Finite Group Databasebeta

← C73×#18262 #32927666

Subgroups — C73×#18262 #32927666

Order 18688.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3534C211yesmaximal, characteristic
2C73×#3094C211yesmaximal, characteristic, complemented
3C73×#3091C211yesmaximal, characteristic, complemented
4C73×#2498C211yesmaximal, characteristic, complemented
5C73×#1618C211yesmaximal, characteristic, complemented
6C73×#1616C211yesmaximal, characteristic, complemented
7C73×#1615C211yesmaximal, characteristic, complemented
8C73×#1613C211yesmaximal, characteristic, complemented
9C73×#1612C211yesmaximal, characteristic, complemented
10C73×#1610C211yesmaximal, characteristic, complemented
11C73×#1609C211yesmaximal, characteristic, complemented
12C73×#1607C211yesmaximal, characteristic, complemented
13C73×#1504C211yesmaximal, characteristic, complemented
14C2×#327×C73C211yesmaximal, characteristic, complemented
15C73×#1468C211yesmaximal, characteristic, complemented
16#562×C73—21no—
17#560×C73—21no—
18#553×C73—21no—
19#551×C73—21no—
20#546×C73—21no—
21#546×C73—21no—
22#546×C73—21no—
23D42×C73—21no—
24#540×C73—21no—
25#539×C73—21no—
26#539×C73C2211yescharacteristic
27#538×C73—21no—
28#538×C73C2211yescharacteristic
29#537×C73C2211yescharacteristic
30#534×C73—21no—
31#534×C73C2211yescharacteristic
32#525×C73C2211yescharacteristic
33C2×#123×C73C2211yescharacteristic
34C2×#121×C73C2211yescharacteristic
35C2×#117×C73C2211yescharacteristic, complemented
36#485×C73—21no—
37#484×C73C2211yescharacteristic, complemented
38#483×C73C2211yescharacteristic, complemented
39#482×C73—21no—
40#482×C73—21no—
41#482×C73—21no—
42#481×C73C2211yescharacteristic
43#481×C73C2211yescharacteristic, complemented
44#481×C73C2211yescharacteristic, complemented
45#480×C73C2211yescharacteristic
46#480×C73C2211yescharacteristic, complemented
47#480×C73C2211yescharacteristic, complemented
48#428×C73—21no—
49#427×C73—21no—
50#418×C73—21no—
51#416×C73—21no—
52#407×C73C2211yescharacteristic, complemented
53C2×C22⋊C8×C73C2211yescharacteristic, complemented
54#400×C73C2211yescharacteristic, complemented
55#399×C73C2211yescharacteristic, complemented
56#398×C73C2211yescharacteristic, complemented
57#397×C73C2211yescharacteristic, complemented
58#388×C73—21no—
59#387×C73—21no—
60#386×C73—21no—
61#380×C73—21no—
62C2×#95×C73C2211yescharacteristic, complemented
63#328×C73C2211yescharacteristic, complemented
64#328×C73C2211yescharacteristic, complemented
65#327×C73C2211yescharacteristic
66#327×C73C2211yescharacteristic
67#327×C73C2211yescharacteristic, complemented
68#327×C73C2211yescharacteristic, complemented
69#327×C73C2211yescharacteristic, complemented
70#327×C73C2211yescharacteristic, complemented
71#324×C73C2211yescharacteristic, complemented
72#324×C73C2211yescharacteristic, complemented
73#323×C73C2211yescharacteristic, complemented
74#323×C73C2211yescharacteristic, complemented
75C2×#41×C73—21no—
76C2×#41×C73D411yescharacteristic
77C22×D4×C73—21no—
78C22×D4×C73—21no—
79C22×D4×C73—21no—
80C22×D4×C73D411yescharacteristic
81C22×D4×C73D411yescharacteristic
82C23×C4×C73—21no—
