yescharacteristic, complemented
69#339×C73C2211yescharacteristic, complemented
70#339×C73C2211yescharacteristic, complemented
71H(5,𝔽2)×C73—22no—
72H(5,𝔽2)×C73—22no—
73H(5,𝔽2)×C73—41no—
74H(5,𝔽2)×C73—41no—
75C2×#41×C73—21no—
76C2×#41×C73—21no—
77C2×#41×C73—21no—
78C2×#41×C73—21no—
79C2×#41×C73—22no—
80C2×#41×C73—22no—
81C2×#41×C73—41no—
82C2×#41×C73—41no—
83C2×#41×C73D411yescharacteristic
84C2×#41×C73D411yescharacteristic
85C2×#41×C73C2311yescharacteristic
86C2×#41×C73C2311yescharacteristic
87C2×#41×C73C2311yescharacteristic
88C22×Q8×C73D411yescharacteristic
89C22×D4×C73—21no—
90C22×D4×C73—22no—
91C22×D4×C73—22no—
92C22×D4×C73—21no—
93C22×D4×C73—21no—
94C22×D4×C73D411yescharacteristic
95C22×D4×C73D412yes—
96C22×D4×C73C2311yescharacteristic
97C23×C4×C73—21no—
98C23×C4×C73C2311yescharacteristic
99C2×M16×C73—21no—
100C2×M16×C73—41no—
101C2×M16×C73—41no—
102C2×M16×C73C2311yescharacteristic
103C2×M16×C73C2311yescharacteristic
104C2×M16×C73C2311yescharacteristic
105C2×M16×C73C2311yescharacteristic
106C22×C8×C73—21no—
107#127×C73—22no—
108#127×C73—21no—
109#124×C73—22no—
110#124×C73—21no—
111#123×C73—22no—
112#123×C73—21no—
113C22⋊Q8×C73—22no—
114C22⋊Q8×C73—21no—
115C22⋊Q8×C73—21no—
116C22⋊Q8×C73D411yescharacteristic
117C22⋊Q8×C73D411yescharacteristic
118#121×C73—22no—
119#121×C73—22no—
120#121×C73—22no—
121#121×C73—22no—
122#121×C73—22no—
123#121×C73—21no—
124#121×C73—21no—
125#121×C73—21no—
126#121×C73—21no—
127#121×C73—21no—
128#121×C73—21no—
129#121×C73—22no—
130#121×C73—21no—
131#121×C73—21no—
132#121×C73D411yescharacteristic
133#121×C73D411yescharacteristic
134#120×C73—22no—
135#120×C73—22no—
136#120×C73—22no—
137#120×C73—21no—
138#120×C73—22no—
139C4×Q8×C73—21no—
140C4×D4×C73—22no—
141C4×D4×C73—22no—
142C4×D4×C73—21no—
143C4×D4×C73—22no—
144C4×D4×C73—21no—
145C4×D4×C73—21no—
146#117×C73—21no—
147#117×C73—21no—
148#117×C73—21no—
149#117×C73—21no—
150#117×C73—21no—
151#117×C73C2311yescharacteristic
152C2×C4⋊C4×C73—21no—
153C2×C4⋊C4×C73—22no—
154C2×C4⋊C4×C73C2311yescharacteristic
155C2×C4⋊C4×C73C2311yescharacteristic
156C2×C4⋊C4×C73C2311yescharacteristic
157C2×C22⋊C4×C73—22no—
158C2×C22⋊C4×C73—21no—
159C2×C22⋊C4×C73—22no—
160C2×C22⋊C4×C73—21no—
161C2×C22⋊C4×C73—22no—
162C2×C22⋊C4×C73D412yes—
163C2×C42×C73—21no—
164C2×C42×C73C2311yescharacteristic
165C2×C42×C73C2311yescharacteristic
166#107×C73—21no—
167#107×C73—21no—
168#106×C73—21no—
169#106×C73—21no—
170#104×C73—22no—
171#104×C73—22no—
172#104×C73—41no—
173#104×C73—41no—
174#104×C73—41no—
175#104×C73—41no—
176#103×C73—21no—
177#103×C73—21no—
178#103×C73—21no—
179#103×C73—21no—
180#103×C73—21no—
181#103×C73—21no—
182#102×C73—21no—
183#102×C73—21no—
184#102×C73—21no—
185#102×C73—21no—
186#102×C73—21no—
187#102×C73—21no—
188#100×C73—41no—
189#100×C73—41no—
190C22⋊C8×C73—21no—
191C22⋊C8×C73—21no—
