Finite Group Databasebeta

← C73×#62558 #32971962

Subgroups — C73×#62558 #32971962

Order 18688.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3559C211yesmaximal, characteristic, complemented
2C73×#3558C211yesmaximal, characteristic, complemented
3C73×#3370C212yesmaximal, complemented
4C73×#3361C212yesmaximal, complemented
5C73×#3322C212yesmaximal, complemented
6C73×#3318C212yesmaximal, complemented
7C73×#3308C212yesmaximal, complemented
8C73×#3301C212yesmaximal, complemented
9C73×#3297C212yesmaximal, complemented
10C73×#3294C212yesmaximal, complemented
11C73×#3243C212yesmaximal, complemented
12C73×#3234C211yesmaximal, characteristic, complemented
13C73×#3220C212yesmaximal, complemented
14C73×#3213C211yesmaximal, characteristic, complemented
15C73×#3179C212yesmaximal, complemented
16C73×#3169C211yesmaximal, characteristic, complemented
17C73×#3136C212yesmaximal, complemented
18C2×#488×C73C211yesmaximal, characteristic, complemented
19C73×#2966C211yesmaximal, characteristic, complemented
20#563×C73—21no—
21#562×C73—21no—
22#562×C73—21no—
23H(3,𝔽4)×C73—21no—
24#559×C73C2212yes—
25#554×C73C2212yescomplemented
26#553×C73C2212yescomplemented
27#553×C73C2212yescomplemented
28#548×C73C2212yes—
29#547×C73—22no—
30#547×C73C2212yescomplemented
31#546×C73—22no—
32#546×C73C2212yes—
33D42×C73C2212yes—
34#544×C73C2212yescomplemented
35#542×C73C2212yes—
36#540×C73C2212yescomplemented
37#539×C73—22no—
38#539×C73—21no—
39#538×C73—22no—
40#538×C73—21no—
41#537×C73—21no—
42#535×C73C2212yes—
43#534×C73—21no—
44#532×C73C2211yescharacteristic
45#532×C73C2211yescharacteristic, complemented
46#529×C73C2211yescharacteristic
47C2×#125×C73C2211yescharacteristic, complemented
48C2×#124×C73C2211yescharacteristic
49#501×C73C2212yescomplemented
50#500×C73C2211yescharacteristic, complemented
51#496×C73C2212yescomplemented
52#493×C73C2211yescharacteristic, complemented
53#490×C73C2212yes—
54#490×C73C2212yescomplemented
55#489×C73C2212yescomplemented
56#489×C73C2212yescomplemented
57#488×C73C2212yescomplemented
58#488×C73C2212yescomplemented
59#488×C73C2212yescomplemented
60#488×C73C2212yescomplemented
61#488×C73C2212yescomplemented
62#486×C73C2212yes—
63#486×C73C2211yescharacteristic, complemented
64#486×C73C2211yescharacteristic, complemented
65#485×C73C2212yescomplemented
66#484×C73C2212yescomplemented
67#482×C73C2212yes—
68#481×C73C2212yescomplemented
69#480×C73C2212yes—
70#480×C73C2212yescomplemented
71#479×C73C2212yescomplemented
72#478×C73C2212yescomplemented
73#478×C73C2212yescomplemented
74#478×C73C2212yescomplemented
75#477×C73C2212yescomplemented
76#474×C73C2212yescomplemented
77#469×C73C2212yes—
78#468×C73C2212yescomplemented
79#466×C73C2212yes—
80#466×C73C2212yescomplemented
81#466×C73C2212yescomplemented
82#465×C73C2212yescomplemented
83#463×C73C2212yescomplemented
84#463×C73C2212yescomplemented
85#463×C73C2212yescomplemented
86#463×C73C2212yescomplemented
87#459×C73C2212yes—
88#459×C73C2212yes—
89#449×C73C2212yescomplemented
90#449×C73C2212yescomplemented
91#448×C73C2212yescomplemented
92#447×C73C2212yes—
93#447×C73C2212yescomplemented
94#447×C73C2212yescomplemented
95#446×C73C2211yescharacteristic, complemented
96C8×Q8×C73C2211yescharacteristic, complemented
97#442×C73C2212yescomplemented
98#440×C73C2212yescomplemented
99C4×SD16×C73C2212yescomplemented
100C4×D8×C73C2212yescomplemented
101C4×D8×C73C2212yescomplemented
102C4×D8×C73C2212yescomplemented
103#436×C73C2211yescharacteristic, complemented
104#435×C73C2212yescomplemented
105C8×D4×C73C2212yescomplemented
