Finite Group Databasebeta

← #33095101

Subgroups — #33095101

Order 18688.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988554C211yesmaximal, characteristic, complemented
2#22612523C211yesmaximal, characteristic, complemented
3#22610370C211yesmaximal, characteristic, complemented
4#22610365C211yesmaximal, characteristic, complemented
5#22610360C211yesmaximal, characteristic, complemented
6#22610355C211yesmaximal, characteristic, complemented
7#22610254C211yesmaximal, characteristic, complemented
8#22610249C211yesmaximal, characteristic, complemented
9#22610244C211yesmaximal, characteristic, complemented
10#22610239C211yesmaximal, characteristic, complemented
11#22610021C211yesmaximal, characteristic, complemented
12#22610017C211yesmaximal, characteristic, complemented
13#22609871C211yesmaximal, characteristic, complemented
14#22609871C211yesmaximal, characteristic, complemented
15C2×#537×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556550C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20C2×#14556515C2211yescharacteristic
21C2×#14556515C2211yescharacteristic
22C2×#14556515C2211yescharacteristic
23C2×#14556515C2211yescharacteristic
24C2×#14556512C2211yescharacteristic
25C2×#14556512C2211yescharacteristic
26C2×#14556512C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28#17988554—24no—
29C2×C22⋊#10596831C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×C22⋊#10596831C2211yescharacteristic
33#17988494—21no—
34#17988490—21no—
35#17988467—21no—
36#17988467—21no—
37#17988447C2211yescharacteristic
38#17988447C2211yescharacteristic
39#17988447C2211yescharacteristic
40#17988447C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49C22×#41×C73C2211yescharacteristic
50C22×#41×C73C2211yescharacteristic
51#537×C73—24no—
52#537×C73C418yescomplemented
53C2×C22⋊Q8×C73—21no—
54C2×C22⋊Q8×C73C2211yescharacteristic
55C2×C22⋊Q8×C73C2211yescharacteristic
56C2×#121×C73—21no—
57C2×#121×C73—21no—
58C2×#121×C73—21no—
59C2×#121×C73C2211yescharacteristic
60C2×#121×C73C2211yescharacteristic
61C22×C4⋊C4×C73C2211yescharacteristic
62C23×Dic73—21no—
63C2×#11924012—22no—
64C2×#11924012—41no—
65C2×#11924012—41no—
66C22×#10596831—22no—
67C22×#10596831—41no—
68C22×#10596831—41no—
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73#14556550—41no—
74#14556550—41no—
75C2×C4⋊Dic73—21no—
76C2×C4⋊Dic73—41no—
77C2×C4⋊Dic73—41no—
78C2×C4⋊Dic73C2311yescharacteristic
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C22⋊Dic73—21no—
83C2×C22⋊Dic73—21no—
84C2×C22⋊Dic73—21no—
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C4×Dic73—21no—
88#14556515—41no—
89#14556515—41no—
90#14556515—41no—
91#14556515—41no—
92#14556512—41no—
93#14556512—41no—
94#14556512—41no—
95#14556512—41no—
96C22⋊#10596831—22no—
97C22⋊#10596831—22no—
98C22⋊#10596831—22no—
99C22⋊#10596831—22no—
100#14556498—21no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104C2×#41×C73—22no—
105C2×#41×C73—41no—
106C2×#41×C73—41no—
107C2×#41×C73—41no—
108C2×#41×C73—41no—
109C2×#41×C73—41no—
110C2×#41×C73—41no—
111C2×#41×C73—41no—
112C2×#41×C73—41no—
113C2×#41×C73C2×C414yes—
114C2×#41×C73C2×C414yescomplemented
115C2×#41×C73D414yes—
