Finite Group Databasebeta

← C73×#18618 #32928022

Subgroups — C73×#18618 #32928022

Order 18688.

1084 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3519C211yesmaximal, characteristic, complemented
2C73×#3247C211yesmaximal, characteristic, complemented
3C73×#3147C211yesmaximal, characteristic, complemented
4C73×#3109C211yesmaximal, characteristic, complemented
5C73×#1634C211yesmaximal, characteristic, complemented
6C73×#1632C211yesmaximal, characteristic, complemented
7C73×#1631C211yesmaximal, characteristic, complemented
8C73×#1629C211yesmaximal, characteristic, complemented
9C73×#1624C211yesmaximal, characteristic, complemented
10C73×#1622C211yesmaximal, characteristic, complemented
11C73×#1621C211yesmaximal, characteristic, complemented
12C73×#1619C211yesmaximal, characteristic, complemented
13C73×#1551C211yesmaximal, characteristic, complemented
14C73×#1494C211yesmaximal, characteristic, complemented
15C2×D4⋊C8×C73C211yesmaximal, characteristic, complemented
16C2×#135×C73—22no—
17#555×C73C2211yescharacteristic
18#554×C73C2211yescharacteristic
19#553×C73—21no—
20#553×C73—21no—
21#550×C73C2211yescharacteristic
22#546×C73—22no—
23#546×C73—21no—
24D42×C73—21no—
25D42×C73C2211yescharacteristic
26#540×C73—21no—
27#538×C73—22no—
28#532×C73C2211yescharacteristic
29#532×C73C2211yescharacteristic, complemented
30#529×C73C2211yescharacteristic
31#525×C73—21no—
32C2×#121×C73—21no—
33#518×C73—21no—
34C2×C4×D4×C73C2211yescharacteristic
35#495×C73—22no—
36#494×C73C2211yescharacteristic, complemented
37#493×C73C2211yescharacteristic, complemented
38#492×C73C2211yescharacteristic, complemented
39#492×C73C2211yescharacteristic, complemented
40#481×C73—21no—
41#478×C73—21no—
42#477×C73C2211yescharacteristic, complemented
43#476×C73C2211yescharacteristic
44#476×C73C2211yescharacteristic, complemented
45#476×C73C2211yescharacteristic, complemented
46#466×C73—21no—
47#465×C73—21no—
48#463×C73—21no—
49#460×C73C2211yescharacteristic, complemented
50#459×C73C2211yescharacteristic
51#459×C73C2211yescharacteristic, complemented
52#459×C73C2211yescharacteristic, complemented
53#447×C73—21no—
54#442×C73—21no—
55#442×C73—21no—
56#432×C73C2211yescharacteristic, complemented
57C2×C4⋊C8×C73C2211yescharacteristic, complemented
58C2×C4×C8×C73C2211yescharacteristic, complemented
59#333×C73C2211yescharacteristic, complemented
60#333×C73C2211yescharacteristic, complemented
61#331×C73C2211yescharacteristic, complemented
62#331×C73C2211yescharacteristic, complemented
63Q8⋊C8×C73C2211yescharacteristic, complemented
64Q8⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67D4⋊C8×C73C2211yescharacteristic, complemented
68D4⋊C8×C73C2211yescharacteristic, complemented
69D4⋊C8×C73C2211yescharacteristic, complemented
70D4⋊C8×C73C2211yescharacteristic, complemented
71C2×#41×C73—21no—
72C2×#41×C73—21no—
73C2×#41×C73D412yes—
74C22×D4×C73—22no—
75C22×D4×C73—21no—
76C22×D4×C73—21no—
77C22×D4×C73D411yescharacteristic
78C23×C4×C73—21no—
79#135×C73—48no—
80C2×Q16×C73—22no—
81C2×SD16×C73—22no—
82C2×SD16×C73—22no—
83C2×SD16×C73—21no—
84C2×D8×C73—21no—
85C2×D8×C73—21no—
86C2×D8×C73—22no—
