Finite Group Databasebeta

← C73×#18823 #32928227

Subgroups — C73×#18823 #32928227

Order 18688.

912 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3520C211yesmaximal, characteristic
2C73×#3252C211yesmaximal, characteristic, complemented
3C73×#3231C211yesmaximal, characteristic, complemented
4C73×#3077C211yesmaximal, characteristic, complemented
5C73×#1654C211yesmaximal, characteristic, complemented
6C73×#1652C211yesmaximal, characteristic, complemented
7C73×#1649C211yesmaximal, characteristic, complemented
8C73×#1647C211yesmaximal, characteristic, complemented
9C73×#1638C211yesmaximal, characteristic, complemented
10C73×#1637C211yesmaximal, characteristic, complemented
11C73×#1635C211yesmaximal, characteristic, complemented
12C73×#1635C211yesmaximal, characteristic, complemented
13C73×#1561C211yesmaximal, characteristic, complemented
14C73×#1495C211yesmaximal, characteristic, complemented
15C73×#1486C211yesmaximal, characteristic, complemented
16#556×C73C2211yescharacteristic
17#554×C73—21no—
18#552×C73—21no—
19#551×C73—22no—
20D4×Q8×C73C2211yescharacteristic
21#548×C73—21no—
22#547×C73C2211yescharacteristic
23#547×C73C2211yescharacteristic
24#546×C73—21no—
25#542×C73—21no—
26#539×C73—22no—
27#533×C73C2211yescharacteristic
28#533×C73C2211yescharacteristic
29#529×C73C2211yescharacteristic
30#525×C73—21no—
31C2×C22⋊Q8×C73—21no—
32#520×C73—21no—
33C2×C4×D4×C73C2211yescharacteristic
34#500×C73C2211yescharacteristic, complemented
35#498×C73C2211yescharacteristic, complemented
36#487×C73C2211yescharacteristic, complemented
37#487×C73C2211yescharacteristic, complemented
38#485×C73—22no—
39#479×C73—22no—
40#479×C73—21no—
41#478×C73—21no—
42#478×C73—21no—
43#477×C73C2211yescharacteristic, complemented
44#476×C73C2211yescharacteristic
45#476×C73C2211yescharacteristic
46#476×C73C2211yescharacteristic, complemented
47#474×C73C2211yescharacteristic
48#474×C73C2211yescharacteristic
49#470×C73—21no—
50#468×C73—21no—
51#464×C73—21no—
52#462×C73C2211yescharacteristic, complemented
53#461×C73C2211yescharacteristic, complemented
54#431×C73C2211yescharacteristic
55#428×C73—21no—
56#423×C73C2211yescharacteristic
57#423×C73C2211yescharacteristic
58#418×C73—21no—
59#332×C73C2211yescharacteristic, complemented
60#332×C73C2211yescharacteristic, complemented
61#332×C73C2211yescharacteristic, complemented
62#332×C73C2211yescharacteristic, complemented
63Q8⋊C8×C73C2211yescharacteristic, complemented
64Q8⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67D4⋊C8×C73C2211yescharacteristic
68D4⋊C8×C73C2211yescharacteristic
69D4⋊C8×C73C2211yescharacteristic, complemented
70D4⋊C8×C73C2211yescharacteristic, complemented
71C2×#41×C73—21no—
72C2×#41×C73—21no—
73C22×Q8×C73—21no—
74C22×D4×C73D411yescharacteristic
75C23×C4×C73—21no—
76C2×Q16×C73—21no—
77C2×SD16×C73—21no—
78C2×M16×C73—21no—
79C2×M16×C73—21no—
80C4⋊Q8×C73—21no—
81C4⋊Q8×C73C2311yescharacteristic
82C4⋊Q8×C73C2311yescharacteristic
83C4⋊Q8×C73C2311yescharacteristic
84C4⋊Q8×C73C2311yescharacteristic
85#126×C73—22no—
86#126×C73—22no—
87#126×C73—21no—
88#125×C73—22no—
89#125×C73—21no—
90#125×C73D411yescharacteristic
91#125×C73D412yes—
92#124×C73—22no—
93#124×C73—21no—
94#124×C73D411yescharacteristic
95#123×C73—22no—
96#123×C73—22no—
97#123×C73—21no—
98#123×C73—22no—
99#123×C73—22no—
100C22⋊Q8×C73—22no—
101C22⋊Q8×C73—22no—
102C22⋊Q8×C73—22no—
103C22⋊Q8×C73—21no—
104C22⋊Q8×C73—21no—
105C22⋊Q8×C73—21no—
106C22⋊Q8×C73—21no—
