Finite Group Databasebeta

← C73×#18795 #32928199

Subgroups — C73×#18795 #32928199

Order 18688.

956 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3475C211yesmaximal, characteristic, complemented
2C73×#3210C211yesmaximal, characteristic, complemented
3C73×#3109C211yesmaximal, characteristic, complemented
4C73×#3106C211yesmaximal, characteristic, complemented
5C73×#1638C211yesmaximal, characteristic, complemented
6C73×#1635C211yesmaximal, characteristic, complemented
7C73×#1634C211yesmaximal, characteristic, complemented
8C73×#1632C211yesmaximal, characteristic, complemented
9C73×#1628C211yesmaximal, characteristic, complemented
10C73×#1625C211yesmaximal, characteristic, complemented
11C73×#1624C211yesmaximal, characteristic, complemented
12C73×#1622C211yesmaximal, characteristic, complemented
13C73×#1554C211yesmaximal, characteristic, complemented
14C73×#1488C211yesmaximal, characteristic, complemented
15C73×#1478C211yesmaximal, characteristic, complemented
16#556×C73C2211yescharacteristic
17#555×C73C2211yescharacteristic
18#554×C73C2211yescharacteristic
19#553×C73—21no—
20#552×C73—21no—
21#552×C73—21no—
22#551×C73—22no—
23#547×C73C2211yescharacteristic
24#546×C73—21no—
25#533×C73C2211yescharacteristic
26#532×C73C2211yescharacteristic
27#529×C73—22no—
28#529×C73—21no—
29#525×C73—21no—
30C4×#41×C73—21no—
31C4×#41×C73C2211yescharacteristic
32C2×C4×D4×C73C2211yescharacteristic
33C2×#117×C73—21no—
34#494×C73C2211yescharacteristic, complemented
35#492×C73C2211yescharacteristic, complemented
36#487×C73C2211yescharacteristic, complemented
37#486×C73C2211yescharacteristic, complemented
38#482×C73—21no—
39#481×C73—21no—
40#477×C73C2211yescharacteristic, complemented
41#476×C73C2211yescharacteristic
42#476×C73C2211yescharacteristic
43#476×C73C2211yescharacteristic, complemented
44#464×C73—22no—
45#460×C73C2211yescharacteristic, complemented
46#459×C73C2211yescharacteristic
47#459×C73C2211yescharacteristic
48#459×C73C2211yescharacteristic, complemented
49#452×C73—22no—
50#449×C73—21no—
51#447×C73—21no—
52#442×C73—21no—
53#442×C73—21no—
54C4×SD16×C73—21no—
55C4×D8×C73—21no—
56#432×C73C2211yescharacteristic
57#431×C73C2211yescharacteristic
58#431×C73C2211yescharacteristic
59#333×C73C2211yescharacteristic, complemented
60#333×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—
73C2×#41×C73D411yescharacteristic
74C22×D4×C73D411yescharacteristic
75C23×C4×C73—21no—
76C2×Q16×C73—22no—
77C2×SD16×C73—21no—
78C2×SD16×C73—22no—
79C2×D8×C73—21no—
80C2×D8×C73—21no—
81C2×D8×C73—21no—
82C4⋊Q8×C73C2311yescharacteristic
83C4⋊Q8×C73C2311yescharacteristic
84C4⋊Q8×C73C2311yescharacteristic
85#127×C73C2311yescharacteristic
86#126×C73—22no—
87#126×C73—22no—
88#126×C73—22no—
89#125×C73—22no—
90#125×C73—21no—
91#125×C73—21no—
92#124×C73—22no—
93#124×C73—21no—
94#124×C73—21no—
95#123×C73—22no—
96#123×C73—22no—
97#123×C73—22no—
98#123×C73—22no—
99C22⋊Q8×C73—21no—
100C22⋊Q8×C73—21no—
101C22⋊Q8×C73—22no—
102C22⋊Q8×C73—21no—
103C22⋊Q8×C73—21no—
104C22⋊Q8×C73D412yes—
105#121×C73—22no—
106#121×C73—21no—
107#121×C73—21no—
108#121×C73—21no—
109#121×C73—21no—
110#121×C73—21no—
111#120×C73—22no—
112C4×Q8×C73—21no—
113C4×Q8×C73—21no—
114C4×Q8×C73D411yescharacteristic
115C4×Q8×C73D412yes—
116C4×Q8×C73C2311yescharacteristic
117C4×D4×C73—22no—
118C4×D4×C73—22no—
119C4×D4×C73—22no—
120C4×D4×C73—21no—
121C4×D4×C73—21no—
122C4×D4×C73—21no—
123C4×D4×C73—21no—
