Finite Group Databasebeta

← C73×#18414 #32927818

Subgroups — C73×#18414 #32927818

Order 18688.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3534C211yesmaximal, characteristic, complemented
2C73×#3194C211yesmaximal, characteristic, complemented
3C73×#3186C211yesmaximal, characteristic, complemented
4C73×#2661C211yesmaximal, characteristic, complemented
5C73×#1612C211yesmaximal, characteristic, complemented
6C73×#1610C211yesmaximal, characteristic, complemented
7C73×#1609C211yesmaximal, characteristic, complemented
8C73×#1607C211yesmaximal, characteristic, complemented
9C73×#1600C211yesmaximal, characteristic, complemented
10C73×#1598C211yesmaximal, characteristic, complemented
11C73×#1597C211yesmaximal, characteristic, complemented
12C73×#1595C211yesmaximal, characteristic, complemented
13C73×#1507C211yesmaximal, characteristic, complemented
14C73×#1501C211yesmaximal, 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×#121×C73C2211yescharacteristic, complemented
36#483×C73C2211yescharacteristic, complemented
37#482×C73—21no—
38#480×C73—21no—
39#480×C73C2211yescharacteristic
40#480×C73C2211yescharacteristic, complemented
41#480×C73C2211yescharacteristic, complemented
42#469×C73—21no—
43#468×C73—21no—
44#466×C73—21no—
45#466×C73—21no—
46#450×C73C2211yescharacteristic, complemented
47#449×C73—21no—
48#447×C73—21no—
49#447×C73C2211yescharacteristic
50#447×C73C2211yescharacteristic, complemented
51#447×C73C2211yescharacteristic, complemented
52#407×C73C2211yescharacteristic, complemented
53C2×C22⋊C8×C73C2211yescharacteristic, complemented
54#398×C73C2211yescharacteristic, complemented
55#397×C73C2211yescharacteristic, complemented
56#394×C73—21no—
57#394×C73C2211yescharacteristic, complemented
58#392×C73—21no—
59#392×C73C2211yescharacteristic, complemented
60#390×C73—21no—
61#388×C73—21no—
62C4×C22⋊C4×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, complemented
77C22×D4×C73—21no—
78C22×D4×C73—21no—
79C22×D4×C73—21no—
80C22×D4×C73—21no—
81C22×D4×C73—21no—
82C22×D4×C73D411yescharacteristic
83C22×D4×C73D411yescharacteristic, complemented
84C22×D4×C73C2311yescharacteristic
85C23×C4×C73C2311yescharacteristic
86C2×SD16×C73—21no—
87C2×D8×C73—21no—
88C2×D8×C73—21no—
89C2×D8×C73—21no—
90C2×M16×C73—21no—
91C22×C8×C73—21no—
92#127×C73—21no—
93#126×C73—21no—
94#126×C73—21no—
95#126×C73—21no—
96#126×C73—21no—
97#125×C73—21no—
98#125×C73—21no—
99#124×C73—21no—
100#124×C73—21no—
101#124×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—
110#123×C73—21no—
111#123×C73—21no—
112#123×C73—21no—
113#123×C73—21no—
114#123×C73—21no—
115#123×C73—21no—
116C22⋊Q8×C73—21no—
117C22⋊Q8×C73—21no—
118C22⋊Q8×C73—21no—
119C22⋊Q8×C73—21no—
120C22⋊Q8×C73—21no—
121C22⋊Q8×C73D411yescharacteristic, complemented
122C22⋊Q8×C73C2311yescharacteristic
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×C73—21no—
133#121×C73—21no—
134#121×C73—21no—
135#121×C73—21no—
136#121×C73—21no—
137#121×C73—21no—
138#121×C73—21no—
139#121×C73—21no—
140#121×C73—21no—
141#121×C73—21no—
142#121×C73D411yescharacteristic, complemented
143#121×C73D411yescharacteristic, complemented
144#121×C73D411yescharacteristic, complemented
145#121×C73C2311yescharacteristic
146#121×C73C2311yescharacteristic
147#121×C73C2311yescharacteristic
148#120×C73—21no—
149#120×C73—21no—
150#120×C73—21no—
151#120×C73—21no—
152#120×C73—21no—
153#120×C73—21no—
154#120×C73—21no—
155#120×C73—21no—
156C4×D4×C73—21no—
157C4×D4×C73—21no—
158C4×D4×C73—21no—
159C4×D4×C73—21no—
160C4×D4×C73—21no—
161C4×D4×C73—21no—
162C4×D4×C73—21no—
