Finite Group Databasebeta

← #33091846

Subgroups — #33091846

Order 18688.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989354C211yesmaximal, characteristic, complemented
2C2×#17988709C211yesmaximal, characteristic, complemented
3C2×#17988704C211yesmaximal, characteristic, complemented
4#22618635C211yesmaximal, characteristic, complemented
5#22610260C211yesmaximal, characteristic, complemented
6#22610260C211yesmaximal, characteristic, complemented
7#22610234C211yesmaximal, characteristic, complemented
8#22610208C211yesmaximal, characteristic, complemented
9#22610208C211yesmaximal, characteristic, complemented
10#22610138C211yesmaximal, characteristic, complemented
11#22609875C211yesmaximal, characteristic, complemented
12#22609778C211yesmaximal, characteristic, complemented
13#22609771C211yesmaximal, characteristic, complemented
14#22609717C211yesmaximal, characteristic, complemented
15C73×#3002C211yesmaximal, characteristic
16#17989354—24no—
17#17989354—24no—
18C2×#14556598—21no—
19C2×#14556598—21no—
20C2×#14556598C2211yescharacteristic
21C2×#14556598C2211yescharacteristic
22C2×#14556598C2211yescharacteristic
23C2×#14556598C2211yescharacteristic
24C2×#14556598C2211yescharacteristic, complemented
25C22×#11924012—21no—
26C22×#11924012—21no—
27C22×#11924012C2211yescharacteristic
28C22×#11924012C2211yescharacteristic
29#17988709—24no—
30#17988704—24no—
31#17988665—21no—
32#17988665—21no—
33#17988659—21no—
34#17988659—21no—
35C2×#14556527C2211yescharacteristic, complemented
36C2×#14556527C2211yescharacteristic, complemented
37#17988614C2211yescharacteristic, complemented
38C2×#14556518C2211yescharacteristic
39C2×#14556518C2211yescharacteristic
40C2×#14556518C2211yescharacteristic
41C2×#14556518C2211yescharacteristic
42C2×#14556518C2211yescharacteristic, complemented
43C2×#14556518C2211yescharacteristic, complemented
44#17988554C2211yescharacteristic, complemented
45#17988551C2211yescharacteristic
46#17988543C2211yescharacteristic, complemented
47C2×#14556501C2211yescharacteristic, complemented
48C2×C8×Dic73C2211yescharacteristic, complemented
49C4×C22⋊Dic73C2211yescharacteristic
50#17988352C2211yescharacteristic, complemented
51#17988352C2211yescharacteristic, complemented
52#17988346C2211yescharacteristic, complemented
53#17988346C2211yescharacteristic, complemented
54#17988341C2211yescharacteristic, complemented
55#17988341C2211yescharacteristic, complemented
56C22×#41×C73C2211yescharacteristic
57C2×#135×C73C2211yescharacteristic
58C2×#135×C73C2211yescharacteristic
59#525×C73C2211yescharacteristic
60#452×C73C411yescharacteristic, complemented
61#452×C73C411yescharacteristic, complemented
62#451×C73C411yescharacteristic, complemented
63#450×C73C411yescharacteristic, complemented
64#449×C73C411yescharacteristic, complemented
65#449×C73C411yescharacteristic, complemented
66#448×C73C411yescharacteristic, complemented
67#447×C73C411yescharacteristic, complemented
68#416×C73C2211yescharacteristic