106C8×D4×C73C2211yescharacteristic, complemented
107#433×C73C2212yescomplemented
108#432×C73C2211yescharacteristic, complemented
109#418×C73C2212yescomplemented
110#417×C73C2212yescomplemented
111#416×C73C2212yescomplemented
112C2×#103×C73C2211yescharacteristic, complemented
113C2×#103×C73C2211yescharacteristic, complemented
114C2×#102×C73C2211yescharacteristic
115C2×#102×C73C2211yescharacteristic
116C2×#102×C73C2212yescomplemented
117#405×C73C2212yescomplemented
118C2×C4×C8×C73C2211yescharacteristic, complemented
119C2×#41×C73—22no—
120C2×#41×C73—21no—
121C2×#41×C73—21no—
122C2×#41×C73C2312yes—
123C22×Q8×C73C2311yescharacteristic
124C22×D4×C73—22no—
125C22×D4×C73C2311yescharacteristic
126C22×D4×C73C2312yes—
127C2×SD16×C73C2312yes—
128C2×SD16×C73C2312yes—
129C2×D8×C73C2312yes—
130C2×D8×C73C2312yes—
131C2×D8×C73C2312yes—
132C2×D8×C73C2312yes—
133C2×M16×C73C2312yes—
134C22×C8×C73C2311yescharacteristic
135C22×C8×C73C2311yescharacteristic
136C22×C8×C73C2312yes—
137C4⋊Q8×C73—22no—
138C4⋊Q8×C73C2312yes—
139C4⋊Q8×C73C2311yescharacteristic
140C4⋊Q8×C73C2311yescharacteristic
141#127×C73C2312yes—
142#127×C73C2311yescharacteristic
143#127×C73C2311yescharacteristic
144#126×C73—22no—
145#126×C73—22no—
146#126×C73—22no—
147#126×C73D412yes—
148#125×C73—22no—
149#125×C73—21no—
150#125×C73—21no—
151#125×C73D411yescharacteristic
152#125×C73C2312yes—
153#125×C73C2312yes—
154#125×C73C2312yes—
155#124×C73—22no—
156#124×C73—22no—
157#124×C73—22no—
158#124×C73—21no—
159#124×C73—21no—
160#124×C73—21no—
161#124×C73—21no—
162#124×C73D411yescharacteristic
163#124×C73C2312yes—
164#124×C73C2312yes—
165#124×C73C2312yes—
166#123×C73—22no—
167#123×C73—22no—
168#123×C73—22no—
169#123×C73—22no—
170#123×C73—22no—
171#123×C73—22no—
172#123×C73—22no—
173#123×C73—22no—
174#123×C73—22no—
175#123×C73—22no—
176#123×C73D412yes—
177C22⋊Q8×C73—22no—
178C22⋊Q8×C73—22no—
179C22⋊Q8×C73—22no—
180C22⋊Q8×C73—22no—
181C22⋊Q8×C73—22no—
182C22⋊Q8×C73—22no—
183C22⋊Q8×C73—22no—
184C22⋊Q8×C73—22no—
185C22⋊Q8×C73D411yescharacteristic
186C22⋊Q8×C73C2312yes—
187#121×C73—22no—
188#121×C73—22no—
189#121×C73—22no—
190#121×C73—21no—
191#121×C73—21no—
192#121×C73—22no—
193#121×C73—22no—
194#121×C73—22no—
195#121×C73—22no—
196#121×C73—22no—
197#121×C73—22no—
198#121×C73D411yescharacteristic
199#121×C73C2312yes—
200#121×C73C2312yes—
201#121×C73C2312yes—
202#121×C73C2312yes—
203#121×C73C2312yes—
204#120×C73—22no—
205#120×C73—22no—
206#120×C73—22no—
207#120×C73—22no—
208#120×C73—22no—
209C4×Q8×C73C2312yes—
210C4×Q8×C73C2311yescharacteristic
211C4×D4×C73—22no—
212C4×D4×C73—22no—
213C4×D4×C73—22no—
214C4×D4×C73—22no—
215C4×D4×C73—21no—
216C4×D4×C73—21no—
217C4×D4×C73C2312yes—
218C4×D4×C73C2312yes—
219C4×D4×C73C2312yes—
220C4×D4×C73C2312yes—
221C4×D4×C73C2312yes—
222C4×D4×C73C2312yes—
223C4×D4×C73C2311yescharacteristic
224#117×C73C2312yes—
225#117×C73C2312yes—
226C2×C4⋊C4×C73—21no—
227C2×C4⋊C4×C73—21no—
228C2×C4⋊C4×C73—22no—
229C2×C4⋊C4×C73C2311yescharacteristic
230C2×C4⋊C4×C73C2311yescharacteristic
231C2×C4⋊C4×C73C2312yes—
232C2×C22⋊C4×C73—21no—
233C2×C22⋊C4×C73—21no—
234C2×C22⋊C4×C73—22no—
235C2×C42×C73C2311yescharacteristic
236#107×C73C2312yes—
237#107×C73C2312yes—
238#107×C73C2312yes—
239#107×C73C2312yes—
240#106×C73C2312yes—
241#106×C73C2312yes—
242C4⋊C8×C73C2311yescharacteristic
243C4⋊C8×C73C2311yescharacteristic
244C4⋊C8×C73C2312yes—
245C4⋊C8×C73C2312yes—
246#103×C73C2312yes—
247#103×C73C2312yes—
248#103×C73C2312yes—
249#103×C73C2312yes—
250#103×C73C2312yes—
251#103×C73C2312yes—
252#102×C73C2312yes—
253#102×C73C2312yes—
254#102×C73C2312yes—