192#95×C73—21no—
193#95×C73—22no—
194C24×C73—22no—
195C24×C73—21no—
196C24×C73C2×D412yes—
197C24×C73C2×D411yescharacteristic
198#41×C73—21no—
199#41×C73—21no—
200#41×C73—22no—
201#41×C73—22no—
202#41×C73—21no—
203#41×C73—21no—
204#41×C73—21no—
205#41×C73—21no—
206#41×C73—21no—
207#41×C73—21no—
208#41×C73—21no—
209#41×C73—21no—
210#41×C73—42no—
211#41×C73—42no—
212#41×C73—41no—
213#41×C73—41no—
214#41×C73—42no—
215#41×C73—42no—
216#41×C73—42no—
217#41×C73—42no—
218#41×C73—42no—
219#41×C73—42no—
220#41×C73#4112yes—
221#41×C73#4112yes—
222C2×Q8×C73—21no—
223C2×Q8×C73—22no—
224C2×Q8×C73—41no—
225C2×Q8×C73C2×D411yescharacteristic
226C2×Q8×C73C2×D411yescharacteristic
227C2×Q8×C73C2×D411yescharacteristic
228C2×D4×C73—21no—
229C2×D4×C73—22no—
230C2×D4×C73—22no—
231C2×D4×C73—22no—
232C2×D4×C73—22no—
233C2×D4×C73—21no—
234C2×D4×C73—21no—
235C2×D4×C73—21no—
236C2×D4×C73—21no—
237C2×D4×C73—21no—
238C2×D4×C73—22no—
239C2×D4×C73—22no—
240C2×D4×C73—22no—
241C2×D4×C73—21no—
242C2×D4×C73—22no—
243C2×D4×C73—21no—
244C2×D4×C73—21no—
245C2×D4×C73—21no—
246C2×D4×C73—21no—
247C2×D4×C73—21no—
248C2×D4×C73—21no—
249C2×D4×C73—21no—
250C2×D4×C73—41no—
251C2×D4×C73—42no—
252C2×D4×C73—42no—
253C2×D4×C73—42no—
254C2×D4×C73—42no—
255C2×D4×C73—44no—
256C2×D4×C73—44no—
257C2×D4×C73—42no—
258C2×D4×C73—42no—
259C2×D4×C73—82no—
260C2×D4×C73—84no—
261C2×D4×C73C2×D411yescharacteristic
262C2×D4×C73C2×D411yescharacteristic
263C2×D4×C73C2×D411yescharacteristic
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—22no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—22no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73—42no—
281C22×C4×C73—42no—
282C22×C4×C73C2×D411yescharacteristic
283C22×C4×C73C2×D411yescharacteristic
284C22×C4×C73C2×D411yescharacteristic
285C22×C4×C73C2×D411yescharacteristic
286C22×C4×C73C2×D411yescharacteristic
287C22×C4×C73C2×D412yes—
288C22×C4×C73C2411yescharacteristic
289M16×C73—21no—
290M16×C73—21no—
291M16×C73—21no—
292M16×C73—21no—
293M16×C73—21no—
294M16×C73—21no—
295M16×C73—21no—
296M16×C73—21no—
297M16×C73—42no—
298C2×C8×C73—21no—
299C2×C8×C73—21no—
300C2×C8×C73—21no—
301C2×C8×C73—21no—
302C2×C8×C73—42no—
303C4⋊C4×C73—22no—
304C4⋊C4×C73—22no—
305C4⋊C4×C73—21no—
306C4⋊C4×C73—21no—
307C4⋊C4×C73—21no—
308C4⋊C4×C73—21no—
309C4⋊C4×C73—21no—
310C4⋊C4×C73—21no—
311C4⋊C4×C73—21no—
312C4⋊C4×C73—21no—
313C4⋊C4×C73—82no—
314C4⋊C4×C73C2×D411yescharacteristic
315C4⋊C4×C73C2×D411yescharacteristic
316C22⋊C4×C73—22no—
317C22⋊C4×C73—22no—
318C22⋊C4×C73—22no—
319C22⋊C4×C73—22no—
320C22⋊C4×C73—22no—
321C22⋊C4×C73—21no—
322C22⋊C4×C73—21no—
323C22⋊C4×C73—21no—
324C22⋊C4×C73—21no—
325C22⋊C4×C73—22no—
326C22⋊C4×C73—22no—
327C22⋊C4×C73—21no—
328C22⋊C4×C73—42no—
329C22⋊C4×C73—44no—
330C22⋊C4×C73—41no—
331C22⋊C4×C73—41no—
332C22⋊C4×C73—82no—
333C42×C73—22no—
334C42×C73—21no—