69#416×C73C2211yescharacteristic
70C2×C22⋊C8×C73C2211yescharacteristic
71#14556598—28no—
72#14556598—28no—
73#14556598—22no—
74#14556598—22no—
75#14556598—22no—
76#14556598—22no—
77#14556598—22no—
78#14556598—22no—
79#14556598—22no—
80#14556598—22no—
81#14556598D414yescomplemented
82#14556598D414yescomplemented
83C2×#11924012—28no—
84C2×#11924012—28no—
85C2×#11924012—22no—
86C2×#11924012—22no—
87C2×#11924012—21no—
88C2×#11924012—21no—
89C2×#11924012—21no—
90C2×#11924012—21no—
91C2×#11924012—22no—
92C2×#11924012—22no—
93C2×#11924012—21no—
94C2×#11924012—21no—
95C2×#11924012D411yescharacteristic
96C2×#11924012D411yescharacteristic
97C2×#11924012D411yescharacteristic
98C2×#11924012D411yescharacteristic
99C2×#11924012C2311yescharacteristic
100C2×#11924012C2311yescharacteristic
101C2×#11924012C2311yescharacteristic
102C2×#11924012C2311yescharacteristic
103C22×#10596831—21no—
104C22×#10596831—21no—
105C22×#10596831—21no—
106C22×#10596831—21no—
107C22×#10596831—21no—
108C22×#10596831—21no—
109C22×#10596831C2311yescharacteristic
110C22×#10596831C2311yescharacteristic
111C2×C22⋊Dic73—21no—
112C2×C4×Dic73C2311yescharacteristic
113C2×C4×Dic73C2311yescharacteristic
114#14556527—22no—
115#14556527—22no—
116C4⋊#10596831—21no—
117C4⋊#10596831—21no—
118#14556518—22no—
119#14556518—22no—
120#14556518—22no—
121#14556518—22no—
122#14556518—22no—
123#14556518—22no—
124C22⋊#10596831—21no—
125C22⋊#10596831—21no—
126C22⋊#10596831—21no—
127C22⋊#10596831—21no—
128#14556502—21no—
129#14556501—22no—
130C4×#10596831—21no—
131C8×Dic73—22no—
132#14556498—21no—
133C2×#41×C73—22no—
134C2×#41×C73—22no—
135C2×#41×C73—22no—
136C2×#41×C73—22no—
137C2×#41×C73—21no—
138C2×#41×C73—21no—
139C2×#41×C73C2×C411yescharacteristic
140C2×#41×C73C2×C411yescharacteristic
141C2×#41×C73C2311yescharacteristic
142C2×#41×C73C2311yescharacteristic
143C2×#41×C73C2311yescharacteristic
144C22×Q8×C73C2×C411yescharacteristic
145C22×D4×C73—21no—
146C22×D4×C73C2×C411yescharacteristic
147C23×C4×C73—21no—
148C23×C4×C73C2311yescharacteristic
149#135×C73—22no—
150#135×C73—22no—
151#135×C73—22no—
152#135×C73—22no—
153C2×Q16×C73C2×C411yescharacteristic
154C2×Q16×C73C2×C411yescharacteristic
155C2×SD16×C73C2×C411yescharacteristic
156C2×SD16×C73C2×C411yescharacteristic
157C2×SD16×C73C2×C411yescharacteristic
158C2×SD16×C73C2×C411yescharacteristic
159C2×D8×C73C2×C411yescharacteristic
160C2×D8×C73C2×C411yescharacteristic
161C22×C8×C73C2311yescharacteristic
162C22×C8×C73C2311yescharacteristic
163#123×C73—21no—
164C22⋊Q8×C73C2×C411yescharacteristic
165C22⋊Q8×C73C2×C411yescharacteristic
166#121×C73C2×C411yescharacteristic
167#121×C73C2×C411yescharacteristic
168#120×C73—21no—
169C4×D4×C73—21no—
170C4×D4×C73—21no—
171#117×C73C2311yescharacteristic
172#103×C73C2×C411yescharacteristic
173#103×C73C2×C411yescharacteristic
174#103×C73C2×C411yescharacteristic
175#103×C73C2×C411yescharacteristic
176#102×C73C2×C411yescharacteristic
177#102×C73C2×C411yescharacteristic