255#102×C73C2312yes—
256#102×C73C2312yes—
257#102×C73C2312yes—
258#102×C73C2312yes—
259#102×C73C2312yes—
260#102×C73C2312yes—
261#102×C73C2312yes—
262#102×C73C2312yes—
263#102×C73C2312yes—
264#102×C73C2312yes—
265#102×C73C2312yes—
266C22⋊C8×C73C2312yes—
267C22⋊C8×C73C2312yes—
268C22⋊C8×C73C2312yes—
269#97×C73C2312yes—
270#97×C73C2312yes—
271C4×C8×C73C2311yescharacteristic
272C4×C8×C73C2311yescharacteristic
273C4×C8×C73C2311yescharacteristic
274C4×C8×C73C2311yescharacteristic
275C4×C8×C73C2312yes—
276C24×C73—21no—
277C24×C73—22no—
278#41×C73—42no—
279#41×C73—42no—
280#41×C73—82no—
281#41×C73—82no—
282#41×C73—84no—
283C2×Q8×C73—22no—
284C2×Q8×C73—21no—
285C2×Q8×C73—21no—
286C2×Q8×C73—21no—
287C2×Q8×C73—41no—
288C2×Q8×C73—41no—
289C2×Q8×C73C2×D411yescharacteristic
290C2×Q8×C73C2412yes—
291C2×D4×C73—22no—
292C2×D4×C73—22no—
293C2×D4×C73—22no—
294C2×D4×C73—22no—
295C2×D4×C73—22no—
296C2×D4×C73—22no—
297C2×D4×C73—22no—
298C2×D4×C73—21no—
299C2×D4×C73—21no—
300C2×D4×C73—21no—
301C2×D4×C73—21no—
302C2×D4×C73—22no—
303C2×D4×C73—22no—
304C2×D4×C73—21no—
305C2×D4×C73—41no—
306C2×D4×C73—41no—
307C2×D4×C73—42no—
308C2×D4×C73—42no—
309C2×D4×C73—84no—
310C2×D4×C73C2×D412yes—
311C2×D4×C73C2×D411yescharacteristic
312C2×D4×C73C2412yes—
313C2×D4×C73C2412yes—
314C2×D4×C73C2412yes—
315C22×C4×C73—21no—
316C22×C4×C73—21no—
317C22×C4×C73—21no—
318C22×C4×C73—22no—
319C22×C4×C73—22no—
320C22×C4×C73—22no—
321C22×C4×C73—22no—
322C22×C4×C73—22no—
323C22×C4×C73—22no—
324C22×C4×C73—22no—
325C22×C4×C73C2×D411yescharacteristic
326C22×C4×C73C2×D411yescharacteristic
327C22×C4×C73C2411yescharacteristic
328C22×C4×C73C2412yes—
329SD16×C73—42no—
330SD16×C73—42no—
331D8×C73—42no—
332D8×C73—42no—
333D8×C73—42no—
334D8×C73—42no—
335M16×C73—42no—
336C2×C8×C73—41no—
337C2×C8×C73—42no—
338C2×C8×C73—41no—
339C2×C8×C73C2411yescharacteristic
340C2×C8×C73C2411yescharacteristic
341C2×C8×C73C2411yescharacteristic
342C2×C8×C73C2411yescharacteristic
343C2×C8×C73C2412yes—
344C2×C8×C73C2412yes—
345C4⋊C4×C73—22no—
346C4⋊C4×C73—22no—
347C4⋊C4×C73—22no—
348C4⋊C4×C73—22no—
349C4⋊C4×C73—22no—
350C4⋊C4×C73—22no—
351C4⋊C4×C73—21no—
352C4⋊C4×C73—22no—
353C4⋊C4×C73—21no—
354C4⋊C4×C73—22no—
355C4⋊C4×C73—21no—
356C4⋊C4×C73—21no—
357C4⋊C4×C73—22no—
358C4⋊C4×C73—22no—
359C4⋊C4×C73C2×D412yes—
360C4⋊C4×C73C2×D412yes—
361C4⋊C4×C73C2×D412yes—
362C4⋊C4×C73C2×D412yes—
363C4⋊C4×C73C2×D411yescharacteristic
364C4⋊C4×C73C2×D411yescharacteristic
365C4⋊C4×C73C2412yes—
366C4⋊C4×C73C2412yes—
367C4⋊C4×C73C2412yes—
368C4⋊C4×C73C2412yes—
369C22⋊C4×C73—22no—
370C22⋊C4×C73—22no—
371C22⋊C4×C73—22no—
372C22⋊C4×C73—22no—
373C22⋊C4×C73—22no—
374C22⋊C4×C73—22no—
375C22⋊C4×C73—22no—
376C22⋊C4×C73—22no—
377C22⋊C4×C73—22no—
378C22⋊C4×C73—22no—
379C22⋊C4×C73—22no—
380C22⋊C4×C73—22no—
381C22⋊C4×C73—22no—
382C22⋊C4×C73—22no—
383C22⋊C4×C73—22no—
384C22⋊C4×C73—22no—
385C22⋊C4×C73—22no—
386C22⋊C4×C73—22no—
387C22⋊C4×C73C2×D412yes—
388C22⋊C4×C73C2×D412yes—
389C22⋊C4×C73C2×D412yes—
390C22⋊C4×C73C2×D412yes—
391C22⋊C4×C73C2×D412yes—
392C42×C73—22no—
393C42×C73—22no—
394C42×C73C2×D411yescharacteristic
395C42×C73C2×D411yescharacteristic
396C42×C73C2411yescharacteristic
397C42×C73C2411yescharacteristic
398C42×C73C2412yes—
399C23×C73—22no—
400C23×C73—22no—
401C23×C73—22no—
402C23×C73—42no—
403C23×C73—81no—
404C23×C73—82no—
405C23×C73—82no—
406C23×C73—81no—
407C23×C73—82no—
408C23×C73C22×D412yes—
409C23×C73C22×D411yescharacteristic
410Q8×C73—22no—
411Q8×C73—22no—
412Q8×C73—41no—
413Q8×C73—81no—
414Q8×C73—81no—
415Q8×C73—81no—
416Q8×C73—82no—
417D4×C73—24no—
418D4×C73—22no—
419D4×C73—22no—