107C22⋊Q8×C73—21no—
108C22⋊Q8×C73—22no—
109C22⋊Q8×C73—21no—
110C22⋊Q8×C73—21no—
111C22⋊Q8×C73—21no—
112C22⋊Q8×C73D411yescharacteristic
113#121×C73—22no—
114#121×C73—21no—
115#121×C73—21no—
116#121×C73D411yescharacteristic
117#120×C73—22no—
118C4×Q8×C73—21no—
119C4×Q8×C73—21no—
120C4×Q8×C73—21no—
121C4×Q8×C73—21no—
122C4×Q8×C73—21no—
123C4×Q8×C73C2311yescharacteristic
124C4×D4×C73—22no—
125C4×D4×C73—22no—
126C4×D4×C73—22no—
127C4×D4×C73—21no—
128C4×D4×C73—21no—
129C4×D4×C73—21no—
130C4×D4×C73—21no—
131C4×D4×C73D411yescharacteristic
132C4×D4×C73D411yescharacteristic
133C4×D4×C73C2311yescharacteristic
134C4×D4×C73C2311yescharacteristic
135C4×D4×C73C2311yescharacteristic
136#117×C73—22no—
137#117×C73—21no—
138#117×C73—21no—
139#117×C73—21no—
140#117×C73D412yes—
141C2×C4⋊C4×C73—22no—
142C2×C4⋊C4×C73—21no—
143C2×C4⋊C4×C73—21no—
144C2×C4⋊C4×C73D411yescharacteristic
145C2×C22⋊C4×C73—22no—
146C2×C22⋊C4×C73—21no—
147C2×C42×C73C2311yescharacteristic
148#107×C73—21no—
149#107×C73—21no—
150#107×C73—21no—
151#107×C73—22no—
152#106×C73—21no—
153#106×C73—21no—
154#106×C73—21no—
155#106×C73—22no—
156C4⋊C8×C73—21no—
157C4⋊C8×C73—21no—
158C4⋊C8×C73—21no—
159C4⋊C8×C73C2311yescharacteristic
160C4⋊C8×C73C2311yescharacteristic
161C4⋊C8×C73C2311yescharacteristic
162C4⋊C8×C73C2311yescharacteristic
163#103×C73—21no—
164#103×C73—21no—
165#103×C73—21no—
166#103×C73—22no—
167#103×C73—22no—
168#102×C73—21no—
169#102×C73—21no—
170#102×C73—21no—
171#102×C73—21no—
172#102×C73—21no—
173C22⋊C8×C73—21no—
174C4×C8×C73C2311yescharacteristic
175C4×C8×C73C2311yescharacteristic
176C24×C73—21no—
177#41×C73—42no—
178#41×C73—42no—
179#41×C73—81no—
180#41×C73—81no—
181C2×Q8×C73—22no—
182C2×Q8×C73—21no—
183C2×Q8×C73—21no—
184C2×Q8×C73—21no—
185C2×Q8×C73—21no—
186C2×Q8×C73—81no—
187C2×Q8×C73—81no—
188C2×Q8×C73C2×D411yescharacteristic
189C2×D4×C73—22no—
190C2×D4×C73—22no—
191C2×D4×C73—21no—
192C2×D4×C73—22no—
193C2×D4×C73—21no—
194C2×D4×C73—41no—
195C2×D4×C73C2×D411yescharacteristic
196C2×D4×C73C2×D411yescharacteristic
197C2×D4×C73C2×D411yescharacteristic
198C22×C4×C73—22no—
199C22×C4×C73—22no—
200C22×C4×C73—22no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—81no—
208C22×C4×C73—81no—
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212Q16×C73—81no—
213SD16×C73—81no—
214M16×C73—42no—
215M16×C73—81no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C4⋊C4×C73—22no—
223C4⋊C4×C73—22no—
224C4⋊C4×C73—22no—
225C4⋊C4×C73—22no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—22no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—22no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—41no—
240C4⋊C4×C73—41no—
241C4⋊C4×C73C2×D411yescharacteristic
242C4⋊C4×C73C2×D412yes—
243C4⋊C4×C73C2×D411yescharacteristic
244C4⋊C4×C73C2×D412yes—
245C4⋊C4×C73C2×D411yescharacteristic
246C4⋊C4×C73C2×D411yescharacteristic
247C22⋊C4×C73—22no—
248C22⋊C4×C73—22no—
249C22⋊C4×C73—22no—
250C22⋊C4×C73—22no—
251C22⋊C4×C73—22no—
252C22⋊C4×C73—21no—
253C22⋊C4×C73—22no—
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—41no—
263C42×C73—22no—
264C42×C73—22no—
265C42×C73—21no—
266C42×C73—41no—
267C42×C73C2×D411yescharacteristic
268C42×C73C2×D411yescharacteristic
269C42×C73C2×D411yescharacteristic
270C42×C73C2411yescharacteristic
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—42no—
275C23×C73—42no—
276C23×C73—81no—
277C23×C73#12011yescharacteristic
278Q8×C73—21no—
279Q8×C73—21no—
280Q8×C73—42no—
281Q8×C73—41no—
282Q8×C73—41no—