178#102×C73C2×C411yescharacteristic
179#102×C73C2×C411yescharacteristic
180C22⋊C8×C73C2×C411yescharacteristic
181C22⋊C8×C73C2×C411yescharacteristic
182C22⋊C8×C73C2×C411yescharacteristic
183C22⋊C8×C73C2×C411yescharacteristic
184C22×Dic73—21no—
185C22×Dic73—21no—
186#11924012—24no—
187#11924012—24no—
188#11924012—24no—
189#11924012—21no—
190#11924012—21no—
191#11924012—22no—
192#11924012—22no—
193#11924012—24no—
194#11924012—24no—
195#11924012—22no—
196#11924012—22no—
197#11924012—21no—
198#11924012—21no—
199#11924012—21no—
200#11924012—21no—
201#11924012—42no—
202#11924012C2×D412yes—
203#11924012C2×D412yes—
204C2×#10596831—24no—
205C2×#10596831—24no—
206C2×#10596831—24no—
207C2×#10596831—21no—
208C2×#10596831—21no—
209C2×#10596831—21no—
210C2×#10596831—21no—
211C2×#10596831—24no—
212C2×#10596831—24no—
213C2×#10596831—21no—
214C2×#10596831—21no—
215C2×#10596831—42no—
216C2×#10596831C2×D411yescharacteristic
217C2×#10596831C2×D411yescharacteristic
218C2×#10596831C2×D412yes—
219C2×#10596831C2×D411yescharacteristic
220C2×#10596831C2×D412yes—
221C2×#10596831C2×D411yescharacteristic
222C22⋊Dic73—42no—
223C4×Dic73—21no—
224C4×Dic73—21no—
225C4×Dic73—21no—
226C4×Dic73—21no—
227C24×C73—21no—
228C24×C73#4111yescharacteristic
229#41×C73—24no—
230#41×C73—24no—
231#41×C73—24no—
232#41×C73—24no—
233#41×C73—22no—
234#41×C73—22no—
235#41×C73—22no—
236#41×C73—22no—
237#41×C73—21no—
238#41×C73—21no—
239#41×C73—21no—
240#41×C73—21no—
241#41×C73—21no—
242#41×C73—21no—
243#41×C73—21no—
244#41×C73—21no—
245#41×C73C2×D412yes—
246#41×C73C2×D412yes—
247#41×C73#4112yes—
248#41×C73#4112yes—
249C2×Q8×C73—22no—
250C2×Q8×C73—22no—
251C2×Q8×C73—21no—
252C2×Q8×C73C22×C411yescharacteristic
253C2×Q8×C73C22×C411yescharacteristic
254C2×Q8×C73C22×C411yescharacteristic
255C2×D4×C73—24no—
256C2×D4×C73—24no—
257C2×D4×C73—21no—
258C2×D4×C73—21no—
259C2×D4×C73—21no—
260C2×D4×C73—21no—
261C2×D4×C73—22no—
262C2×D4×C73—22no—
263C2×D4×C73—21no—
264C2×D4×C73—21no—
265C2×D4×C73—21no—
266C2×D4×C73—21no—
267C2×D4×C73C22×C411yescharacteristic
268C2×D4×C73C22×C411yescharacteristic
269C2×D4×C73C22×C411yescharacteristic
270C22×C4×C73—24no—
271C22×C4×C73—24no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73—21no—
281C22×C4×C73—21no—
282C22×C4×C73C22×C411yescharacteristic
283C22×C4×C73C22×C411yescharacteristic
284C22×C4×C73C2×D411yescharacteristic
285C22×C4×C73C2×D411yescharacteristic
286C22×C4×C73#4111yescharacteristic
287C22×C4×C73C2411yescharacteristic
288Q16×C73—22no—
289Q16×C73—22no—
290SD16×C73—22no—
291SD16×C73—22no—
292SD16×C73—22no—
293SD16×C73—22no—
294D8×C73—22no—
295D8×C73—22no—
296C2×C8×C73—21no—
297C2×C8×C73—21no—
298C2×C8×C73—21no—
299C2×C8×C73—21no—
300C2×C8×C73C22×C411yescharacteristic
301C2×C8×C73C22×C411yescharacteristic
302C2×C8×C73C22×C411yescharacteristic
303C2×C8×C73C22×C411yescharacteristic
304C4⋊C4×C73—21no—
305C4⋊C4×C73—21no—
306C4⋊C4×C73C22×C411yescharacteristic
307C4⋊C4×C73C22×C411yescharacteristic
308C22⋊C4×C73—21no—