335C42×C73—21no—
336C42×C73—21no—
337C42×C73—21no—
338C42×C73—21no—
339C42×C73—41no—
340C42×C73—41no—
341C23×C73—21no—
342C23×C73—21no—
343C23×C73—21no—
344C23×C73—22no—
345C23×C73—21no—
346C23×C73—21no—
347C23×C73—22no—
348C23×C73—22no—
349C23×C73—41no—
350C23×C73—41no—
351C23×C73—42no—
352C23×C73—42no—
353C23×C73—44no—
354C23×C73—42no—
355C23×C73—42no—
356C23×C73—81no—
357C23×C73—82no—
358C23×C73—82no—
359C23×C73#12011yescharacteristic
360C23×C73#12011yescharacteristic
361C23×C73C22×D411yescharacteristic
362Q8×C73—21no—
363Q8×C73—21no—
364Q8×C73—21no—
365Q8×C73—21no—
366Q8×C73—21no—
367Q8×C73—42no—
368Q8×C73#12312yes—
369D4×C73—22no—
370D4×C73—22no—
371D4×C73—21no—
372D4×C73—21no—
373D4×C73—21no—
374D4×C73—21no—
375D4×C73—21no—
376D4×C73—42no—
377D4×C73—42no—
378D4×C73—44no—
379D4×C73—42no—
380D4×C73—44no—
381D4×C73—44no—
382D4×C73—42no—
383D4×C73—41no—
384D4×C73—41no—
385D4×C73—41no—
386D4×C73—41no—
387D4×C73—41no—
388D4×C73—41no—
389D4×C73—41no—
390D4×C73—41no—
391D4×C73—81no—
392D4×C73—82no—
393D4×C73—82no—
394D4×C73—82no—
395D4×C73—82no—
396D4×C73#12312yes—
397C2×C4×C73—21no—
398C2×C4×C73—21no—
399C2×C4×C73—21no—
400C2×C4×C73—21no—
401C2×C4×C73—21no—
402C2×C4×C73—21no—
403C2×C4×C73—21no—
404C2×C4×C73—21no—
405C2×C4×C73—21no—
406C2×C4×C73—21no—
407C2×C4×C73—21no—
408C2×C4×C73—22no—
409C2×C4×C73—22no—
410C2×C4×C73—22no—
411C2×C4×C73—21no—
412C2×C4×C73—22no—
413C2×C4×C73—21no—
414C2×C4×C73—21no—
415C2×C4×C73—21no—
416C2×C4×C73—42no—
417C2×C4×C73—42no—
418C2×C4×C73—42no—
419C2×C4×C73—44no—
420C2×C4×C73—41no—
421C2×C4×C73—41no—
422C2×C4×C73—41no—
423C2×C4×C73—41no—
424C2×C4×C73—41no—
425C2×C4×C73—41no—
426C2×C4×C73—42no—
427C2×C4×C73—41no—
428C2×C4×C73—42no—
429C2×C4×C73—41no—
430C2×C4×C73—42no—
431C2×C4×C73—41no—
432C2×C4×C73—41no—
433C2×C4×C73—41no—
434C2×C4×C73—82no—
435C2×C4×C73#12011yescharacteristic
436C2×C4×C73#12011yescharacteristic
437C2×C4×C73C22×D411yescharacteristic
438C2×C4×C73C22×D411yescharacteristic
439C2×C4×C73C2×#4111yescharacteristic
440C2×C4×C73C2×#4111yescharacteristic
441C2×C4×C73H(5,𝔽2)11yescharacteristic
442C2×C4×C73H(5,𝔽2)11yescharacteristic
443C8×C73—41no—
444C8×C73—41no—
445C8×C73—41no—
446C8×C73—41no—
447C22×C73—21no—
448C22×C73—21no—
449C22×C73—21no—
450C22×C73—21no—
451C22×C73—22no—
452C22×C73—21no—
453C22×C73—21no—
454C22×C73—21no—
455C22×C73—21no—
456C22×C73—41no—
457C22×C73—41no—
458C22×C73—41no—
459C22×C73—41no—
460C22×C73—42no—
461C22×C73—41no—
462C22×C73—42no—
463C22×C73—41no—
464C22×C73—42no—
465C22×C73—41no—
466C22×C73—41no—
467C22×C73—81no—
468C22×C73—81no—
469C22×C73—82no—
470C22×C73—82no—
471C22×C73—84no—
472C22×C73—164no—
473C22×C73C2×#12011yescharacteristic
474C22×C73#54611yescharacteristic
475C22×C73#54611yescharacteristic
476C4×C73—21no—
477C4×C73—21no—
478C4×C73—22no—
479C4×C73—42no—
480C4×C73—41no—