124C4×D4×C73—21no—
125C4×D4×C73—21no—
126C4×D4×C73—21no—
127C4×D4×C73D411yescharacteristic
128C4×D4×C73D411yescharacteristic
129C4×D4×C73D411yescharacteristic
130C4×D4×C73C2311yescharacteristic
131C4×D4×C73C2311yescharacteristic
132C4×D4×C73C2311yescharacteristic
133#117×C73—22no—
134#117×C73—22no—
135#117×C73—22no—
136#117×C73—21no—
137#117×C73—21no—
138#117×C73—21no—
139#117×C73—21no—
140#117×C73—21no—
141#117×C73D411yescharacteristic
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×C73—22no—
148C2×C42×C73—21no—
149C2×C42×C73C2311yescharacteristic
150#107×C73—21no—
151#106×C73—21no—
152#106×C73—21no—
153#106×C73—21no—
154C4⋊C8×C73—21no—
155C4⋊C8×C73C2311yescharacteristic
156C4⋊C8×C73C2311yescharacteristic
157C4⋊C8×C73C2311yescharacteristic
158C4⋊C8×C73C2311yescharacteristic
159#103×C73—21no—
160#103×C73—22no—
161#102×C73—21no—
162#102×C73—21no—
163#102×C73—21no—
164#102×C73—21no—
165#102×C73—21no—
166#102×C73—21no—
167#102×C73—21no—
168#102×C73—22no—
169C22⋊C8×C73—21no—
170C22⋊C8×C73—21no—
171C22⋊C8×C73—21no—
172#97×C73—21no—
173C4×C8×C73—21no—
174C4×C8×C73C2311yescharacteristic
175C4×C8×C73C2311yescharacteristic
176C24×C73—21no—
177#41×C73—41no—
178#41×C73—41no—
179#41×C73—42no—
180#41×C73—42no—
181#41×C73—82no—
182C2×Q8×C73—21no—
183C2×Q8×C73—21no—
184C2×Q8×C73C2×D411yescharacteristic
185C2×Q8×C73C2×D412yes—
186C2×D4×C73—22no—
187C2×D4×C73—22no—
188C2×D4×C73—21no—
189C2×D4×C73—22no—
190C2×D4×C73—21no—
191C2×D4×C73—21no—
192C2×D4×C73—21no—
193C2×D4×C73—21no—
194C2×D4×C73—41no—
195C2×D4×C73—41no—
196C2×D4×C73C2×D411yescharacteristic
197C2×D4×C73C2×D411yescharacteristic
198C2×D4×C73C2×D411yescharacteristic
199C22×C4×C73—22no—
200C22×C4×C73—21no—
201C22×C4×C73—22no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—42no—
210C22×C4×C73—42no—
211C22×C4×C73—41no—
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215Q16×C73—82no—
216SD16×C73—42no—
217SD16×C73—82no—
218D8×C73—42no—
219D8×C73—42no—
220D8×C73—42no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C4⋊C4×C73—22no—
228C4⋊C4×C73—22no—
229C4⋊C4×C73—22no—
230C4⋊C4×C73—22no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—22no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—22no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73C2×D412yes—
242C4⋊C4×C73C2×D411yescharacteristic
243C4⋊C4×C73C2×D411yescharacteristic
244C4⋊C4×C73C2×D411yescharacteristic
245C4⋊C4×C73C2×D411yescharacteristic
246C22⋊C4×C73—22no—
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—41no—
261C22⋊C4×C73—41no—
262C42×C73—22no—
263C42×C73—22no—
264C42×C73—21no—
265C42×C73—22no—
266C42×C73—21no—
267C42×C73—21no—
268C42×C73C2×D411yescharacteristic
269C42×C73C2×D411yescharacteristic
270C42×C73C2×D411yescharacteristic
271C42×C73C2411yescharacteristic
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—42no—
276C23×C73—42no—
277C23×C73—41no—
278C23×C73—81no—
279C23×C73#12011yescharacteristic
280Q8×C73—21no—
281Q8×C73—21no—
282Q8×C73—42no—
283Q8×C73—42no—
284Q8×C73—41no—
285Q8×C73—41no—
286D4×C73—21no—
287D4×C73—21no—
288D4×C73—21no—
289D4×C73—21no—
290D4×C73—21no—
291D4×C73—42no—
292D4×C73—42no—
293D4×C73—44no—
294D4×C73—42no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—41no—
298D4×C73—41no—
299D4×C73—82no—
300D4×C73—82no—
301D4×C73#13512yes—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—21no—
313C2×C4×C73—41no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73—42no—