283Q8×C73—41no—
284Q8×C73—41no—
285Q8×C73—41no—
286Q8×C73—41no—
287Q8×C73—82no—
288D4×C73—21no—
289D4×C73—21no—
290D4×C73—21no—
291D4×C73—21no—
292D4×C73—21no—
293D4×C73—42no—
294D4×C73—42no—
295D4×C73—44no—
296D4×C73—82no—
297D4×C73#13712yes—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—22no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—22no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—41no—
310C2×C4×C73—44no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—81no—
320C2×C4×C73—81no—
321C2×C4×C73—81no—
322C2×C4×C73—82no—
323C2×C4×C73—82no—
324C2×C4×C73#12011yescharacteristic
325C2×C4×C73#12011yescharacteristic
326C2×C4×C73#12011yescharacteristic
327C2×C4×C73C22×D411yescharacteristic
328C2×C4×C73C22×D411yescharacteristic
329C2×C4×C73C22×D411yescharacteristic
330C8×C73—41no—
331C8×C73—41no—
332C8×C73—41no—
333C8×C73—41no—
334C8×C73—41no—
335C8×C73—41no—
336C22×C73—21no—
337C22×C73—22no—
338C22×C73—21no—
339C22×C73—21no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—84no—
349C22×C73C2×#12011yescharacteristic
350C4×C73—21no—
351C4×C73—21no—
352C4×C73—21no—
353C4×C73—21no—
354C4×C73—41no—
355C4×C73—42no—
356C4×C73—41no—
357C4×C73—41no—
358C4×C73—42no—
359C4×C73—41no—
360C4×C73—41no—
361C4×C73—81no—
362C4×C73—81no—
363C4×C73C2×#13711yescharacteristic
364C4×C73#57511yescharacteristic
365C4×C73#57611yescharacteristic
366C4×C73#57711yescharacteristic
367#18823C7311yesmaximal, characteristic, direct product factor, Sylow
368C2×C73—41no—
369C2×C73—42no—
370C2×C73—81no—
371C2×C73—81no—
372C2×C73#300711yescharacteristic
373C2×C73#301211yescharacteristic
374C2×C73#302011yescharacteristic
375#3520C2×C7311yescharacteristic
376#3252C2×C7311yescharacteristic, complemented
377#3231C2×C7311yescharacteristic, complemented
378#3077C2×C7311yescharacteristic, complemented
379#1654C2×C7311yescharacteristic, complemented
380#1652C2×C7311yescharacteristic, complemented
381#1649C2×C7311yescharacteristic, complemented
382#1647C2×C7311yescharacteristic, complemented
383#1638C2×C7311yescharacteristic, complemented
384#1637C2×C7311yescharacteristic, complemented
385#1635C2×C7311yescharacteristic, complemented
386#1635C2×C7311yescharacteristic, complemented
387#1561C2×C7311yescharacteristic, complemented
388#1495C2×C7311yescharacteristic, complemented
389#1486C2×C7311yescharacteristic, complemented
390C73#1882311yescharacteristic, direct product factor, Sylow
391#556C22×C7311yescharacteristic
392#554—21no—
393#552—21no—
394#551—22no—
395D4×Q8C22×C7311yescharacteristic
396#548—21no—
397#547C22×C7311yescharacteristic
398#547C22×C7311yescharacteristic
399#546—21no—
400#542—21no—
401#539—22no—
402#533C22×C7311yescharacteristic
403#533C22×C7311yescharacteristic
404#529C22×C7311yescharacteristic
405#525—21no—
406C2×C22⋊Q8—21no—
407#520—21no—
408C2×C4×D4C22×C7311yescharacteristic
409#500C22×C7311yescharacteristic, complemented
410#498C22×C7311yescharacteristic, complemented
411#487C22×C7311yescharacteristic, complemented
412#487C22×C7311yescharacteristic, complemented
413#485—22no—
414#479—22no—
415#479—21no—
416#478—21no—
417#478—21no—
418#477C22×C7311yescharacteristic, complemented
419#476C22×C7311yescharacteristic
420#476C22×C7311yescharacteristic
421#476C22×C7311yescharacteristic, complemented
422#474C22×C7311yescharacteristic
423#474C22×C7311yescharacteristic
424#470—21no—
425#468—21no—
426#464—21no—
427#462C22×C7311yescharacteristic, complemented