116C22×Q8×C73D411yescharacteristic
117C22×Q8×C73C2311yescharacteristic
118C22×D4×C73—21no—
119C22×D4×C73—21no—
120C22×D4×C73—21no—
121C22×D4×C73D411yescharacteristic
122C22×D4×C73D411yescharacteristic
123C22×D4×C73D411yescharacteristic
124C22×D4×C73C2311yescharacteristic
125C23×C4×C73—21no—
126C23×C4×C73—21no—
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C22⋊Q8×C73—28no—
131C22⋊Q8×C73—22no—
132C22⋊Q8×C73—22no—
133C22⋊Q8×C73C2×C414yes—
134C22⋊Q8×C73C2×C414yescomplemented
135#121×C73—28no—
136#121×C73—28no—
137#121×C73—28no—
138#121×C73—22no—
139#121×C73—22no—
140#121×C73C2×C414yes—
141#121×C73C2×C414yescomplemented
142C2×C4⋊C4×C73—21no—
143C2×C4⋊C4×C73—22no—
144C2×C4⋊C4×C73—21no—
145C2×C4⋊C4×C73—21no—
146C2×C4⋊C4×C73C2×C414yescomplemented
147C2×C4⋊C4×C73C2311yescharacteristic
148C2×C4⋊C4×C73C2311yescharacteristic
149C2×C22⋊C4×C73—21no—
150C2×C22⋊C4×C73—21no—
151C2×C22⋊C4×C73—21no—
152C2×C22⋊C4×C73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—42no—
158C22×Dic73—81no—
159C22×Dic73—81no—
160#11924012—44no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—44no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73—21no—
177C4⋊Dic73—21no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73—21no—
182C4⋊Dic73—42no—
183C22⋊Dic73—42no—
184C22⋊Dic73—81no—
185C22⋊Dic73—81no—
186C22⋊Dic73—81no—
187C22⋊Dic73—81no—
188C4×Dic73—42no—
189C24×C73—21no—
190C24×C73C2×D411yescharacteristic
191C24×C73C2×D411yescharacteristic
192C24×C73C2×D411yescharacteristic
193#41×C73—44no—
194#41×C73—44no—
195#41×C73—44no—
196#41×C73—44no—
197#41×C73—44no—
198#41×C73—44no—
199#41×C73—44no—
200#41×C73—44no—
201C2×Q8×C73—21no—
202C2×Q8×C73—21no—
203C2×Q8×C73—21no—
204C2×Q8×C73—21no—
205C2×Q8×C73—21no—
206C2×Q8×C73—41no—
207C2×Q8×C73—41no—
208C2×Q8×C73C22⋊C414yes—
209C2×Q8×C73C22×C412yes—
210C2×D4×C73—24no—
211C2×D4×C73—24no—
212C2×D4×C73—24no—
213C2×D4×C73—21no—
214C2×D4×C73—21no—
215C2×D4×C73—21no—
216C2×D4×C73—21no—
217C2×D4×C73—21no—
218C2×D4×C73—41no—
219C2×D4×C73—41no—
220C2×D4×C73—41no—
221C2×D4×C73—41no—
222C2×D4×C73—41no—
223C2×D4×C73—41no—
224C2×D4×C73—42no—
225C2×D4×C73—42no—
226C2×D4×C73—81no—
227C2×D4×C73—81no—
228C2×D4×C73—81no—
229C2×D4×C73—81no—
230C2×D4×C73C22⋊C414yes—
231C2×D4×C73C22⋊C414yes—
232C2×D4×C73C22⋊C414yes—
233C2×D4×C73C22×C412yes—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—24no—
250C22×C4×C73—24no—
251C22×C4×C73—42no—
252C22×C4×C73—42no—
253C22×C4×C73—81no—
254C22×C4×C73—81no—
255C22×C4×C73C22×C412yes—
256C22×C4×C73C22×C412yes—
257C22×C4×C73C22×C412yes—
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D412yes—
262C22×C4×C73C2×D412yes—
263C22×C4×C73C2×D412yes—
264C22×C4×C73C2411yescharacteristic
265C4⋊C4×C73—24no—
266C4⋊C4×C73—24no—
267C4⋊C4×C73—24no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73C22×C412yes—
271C4⋊C4×C73C22×C412yes—
272C22⋊C4×C73—24no—
273C22⋊C4×C73—24no—
274C22⋊C4×C73—24no—
275C22⋊C4×C73—24no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—21no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—21no—
285C23×C73—21no—
286C23×C73—21no—
287C23×C73—21no—
288C23×C73—21no—
289C23×C73—21no—
290C23×C73—21no—
291C23×C73—21no—
292C23×C73—21no—