420D4×C73—22no—
421D4×C73—22no—
422D4×C73—22no—
423D4×C73—22no—
424D4×C73—41no—
425D4×C73—44no—
426D4×C73—44no—
427D4×C73—81no—
428D4×C73—81no—
429D4×C73—82no—
430D4×C73—82no—
431D4×C73—81no—
432D4×C73—82no—
433D4×C73—81no—
434D4×C73—81no—
435D4×C73—82no—
436D4×C73—82no—
437D4×C73—82no—
438D4×C73—82no—
439C2×C4×C73—22no—
440C2×C4×C73—21no—
441C2×C4×C73—21no—
442C2×C4×C73—22no—
443C2×C4×C73—22no—
444C2×C4×C73—22no—
445C2×C4×C73—22no—
446C2×C4×C73—22no—
447C2×C4×C73—22no—
448C2×C4×C73—22no—
449C2×C4×C73—41no—
450C2×C4×C73—42no—
451C2×C4×C73—82no—
452C2×C4×C73—82no—
453C2×C4×C73—82no—
454C2×C4×C73—82no—
455C2×C4×C73—82no—
456C2×C4×C73—82no—
457C2×C4×C73—81no—
458C2×C4×C73—81no—
459C2×C4×C73—82no—
460C2×C4×C73C22×D412yes—
461C2×C4×C73C22×D412yes—
462C2×C4×C73C22×D411yescharacteristic
463C2×C4×C73C22×D411yescharacteristic
464C2×C4×C73C22×D411yescharacteristic
465C2×C4×C73C22×D411yescharacteristic
466C2×C4×C73C22×D411yescharacteristic
467C2×C4×C73C22×D412yes—
468C2×C4×C73C2511yescharacteristic
469C8×C73—21no—
470C8×C73—21no—
471C8×C73—21no—
472C8×C73—21no—
473C8×C73—22no—
474C8×C73—22no—
475C22×C73—21no—
476C22×C73—21no—
477C22×C73—22no—
478C22×C73—22no—
479C22×C73—22no—
480C22×C73—42no—
481C22×C73—42no—
482C22×C73—42no—
483C22×C73—42no—
484C22×C73—42no—
485C22×C73—42no—
486C22×C73—42no—
487C22×C73—42no—
488C22×C73—42no—
489C22×C73—162no—
490C22×C73—164no—
491C22×C73#57612yes—
492C22×C73C23×D411yescharacteristic
493C4×C73—21no—
494C4×C73—21no—
495C4×C73—22no—
496C4×C73—22no—
497C4×C73—21no—
498C4×C73—21no—
499C4×C73—21no—
500C4×C73—22no—
501C4×C73—42no—
502C4×C73—42no—
503C4×C73—42no—
504C4×C73—42no—
505C4×C73—42no—
506C4×C73#58511yescharacteristic
507C4×C73#58511yescharacteristic
508#62558C7311yesmaximal, characteristic, direct product factor, Sylow
509C2×C73—22no—
510C2×C73—42no—
511C2×C73—82no—
512C2×C73—82no—
513C2×C73—82no—
514C2×C73#350011yescharacteristic
515C2×C73C2×#57611yescharacteristic
516C2×C73#358411yescharacteristic
517#3559C2×C7311yescharacteristic, complemented
518#3558C2×C7311yescharacteristic, complemented
519#3370C2×C7312yescomplemented
520#3361C2×C7312yescomplemented
521#3322C2×C7312yescomplemented
522#3318C2×C7312yescomplemented
523#3308C2×C7312yescomplemented
524#3301C2×C7312yescomplemented
525#3297C2×C7312yescomplemented
526#3294C2×C7312yescomplemented
527#3243C2×C7312yescomplemented
528#3234C2×C7311yescharacteristic, complemented
529#3220C2×C7312yescomplemented
530#3213C2×C7311yescharacteristic, complemented
531#3179C2×C7312yescomplemented
532#3169C2×C7311yescharacteristic, complemented
533#3136C2×C7312yescomplemented
534C2×#488C2×C7311yescharacteristic, complemented
535#2966C2×C7311yescharacteristic, complemented
536C73#6255811yescharacteristic, direct product factor, Sylow
537#563—21no—
538#562—21no—
539#562—21no—
540H(3,𝔽4)—21no—
541#559C22×C7312yes—
542#554C22×C7312yescomplemented
543#553C22×C7312yescomplemented
544#553C22×C7312yescomplemented
545#548C22×C7312yes—
546#547—22no—
547#547C22×C7312yescomplemented
548#546—22no—
549#546C22×C7312yes—
550D42C22×C7312yes—
551#544C22×C7312yescomplemented
552#542C22×C7312yes—
553#540C22×C7312yescomplemented
554#539—22no—
555#539—21no—
556#538—22no—
557#538—21no—
558#537—21no—
559#535C22×C7312yes—
560#534—21no—
561#532C22×C7311yescharacteristic
562#532C22×C7311yescharacteristic, complemented
563#529C22×C7311yescharacteristic
564C2×#125C22×C7311yescharacteristic, complemented
565C2×#124C22×C7311yescharacteristic
566#501C22×C7312yescomplemented
567#500C22×C7311yescharacteristic, complemented