317C2×C4×C73—42no—
318C2×C4×C73—44no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—81no—
327C2×C4×C73—82no—
328C2×C4×C73—82no—
329C2×C4×C73#12011yescharacteristic
330C2×C4×C73#12011yescharacteristic
331C2×C4×C73#12011yescharacteristic
332C2×C4×C73C22×D411yescharacteristic
333C2×C4×C73C22×D411yescharacteristic
334C2×C4×C73C22×D411yescharacteristic
335C8×C73—41no—
336C8×C73—41no—
337C8×C73—41no—
338C8×C73—41no—
339C8×C73—41no—
340C8×C73—41no—
341C22×C73—21no—
342C22×C73—22no—
343C22×C73—21no—
344C22×C73—21no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—84no—
354C22×C73—81no—
355C22×C73—81no—
356C22×C73—81no—
357C22×C73C2×#12011yescharacteristic
358C4×C73—21no—
359C4×C73—21no—
360C4×C73—21no—
361C4×C73—21no—
362C4×C73—41no—
363C4×C73—42no—
364C4×C73—41no—
365C4×C73—41no—
366C4×C73—41no—
367C4×C73—41no—
368C4×C73—42no—
369C4×C73—81no—
370C4×C73C2×#13511yescharacteristic
371C4×C73#57511yescharacteristic
372C4×C73#57511yescharacteristic
373C4×C73#57511yescharacteristic
374#18795C7311yesmaximal, characteristic, direct product factor, Sylow
375C2×C73—41no—
376C2×C73—42no—
377C2×C73—81no—
378C2×C73—81no—
379C2×C73—161no—
380C2×C73#300211yescharacteristic
381C2×C73#300511yescharacteristic
382C2×C73#302111yescharacteristic
383#3475C2×C7311yescharacteristic, complemented
384#3210C2×C7311yescharacteristic, complemented
385#3109C2×C7311yescharacteristic, complemented
386#3106C2×C7311yescharacteristic, complemented
387#1638C2×C7311yescharacteristic, complemented
388#1635C2×C7311yescharacteristic, complemented
389#1634C2×C7311yescharacteristic, complemented
390#1632C2×C7311yescharacteristic, complemented
391#1628C2×C7311yescharacteristic, complemented
392#1625C2×C7311yescharacteristic, complemented
393#1624C2×C7311yescharacteristic, complemented
394#1622C2×C7311yescharacteristic, complemented
395#1554C2×C7311yescharacteristic, complemented
396#1488C2×C7311yescharacteristic, complemented
397#1478C2×C7311yescharacteristic, complemented
398C73#1879511yescharacteristic, direct product factor, Sylow
399#556C22×C7311yescharacteristic
400#555C22×C7311yescharacteristic
401#554C22×C7311yescharacteristic
402#553—21no—
403#552—21no—
404#552—21no—
405#551—22no—
406#547C22×C7311yescharacteristic
407#546—21no—
408#533C22×C7311yescharacteristic
409#532C22×C7311yescharacteristic
410#529—22no—
411#529—21no—
412#525—21no—
413C4×#41—21no—
414C4×#41C22×C7311yescharacteristic
415C2×C4×D4C22×C7311yescharacteristic
416C2×#117—21no—
417#494C22×C7311yescharacteristic, complemented
418#492C22×C7311yescharacteristic, complemented
419#487C22×C7311yescharacteristic, complemented
420#486C22×C7311yescharacteristic, complemented
421#482—21no—
422#481—21no—
423#477C22×C7311yescharacteristic, complemented
424#476C22×C7311yescharacteristic
425#476C22×C7311yescharacteristic
426#476C22×C7311yescharacteristic, complemented
427#464—22no—
428#460C22×C7311yescharacteristic, complemented
429#459C22×C7311yescharacteristic
430#459C22×C7311yescharacteristic
431#459C22×C7311yescharacteristic, complemented
432#452—22no—
433#449—21no—
434#447—21no—
435#442—21no—
436#442—21no—
437C4×SD16—21no—
438C4×D8—21no—
439#432C22×C7311yescharacteristic
440#431C22×C7311yescharacteristic
441#431C22×C7311yescharacteristic
442#333C22×C7311yescharacteristic, complemented
443#333C22×C7311yescharacteristic, complemented
444#332C22×C7311yescharacteristic, complemented