87C2×D8×C73—21no—
88C22×C8×C73—21no—
89C22×C8×C73—21no—
90C4⋊Q8×C73C2311yescharacteristic
91C4⋊Q8×C73C2311yescharacteristic
92#127×C73—21no—
93#127×C73C2311yescharacteristic
94#127×C73C2311yescharacteristic
95#126×C73—22no—
96#126×C73—21no—
97#125×C73—21no—
98#125×C73D411yescharacteristic
99#124×C73—22no—
100#124×C73—21no—
101#124×C73D411yescharacteristic
102#124×C73D412yes—
103#123×C73—22no—
104#123×C73—22no—
105#123×C73—22no—
106#123×C73—21no—
107C22⋊Q8×C73—21no—
108C22⋊Q8×C73—22no—
109C22⋊Q8×C73D411yescharacteristic
110#121×C73—22no—
111#121×C73—22no—
112#121×C73—22no—
113#121×C73—22no—
114#121×C73—21no—
115#121×C73—22no—
116#121×C73—21no—
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×C73D411yescharacteristic
125#120×C73—22no—
126#120×C73—22no—
127#120×C73—22no—
128C4×Q8×C73C2311yescharacteristic
129C4×D4×C73—22no—
130C4×D4×C73—22no—
131C4×D4×C73—22no—
132C4×D4×C73—21no—
133C4×D4×C73—21no—
134C4×D4×C73—21no—
135C4×D4×C73—21no—
136C4×D4×C73—21no—
137C4×D4×C73—21no—
138C4×D4×C73—21no—
139C4×D4×C73—21no—
140C4×D4×C73—21no—
141C4×D4×C73D411yescharacteristic
142C4×D4×C73D411yescharacteristic
143C4×D4×C73C2311yescharacteristic
144C4×D4×C73C2311yescharacteristic
145C4×D4×C73C2311yescharacteristic
146#117×C73—21no—
147#117×C73—21no—
148#117×C73—21no—
149C2×C4⋊C4×C73—21no—
150C2×C4⋊C4×C73D411yescharacteristic
151C2×C22⋊C4×C73—22no—
152C2×C22⋊C4×C73—22no—
153C2×C22⋊C4×C73—21no—
154C2×C42×C73C2311yescharacteristic
155#107×C73—21no—
156#106×C73—21no—
157#106×C73—21no—
158#106×C73—21no—
159C4⋊C8×C73—21no—
160C4⋊C8×C73C2311yescharacteristic
161C4⋊C8×C73C2311yescharacteristic
162C4⋊C8×C73C2311yescharacteristic
163C4⋊C8×C73C2311yescharacteristic
164#103×C73—21no—
165#102×C73—21no—
166#102×C73—21no—
167#102×C73—21no—
168#102×C73—21no—
169#102×C73—21no—
170#102×C73—21no—
171#102×C73—21no—
172C22⋊C8×C73—21no—
173#97×C73—21no—
174C4×C8×C73—21no—
175C4×C8×C73C2311yescharacteristic
176C4×C8×C73C2311yescharacteristic
177C24×C73—22no—
178C24×C73—21no—
179#41×C73—44no—
180#41×C73—44no—
181#41×C73—81no—
182#41×C73—81no—
183C2×Q8×C73—21no—
184C2×Q8×C73C2×D411yescharacteristic
185C2×Q8×C73C2×D412yes—
186C2×D4×C73—22no—
187C2×D4×C73—22no—
188C2×D4×C73—22no—
189C2×D4×C73—21no—
190C2×D4×C73—22no—
191C2×D4×C73—22no—
192C2×D4×C73—22no—
193C2×D4×C73—22no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—41no—
201C2×D4×C73—42no—
202C2×D4×C73—42no—
203C2×D4×C73—41no—
204C2×D4×C73—81no—
205C2×D4×C73—81no—
206C2×D4×C73—84no—
207C2×D4×C73C2×D411yescharacteristic
208C2×D4×C73C2×D411yescharacteristic
209C2×D4×C73C2×D411yescharacteristic
210C2×D4×C73C2×D412yes—
211C22×C4×C73—22no—
212C22×C4×C73—22no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—22no—
219C22×C4×C73—21no—
220C22×C4×C73—41no—
221C22×C4×C73—81no—
222C22×C4×C73—81no—
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2×D411yescharacteristic
226Q16×C73—44no—
227SD16×C73—44no—
228SD16×C73—44no—
229SD16×C73—81no—
230D8×C73—44no—
231D8×C73—42no—
232D8×C73—42no—
233D8×C73—81no—
234C2×C8×C73—24no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—81no—
242C4⋊C4×C73—22no—
243C4⋊C4×C73—22no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73—21no—