83C23×C4×C73C2311yescharacteristic
84C2×M16×C73—21no—
85C22×C8×C73—21no—
86#127×C73—21no—
87#126×C73—21no—
88#126×C73—21no—
89#126×C73—21no—
90#126×C73—21no—
91#125×C73—21no—
92#125×C73—21no—
93#124×C73—21no—
94#124×C73—21no—
95#124×C73—21no—
96#123×C73—21no—
97#123×C73—21no—
98#123×C73—21no—
99#123×C73—21no—
100#123×C73—21no—
101#123×C73—21no—
102#123×C73—21no—
103#123×C73—21no—
104#123×C73—21no—
105#123×C73—21no—
106#123×C73—21no—
107#123×C73—21no—
108#123×C73—21no—
109#123×C73—21no—
110C22⋊Q8×C73—21no—
111C22⋊Q8×C73—21no—
112C22⋊Q8×C73—21no—
113C22⋊Q8×C73—21no—
114C22⋊Q8×C73—21no—
115C22⋊Q8×C73D411yescharacteristic
116C22⋊Q8×C73C2311yescharacteristic
117#121×C73—21no—
118#121×C73—21no—
119#121×C73—21no—
120#121×C73—21no—
121#121×C73—21no—
122#121×C73—21no—
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—21no—
130#121×C73—21no—
131#121×C73—21no—
132#121×C73D411yescharacteristic
133#121×C73D411yescharacteristic
134#121×C73D411yescharacteristic
135#121×C73C2311yescharacteristic
136#121×C73C2311yescharacteristic
137#121×C73C2311yescharacteristic
138#120×C73—21no—
139#120×C73—21no—
140#120×C73—21no—
141#120×C73—21no—
142#120×C73—21no—
143#120×C73—21no—
144#120×C73—21no—
145#120×C73—21no—
146C4×D4×C73—21no—
147C4×D4×C73—21no—
148C4×D4×C73—21no—
149C4×D4×C73—21no—
150C4×D4×C73—21no—
151C4×D4×C73—21no—
152C4×D4×C73—21no—
153C4×D4×C73—21no—
154#117×C73—21no—
155#117×C73—21no—
156#117×C73—21no—
157#117×C73—21no—
158#117×C73—21no—
159#117×C73D411yescharacteristic
160C2×C4⋊C4×C73—21no—
161C2×C4⋊C4×C73—21no—
162C2×C4⋊C4×C73D411yescharacteristic
163C2×C4⋊C4×C73D411yescharacteristic
164C2×C4⋊C4×C73C2311yescharacteristic
165C2×C4⋊C4×C73C2311yescharacteristic
166C2×C4⋊C4×C73C2311yescharacteristic
167C2×C22⋊C4×C73—21no—
168C2×C22⋊C4×C73—21no—
169C2×C22⋊C4×C73—21no—
170C2×C22⋊C4×C73—21no—
171C2×C22⋊C4×C73—21no—
172C2×C22⋊C4×C73—21no—
173C2×C22⋊C4×C73D411yescharacteristic
174C2×C22⋊C4×C73D411yescharacteristic
175C2×C22⋊C4×C73C2311yescharacteristic
176C2×C42×C73—21no—
177#107×C73—21no—
178#107×C73—21no—
179#107×C73—21no—
180#107×C73—21no—
181#106×C73—21no—
182#106×C73—21no—
183#106×C73—21no—
184#106×C73—21no—
185#103×C73—21no—
186#103×C73—21no—
187#102×C73—21no—
188#102×C73—21no—
189#102×C73—21no—
190#102×C73—21no—
191#102×C73—21no—
192#102×C73—21no—
193C22⋊C8×C73—21no—
194C22⋊C8×C73—21no—
195C22⋊C8×C73C2311yescharacteristic
196C22⋊C8×C73C2311yescharacteristic
197C22⋊C8×C73C2311yescharacteristic
198C22⋊C8×C73C2311yescharacteristic
199#95×C73—21no—
200#95×C73—21no—
201#95×C73—21no—
202#95×C73—21no—
203#95×C73—21no—
204#95×C73C2311yescharacteristic
205#95×C73C2311yescharacteristic
206C24×C73—21no—
207C24×C73—21no—
208C24×C73C2×D411yescharacteristic
209C24×C73C2×D411yescharacteristic
210#41×C73—42no—
211#41×C73—81no—
212#41×C73—81no—
213C2×Q8×C73—21no—
214C2×Q8×C73C2×D411yescharacteristic
215C2×D4×C73—21no—
216C2×D4×C73—21no—
217C2×D4×C73—21no—
218C2×D4×C73—21no—
219C2×D4×C73—21no—
220C2×D4×C73—21no—
221C2×D4×C73—21no—
222C2×D4×C73—21no—
223C2×D4×C73—21no—
224C2×D4×C73—21no—
225C2×D4×C73—21no—
226C2×D4×C73—21no—
227C2×D4×C73—21no—