481C4×C73—41no—
482C4×C73—41no—
483C4×C73—42no—
484C4×C73—41no—
485C4×C73—81no—
486C4×C73—81no—
487C4×C73—81no—
488C4×C73C2×#12311yescharacteristic
489C4×C73#53411yescharacteristic
490C4×C73#54611yescharacteristic
491C4×C73#54611yescharacteristic
492#24031C7311yesmaximal, characteristic, direct product factor, Sylow
493C2×C73—21no—
494C2×C73—21no—
495C2×C73—41no—
496C2×C73—41no—
497C2×C73—42no—
498C2×C73—81no—
499C2×C73—82no—
500C2×C73—81no—
501C2×C73#240511yescharacteristic
502C2×C73#301811yescharacteristic
503C2×C73#301911yescharacteristic
504#3488C2×C7311yescharacteristic
505#3093C2×C7311yescharacteristic, complemented
506#2896C2×C7311yescharacteristic, complemented
507#2500C2×C7311yescharacteristic, complemented
508#2040C2×C7311yescharacteristic, complemented
509#2039C2×C7311yescharacteristic, complemented
510#2037C2×C7311yescharacteristic, complemented
511#2037C2×C7311yescharacteristic, complemented
512#1900C2×C7311yescharacteristic, complemented
513#1871C2×C7311yescharacteristic, complemented
514#1860C2×C7311yescharacteristic, complemented
515#1859C2×C7311yescharacteristic, complemented
516#1792C2×C7311yescharacteristic, complemented
517#1792C2×C7311yescharacteristic, complemented
518#1789C2×C7311yescharacteristic, complemented
519C73#2403111yescharacteristic, direct product factor, Sylow
520C2×H(5,𝔽2)C22×C7311yescharacteristic
521C22×#41C22×C7311yescharacteristic
522C22×M16C22×C7311yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C7311yescharacteristic
531#535—21no—
532#535C22×C7311yescharacteristic
533#525—21no—
534#525C22×C7311yescharacteristic
535C2×#121—21no—
536C2×#121C22×C7311yescharacteristic
537#520C22×C7311yescharacteristic
538C2×#117C22×C7311yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C7311yescharacteristic, complemented
544#428C22×C7311yescharacteristic, complemented
545C2×#104C22×C7311yescharacteristic
546C2×#104C22×C7311yescharacteristic
547C2×#104C22×C7311yescharacteristic, complemented
548C2×#104C22×C7311yescharacteristic, complemented
549C2×#104C22×C7311yescharacteristic, complemented
550C2×#104C22×C7311yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C7311yescharacteristic
554#417C22×C7311yescharacteristic
555#417C22×C7311yescharacteristic, complemented
556#417C22×C7311yescharacteristic, complemented
557#417C22×C7311yescharacteristic, complemented
558#417C22×C7311yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C7311yescharacteristic, complemented
562C2×#100C22×C7311yescharacteristic, complemented
563#407C22×C7311yescharacteristic, complemented
564#394—22no—
565#390C22×C7311yescharacteristic, complemented
566#390C22×C7311yescharacteristic, complemented
567#388—22no—
568#384C22×C7311yescharacteristic, complemented
569#382C22×C7311yescharacteristic, complemented
570C4×C22⋊C4C22×C7311yescharacteristic, complemented