293C23×C73—21no—
294C23×C73—22no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73C2×C22⋊C412yes—
302C23×C73C2×C22⋊C412yes—
303C23×C73C2×C22⋊C412yes—
304C23×C73C22×D411yescharacteristic
305Q8×C73—22no—
306Q8×C73—22no—
307Q8×C73—44no—
308Q8×C73—41no—
309Q8×C73—41no—
310D4×C73—22no—
311D4×C73—22no—
312D4×C73—44no—
313D4×C73—44no—
314D4×C73—44no—
315D4×C73—48no—
316D4×C73—41no—
317D4×C73—41no—
318D4×C73—84no—
319D4×C73—84no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—48no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—84no—
349C2×C4×C73C2×C22⋊C412yes—
350C2×C4×C73C2×C22⋊C412yes—
351C2×C4×C73C2×C22⋊C412yes—
352C2×C4×C73C23×C411yescharacteristic
353C2×C4×C73C22×D411yescharacteristic
354C2×C4×C73H(5,𝔽2)11yescharacteristic
355C2×C4×C73H(5,𝔽2)11yescharacteristic
356C2×C4×C73H(5,𝔽2)11yescharacteristic
357C2×C4×C73H(5,𝔽2)11yescharacteristic
358C2×Dic73—41no—
359C2×Dic73—41no—
360C2×Dic73—41no—
361C2×Dic73—41no—
362C2×Dic73—41no—
363C2×Dic73—41no—
364C2×Dic73—41no—
365C2×Dic73—41no—
366C2×Dic73—41no—
367C2×Dic73—41no—
368C2×Dic73—41no—
369C2×Dic73—41no—
370C2×Dic73—84no—
371#10596831—41no—
372#10596831—41no—
373#10596831—41no—
374#10596831—41no—
375C22×C73—22no—
376C22×C73—22no—
377C22×C73—22no—
378C22×C73—22no—
379C22×C73—22no—
380C22×C73—22no—
381C22×C73—22no—
382C22×C73—22no—
383C22×C73—22no—
384C22×C73—41no—
385C22×C73—41no—
386C22×C73—41no—
387C22×C73—41no—
388C22×C73—41no—
389C22×C73—41no—
390C22×C73—41no—
391C22×C73—41no—
392C22×C73—41no—
393C22×C73—41no—
394C22×C73—41no—
395C22×C73—41no—
396C22×C73—42no—
397C22×C73—42no—
398C22×C73—42no—
399C22×C73—81no—
400C22×C73—81no—
401C22×C73—81no—
402C22×C73—81no—
403C22×C73C22×C22⋊C411yescharacteristic
404C22×C73#53411yescharacteristic
405C22×C73#53411yescharacteristic
406C22×C73#57611yescharacteristic
407C22×C73#57711yescharacteristic
408C22×C73#57711yescharacteristic
409C22×C73#57811yescharacteristic
410C4×C73—22no—
411C4×C73—22no—
412C4×C73—22no—
413C4×C73—42no—
414C4×C73—42no—
415C4×C73—42no—
416C4×C73#51811yescharacteristic
417C4×C73#51811yescharacteristic
418C4×C73#53411yescharacteristic
419C4×C73#53411yescharacteristic
420Dic73—81no—
421Dic73—81no—
422Dic73—81no—
423Dic73—81no—
424#21772—731nomaximal, Sylow
425C2×C73—42no—
426C2×C73—42no—
427C2×C73—42no—
428C2×C73—82no—
429C2×C73#230811yescharacteristic
430C2×C73#289711yescharacteristic
431C2×C73#289811yescharacteristic
432C2×C73#319811yescharacteristic
433C2×C73#320111yescharacteristic
434C2×C73#320311yescharacteristic
435C2×C73#320411yescharacteristic
436C2×#537D7311yescharacteristic
437C2×#408—731no—
438#2311—731no—
439#1895—731no—
440#1894—731no—
441#1893—731no—
442#1892—731no—
443#1875—731no—
444#1874—731no—
445#1873—731no—
446#1872—731no—
447#1824—731no—
448#1823—731no—
449#1788—731no—
450#1788—731no—
451C73#2177211yescharacteristic, complemented, Sylow
452C22×#41C2×D7311yescharacteristic
453C22×#41C2×D7311yescharacteristic
454C22×M16—731no—
455C23×C8—731no—
456#537—24no—
457#537Dic7318yescomplemented
458C2×C22⋊Q8—21no—
459C2×C22⋊Q8C2×D7311yescharacteristic
460C2×C22⋊Q8C2×D7311yescharacteristic
461C2×#121—21no—
462C2×#121—21no—
463C2×#121—21no—