228C2×D4×C73—21no—
229C2×D4×C73—21no—
230C2×D4×C73—21no—
231C2×D4×C73—21no—
232C2×D4×C73—42no—
233C2×D4×C73—42no—
234C2×D4×C73—81no—
235C2×D4×C73—81no—
236C2×D4×C73—81no—
237C2×D4×C73—81no—
238C2×D4×C73—82no—
239C2×D4×C73C2×D411yescharacteristic
240C2×D4×C73C2×D411yescharacteristic
241C2×D4×C73C2×D411yescharacteristic
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—42no—
254C22×C4×C73—42no—
255C22×C4×C73—42no—
256C22×C4×C73—81no—
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2×D411yescharacteristic
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2411yescharacteristic
266M16×C73—42no—
267C2×C8×C73—21no—
268C2×C8×C73—21no—
269C2×C8×C73—21no—
270C2×C8×C73—21no—
271C2×C8×C73—42no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73—21no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73—21no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—21no—
280C4⋊C4×C73—21no—
281C4⋊C4×C73—21no—
282C4⋊C4×C73—21no—
283C4⋊C4×C73—21no—
284C4⋊C4×C73—21no—
285C4⋊C4×C73—21no—
286C4⋊C4×C73—21no—
287C4⋊C4×C73—21no—
288C4⋊C4×C73—21no—
289C4⋊C4×C73—42no—
290C4⋊C4×C73—81no—
291C4⋊C4×C73C2×D411yescharacteristic
292C4⋊C4×C73C2×D411yescharacteristic
293C4⋊C4×C73C2×D411yescharacteristic
294C4⋊C4×C73C2×D411yescharacteristic
295C22⋊C4×C73—21no—
296C22⋊C4×C73—21no—
297C22⋊C4×C73—21no—
298C22⋊C4×C73—21no—
299C22⋊C4×C73—21no—
300C22⋊C4×C73—21no—
301C22⋊C4×C73—21no—
302C22⋊C4×C73—21no—
303C22⋊C4×C73—21no—
304C22⋊C4×C73—21no—
305C22⋊C4×C73—21no—
306C22⋊C4×C73—21no—
307C22⋊C4×C73—21no—
308C22⋊C4×C73—21no—
309C22⋊C4×C73—21no—
310C22⋊C4×C73—21no—
311C22⋊C4×C73—21no—
312C22⋊C4×C73—21no—
313C22⋊C4×C73—21no—
314C22⋊C4×C73—21no—
315C22⋊C4×C73—21no—
316C22⋊C4×C73—21no—
317C22⋊C4×C73—21no—
318C22⋊C4×C73—21no—
319C22⋊C4×C73—21no—
320C22⋊C4×C73—42no—
321C22⋊C4×C73—41no—
322C22⋊C4×C73—41no—
323C22⋊C4×C73—81no—
324C42×C73—21no—
325C42×C73—21no—
326C42×C73—21no—
327C42×C73—41no—
328C42×C73—41no—
329C23×C73—21no—
330C23×C73—21no—
331C23×C73—22no—
332C23×C73—21no—
333C23×C73—21no—
334C23×C73—21no—
335C23×C73—21no—
336C23×C73—21no—
337C23×C73—21no—
338C23×C73—41no—
339C23×C73—41no—
340C23×C73—41no—
341C23×C73—42no—
342C23×C73—81no—
343C23×C73—81no—
344C23×C73—81no—
345C23×C73—81no—
346C23×C73—81no—
347C23×C73#12011yescharacteristic
348C23×C73#12011yescharacteristic
349C23×C73C22×D411yescharacteristic
350Q8×C73—41no—
351Q8×C73—81no—
352D4×C73—41no—
353D4×C73—41no—
354D4×C73—41no—
355D4×C73—41no—
356D4×C73—41no—
357D4×C73—41no—
358D4×C73—41no—
359D4×C73—41no—
360D4×C73—41no—
361D4×C73—42no—
362D4×C73—42no—
363D4×C73—81no—
364D4×C73—81no—
365D4×C73—81no—
366D4×C73—81no—
367D4×C73—81no—
368D4×C73—81no—
369D4×C73—81no—
370D4×C73—81no—
371D4×C73—81no—
372D4×C73—81no—
373D4×C73—81no—
374D4×C73—81no—
375C2×C4×C73—22no—
376C2×C4×C73—22no—
377C2×C4×C73—22no—
378C2×C4×C73—21no—
379C2×C4×C73—21no—
380C2×C4×C73—21no—
381C2×C4×C73—21no—
382C2×C4×C73—21no—
383C2×C4×C73—21no—
384C2×C4×C73—21no—
385C2×C4×C73—21no—
386C2×C4×C73—21no—
387C2×C4×C73—21no—
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×C73—41no—
396C2×C4×C73—41no—
397C2×C4×C73—41no—
398C2×C4×C73—41no—