568#496C22×C7312yescomplemented
569#493C22×C7311yescharacteristic, complemented
570#490C22×C7312yes—
571#490C22×C7312yescomplemented
572#489C22×C7312yescomplemented
573#489C22×C7312yescomplemented
574#488C22×C7312yescomplemented
575#488C22×C7312yescomplemented
576#488C22×C7312yescomplemented
577#488C22×C7312yescomplemented
578#488C22×C7312yescomplemented
579#486C22×C7312yes—
580#486C22×C7311yescharacteristic, complemented
581#486C22×C7311yescharacteristic, complemented
582#485C22×C7312yescomplemented
583#484C22×C7312yescomplemented
584#482C22×C7312yes—
585#481C22×C7312yescomplemented
586#480C22×C7312yes—
587#480C22×C7312yescomplemented
588#479C22×C7312yescomplemented
589#478C22×C7312yescomplemented
590#478C22×C7312yescomplemented
591#478C22×C7312yescomplemented
592#477C22×C7312yescomplemented
593#474C22×C7312yescomplemented
594#469C22×C7312yes—
595#468C22×C7312yescomplemented
596#466C22×C7312yes—
597#466C22×C7312yescomplemented
598#466C22×C7312yescomplemented
599#465C22×C7312yescomplemented
600#463C22×C7312yescomplemented
601#463C22×C7312yescomplemented
602#463C22×C7312yescomplemented
603#463C22×C7312yescomplemented
604#459C22×C7312yes—
605#459C22×C7312yes—
606#449C22×C7312yescomplemented
607#449C22×C7312yescomplemented
608#448C22×C7312yescomplemented
609#447C22×C7312yes—
610#447C22×C7312yescomplemented
611#447C22×C7312yescomplemented
612#446C22×C7311yescharacteristic, complemented
613C8×Q8C22×C7311yescharacteristic, complemented
614#442C22×C7312yescomplemented
615#440C22×C7312yescomplemented
616C4×SD16C22×C7312yescomplemented
617C4×D8C22×C7312yescomplemented
618C4×D8C22×C7312yescomplemented
619C4×D8C22×C7312yescomplemented
620#436C22×C7311yescharacteristic, complemented
621#435C22×C7312yescomplemented
622C8×D4C22×C7312yescomplemented
623C8×D4C22×C7311yescharacteristic, complemented
624#433C22×C7312yescomplemented
625#432C22×C7311yescharacteristic, complemented
626#418C22×C7312yescomplemented
627#417C22×C7312yescomplemented
628#416C22×C7312yescomplemented
629C2×#103C22×C7311yescharacteristic, complemented
630C2×#103C22×C7311yescharacteristic, complemented
631C2×#102C22×C7311yescharacteristic
632C2×#102C22×C7311yescharacteristic
633C2×#102C22×C7312yescomplemented
634#405C22×C7312yescomplemented
635C2×C4×C8C22×C7311yescharacteristic, complemented
636C2×#41—22no—
637C2×#41—21no—
638C2×#41—21no—
639C2×#41C23×C7312yes—
640C22×Q8C23×C7311yescharacteristic
641C22×D4—22no—
642C22×D4C23×C7311yescharacteristic
643C22×D4C23×C7312yes—
644C2×SD16C23×C7312yes—
645C2×SD16C23×C7312yes—
646C2×D8C23×C7312yes—
647C2×D8C23×C7312yes—
648C2×D8C23×C7312yes—
649C2×D8C23×C7312yes—
650C2×M16C23×C7312yes—
651C22×C8C23×C7311yescharacteristic
652C22×C8C23×C7311yescharacteristic
653C22×C8C23×C7312yes—
654C4⋊Q8—22no—
655C4⋊Q8C23×C7311yescharacteristic
656C4⋊Q8C23×C7311yescharacteristic
657C4⋊Q8C23×C7312yes—
658#127C23×C7311yescharacteristic
659#127C23×C7311yescharacteristic
660#127C23×C7312yes—
661#126—22no—
662#126—22no—
663#126—22no—
664#126D4×C7312yes—
665#125—22no—
666#125—21no—
667#125—21no—
668#125D4×C7311yescharacteristic
669#125C23×C7312yes—
670#125C23×C7312yes—
671#125C23×C7312yes—
672#124—22no—
673#124—22no—
674#124—22no—
675#124—21no—
676#124—21no—
677#124—21no—
678#124—21no—
679#124D4×C7311yescharacteristic
680#124C23×C7312yes—
681#124C23×C7312yes—
682#124C23×C7312yes—
683#123—22no—
684#123—22no—
685#123—22no—
686#123—22no—
687#123—22no—
688#123—22no—
689#123—22no—
690#123—22no—
691#123—22no—
692#123—22no—
693#123D4×C7312yes—
694C22⋊Q8—22no—
695C22⋊Q8—22no—
696C22⋊Q8—22no—
697C22⋊Q8—22no—
698C22⋊Q8—22no—