253C4⋊C4×C73C2×D411yescharacteristic
254C4⋊C4×C73C2×D411yescharacteristic
255C4⋊C4×C73C2×D411yescharacteristic
256C4⋊C4×C73C2×D411yescharacteristic
257C22⋊C4×C73—22no—
258C22⋊C4×C73—22no—
259C22⋊C4×C73—22no—
260C22⋊C4×C73—22no—
261C22⋊C4×C73—22no—
262C22⋊C4×C73—21no—
263C22⋊C4×C73—21no—
264C22⋊C4×C73—21no—
265C22⋊C4×C73—21no—
266C22⋊C4×C73—22no—
267C22⋊C4×C73—21no—
268C22⋊C4×C73—21no—
269C22⋊C4×C73—22no—
270C22⋊C4×C73—21no—
271C22⋊C4×C73—21no—
272C22⋊C4×C73—21no—
273C22⋊C4×C73—41no—
274C22⋊C4×C73—41no—
275C42×C73—22no—
276C42×C73—21no—
277C42×C73C2×D411yescharacteristic
278C42×C73C2×D411yescharacteristic
279C42×C73C2×D411yescharacteristic
280C42×C73C2411yescharacteristic
281C23×C73—21no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—22no—
285C23×C73—42no—
286C23×C73—44no—
287C23×C73—42no—
288C23×C73—41no—
289C23×C73—81no—
290C23×C73—82no—
291C23×C73—82no—
292C23×C73#12011yescharacteristic
293Q8×C73—21no—
294Q8×C73—21no—
295Q8×C73—42no—
296Q8×C73—42no—
297D4×C73—21no—
298D4×C73—21no—
299D4×C73—21no—
300D4×C73—21no—
301D4×C73—21no—
302D4×C73—42no—
303D4×C73—42no—
304D4×C73—42no—
305D4×C73—44no—
306D4×C73—42no—
307D4×C73—44no—
308D4×C73—41no—
309D4×C73—41no—
310D4×C73—41no—
311D4×C73—41no—
312D4×C73—41no—
313D4×C73—41no—
314D4×C73—41no—
315D4×C73—41no—
316D4×C73—82no—
317D4×C73—82no—
318D4×C73—82no—
319D4×C73—82no—
320D4×C73—82no—
321D4×C73#13512yescomplemented
322C2×C4×C73—22no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—22no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—81no—
341C2×C4×C73—81no—
342C2×C4×C73—82no—
343C2×C4×C73—82no—
344C2×C4×C73—81no—
345C2×C4×C73—82no—
346C2×C4×C73—82no—
347C2×C4×C73#12011yescharacteristic
348C2×C4×C73#12011yescharacteristic
349C2×C4×C73#12011yescharacteristic
350C2×C4×C73C22×D411yescharacteristic
351C2×C4×C73C22×D411yescharacteristic
352C2×C4×C73C22×D411yescharacteristic
353C8×C73—22no—
354C8×C73—22no—
355C8×C73—41no—
356C8×C73—41no—
357C8×C73—41no—
358C8×C73—41no—
359C22×C73—21no—
360C22×C73—21no—
361C22×C73—22no—
362C22×C73—41no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—42no—
367C22×C73—41no—
368C22×C73—42no—
369C22×C73—41no—
370C22×C73—42no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73—84no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73—164no—
378C22×C73#45312yes—
379C22×C73C2×#12011yescharacteristic
380C4×C73—21no—
381C4×C73—21no—
382C4×C73—21no—
383C4×C73—21no—
384C4×C73—41no—
385C4×C73—41no—
386C4×C73—41no—
387C4×C73—41no—
388C4×C73—41no—
389C4×C73—42no—
390C4×C73—81no—
391C4×C73C2×#13511yescharacteristic
392C4×C73#57511yescharacteristic
393C4×C73#57611yescharacteristic
394C4×C73#57711yescharacteristic
395#18618C7311yesmaximal, characteristic, direct product factor, Sylow
396C2×C73—22no—
397C2×C73—42no—
398C2×C73—81no—
399C2×C73—82no—
400C2×C73—81no—
401C2×C73—161no—
402C2×C73#300211yescharacteristic
403C2×C73#301211yescharacteristic
404C2×C73C2×#45311yescharacteristic
405#3519C2×C7311yescharacteristic, complemented
406#3247C2×C7311yescharacteristic, complemented
407#3147C2×C7311yescharacteristic, complemented