399C2×C4×C73—41no—
400C2×C4×C73—41no—
401C2×C4×C73—41no—
402C2×C4×C73—41no—
403C2×C4×C73—41no—
404C2×C4×C73—41no—
405C2×C4×C73—81no—
406C2×C4×C73—81no—
407C2×C4×C73—81no—
408C2×C4×C73—81no—
409C2×C4×C73—81no—
410C2×C4×C73—81no—
411C2×C4×C73—81no—
412C2×C4×C73—84no—
413C2×C4×C73#12011yescharacteristic
414C2×C4×C73#12011yescharacteristic
415C2×C4×C73C22×D411yescharacteristic
416C2×C4×C73C22×D411yescharacteristic
417C8×C73—41no—
418C8×C73—41no—
419C8×C73—41no—
420C8×C73—41no—
421C22×C73—21no—
422C22×C73—21no—
423C22×C73—21no—
424C22×C73—21no—
425C22×C73—21no—
426C22×C73—21no—
427C22×C73—21no—
428C22×C73—42no—
429C22×C73—42no—
430C22×C73—41no—
431C22×C73—41no—
432C22×C73—41no—
433C22×C73—41no—
434C22×C73—41no—
435C22×C73—41no—
436C22×C73—41no—
437C22×C73—41no—
438C22×C73—41no—
439C22×C73—41no—
440C22×C73—41no—
441C22×C73—41no—
442C22×C73—81no—
443C22×C73—81no—
444C22×C73—162no—
445C22×C73—162no—
446C22×C73#45812yes—
447C22×C73C2×#12011yescharacteristic
448C22×C73#57611yescharacteristic
449C22×C73#57711yescharacteristic
450C4×C73—21no—
451C4×C73—21no—
452C4×C73—21no—
453C4×C73—21no—
454C4×C73—42no—
455C4×C73—41no—
456C4×C73—41no—
457C4×C73—41no—
458C4×C73—41no—
459C4×C73—41no—
460C4×C73—41no—
461C4×C73—41no—
462C4×C73—41no—
463C4×C73—81no—
464C4×C73—81no—
465C4×C73—81no—
466#18262C7311yesmaximal, characteristic, direct product factor, Sylow
467C2×C73—21no—
468C2×C73—21no—
469C2×C73—22no—
470C2×C73—41no—
471C2×C73—81no—
472C2×C73—81no—
473C2×C73—81no—
474C2×C73—81no—
475C2×C73#301211yescharacteristic
476C2×C73#301811yescharacteristic
477C2×C73C2×#45811yescharacteristic
478#3534C2×C7311yescharacteristic
479#3094C2×C7311yescharacteristic, complemented
480#3091C2×C7311yescharacteristic, complemented
481#2498C2×C7311yescharacteristic, complemented
482#1618C2×C7311yescharacteristic, complemented
483#1616C2×C7311yescharacteristic, complemented
484#1615C2×C7311yescharacteristic, complemented
485#1613C2×C7311yescharacteristic, complemented
486#1612C2×C7311yescharacteristic, complemented
487#1610C2×C7311yescharacteristic, complemented
488#1609C2×C7311yescharacteristic, complemented
489#1607C2×C7311yescharacteristic, complemented
490#1504C2×C7311yescharacteristic, complemented
491C2×#327C2×C7311yescharacteristic, complemented
492#1468C2×C7311yescharacteristic, complemented
493C73#1826211yescharacteristic, direct product factor, Sylow
494#562—21no—
495#560—21no—
496#553—21no—
497#551—21no—
498#546—21no—
499#546—21no—
500#546—21no—
501D42—21no—
502#540—21no—
503#539—21no—
504#539C22×C7311yescharacteristic
505#538—21no—
506#538C22×C7311yescharacteristic
507#537C22×C7311yescharacteristic
508#534—21no—
509#534C22×C7311yescharacteristic
510#525C22×C7311yescharacteristic
511C2×#123C22×C7311yescharacteristic
512C2×#121C22×C7311yescharacteristic
513C2×#117C22×C7311yescharacteristic, complemented
514#485—21no—
515#484C22×C7311yescharacteristic, complemented
516#483C22×C7311yescharacteristic, complemented
517#482—21no—
518#482—21no—
519#482—21no—
520#481C22×C7311yescharacteristic
521#481C22×C7311yescharacteristic, complemented