699C22⋊Q8—22no—
700C22⋊Q8—22no—
701C22⋊Q8—22no—
702C22⋊Q8D4×C7311yescharacteristic
703C22⋊Q8C23×C7312yes—
704#121—22no—
705#121—22no—
706#121—22no—
707#121—21no—
708#121—21no—
709#121—22no—
710#121—22no—
711#121—22no—
712#121—22no—
713#121—22no—
714#121—22no—
715#121D4×C7311yescharacteristic
716#121C23×C7312yes—
717#121C23×C7312yes—
718#121C23×C7312yes—
719#121C23×C7312yes—
720#121C23×C7312yes—
721#120—22no—
722#120—22no—
723#120—22no—
724#120—22no—
725#120—22no—
726C4×Q8C23×C7312yes—
727C4×Q8C23×C7311yescharacteristic
728C4×D4—22no—
729C4×D4—22no—
730C4×D4—22no—
731C4×D4—22no—
732C4×D4—21no—
733C4×D4—21no—
734C4×D4C23×C7312yes—
735C4×D4C23×C7312yes—
736C4×D4C23×C7312yes—
737C4×D4C23×C7312yes—
738C4×D4C23×C7312yes—
739C4×D4C23×C7312yes—
740C4×D4C23×C7311yescharacteristic
741#117C23×C7312yes—
742#117C23×C7312yes—
743C2×C4⋊C4—21no—
744C2×C4⋊C4—21no—
745C2×C4⋊C4—22no—
746C2×C4⋊C4C23×C7311yescharacteristic
747C2×C4⋊C4C23×C7311yescharacteristic
748C2×C4⋊C4C23×C7312yes—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—22no—
752C2×C42C23×C7311yescharacteristic
753#107C23×C7312yes—
754#107C23×C7312yes—
755#107C23×C7312yes—
756#107C23×C7312yes—
757#106C23×C7312yes—
758#106C23×C7312yes—
759C4⋊C8C23×C7311yescharacteristic
760C4⋊C8C23×C7311yescharacteristic
761C4⋊C8C23×C7312yes—
762C4⋊C8C23×C7312yes—
763#103C23×C7312yes—
764#103C23×C7312yes—
765#103C23×C7312yes—
766#103C23×C7312yes—
767#103C23×C7312yes—
768#103C23×C7312yes—
769#102C23×C7312yes—
770#102C23×C7312yes—
771#102C23×C7312yes—
772#102C23×C7312yes—
773#102C23×C7312yes—
774#102C23×C7312yes—
775#102C23×C7312yes—
776#102C23×C7312yes—
777#102C23×C7312yes—
778#102C23×C7312yes—
779#102C23×C7312yes—
780#102C23×C7312yes—
781#102C23×C7312yes—
782#102C23×C7312yes—
783C22⋊C8C23×C7312yes—
784C22⋊C8C23×C7312yes—
785C22⋊C8C23×C7312yes—
786#97C23×C7312yes—
787#97C23×C7312yes—
788C4×C8C23×C7311yescharacteristic
789C4×C8C23×C7311yescharacteristic
790C4×C8C23×C7311yescharacteristic
791C4×C8C23×C7311yescharacteristic
792C4×C8C23×C7312yes—
793C24—21no—
794C24—22no—
795#41—42no—
796#41—42no—
797#41—82no—
798#41—82no—
799#41—84no—
800C2×Q8—22no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—41no—
805C2×Q8—41no—
806C2×Q8C2×D4×C7311yescharacteristic
807C2×Q8C24×C7312yes—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—21no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—84no—
827C2×D4C2×D4×C7312yes—
828C2×D4C2×D4×C7311yescharacteristic
829C2×D4C24×C7312yes—
830C2×D4C24×C7312yes—
831C2×D4C24×C7312yes—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4C2×D4×C7311yescharacteristic
843C22×C4C2×D4×C7311yescharacteristic
844C22×C4C24×C7311yescharacteristic
845C22×C4C24×C7312yes—
846SD16—42no—
847SD16—42no—
848D8—42no—
849D8—42no—
850D8—42no—
851D8—42no—
852M16—42no—
853C2×C8—41no—
854C2×C8—42no—
855C2×C8—41no—
856C2×C8C24×C7311yescharacteristic
857C2×C8C24×C7311yescharacteristic
858C2×C8C24×C7311yescharacteristic
859C2×C8C24×C7311yescharacteristic
860C2×C8C24×C7312yes—
861C2×C8C24×C7312yes—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—21no—
869C4⋊C4—22no—
870C4⋊C4—21no—
871C4⋊C4—22no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4C2×D4×C7312yes—
877C4⋊C4C2×D4×C7312yes—
878C4⋊C4C2×D4×C7312yes—
879C4⋊C4C2×D4×C7312yes—
880C4⋊C4C2×D4×C7311yescharacteristic
881C4⋊C4C2×D4×C7311yescharacteristic
882C4⋊C4C24×C7312yes—
883C4⋊C4C24×C7312yes—
884C4⋊C4C24×C7312yes—
885C4⋊C4C24×C7312yes—
886C22⋊C4—22no—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—22no—
904C22⋊C4C2×D4×C7312yes—
905C22⋊C4C2×D4×C7312yes—