464C2×#121C2×D7311yescharacteristic
465C2×#121C2×D7311yescharacteristic
466C2×#117—731no—
467C22×C4⋊C4—731no—
468C22×C4⋊C4C2×D7311yescharacteristic
469C2×#103—731no—
470C2×#103—731no—
471C2×#103—731no—
472C2×#103—731no—
473C2×#102—731no—
474C2×#102—731no—
475C2×#102—731no—
476C2×#102—731no—
477#408—1464no—
478C2×C22⋊C8—731no—
479C2×C22⋊C8—731no—
480C2×C22⋊C8—731no—
481C2×C22⋊C8—731no—
482#391—1461no—
483#390—1461no—
484#386—1461no—
485#386—1461no—
486#380—731no—
487#380—731no—
488#380—731no—
489#380—731no—
490#340—731no—
491#340—731no—
492#340—731no—
493#340—731no—
494#340—731no—
495#340—731no—
496#340—731no—
497#340—731no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×Dic7314yes—
508C2×#41C2×Dic7314yescomplemented
509C2×#41C22⋊D7314yes—
510C22×Q8C22⋊D7311yescharacteristic
511C22×Q8C22×D7311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C22⋊D7311yescharacteristic
516C22×D4C22⋊D7311yescharacteristic
517C22×D4C22⋊D7311yescharacteristic
518C22×D4C22×D7311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—1461no—
522C23×C4C22×D7311yescharacteristic
523C23×C4C22×D7311yescharacteristic
524C23×C4C22×D7311yescharacteristic
525C2×M16—2921no—
526C2×M16—2921no—
527C2×M16—1462no—
528C22×C8—2921no—
529C22×C8—2921no—
530C22×C8—731no—
531C22×C8—731no—
532C22×C8—731no—
533C22×C8—731no—
534C22×C8—1462no—
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×Dic7314yes—
539C22⋊Q8C2×Dic7314yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×Dic7314yes—
546#121C2×Dic7314yescomplemented
547#117—2921no—
548#117—2921no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—2921no—
554C2×C4⋊C4—2921no—
555C2×C4⋊C4—731no—
556C2×C4⋊C4—731no—
557C2×C4⋊C4—731no—
558C2×C4⋊C4—731no—
559C2×C4⋊C4—1461no—
560C2×C4⋊C4C2×Dic7314yescomplemented
561C2×C4⋊C4C22×D7311yescharacteristic
562C2×C4⋊C4C22×D7311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—1461no—
568C2×C22⋊C4—1461no—
569C2×C22⋊C4—1461no—
570C2×C22⋊C4—1461no—
571C2×C22⋊C4—1461no—
572C2×C42—1461no—
573#103—2921no—
574#103—2921no—
575#103—2921no—
576#103—2921no—
577#102—2921no—
578#102—2921no—
579#102—2921no—
580#102—2921no—
581C22⋊C8—1462no—
582C22⋊C8—1462no—
583C22⋊C8—1462no—
584C22⋊C8—1462no—
585#95—1461no—
586#95—1461no—
587#95—1461no—
588#95—1461no—
589C24—21no—
590C24C2×C22⋊D7311yescharacteristic
591C24C2×C22⋊D7311yescharacteristic
592C24C2×C22⋊D7311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊Dic7314yes—
609C2×Q8C22×Dic7312yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊Dic7314yes—
631C2×D4C22⋊Dic7314yes—
632C2×D4C22⋊Dic7314yes—
633C2×D4C22×Dic7312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—81no—
655C22×C4—2922no—
656C22×C4—5841no—
657C22×C4—5841no—
658C22×C4—1461no—
659C22×C4—1461no—
660C22×C4—1461no—
661C22×C4—1461no—
662C22×C4C22×Dic7312yes—
663C22×C4C22×Dic7312yes—
664C22×C4C22×Dic7312yes—
665C22×C4C2×C22⋊D7311yescharacteristic
666C22×C4C2×C22⋊D7311yescharacteristic
667C22×C4C2×C22⋊D7311yescharacteristic
668C22×C4C2×C22⋊D7312yes—
669C22×C4C2×C22⋊D7312yes—
670C22×C4C2×C22⋊D7312yes—
671C22×C4C23×D7311yescharacteristic
672M16—2924no—
673C2×C8—2924no—
674C2×C8—1461no—
675C2×C8—1461no—
676C2×C8—1461no—
677C2×C8—1461no—