522#481C22×C7311yescharacteristic, complemented
523#480C22×C7311yescharacteristic
524#480C22×C7311yescharacteristic, complemented
525#480C22×C7311yescharacteristic, complemented
526#428—21no—
527#427—21no—
528#418—21no—
529#416—21no—
530#407C22×C7311yescharacteristic, complemented
531C2×C22⋊C8C22×C7311yescharacteristic, complemented
532#400C22×C7311yescharacteristic, complemented
533#399C22×C7311yescharacteristic, complemented
534#398C22×C7311yescharacteristic, complemented
535#397C22×C7311yescharacteristic, complemented
536#388—21no—
537#387—21no—
538#386—21no—
539#380—21no—
540C2×#95C22×C7311yescharacteristic, complemented
541#328C22×C7311yescharacteristic, complemented
542#328C22×C7311yescharacteristic, complemented
543#327C22×C7311yescharacteristic
544#327C22×C7311yescharacteristic
545#327C22×C7311yescharacteristic, complemented
546#327C22×C7311yescharacteristic, complemented
547#327C22×C7311yescharacteristic, complemented
548#327C22×C7311yescharacteristic, complemented
549#324C22×C7311yescharacteristic, complemented
550#324C22×C7311yescharacteristic, complemented
551#323C22×C7311yescharacteristic, complemented
552#323C22×C7311yescharacteristic, complemented
553C2×#41—21no—
554C2×#41D4×C7311yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C7311yescharacteristic
559C22×D4D4×C7311yescharacteristic
560C23×C4—21no—
561C23×C4C23×C7311yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C7311yescharacteristic
594C22⋊Q8C23×C7311yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C7311yescharacteristic
611#121D4×C7311yescharacteristic
612#121D4×C7311yescharacteristic
613#121C23×C7311yescharacteristic
614#121C23×C7311yescharacteristic
615#121C23×C7311yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C7311yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C7311yescharacteristic
641C2×C4⋊C4D4×C7311yescharacteristic
642C2×C4⋊C4C23×C7311yescharacteristic
643C2×C4⋊C4C23×C7311yescharacteristic
644C2×C4⋊C4C23×C7311yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C7311yescharacteristic
652C2×C22⋊C4D4×C7311yescharacteristic
653C2×C22⋊C4C23×C7311yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C7311yescharacteristic
674C22⋊C8C23×C7311yescharacteristic
675C22⋊C8C23×C7311yescharacteristic
676C22⋊C8C23×C7311yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C7311yescharacteristic
683#95C23×C7311yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C7311yescharacteristic
687C24C2×D4×C7311yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C7311yescharacteristic
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—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C7311yescharacteristic
718C2×D4C2×D4×C7311yescharacteristic
719C2×D4C2×D4×C7311yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C7311yescharacteristic
736C22×C4C2×D4×C7311yescharacteristic
737C22×C4C2×D4×C7311yescharacteristic
738C22×C4C2×D4×C7311yescharacteristic
739C22×C4C2×D4×C7311yescharacteristic
740C22×C4C2×D4×C7311yescharacteristic
741C22×C4C2×D4×C7311yescharacteristic
742C22×C4C2×D4×C7311yescharacteristic