571#343C22×C7311yescharacteristic, complemented
572#343C22×C7311yescharacteristic, complemented
573#339C22×C7311yescharacteristic, complemented
574#339C22×C7311yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C7311yescharacteristic
588C2×#41D4×C7311yescharacteristic
589C2×#41C23×C7311yescharacteristic
590C2×#41C23×C7311yescharacteristic
591C2×#41C23×C7311yescharacteristic
592C22×Q8D4×C7311yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C7311yescharacteristic
599C22×D4D4×C7312yes—
600C22×D4C23×C7311yescharacteristic
601C23×C4—21no—
602C23×C4C23×C7311yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C7311yescharacteristic
607C2×M16C23×C7311yescharacteristic
608C2×M16C23×C7311yescharacteristic
609C2×M16C23×C7311yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C7311yescharacteristic
621C22⋊Q8D4×C7311yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C7311yescharacteristic
637#121D4×C7311yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C7311yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C7311yescharacteristic
659C2×C4⋊C4C23×C7311yescharacteristic
660C2×C4⋊C4C23×C7311yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C7312yes—
667C2×C42—21no—
668C2×C42C23×C7311yescharacteristic
669C2×C42C23×C7311yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C7312yes—
701C24C2×D4×C7311yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C7312yes—
725#41#41×C7312yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C7311yescharacteristic
730C2×Q8C2×D4×C7311yescharacteristic
731C2×Q8C2×D4×C7311yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C7311yescharacteristic
766C2×D4C2×D4×C7311yescharacteristic
767C2×D4C2×D4×C7311yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C7311yescharacteristic
787C22×C4C2×D4×C7311yescharacteristic
788C22×C4C2×D4×C7311yescharacteristic
789C22×C4C2×D4×C7311yescharacteristic
790C22×C4C2×D4×C7311yescharacteristic
791C22×C4C2×D4×C7312yes—
792C22×C4C24×C7311yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C7311yescharacteristic
819C4⋊C4C2×D4×C7311yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C7311yescharacteristic
864C23#120×C7311yescharacteristic
865C23C22×D4×C7311yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C7312yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C7312yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C7311yescharacteristic
940C2×C4#120×C7311yescharacteristic
941C2×C4C22×D4×C7311yescharacteristic
942C2×C4C22×D4×C7311yescharacteristic
943C2×C4C2×#41×C7311yescharacteristic
944C2×C4C2×#41×C7311yescharacteristic
945C2×C4H(5,𝔽2)×C7311yescharacteristic
946C2×C4H(5,𝔽2)×C7311yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—22no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C7311yescharacteristic
978C22#546×C7311yescharacteristic