678C2×C8—1461no—
679C2×C8—1461no—
680C2×C8—1461no—
681C2×C8—1461no—
682C2×C8—1461no—
683C2×C8—1461no—
684C2×C8—1461no—
685C2×C8—1461no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—2922no—
692C4⋊C4—1461no—
693C4⋊C4—1461no—
694C4⋊C4—1461no—
695C4⋊C4—1461no—
696C4⋊C4—1461no—
697C4⋊C4—1461no—
698C4⋊C4—1461no—
699C4⋊C4—1461no—
700C4⋊C4C22×Dic7312yes—
701C4⋊C4C22×Dic7312yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—2922no—
707C22⋊C4—5841no—
708C22⋊C4—5841no—
709C22⋊C4—5841no—
710C22⋊C4—5841no—
711C42—2922no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊Dic7312yes—
738C23C2×C22⋊Dic7312yes—
739C23C2×C22⋊Dic7312yes—
740C23C22×C22⋊D7311yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—2921no—
786C2×C4—2921no—
787C2×C4—2921no—
788C2×C4—2921no—
789C2×C4—2921no—
790C2×C4—2921no—
791C2×C4—2921no—
792C2×C4—2921no—
793C2×C4—2921no—
794C2×C4—2921no—
795C2×C4—2921no—
796C2×C4—2921no—
797C2×C4—5844no—
798C2×C4C2×C22⋊Dic7312yes—
799C2×C4C2×C22⋊Dic7312yes—
800C2×C4C2×C22⋊Dic7312yes—
801C2×C4C23×Dic7311yescharacteristic
802C2×C4C22×C22⋊D7311yescharacteristic
803C2×C4#1455663611yescharacteristic
804C2×C4#1455663611yescharacteristic
805C2×C4#1455663611yescharacteristic
806C2×C4#1455663611yescharacteristic
807C8—2921no—
808C8—2921no—
809C8—2921no—
810C8—2921no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊Dic7311yescharacteristic
840C22#1798914611yescharacteristic
841C22#1798914611yescharacteristic
842C22#1798939011yescharacteristic
843C22#1798939511yescharacteristic
844C22#1798939811yescharacteristic
845C22#1798940211yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—5841no—
853C4—5841no—
854C4—5841no—
855C4—5841no—
856C4#1798906211yescharacteristic
857C4#1798906211yescharacteristic
858C4#1798914611yescharacteristic
859C4#1798914611yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2#2261250911yescharacteristic
865C2#2261845711yescharacteristic
866C2#2261846411yescharacteristic
867C2#2262077711yescharacteristic
868C2#2262080711yescharacteristic
869C2#2262082811yescharacteristic
870C2#2262083711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
Fitting, prime radicalC2×#537×C73C2
socleC23×C73C22×D4
cosocleC22×C4×C73C24
hypercenterC2×#537D73
hypocenterC73#21772
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#17988554C2semidirect
2. #22612523C2semidirect
3. #22610370C2semidirect
4. #22610365C2semidirect
5. #22610360C2semidirect
6. #22610355C2semidirect
7. #22610254C2semidirect
8. #22610249C2semidirect
9. #22610244C2semidirect
10. #22610239C2semidirect
11. #22610021C2semidirect
12. #22610017C2semidirect
13. #22609871C2semidirect
14. #22609871C2semidirect
52. #537×C73C4semidirect
114. C2×#41×C73C2×C4semidirect
134. C22⋊Q8×C73C2×C4semidirect
141. #121×C73C2×C4semidirect
146. C2×C4⋊C4×C73C2×C4semidirect
451. C73#21772semidirect
457. #537Dic73semidirect
508. C2×#41C2×Dic73semidirect
539. C22⋊Q8C2×Dic73semidirect
546. #121C2×Dic73semidirect
560. C2×C4⋊C4C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179885542
#226125232
#226103702
#226103652
#226103602
#226103552
#226102542
#226102492
#226102442
#226102392
#226100212
#226100172
#226098712
C2×#537×C732
#2177273