163C4×D4×C73—21no—
164#117×C73—21no—
165#117×C73D411yescharacteristic, complemented
166C2×C4⋊C4×C73—21no—
167C2×C4⋊C4×C73D411yescharacteristic
168C2×C4⋊C4×C73D411yescharacteristic, complemented
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C22⋊C4×C73—21no—
172C2×C22⋊C4×C73—21no—
173C2×C22⋊C4×C73—21no—
174C2×C22⋊C4×C73—21no—
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73—21no—
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180C2×C22⋊C4×C73D411yescharacteristic
181C2×C22⋊C4×C73D411yescharacteristic
182C2×C22⋊C4×C73C2311yescharacteristic
183C2×C42×C73—21no—
184#107×C73—21no—
185#107×C73—21no—
186#107×C73—21no—
187#106×C73—21no—
188#103×C73—21no—
189#102×C73—21no—
190#102×C73—21no—
191#102×C73—21no—
192#102×C73—21no—
193#102×C73—21no—
194#102×C73—21no—
195#102×C73—21no—
196C22⋊C8×C73—21no—
197C22⋊C8×C73—21no—
198C22⋊C8×C73C2311yescharacteristic
199C22⋊C8×C73C2311yescharacteristic
200C22⋊C8×C73C2311yescharacteristic
201C22⋊C8×C73C2311yescharacteristic
202#95×C73—21no—
203#95×C73—21no—
204#95×C73C2311yescharacteristic
205#95×C73C2311yescharacteristic
206C24×C73—21no—
207C24×C73—21no—
208C24×C73—21no—
209C24×C73C2×D411yescharacteristic
210C24×C73C2×D411yescharacteristic
211#41×C73—81no—
212#41×C73—81no—
213#41×C73—81no—
214C2×Q8×C73—21no—
215C2×Q8×C73C2×D411yescharacteristic
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—21no—
233C2×D4×C73—21no—
234C2×D4×C73—21no—
235C2×D4×C73—42no—
236C2×D4×C73—41no—
237C2×D4×C73—41no—
238C2×D4×C73—81no—
239C2×D4×C73—81no—
240C2×D4×C73—81no—
241C2×D4×C73—81no—
242C2×D4×C73—81no—
243C2×D4×C73—81no—
244C2×D4×C73—81no—
245C2×D4×C73—81no—
246C2×D4×C73—81no—
247C2×D4×C73—81no—
248C2×D4×C73—81no—
249C2×D4×C73—82no—
250C2×D4×C73C2×D411yescharacteristic
251C2×D4×C73C2×D411yescharacteristic
252C2×D4×C73C2×D411yescharacteristic
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—81no—
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2×D411yescharacteristic
266C22×C4×C73C2×D411yescharacteristic
267C22×C4×C73C2×D411yescharacteristic
268C22×C4×C73C2×D411yescharacteristic
269C22×C4×C73C2×D411yescharacteristic
270C22×C4×C73C2×D411yescharacteristic
271C22×C4×C73C2×D411yescharacteristic
272C22×C4×C73C2411yescharacteristic
273SD16×C73—81no—
274D8×C73—81no—
275D8×C73—81no—
276D8×C73—81no—
277M16×C73—81no—
278C2×C8×C73—21no—
279C2×C8×C73—21no—
280C2×C8×C73—21no—
281C2×C8×C73—21no—
282C2×C8×C73—81no—
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—21no—
290C4⋊C4×C73—21no—
291C4⋊C4×C73—21no—
292C4⋊C4×C73—21no—
293C4⋊C4×C73—21no—
294C4⋊C4×C73—21no—
295C4⋊C4×C73—21no—
296C4⋊C4×C73—21no—
297C4⋊C4×C73—21no—
298C4⋊C4×C73—81no—
299C4⋊C4×C73C2×D411yescharacteristic
300C4⋊C4×C73C2×D411yescharacteristic
301C4⋊C4×C73C2×D411yescharacteristic
302C4⋊C4×C73C2×D411yescharacteristic
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—21no—
321C22⋊C4×C73—21no—
322C22⋊C4×C73—21no—
323C22⋊C4×C73—21no—
324C22⋊C4×C73—21no—
325C22⋊C4×C73—21no—
326C22⋊C4×C73—21no—
327C22⋊C4×C73—21no—
328C22⋊C4×C73—42no—
329C22⋊C4×C73—42no—
330C22⋊C4×C73—41no—
331C22⋊C4×C73—41no—
332C22⋊C4×C73—81no—
333C22⋊C4×C73—81no—
334C22⋊C4×C73—81no—
335C42×C73—21no—
336C42×C73—21no—
337C42×C73—21no—
338C42×C73—81no—
339C23×C73—21no—
340C23×C73—21no—
341C23×C73—21no—
342C23×C73—21no—
343C23×C73—21no—
344C23×C73—21no—
345C23×C73—21no—
346C23×C73—21no—
347C23×C73—41no—
348C23×C73—41no—
349C23×C73—42no—
350C23×C73—41no—
351C23×C73—41no—
352C23×C73—41no—
353C23×C73—41no—
354C23×C73—41no—
355C23×C73—41no—
356C23×C73—41no—
357C23×C73—41no—
358C23×C73—41no—