743C22×C4C24×C7311yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C7311yescharacteristic
770C4⋊C4C2×D4×C7311yescharacteristic
771C4⋊C4C2×D4×C7311yescharacteristic
772C4⋊C4C2×D4×C7311yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C7311yescharacteristic
826C23#120×C7311yescharacteristic
827C23C22×D4×C7311yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C7311yescharacteristic
892C2×C4#120×C7311yescharacteristic
893C2×C4C22×D4×C7311yescharacteristic
894C2×C4C22×D4×C7311yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22#458×C7312yes—
925C22C2×#120×C7311yescharacteristic
926C22#576×C7311yescharacteristic
927C22#577×C7311yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C73×#301211yescharacteristic
953C2C73×#301811yescharacteristic
954C2C2×#458×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3094C2semidirect
3. C73×#3091C2semidirect
4. C73×#2498C2semidirect
5. C73×#1618C2semidirect
6. C73×#1616C2semidirect
7. C73×#1615C2semidirect
8. C73×#1613C2semidirect
9. C73×#1612C2semidirect
10. C73×#1610C2semidirect
11. C73×#1609C2semidirect
12. C73×#1607C2semidirect
13. C73×#1504C2semidirect
14. C2×#327×C73C2semidirect
15. C73×#1468C2semidirect
35. C2×#117×C73C22semidirect
37. #484×C73C22semidirect
38. #483×C73C22semidirect
43. #481×C73C22semidirect
44. #481×C73C22semidirect
46. #480×C73C22semidirect
47. #480×C73C22semidirect
52. #407×C73C22semidirect
53. C2×C22⋊C8×C73C22semidirect
54. #400×C73C22semidirect
55. #399×C73C22semidirect
56. #398×C73C22semidirect
57. #397×C73C22semidirect
62. C2×#95×C73C22semidirect
63. #328×C73C22semidirect
64. #328×C73C22semidirect
67. #327×C73C22semidirect
68. #327×C73C22semidirect
69. #327×C73C22semidirect
70. #327×C73C22semidirect
71. #324×C73C22semidirect
72. #324×C73C22semidirect
73. #323×C73C22semidirect
74. #323×C73C22semidirect
466. #18262C73direct (N × H)
479. #3094C2×C73semidirect
480. #3091C2×C73semidirect
481. #2498C2×C73semidirect
482. #1618C2×C73semidirect
483. #1616C2×C73semidirect
484. #1615C2×C73semidirect
485. #1613C2×C73semidirect
486. #1612C2×C73semidirect
487. #1610C2×C73semidirect
488. #1609C2×C73semidirect
489. #1607C2×C73semidirect
490. #1504C2×C73semidirect
491. C2×#327C2×C73semidirect
492. #1468C2×C73semidirect
493. C73#18262direct (N × H)
513. C2×#117C22×C73semidirect
515. #484C22×C73semidirect
516. #483C22×C73semidirect
521. #481C22×C73semidirect
522. #481C22×C73semidirect
524. #480C22×C73semidirect
525. #480C22×C73semidirect
530. #407C22×C73semidirect
531. C2×C22⋊C8C22×C73semidirect
532. #400C22×C73semidirect
533. #399C22×C73semidirect
534. #398C22×C73semidirect
535. #397C22×C73semidirect
540. C2×#95C22×C73semidirect
541. #328C22×C73semidirect
542. #328C22×C73semidirect
545. #327C22×C73semidirect
546. #327C22×C73semidirect
547. #327C22×C73semidirect
548. #327C22×C73semidirect
549. #324C22×C73semidirect
550. #324C22×C73semidirect
551. #323C22×C73semidirect
552. #323C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35342
C73×#30942
C73×#30912
C73×#24982
C73×#16182
C73×#16162
C73×#16152
C73×#16132
C73×#16122
C73×#16102
C73×#16092
C73×#16072
C73×#15042
C2×#327×C732
C73×#14682
#1826273