445#332C22×C7311yescharacteristic, complemented
446Q8⋊C8C22×C7311yescharacteristic, complemented
447Q8⋊C8C22×C7311yescharacteristic, complemented
448D4⋊C8C22×C7311yescharacteristic
449D4⋊C8C22×C7311yescharacteristic
450D4⋊C8C22×C7311yescharacteristic
451D4⋊C8C22×C7311yescharacteristic
452D4⋊C8C22×C7311yescharacteristic, complemented
453D4⋊C8C22×C7311yescharacteristic, complemented
454C2×#41—21no—
455C2×#41—21no—
456C2×#41D4×C7311yescharacteristic
457C22×D4D4×C7311yescharacteristic
458C23×C4—21no—
459C2×Q16—22no—
460C2×SD16—21no—
461C2×SD16—22no—
462C2×D8—21no—
463C2×D8—21no—
464C2×D8—21no—
465C4⋊Q8C23×C7311yescharacteristic
466C4⋊Q8C23×C7311yescharacteristic
467C4⋊Q8C23×C7311yescharacteristic
468#127C23×C7311yescharacteristic
469#126—22no—
470#126—22no—
471#126—22no—
472#125—22no—
473#125—21no—
474#125—21no—
475#124—22no—
476#124—21no—
477#124—21no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—22no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8D4×C7312yes—
488#121—22no—
489#121—21no—
490#121—21no—
491#121—21no—
492#121—21no—
493#121—21no—
494#120—22no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8D4×C7311yescharacteristic
498C4×Q8D4×C7312yes—
499C4×Q8C23×C7311yescharacteristic
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4D4×C7311yescharacteristic
511C4×D4D4×C7311yescharacteristic
512C4×D4D4×C7311yescharacteristic
513C4×D4C23×C7311yescharacteristic
514C4×D4C23×C7311yescharacteristic
515C4×D4C23×C7311yescharacteristic
516#117—22no—
517#117—22no—
518#117—22no—
519#117—21no—
520#117—21no—
521#117—21no—
522#117—21no—
523#117—21no—
524#117D4×C7311yescharacteristic
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4D4×C7311yescharacteristic
528C2×C22⋊C4—22no—
529C2×C22⋊C4—21no—
530C2×C42—22no—
531C2×C42—21no—
532C2×C42C23×C7311yescharacteristic
533#107—21no—
534#106—21no—
535#106—21no—
536#106—21no—
537C4⋊C8—21no—
538C4⋊C8C23×C7311yescharacteristic
539C4⋊C8C23×C7311yescharacteristic
540C4⋊C8C23×C7311yescharacteristic
541C4⋊C8C23×C7311yescharacteristic
542#103—21no—
543#103—22no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549#102—21no—
550#102—21no—
551#102—22no—
552C22⋊C8—21no—
553C22⋊C8—21no—
554C22⋊C8—21no—
555#97—21no—
556C4×C8—21no—
557C4×C8C23×C7311yescharacteristic
558C4×C8C23×C7311yescharacteristic
559C24—21no—
560#41—41no—
561#41—41no—
562#41—42no—
563#41—42no—
564#41—82no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C2×D4×C7311yescharacteristic
568C2×Q8C2×D4×C7312yes—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4C2×D4×C7311yescharacteristic
580C2×D4C2×D4×C7311yescharacteristic
581C2×D4C2×D4×C7311yescharacteristic
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—41no—
595C22×C4C2×D4×C7311yescharacteristic
596C22×C4C2×D4×C7311yescharacteristic
597C22×C4C2×D4×C7311yescharacteristic
598Q16—82no—
599SD16—42no—
600SD16—82no—
601D8—42no—
602D8—42no—
603D8—42no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4C2×D4×C7312yes—
625C4⋊C4C2×D4×C7311yescharacteristic
626C4⋊C4C2×D4×C7311yescharacteristic
627C4⋊C4C2×D4×C7311yescharacteristic
628C4⋊C4C2×D4×C7311yescharacteristic
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—41no—
644C22⋊C4—41no—
645C42—22no—
646C42—22no—
647C42—21no—
648C42—22no—
649C42—21no—
650C42—21no—
651C42C2×D4×C7311yescharacteristic
652C42C2×D4×C7311yescharacteristic
653C42C2×D4×C7311yescharacteristic
654C42C24×C7311yescharacteristic
655C23—21no—