428#461C22×C7311yescharacteristic, complemented
429#431C22×C7311yescharacteristic
430#428—21no—
431#423C22×C7311yescharacteristic
432#423C22×C7311yescharacteristic
433#418—21no—
434#332C22×C7311yescharacteristic, complemented
435#332C22×C7311yescharacteristic, complemented
436#332C22×C7311yescharacteristic, complemented
437#332C22×C7311yescharacteristic, complemented
438Q8⋊C8C22×C7311yescharacteristic, complemented
439Q8⋊C8C22×C7311yescharacteristic, complemented
440D4⋊C8C22×C7311yescharacteristic
441D4⋊C8C22×C7311yescharacteristic
442D4⋊C8C22×C7311yescharacteristic
443D4⋊C8C22×C7311yescharacteristic
444D4⋊C8C22×C7311yescharacteristic, complemented
445D4⋊C8C22×C7311yescharacteristic, complemented
446C2×#41—21no—
447C2×#41—21no—
448C22×Q8—21no—
449C22×D4D4×C7311yescharacteristic
450C23×C4—21no—
451C2×Q16—21no—
452C2×SD16—21no—
453C2×M16—21no—
454C2×M16—21no—
455C4⋊Q8—21no—
456C4⋊Q8C23×C7311yescharacteristic
457C4⋊Q8C23×C7311yescharacteristic
458C4⋊Q8C23×C7311yescharacteristic
459C4⋊Q8C23×C7311yescharacteristic
460#126—22no—
461#126—22no—
462#126—21no—
463#125—22no—
464#125—21no—
465#125D4×C7311yescharacteristic
466#125D4×C7312yes—
467#124—22no—
468#124—21no—
469#124D4×C7311yescharacteristic
470#123—22no—
471#123—22no—
472#123—21no—
473#123—22no—
474#123—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—22no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8D4×C7311yescharacteristic
488#121—22no—
489#121—21no—
490#121—21no—
491#121D4×C7311yescharacteristic
492#120—22no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8C23×C7311yescharacteristic
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4D4×C7311yescharacteristic
507C4×D4D4×C7311yescharacteristic
508C4×D4C23×C7311yescharacteristic
509C4×D4C23×C7311yescharacteristic
510C4×D4C23×C7311yescharacteristic
511#117—22no—
512#117—21no—
513#117—21no—
514#117—21no—
515#117D4×C7312yes—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C7311yescharacteristic
520C2×C22⋊C4—22no—
521C2×C22⋊C4—21no—
522C2×C42C23×C7311yescharacteristic
523#107—21no—
524#107—21no—
525#107—21no—
526#107—22no—
527#106—21no—
528#106—21no—
529#106—21no—
530#106—22no—
531C4⋊C8—21no—
532C4⋊C8—21no—
533C4⋊C8—21no—
534C4⋊C8C23×C7311yescharacteristic
535C4⋊C8C23×C7311yescharacteristic
536C4⋊C8C23×C7311yescharacteristic
537C4⋊C8C23×C7311yescharacteristic
538#103—21no—
539#103—21no—
540#103—21no—
541#103—22no—
542#103—22no—
543#102—21no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—21no—
548C22⋊C8—21no—
549C4×C8C23×C7311yescharacteristic
550C4×C8C23×C7311yescharacteristic
551C24—21no—
552#41—42no—
553#41—42no—
554#41—81no—
555#41—81no—
556C2×Q8—22no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—81no—
562C2×Q8—81no—
563C2×Q8C2×D4×C7311yescharacteristic
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—41no—
570C2×D4C2×D4×C7311yescharacteristic
571C2×D4C2×D4×C7311yescharacteristic
572C2×D4C2×D4×C7311yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C7311yescharacteristic
585C22×C4C2×D4×C7311yescharacteristic
586C22×C4C2×D4×C7311yescharacteristic
587Q16—81no—
588SD16—81no—
589M16—42no—
590M16—81no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4C2×D4×C7311yescharacteristic
617C4⋊C4C2×D4×C7312yes—
618C4⋊C4C2×D4×C7311yescharacteristic
619C4⋊C4C2×D4×C7312yes—
620C4⋊C4C2×D4×C7311yescharacteristic
621C4⋊C4C2×D4×C7311yescharacteristic
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—21no—
628C22⋊C4—22no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—41no—