359C23×C73—81no—
360C23×C73—81no—
361C23×C73—81no—
362C23×C73—81no—
363C23×C73—81no—
364C23×C73#12011yescharacteristic
365C23×C73#12011yescharacteristic
366C23×C73C22×D411yescharacteristic
367Q8×C73—41no—
368Q8×C73—81no—
369D4×C73—41no—
370D4×C73—41no—
371D4×C73—41no—
372D4×C73—41no—
373D4×C73—41no—
374D4×C73—41no—
375D4×C73—41no—
376D4×C73—42no—
377D4×C73—42no—
378D4×C73—41no—
379D4×C73—41no—
380D4×C73—41no—
381D4×C73—41no—
382D4×C73—41no—
383D4×C73—41no—
384D4×C73—81no—
385D4×C73—81no—
386D4×C73—81no—
387D4×C73—81no—
388D4×C73—81no—
389D4×C73—81no—
390D4×C73—81no—
391D4×C73—81no—
392D4×C73—81no—
393D4×C73—81no—
394D4×C73—81no—
395D4×C73—81no—
396D4×C73—84no—
397D4×C73—82no—
398D4×C73—82no—
399C2×C4×C73—22no—
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—21no—
409C2×C4×C73—21no—
410C2×C4×C73—41no—
411C2×C4×C73—41no—
412C2×C4×C73—41no—
413C2×C4×C73—41no—
414C2×C4×C73—41no—
415C2×C4×C73—41no—
416C2×C4×C73—41no—
417C2×C4×C73—41no—
418C2×C4×C73—41no—
419C2×C4×C73—41no—
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—81no—
427C2×C4×C73—81no—
428C2×C4×C73—81no—
429C2×C4×C73—81no—
430C2×C4×C73—81no—
431C2×C4×C73—81no—
432C2×C4×C73—81no—
433C2×C4×C73#12011yescharacteristic
434C2×C4×C73#12011yescharacteristic
435C2×C4×C73C22×D411yescharacteristic
436C2×C4×C73C22×D411yescharacteristic
437C8×C73—41no—
438C8×C73—41no—
439C8×C73—41no—
440C8×C73—41no—
441C22×C73—21no—
442C22×C73—21no—
443C22×C73—21no—
444C22×C73—21no—
445C22×C73—21no—
446C22×C73—21no—
447C22×C73—21no—
448C22×C73—21no—
449C22×C73—41no—
450C22×C73—41no—
451C22×C73—41no—
452C22×C73—41no—
453C22×C73—41no—
454C22×C73—41no—
455C22×C73—41no—
456C22×C73—41no—
457C22×C73—41no—
458C22×C73—41no—
459C22×C73—41no—
460C22×C73—41no—
461C22×C73—81no—
462C22×C73—81no—
463C22×C73—81no—
464C22×C73—81no—
465C22×C73—81no—
466C22×C73—81no—
467C22×C73—81no—
468C22×C73—81no—
469C22×C73—81no—
470C22×C73—81no—
471C22×C73—81no—
472C22×C73—162no—
473C22×C73—162no—
474C22×C73C2×#12011yescharacteristic
475C22×C73#57611yescharacteristic
476C22×C73#57611yescharacteristic
477C4×C73—21no—
478C4×C73—21no—
479C4×C73—21no—
480C4×C73—21no—
481C4×C73—42no—
482C4×C73—41no—
483C4×C73—41no—
484C4×C73—41no—
485C4×C73—41no—
486C4×C73—41no—
487C4×C73—41no—
488C4×C73—41no—
489C4×C73—41no—
490C4×C73—81no—
491C4×C73—81no—
492#18414C7311yesmaximal, characteristic, direct product factor, Sylow
493C2×C73—21no—
494C2×C73—21no—
495C2×C73—41no—
496C2×C73—41no—
497C2×C73—81no—
498C2×C73—81no—
499C2×C73—81no—
500C2×C73—81no—
501C2×C73—161no—
502C2×C73#300811yescharacteristic
503C2×C73#301811yescharacteristic
504C2×C73#302611yescharacteristic
505#3534C2×C7311yescharacteristic, complemented
506#3194C2×C7311yescharacteristic, complemented
507#3186C2×C7311yescharacteristic, complemented
508#2661C2×C7311yescharacteristic, complemented
509#1612C2×C7311yescharacteristic, complemented
510#1610C2×C7311yescharacteristic, complemented
511#1609C2×C7311yescharacteristic, complemented
512#1607C2×C7311yescharacteristic, complemented
513#1600C2×C7311yescharacteristic, complemented
514#1598C2×C7311yescharacteristic, complemented
515#1597C2×C7311yescharacteristic, complemented
516#1595C2×C7311yescharacteristic, complemented
517#1507C2×C7311yescharacteristic, complemented
518#1501C2×C7311yescharacteristic, complemented
519#1468C2×C7311yescharacteristic, complemented
520C73#1841411yescharacteristic, direct product factor, Sylow
521#562—21no—
522#560—21no—
523#553—21no—
524#551—21no—
525#546—21no—
526#546—21no—
527#546—21no—
528D42—21no—
529#540—21no—