408#3109C2×C7311yescharacteristic, complemented
409#1634C2×C7311yescharacteristic, complemented
410#1632C2×C7311yescharacteristic, complemented
411#1631C2×C7311yescharacteristic, complemented
412#1629C2×C7311yescharacteristic, complemented
413#1624C2×C7311yescharacteristic, complemented
414#1622C2×C7311yescharacteristic, complemented
415#1621C2×C7311yescharacteristic, complemented
416#1619C2×C7311yescharacteristic, complemented
417#1551C2×C7311yescharacteristic, complemented
418#1494C2×C7311yescharacteristic, complemented
419C2×D4⋊C8C2×C7311yescharacteristic, complemented
420C73#1861811yescharacteristic, direct product factor, Sylow
421C2×#135—22no—
422#555C22×C7311yescharacteristic
423#554C22×C7311yescharacteristic
424#553—21no—
425#553—21no—
426#550C22×C7311yescharacteristic
427#546—22no—
428#546—21no—
429D42—21no—
430D42C22×C7311yescharacteristic
431#540—21no—
432#538—22no—
433#532C22×C7311yescharacteristic
434#532C22×C7311yescharacteristic, complemented
435#529C22×C7311yescharacteristic
436#525—21no—
437C2×#121—21no—
438#518—21no—
439C2×C4×D4C22×C7311yescharacteristic
440#495—22no—
441#494C22×C7311yescharacteristic, complemented
442#493C22×C7311yescharacteristic, complemented
443#492C22×C7311yescharacteristic, complemented
444#492C22×C7311yescharacteristic, complemented
445#481—21no—
446#478—21no—
447#477C22×C7311yescharacteristic, complemented
448#476C22×C7311yescharacteristic
449#476C22×C7311yescharacteristic, complemented
450#476C22×C7311yescharacteristic, complemented
451#466—21no—
452#465—21no—
453#463—21no—
454#460C22×C7311yescharacteristic, complemented
455#459C22×C7311yescharacteristic
456#459C22×C7311yescharacteristic, complemented
457#459C22×C7311yescharacteristic, complemented
458#447—21no—
459#442—21no—
460#442—21no—
461#432C22×C7311yescharacteristic, complemented
462C2×C4⋊C8C22×C7311yescharacteristic, complemented
463C2×C4×C8C22×C7311yescharacteristic, complemented
464#333C22×C7311yescharacteristic, complemented
465#333C22×C7311yescharacteristic, complemented
466#331C22×C7311yescharacteristic, complemented
467#331C22×C7311yescharacteristic, complemented
468Q8⋊C8C22×C7311yescharacteristic, complemented
469Q8⋊C8C22×C7311yescharacteristic, complemented
470D4⋊C8C22×C7311yescharacteristic
471D4⋊C8C22×C7311yescharacteristic
472D4⋊C8C22×C7311yescharacteristic, complemented
473D4⋊C8C22×C7311yescharacteristic, complemented
474D4⋊C8C22×C7311yescharacteristic, complemented
475D4⋊C8C22×C7311yescharacteristic, complemented
476C2×#41—21no—
477C2×#41—21no—
478C2×#41D4×C7312yes—
479C22×D4—22no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4D4×C7311yescharacteristic
483C23×C4—21no—
484#135—48no—
485C2×Q16—22no—
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16—21no—
489C2×D8—22no—
490C2×D8—21no—
491C2×D8—21no—
492C2×D8—21no—
493C22×C8—21no—
494C22×C8—21no—
495C4⋊Q8C23×C7311yescharacteristic
496C4⋊Q8C23×C7311yescharacteristic
497#127—21no—
498#127C23×C7311yescharacteristic
499#127C23×C7311yescharacteristic
500#126—22no—
501#126—21no—
502#125—21no—
503#125D4×C7311yescharacteristic
504#124—22no—
505#124—21no—
506#124D4×C7311yescharacteristic
507#124D4×C7312yes—