656C23—21no—
657C23—21no—
658C23—42no—
659C23—42no—
660C23—41no—
661C23—81no—
662C23#120×C7311yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—42no—
666Q8—42no—
667Q8—41no—
668Q8—41no—
669D4—21no—
670D4—21no—
671D4—21no—
672D4—21no—
673D4—21no—
674D4—42no—
675D4—42no—
676D4—44no—
677D4—42no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—82no—
683D4—82no—
684D4#135×C7312yes—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—81no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4#120×C7311yescharacteristic
713C2×C4#120×C7311yescharacteristic
714C2×C4#120×C7311yescharacteristic
715C2×C4C22×D4×C7311yescharacteristic
716C2×C4C22×D4×C7311yescharacteristic
717C2×C4C22×D4×C7311yescharacteristic
718C8—41no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C22—21no—
725C22—22no—
726C22—21no—
727C22—21no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—84no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22C2×#120×C7311yescharacteristic
741C4—21no—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—41no—
746C4—42no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—42no—
752C4—81no—
753C4C2×#135×C7311yescharacteristic
754C4#575×C7311yescharacteristic
755C4#575×C7311yescharacteristic
756C4#575×C7311yescharacteristic
757C2—41no—
758C2—42no—
759C2—81no—
760C2—81no—
761C2—161no—
762C2C73×#300211yescharacteristic
763C2C73×#300511yescharacteristic
764C2C73×#302111yescharacteristic
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×#3475C2semidirect
2. C73×#3210C2semidirect
3. C73×#3109C2semidirect
4. C73×#3106C2semidirect
5. C73×#1638C2semidirect
6. C73×#1635C2semidirect
7. C73×#1634C2semidirect
8. C73×#1632C2semidirect
9. C73×#1628C2semidirect
10. C73×#1625C2semidirect
11. C73×#1624C2semidirect
12. C73×#1622C2semidirect
13. C73×#1554C2semidirect
14. C73×#1488C2semidirect
15. C73×#1478C2semidirect
34. #494×C73C22semidirect
35. #492×C73C22semidirect
36. #487×C73C22semidirect
37. #486×C73C22semidirect
40. #477×C73C22semidirect
43. #476×C73C22semidirect
45. #460×C73C22semidirect
48. #459×C73C22semidirect
59. #333×C73C22semidirect
60. #333×C73C22semidirect
61. #332×C73C22semidirect
62. #332×C73C22semidirect
63. Q8⋊C8×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
69. D4⋊C8×C73C22semidirect
70. D4⋊C8×C73C22semidirect
374. #18795C73direct (N × H)
383. #3475C2×C73semidirect
384. #3210C2×C73semidirect
385. #3109C2×C73semidirect
386. #3106C2×C73semidirect
387. #1638C2×C73semidirect
388. #1635C2×C73semidirect
389. #1634C2×C73semidirect
390. #1632C2×C73semidirect
391. #1628C2×C73semidirect
392. #1625C2×C73semidirect
393. #1624C2×C73semidirect
394. #1622C2×C73semidirect
395. #1554C2×C73semidirect
396. #1488C2×C73semidirect
397. #1478C2×C73semidirect
398. C73#18795direct (N × H)
417. #494C22×C73semidirect
418. #492C22×C73semidirect
419. #487C22×C73semidirect
420. #486C22×C73semidirect
423. #477C22×C73semidirect
426. #476C22×C73semidirect
428. #460C22×C73semidirect
431. #459C22×C73semidirect
442. #333C22×C73semidirect
443. #333C22×C73semidirect
444. #332C22×C73semidirect
445. #332C22×C73semidirect
446. Q8⋊C8C22×C73semidirect
447. Q8⋊C8C22×C73semidirect
452. D4⋊C8C22×C73semidirect
453. D4⋊C8C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34752
C73×#32102
C73×#31092
C73×#31062
C73×#16382
C73×#16352
C73×#16342
C73×#16322
C73×#16282
C73×#16252
C73×#16242
C73×#16222
C73×#15542
C73×#14882
C73×#14782
#1879573