906C22⋊C4C2×D4×C7312yes—
907C22⋊C4C2×D4×C7312yes—
908C22⋊C4C2×D4×C7312yes—
909C42—22no—
910C42—22no—
911C42C2×D4×C7311yescharacteristic
912C42C2×D4×C7311yescharacteristic
913C42C24×C7311yescharacteristic
914C42C24×C7311yescharacteristic
915C42C24×C7312yes—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—42no—
920C23—81no—
921C23—82no—
922C23—82no—
923C23—81no—
924C23—82no—
925C23C22×D4×C7312yes—
926C23C22×D4×C7311yescharacteristic
927Q8—22no—
928Q8—22no—
929Q8—41no—
930Q8—81no—
931Q8—81no—
932Q8—81no—
933Q8—82no—
934D4—24no—
935D4—22no—
936D4—22no—
937D4—22no—
938D4—22no—
939D4—22no—
940D4—22no—
941D4—41no—
942D4—44no—
943D4—44no—
944D4—82no—
945D4—81no—
946D4—82no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—82no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4—82no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—41no—
967C2×C4—42no—
968C2×C4—82no—
969C2×C4—82no—
970C2×C4—82no—
971C2×C4—82no—
972C2×C4—82no—
973C2×C4—82no—
974C2×C4—81no—
975C2×C4—82no—
976C2×C4—81no—
977C2×C4C22×D4×C7312yes—
978C2×C4C22×D4×C7312yes—
979C2×C4C22×D4×C7311yescharacteristic
980C2×C4C22×D4×C7311yescharacteristic
981C2×C4C22×D4×C7311yescharacteristic
982C2×C4C22×D4×C7311yescharacteristic
983C2×C4C22×D4×C7311yescharacteristic
984C2×C4C22×D4×C7312yes—
985C2×C4C25×C7311yescharacteristic
986C8—21no—
987C8—21no—
988C8—21no—
989C8—21no—
990C8—22no—
991C8—22no—
992C22—21no—
993C22—21no—
994C22—22no—
995C22—22no—
996C22—22no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—162no—
1007C22—164no—
1008C22#576×C7312yes—
1009C22C23×D4×C7311yescharacteristic
1010C4—22no—
1011C4—21no—
1012C4—21no—
1013C4—21no—
1014C4—22no—
1015C4—21no—
1016C4—21no—
1017C4—22no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4#585×C7311yescharacteristic
1024C4#585×C7311yescharacteristic
1025C2—22no—
1026C2—42no—
1027C2—82no—
1028C2—82no—
1029C2—82no—
1030C2C73×#350011yescharacteristic
1031C2C2×#576×C7311yescharacteristic
1032C2C73×#358411yescharacteristic
subgroupG/H
center, socleC22×C73C23×D4
commutator, Frattini, cosocleC2×C4C25×C73
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ #529×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3559C2semidirect
2. C73×#3558C2semidirect
3. C73×#3370C2semidirect
4. C73×#3361C2semidirect
5. C73×#3322C2semidirect
6. C73×#3318C2semidirect
7. C73×#3308C2semidirect
8. C73×#3301C2semidirect
9. C73×#3297C2semidirect
10. C73×#3294C2semidirect
11. C73×#3243C2semidirect
12. C73×#3234C2semidirect
13. C73×#3220C2semidirect
14. C73×#3213C2semidirect
15. C73×#3179C2semidirect
16. C73×#3169C2semidirect
17. C73×#3136C2semidirect
18. C2×#488×C73C2semidirect
19. C73×#2966C2semidirect
25. #554×C73C22semidirect
26. #553×C73C22semidirect
27. #553×C73C22semidirect
30. #547×C73C22semidirect
34. #544×C73C22semidirect
36. #540×C73C22semidirect
45. #532×C73C22semidirect
47. C2×#125×C73C22semidirect
49. #501×C73C22semidirect
50. #500×C73C22semidirect
51. #496×C73C22semidirect
52. #493×C73C22semidirect
54. #490×C73C22semidirect
55. #489×C73C22semidirect
56. #489×C73C22semidirect
57. #488×C73C22semidirect
58. #488×C73C22semidirect
59. #488×C73C22semidirect
60. #488×C73C22semidirect
61. #488×C73C22semidirect
63. #486×C73C22semidirect
64. #486×C73C22semidirect
65. #485×C73C22semidirect
66. #484×C73C22semidirect
68. #481×C73C22semidirect
70. #480×C73C22semidirect
71. #479×C73C22semidirect
72. #478×C73C22semidirect
73. #478×C73C22semidirect
74. #478×C73C22semidirect
75. #477×C73C22semidirect
76. #474×C73C22semidirect
78. #468×C73C22semidirect
80. #466×C73C22semidirect
81. #466×C73C22semidirect