638C42—22no—
639C42—22no—
640C42—21no—
641C42—41no—
642C42C2×D4×C7311yescharacteristic
643C42C2×D4×C7311yescharacteristic
644C42C2×D4×C7311yescharacteristic
645C42C24×C7311yescharacteristic
646C23—21no—
647C23—21no—
648C23—21no—
649C23—42no—
650C23—42no—
651C23—81no—
652C23#120×C7311yescharacteristic
653Q8—21no—
654Q8—21no—
655Q8—42no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—82no—
663D4—21no—
664D4—21no—
665D4—21no—
666D4—21no—
667D4—21no—
668D4—42no—
669D4—44no—
670D4—42no—
671D4—82no—
672D4#137×C7312yes—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—44no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4#120×C7311yescharacteristic
700C2×C4#120×C7311yescharacteristic
701C2×C4#120×C7311yescharacteristic
702C2×C4C22×D4×C7311yescharacteristic
703C2×C4C22×D4×C7311yescharacteristic
704C2×C4C22×D4×C7311yescharacteristic
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C8—41no—
711C22—21no—
712C22—22no—
713C22—21no—
714C22—21no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—84no—
724C22C2×#120×C7311yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—42no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4—81no—
738C4C2×#137×C7311yescharacteristic
739C4#575×C7311yescharacteristic
740C4#576×C7311yescharacteristic
741C4#577×C7311yescharacteristic
742C2—41no—
743C2—42no—
744C2—81no—
745C2—81no—
746C2C73×#300711yescharacteristic
747C2C73×#301211yescharacteristic
748C2C73×#302011yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3520C2
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
2. C73×#3252C2semidirect
3. C73×#3231C2semidirect
4. C73×#3077C2semidirect
5. C73×#1654C2semidirect
6. C73×#1652C2semidirect
7. C73×#1649C2semidirect
8. C73×#1647C2semidirect
9. C73×#1638C2semidirect
10. C73×#1637C2semidirect
11. C73×#1635C2semidirect
12. C73×#1635C2semidirect
13. C73×#1561C2semidirect
14. C73×#1495C2semidirect
15. C73×#1486C2semidirect
34. #500×C73C22semidirect
35. #498×C73C22semidirect
36. #487×C73C22semidirect
37. #487×C73C22semidirect
43. #477×C73C22semidirect
46. #476×C73C22semidirect
52. #462×C73C22semidirect
53. #461×C73C22semidirect
59. #332×C73C22semidirect
60. #332×C73C22semidirect
61. #332×C73C22semidirect
62. #332×C73C22semidirect
63. Q8⋊C8×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
69. D4⋊C8×C73C22semidirect
70. D4⋊C8×C73C22semidirect
367. #18823C73direct (N × H)
376. #3252C2×C73semidirect
377. #3231C2×C73semidirect
378. #3077C2×C73semidirect
379. #1654C2×C73semidirect
380. #1652C2×C73semidirect
381. #1649C2×C73semidirect
382. #1647C2×C73semidirect
383. #1638C2×C73semidirect
384. #1637C2×C73semidirect
385. #1635C2×C73semidirect
386. #1635C2×C73semidirect
387. #1561C2×C73semidirect
388. #1495C2×C73semidirect
389. #1486C2×C73semidirect
390. C73#18823direct (N × H)
409. #500C22×C73semidirect
410. #498C22×C73semidirect
411. #487C22×C73semidirect
412. #487C22×C73semidirect
418. #477C22×C73semidirect
421. #476C22×C73semidirect
427. #462C22×C73semidirect
428. #461C22×C73semidirect
434. #332C22×C73semidirect
435. #332C22×C73semidirect
436. #332C22×C73semidirect
437. #332C22×C73semidirect
438. Q8⋊C8C22×C73semidirect
439. Q8⋊C8C22×C73semidirect
444. D4⋊C8C22×C73semidirect
445. D4⋊C8C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35202
C73×#32522
C73×#32312
C73×#30772
C73×#16542
C73×#16522
C73×#16492
C73×#16472
C73×#16382
C73×#16372
C73×#16352
C73×#15612
C73×#14952
C73×#14862
#1882373