979C22#546×C7311yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—42no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C7311yescharacteristic
993C4#534×C7311yescharacteristic
994C4#546×C7311yescharacteristic
995C4#546×C7311yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C73×#240511yescharacteristic
1005C2C73×#301811yescharacteristic
1006C2C73×#301911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3488C2
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
2. C73×#3093C2semidirect
3. C73×#2896C2semidirect
4. C73×#2500C2semidirect
5. C73×#2040C2semidirect
6. C73×#2039C2semidirect
7. C73×#2037C2semidirect
8. C73×#2037C2semidirect
9. C73×#1900C2semidirect
10. C73×#1871C2semidirect
11. C73×#1860C2semidirect
12. C73×#1859C2semidirect
13. C73×#1792C2semidirect
14. C73×#1792C2semidirect
15. C73×#1789C2semidirect
18. C22×M16×C73C22semidirect
34. C2×#117×C73C22semidirect
39. #428×C73C22semidirect
40. #428×C73C22semidirect
43. C2×#104×C73C22semidirect
44. C2×#104×C73C22semidirect
45. C2×#104×C73C22semidirect
46. C2×#104×C73C22semidirect
51. #417×C73C22semidirect
52. #417×C73C22semidirect
53. #417×C73C22semidirect
54. #417×C73C22semidirect
57. C2×#100×C73C22semidirect
58. C2×#100×C73C22semidirect
59. #407×C73C22semidirect
61. #390×C73C22semidirect
62. #390×C73C22semidirect
64. #384×C73C22semidirect
65. #382×C73C22semidirect
66. C4×C22⋊C4×C73C22semidirect
67. #343×C73C22semidirect
68. #343×C73C22semidirect
69. #339×C73C22semidirect
70. #339×C73C22semidirect
492. #24031C73direct (N × H)
505. #3093C2×C73semidirect
506. #2896C2×C73semidirect
507. #2500C2×C73semidirect
508. #2040C2×C73semidirect
509. #2039C2×C73semidirect
510. #2037C2×C73semidirect
511. #2037C2×C73semidirect
512. #1900C2×C73semidirect
513. #1871C2×C73semidirect
514. #1860C2×C73semidirect
515. #1859C2×C73semidirect
516. #1792C2×C73semidirect
517. #1792C2×C73semidirect
518. #1789C2×C73semidirect
519. C73#24031direct (N × H)
522. C22×M16C22×C73semidirect
538. C2×#117C22×C73semidirect
543. #428C22×C73semidirect
544. #428C22×C73semidirect
547. C2×#104C22×C73semidirect
548. C2×#104C22×C73semidirect
549. C2×#104C22×C73semidirect
550. C2×#104C22×C73semidirect
555. #417C22×C73semidirect
556. #417C22×C73semidirect
557. #417C22×C73semidirect
558. #417C22×C73semidirect
561. C2×#100C22×C73semidirect
562. C2×#100C22×C73semidirect
563. #407C22×C73semidirect
565. #390C22×C73semidirect
566. #390C22×C73semidirect
568. #384C22×C73semidirect
569. #382C22×C73semidirect
570. C4×C22⋊C4C22×C73semidirect
571. #343C22×C73semidirect
572. #343C22×C73semidirect
573. #339C22×C73semidirect
574. #339C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34882
C73×#30932
C73×#28962
C73×#25002
C73×#20402
C73×#20392
C73×#20372
C73×#19002
C73×#18712
C73×#18602
C73×#18592
C73×#17922
C73×#17892
#2403173