508#123—22no—
509#123—22no—
510#123—22no—
511#123—21no—
512C22⋊Q8—21no—
513C22⋊Q8—22no—
514C22⋊Q8D4×C7311yescharacteristic
515#121—22no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—21no—
520#121—22no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121D4×C7311yescharacteristic
530#120—22no—
531#120—22no—
532#120—22no—
533C4×Q8C23×C7311yescharacteristic
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4D4×C7311yescharacteristic
547C4×D4D4×C7311yescharacteristic
548C4×D4C23×C7311yescharacteristic
549C4×D4C23×C7311yescharacteristic
550C4×D4C23×C7311yescharacteristic
551#117—21no—
552#117—21no—
553#117—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4D4×C7311yescharacteristic
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—21no—
559C2×C42C23×C7311yescharacteristic
560#107—21no—
561#106—21no—
562#106—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8C23×C7311yescharacteristic
566C4⋊C8C23×C7311yescharacteristic
567C4⋊C8C23×C7311yescharacteristic
568C4⋊C8C23×C7311yescharacteristic
569#103—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577C22⋊C8—21no—
578#97—21no—
579C4×C8—21no—
580C4×C8C23×C7311yescharacteristic
581C4×C8C23×C7311yescharacteristic
582C24—22no—
583C24—21no—
584#41—44no—
585#41—44no—
586#41—81no—
587#41—81no—
588C2×Q8—21no—
589C2×Q8C2×D4×C7311yescharacteristic
590C2×Q8C2×D4×C7312yes—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—41no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—41no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—84no—
612C2×D4C2×D4×C7311yescharacteristic
613C2×D4C2×D4×C7311yescharacteristic
614C2×D4C2×D4×C7311yescharacteristic
615C2×D4C2×D4×C7312yes—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—41no—
626C22×C4—81no—
627C22×C4—81no—
628C22×C4C2×D4×C7311yescharacteristic
629C22×C4C2×D4×C7311yescharacteristic
630C22×C4C2×D4×C7311yescharacteristic
631Q16—44no—
632SD16—44no—
633SD16—44no—
634SD16—81no—
635D8—44no—
636D8—42no—
637D8—42no—
638D8—81no—
639C2×C8—24no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—81no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4C2×D4×C7311yescharacteristic
659C4⋊C4C2×D4×C7311yescharacteristic
660C4⋊C4C2×D4×C7311yescharacteristic
661C4⋊C4C2×D4×C7311yescharacteristic
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C42—22no—
681C42—21no—
682C42C2×D4×C7311yescharacteristic
683C42C2×D4×C7311yescharacteristic
684C42C2×D4×C7311yescharacteristic
685C42C24×C7311yescharacteristic
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—42no—
691C23—44no—
692C23—42no—
693C23—41no—
694C23—81no—
695C23—82no—
696C23—82no—
697C23#120×C7311yescharacteristic
698Q8—21no—
699Q8—21no—
700Q8—42no—
701Q8—42no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—44no—
711D4—42no—
712D4—44no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4#135×C7312yescomplemented
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4—81no—
750C2×C4—82no—
751C2×C4—82no—
752C2×C4#120×C7311yescharacteristic
753C2×C4#120×C7311yescharacteristic
754C2×C4#120×C7311yescharacteristic
755C2×C4C22×D4×C7311yescharacteristic
756C2×C4C22×D4×C7311yescharacteristic