82. #465×C73C22semidirect
83. #463×C73C22semidirect
84. #463×C73C22semidirect
85. #463×C73C22semidirect
86. #463×C73C22semidirect
89. #449×C73C22semidirect
90. #449×C73C22semidirect
91. #448×C73C22semidirect
93. #447×C73C22semidirect
94. #447×C73C22semidirect
95. #446×C73C22semidirect
96. C8×Q8×C73C22semidirect
97. #442×C73C22semidirect
98. #440×C73C22semidirect
99. C4×SD16×C73C22semidirect
100. C4×D8×C73C22semidirect
101. C4×D8×C73C22semidirect
102. C4×D8×C73C22semidirect
103. #436×C73C22semidirect
104. #435×C73C22semidirect
105. C8×D4×C73C22semidirect
106. C8×D4×C73C22semidirect
107. #433×C73C22semidirect
108. #432×C73C22semidirect
109. #418×C73C22semidirect
110. #417×C73C22semidirect
111. #416×C73C22semidirect
112. C2×#103×C73C22semidirect
113. C2×#103×C73C22semidirect
116. C2×#102×C73C22semidirect
117. #405×C73C22semidirect
118. C2×C4×C8×C73C22semidirect
508. #62558C73direct (N × H)
517. #3559C2×C73semidirect
518. #3558C2×C73semidirect
519. #3370C2×C73semidirect
520. #3361C2×C73semidirect
521. #3322C2×C73semidirect
522. #3318C2×C73semidirect
523. #3308C2×C73semidirect
524. #3301C2×C73semidirect
525. #3297C2×C73semidirect
526. #3294C2×C73semidirect
527. #3243C2×C73semidirect
528. #3234C2×C73semidirect
529. #3220C2×C73semidirect
530. #3213C2×C73semidirect
531. #3179C2×C73semidirect
532. #3169C2×C73semidirect
533. #3136C2×C73semidirect
534. C2×#488C2×C73semidirect
535. #2966C2×C73semidirect
536. C73#62558direct (N × H)
542. #554C22×C73semidirect
543. #553C22×C73semidirect
544. #553C22×C73semidirect
547. #547C22×C73semidirect
551. #544C22×C73semidirect
553. #540C22×C73semidirect
562. #532C22×C73semidirect
564. C2×#125C22×C73semidirect
566. #501C22×C73semidirect
567. #500C22×C73semidirect
568. #496C22×C73semidirect
569. #493C22×C73semidirect
571. #490C22×C73semidirect
572. #489C22×C73semidirect
573. #489C22×C73semidirect
574. #488C22×C73semidirect
575. #488C22×C73semidirect
576. #488C22×C73semidirect
577. #488C22×C73semidirect
578. #488C22×C73semidirect
580. #486C22×C73semidirect
581. #486C22×C73semidirect
582. #485C22×C73semidirect
583. #484C22×C73semidirect
585. #481C22×C73semidirect
587. #480C22×C73semidirect
588. #479C22×C73semidirect
589. #478C22×C73semidirect
590. #478C22×C73semidirect
591. #478C22×C73semidirect
592. #477C22×C73semidirect
593. #474C22×C73semidirect
595. #468C22×C73semidirect
597. #466C22×C73semidirect
598. #466C22×C73semidirect
599. #465C22×C73semidirect
600. #463C22×C73semidirect
601. #463C22×C73semidirect
602. #463C22×C73semidirect
603. #463C22×C73semidirect
606. #449C22×C73semidirect
607. #449C22×C73semidirect
608. #448C22×C73semidirect
610. #447C22×C73semidirect
611. #447C22×C73semidirect
612. #446C22×C73semidirect
613. C8×Q8C22×C73semidirect
614. #442C22×C73semidirect
615. #440C22×C73semidirect
616. C4×SD16C22×C73semidirect
617. C4×D8C22×C73semidirect
618. C4×D8C22×C73semidirect
619. C4×D8C22×C73semidirect
620. #436C22×C73semidirect
621. #435C22×C73semidirect
622. C8×D4C22×C73semidirect
623. C8×D4C22×C73semidirect
624. #433C22×C73semidirect
625. #432C22×C73semidirect
626. #418C22×C73semidirect
627. #417C22×C73semidirect
628. #416C22×C73semidirect
629. C2×#103C22×C73semidirect
630. C2×#103C22×C73semidirect
633. C2×#102C22×C73semidirect
634. #405C22×C73semidirect
635. C2×C4×C8C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35592
C73×#35582
C73×#33702
C73×#33612
C73×#33222
C73×#33182
C73×#33082
C73×#33012
C73×#32972
C73×#32942
C73×#32432
C73×#32342
C73×#32202
C73×#32132
C73×#31792
C73×#31692
C73×#31362
C2×#488×C732
C73×#29662
#6255873