530#539—21no—
531#539C22×C7311yescharacteristic
532#538—21no—
533#538C22×C7311yescharacteristic
534#537C22×C7311yescharacteristic
535#534—21no—
536#534C22×C7311yescharacteristic
537#525C22×C7311yescharacteristic
538C2×#123C22×C7311yescharacteristic
539C2×#121C22×C7311yescharacteristic
540C2×#121C22×C7311yescharacteristic, complemented
541#483C22×C7311yescharacteristic, complemented
542#482—21no—
543#480—21no—
544#480C22×C7311yescharacteristic
545#480C22×C7311yescharacteristic, complemented
546#480C22×C7311yescharacteristic, complemented
547#469—21no—
548#468—21no—
549#466—21no—
550#466—21no—
551#450C22×C7311yescharacteristic, complemented
552#449—21no—
553#447—21no—
554#447C22×C7311yescharacteristic
555#447C22×C7311yescharacteristic, complemented
556#447C22×C7311yescharacteristic, complemented
557#407C22×C7311yescharacteristic, complemented
558C2×C22⋊C8C22×C7311yescharacteristic, complemented
559#398C22×C7311yescharacteristic, complemented
560#397C22×C7311yescharacteristic, complemented
561#394—21no—
562#394C22×C7311yescharacteristic, complemented
563#392—21no—
564#392C22×C7311yescharacteristic, complemented
565#390—21no—
566#388—21no—
567C4×C22⋊C4C22×C7311yescharacteristic, complemented
568#328C22×C7311yescharacteristic, complemented
569#328C22×C7311yescharacteristic, complemented
570#327C22×C7311yescharacteristic
571#327C22×C7311yescharacteristic
572#327C22×C7311yescharacteristic, complemented
573#327C22×C7311yescharacteristic, complemented
574#327C22×C7311yescharacteristic, complemented
575#327C22×C7311yescharacteristic, complemented
576#324C22×C7311yescharacteristic, complemented
577#324C22×C7311yescharacteristic, complemented
578#323C22×C7311yescharacteristic, complemented
579#323C22×C7311yescharacteristic, complemented
580C2×#41—21no—
581C2×#41D4×C7311yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C7311yescharacteristic
588C22×D4D4×C7311yescharacteristic, complemented
589C22×D4C23×C7311yescharacteristic
590C23×C4C23×C7311yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C7311yescharacteristic, complemented
627C22⋊Q8C23×C7311yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C7311yescharacteristic, complemented
648#121D4×C7311yescharacteristic, complemented
649#121D4×C7311yescharacteristic, complemented
650#121C23×C7311yescharacteristic
651#121C23×C7311yescharacteristic
652#121C23×C7311yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C7311yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C7311yescharacteristic
673C2×C4⋊C4D4×C7311yescharacteristic, complemented
674C2×C4⋊C4C23×C7311yescharacteristic
675C2×C4⋊C4C23×C7311yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C7311yescharacteristic
686C2×C22⋊C4D4×C7311yescharacteristic
687C2×C22⋊C4C23×C7311yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C7311yescharacteristic
704C22⋊C8C23×C7311yescharacteristic
705C22⋊C8C23×C7311yescharacteristic
706C22⋊C8C23×C7311yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C7311yescharacteristic
710#95C23×C7311yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C7311yescharacteristic
715C24C2×D4×C7311yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C7311yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C7311yescharacteristic
756C2×D4C2×D4×C7311yescharacteristic
757C2×D4C2×D4×C7311yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C7311yescharacteristic
770C22×C4C2×D4×C7311yescharacteristic
771C22×C4C2×D4×C7311yescharacteristic
772C22×C4C2×D4×C7311yescharacteristic
773C22×C4C2×D4×C7311yescharacteristic