757C2×C4C22×D4×C7311yescharacteristic
758C8—22no—
759C8—22no—
760C8—41no—
761C8—41no—
762C8—41no—
763C8—41no—
764C22—21no—
765C22—21no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—84no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—164no—
783C22#453×C7312yes—
784C22C2×#120×C7311yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—81no—
796C4C2×#135×C7311yescharacteristic
797C4#575×C7311yescharacteristic
798C4#576×C7311yescharacteristic
799C4#577×C7311yescharacteristic
800C2—22no—
801C2—42no—
802C2—81no—
803C2—81no—
804C2—82no—
805C2—161no—
806C2C73×#300211yescharacteristic
807C2C73×#301211yescharacteristic
808C2C2×#453×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3519C2semidirect
2. C73×#3247C2semidirect
3. C73×#3147C2semidirect
4. C73×#3109C2semidirect
5. C73×#1634C2semidirect
6. C73×#1632C2semidirect
7. C73×#1631C2semidirect
8. C73×#1629C2semidirect
9. C73×#1624C2semidirect
10. C73×#1622C2semidirect
11. C73×#1621C2semidirect
12. C73×#1619C2semidirect
13. C73×#1551C2semidirect
14. C73×#1494C2semidirect
15. C2×D4⋊C8×C73C2semidirect
29. #532×C73C22semidirect
36. #494×C73C22semidirect
37. #493×C73C22semidirect
38. #492×C73C22semidirect
39. #492×C73C22semidirect
42. #477×C73C22semidirect
44. #476×C73C22semidirect
45. #476×C73C22semidirect
49. #460×C73C22semidirect
51. #459×C73C22semidirect
52. #459×C73C22semidirect
56. #432×C73C22semidirect
57. C2×C4⋊C8×C73C22semidirect
58. C2×C4×C8×C73C22semidirect
59. #333×C73C22semidirect
60. #333×C73C22semidirect
61. #331×C73C22semidirect
62. #331×C73C22semidirect
63. Q8⋊C8×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
67. D4⋊C8×C73C22semidirect
68. D4⋊C8×C73C22semidirect
69. D4⋊C8×C73C22semidirect
70. D4⋊C8×C73C22semidirect
321. D4×C73#135semidirect
395. #18618C73direct (N × H)
405. #3519C2×C73semidirect
406. #3247C2×C73semidirect
407. #3147C2×C73semidirect
408. #3109C2×C73semidirect
409. #1634C2×C73semidirect
410. #1632C2×C73semidirect
411. #1631C2×C73semidirect
412. #1629C2×C73semidirect
413. #1624C2×C73semidirect
414. #1622C2×C73semidirect
415. #1621C2×C73semidirect
416. #1619C2×C73semidirect
417. #1551C2×C73semidirect
418. #1494C2×C73semidirect
419. C2×D4⋊C8C2×C73semidirect
420. C73#18618direct (N × H)
434. #532C22×C73semidirect
441. #494C22×C73semidirect
442. #493C22×C73semidirect
443. #492C22×C73semidirect
444. #492C22×C73semidirect
447. #477C22×C73semidirect
449. #476C22×C73semidirect
450. #476C22×C73semidirect
454. #460C22×C73semidirect
456. #459C22×C73semidirect
457. #459C22×C73semidirect
461. #432C22×C73semidirect
462. C2×C4⋊C8C22×C73semidirect
463. C2×C4×C8C22×C73semidirect
464. #333C22×C73semidirect
465. #333C22×C73semidirect
466. #331C22×C73semidirect
467. #331C22×C73semidirect
468. Q8⋊C8C22×C73semidirect
469. Q8⋊C8C22×C73semidirect
472. D4⋊C8C22×C73semidirect
473. D4⋊C8C22×C73semidirect
474. D4⋊C8C22×C73semidirect
475. D4⋊C8C22×C73semidirect
726. D4#135×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35192
C73×#32472
C73×#31472
C73×#31092
C73×#16342
C73×#16322
C73×#16312
C73×#16292
C73×#16242
C73×#16222
C73×#16212
C73×#16192
C73×#15512
C73×#14942
C2×D4⋊C8×C732
#1861873