774C22×C4C2×D4×C7311yescharacteristic
775C22×C4C2×D4×C7311yescharacteristic
776C22×C4C2×D4×C7311yescharacteristic
777C22×C4C24×C7311yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C7311yescharacteristic
805C4⋊C4C2×D4×C7311yescharacteristic
806C4⋊C4C2×D4×C7311yescharacteristic
807C4⋊C4C2×D4×C7311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C7311yescharacteristic
870C23#120×C7311yescharacteristic
871C23C22×D4×C7311yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C7311yescharacteristic
939C2×C4#120×C7311yescharacteristic
940C2×C4C22×D4×C7311yescharacteristic
941C2×C4C22×D4×C7311yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C7311yescharacteristic
980C22#576×C7311yescharacteristic
981C22#576×C7311yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C73×#300811yescharacteristic
1007C2C73×#301811yescharacteristic
1008C2C73×#302611yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
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
1. C73×#3534C2semidirect
2. C73×#3194C2semidirect
3. C73×#3186C2semidirect
4. C73×#2661C2semidirect
5. C73×#1612C2semidirect
6. C73×#1610C2semidirect
7. C73×#1609C2semidirect
8. C73×#1607C2semidirect
9. C73×#1600C2semidirect
10. C73×#1598C2semidirect
11. C73×#1597C2semidirect
12. C73×#1595C2semidirect
13. C73×#1507C2semidirect
14. C73×#1501C2semidirect
15. C73×#1468C2semidirect
35. C2×#121×C73C22semidirect
36. #483×C73C22semidirect
40. #480×C73C22semidirect
41. #480×C73C22semidirect
46. #450×C73C22semidirect
50. #447×C73C22semidirect
51. #447×C73C22semidirect
52. #407×C73C22semidirect
53. C2×C22⋊C8×C73C22semidirect
54. #398×C73C22semidirect
55. #397×C73C22semidirect
57. #394×C73C22semidirect
59. #392×C73C22semidirect
62. C4×C22⋊C4×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
76. C2×#41×C73D4semidirect
83. C22×D4×C73D4semidirect
121. C22⋊Q8×C73D4semidirect
142. #121×C73D4semidirect
143. #121×C73D4semidirect
144. #121×C73D4semidirect
165. #117×C73D4semidirect
168. C2×C4⋊C4×C73D4semidirect
492. #18414C73direct (N × H)
505. #3534C2×C73semidirect
506. #3194C2×C73semidirect
507. #3186C2×C73semidirect
508. #2661C2×C73semidirect
509. #1612C2×C73semidirect
510. #1610C2×C73semidirect
511. #1609C2×C73semidirect
512. #1607C2×C73semidirect
513. #1600C2×C73semidirect
514. #1598C2×C73semidirect
515. #1597C2×C73semidirect
516. #1595C2×C73semidirect
517. #1507C2×C73semidirect
518. #1501C2×C73semidirect
519. #1468C2×C73semidirect
520. C73#18414direct (N × H)
540. C2×#121C22×C73semidirect
541. #483C22×C73semidirect
545. #480C22×C73semidirect
546. #480C22×C73semidirect
551. #450C22×C73semidirect
555. #447C22×C73semidirect
556. #447C22×C73semidirect
557. #407C22×C73semidirect
558. C2×C22⋊C8C22×C73semidirect
559. #398C22×C73semidirect
560. #397C22×C73semidirect
562. #394C22×C73semidirect
564. #392C22×C73semidirect
567. C4×C22⋊C4C22×C73semidirect
568. #328C22×C73semidirect
569. #328C22×C73semidirect
572. #327C22×C73semidirect
573. #327C22×C73semidirect
574. #327C22×C73semidirect
575. #327C22×C73semidirect
576. #324C22×C73semidirect
577. #324C22×C73semidirect
578. #323C22×C73semidirect
579. #323C22×C73semidirect
581. C2×#41D4×C73semidirect
588. C22×D4D4×C73semidirect
626. C22⋊Q8D4×C73semidirect
647. #121D4×C73semidirect
648. #121D4×C73semidirect
649. #121D4×C73semidirect
670. #117D4×C73semidirect
673. C2×C4⋊C4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35342
C73×#31942
C73×#31862
C73×#26612
C73×#16122
C73×#16102
C73×#16092
C73×#16072
C73×#16002
C73×#15982
C73×#15972
C73×#15952
C73×#15072
C73×#15012
C73×#14682
#1841473