309C22⋊C4×C73—21no—
310C22⋊C4×C73—21no—
311C22⋊C4×C73—21no—
312C22⋊C4×C73—21no—
313C42×C73—21no—
314C23×C73—24no—
315C23×C73—21no—
316C23×C73—21no—
317C23×C73—21no—
318C23×C73—21no—
319C23×C73—21no—
320C23×C73—41no—
321C23×C73—41no—
322C23×C73—81no—
323C23×C73—81no—
324C23×C73C4×D411yescharacteristic
325C23×C73C4×D411yescharacteristic
326C23×C73C2×#4111yescharacteristic
327Q8×C73—24no—
328Q8×C73—21no—
329Q8×C73—21no—
330Q8×C73—21no—
331Q8×C73—21no—
332Q8×C73C4×D412yes—
333Q8×C73C4×D412yes—
334D4×C73—24no—
335D4×C73—24no—
336D4×C73—24no—
337D4×C73—22no—
338D4×C73—22no—
339D4×C73—22no—
340D4×C73—22no—
341D4×C73—21no—
342D4×C73—21no—
343D4×C73—21no—
344D4×C73—21no—
345D4×C73—41no—
346D4×C73—41no—
347D4×C73—81no—
348D4×C73—81no—
349D4×C73C4×D412yes—
350D4×C73C4×D412yes—
351C2×C4×C73—24no—
352C2×C4×C73—24no—
353C2×C4×C73—24no—
354C2×C4×C73—21no—
355C2×C4×C73—21no—
356C2×C4×C73—21no—
357C2×C4×C73—21no—
358C2×C4×C73—21no—
359C2×C4×C73—21no—
360C2×C4×C73—21no—
361C2×C4×C73—21no—
362C2×C4×C73—21no—
363C2×C4×C73—22no—
364C2×C4×C73—22no—
365C2×C4×C73—21no—
366C2×C4×C73—21no—
367C2×C4×C73—22no—
368C2×C4×C73—22no—
369C2×C4×C73—21no—
370C2×C4×C73—21no—
371C2×C4×C73—21no—
372C2×C4×C73—21no—
373C2×C4×C73—41no—
374C2×C4×C73—41no—
375C2×C4×C73C4×D411yescharacteristic
376C2×C4×C73C4×D411yescharacteristic
377C2×C4×C73C23×C411yescharacteristic
378C2×C4×C73C22×D411yescharacteristic
379C2×C4×C73C22×D411yescharacteristic
380C2×C4×C73C22×D411yescharacteristic
381C2×C4×C73C2×#4111yescharacteristic
382C2×C4×C73C2×#4111yescharacteristic
383C2×Dic73—22no—
384C2×Dic73—41no—
385C2×Dic73—41no—
386C2×Dic73—41no—
387C2×Dic73—41no—
388C2×Dic73—41no—
389C8×C73—21no—
390C8×C73—21no—
391C8×C73—21no—
392C8×C73—21no—
393#10596831—22no—
394#10596831—22no—
395#10596831—21no—
396#10596831—21no—
397#10596831—41no—
398#10596831—41no—
399#10596831#12012yes—
400#10596831#12012yes—
401C22×C73—21no—
402C22×C73—21no—
403C22×C73—21no—
404C22×C73—21no—
405C22×C73—21no—
406C22×C73—21no—
407C22×C73—21no—
408C22×C73—21no—
409C22×C73—22no—
410C22×C73—22no—
411C22×C73—41no—
412C22×C73—41no—
413C22×C73—41no—
414C22×C73—41no—
415C22×C73—41no—
416C22×C73—41no—
417C22×C73—41no—
418C22×C73—81no—
419C22×C73—81no—
420C22×C73—84no—
421C22×C73C2×C4×D411yescharacteristic
422C22×C73#52511yescharacteristic
423C22×C73#52511yescharacteristic
424C4×C73—21no—
425C4×C73—22no—
426C4×C73—22no—
427C4×C73—21no—
428C4×C73—41no—
429C4×C73—41no—
430C4×C73—41no—
431C4×C73C2×C4×D411yescharacteristic
432C4×C73C2×C4×D411yescharacteristic
433C4×C73C2×#12011yescharacteristic
434C4×C73#52511yescharacteristic
435Dic73—42no—
436Dic73—81no—
437#21468—731nomaximal, Sylow
438C2×C73—21no—
439C2×C73—21no—
440C2×C73—41no—
441C2×C73—41no—
442C2×C73—42no—
443C2×C73—42no—
444C2×C73—81no—
445C2×C73C4×#12011yescharacteristic
446C2×C73#295611yescharacteristic
447C2×C73#295711yescharacteristic
448C2×#568—731no—
449#3002D7311yescharacteristic
450C2×#444—731no—
451C2×#443—731no—
452#2930—731no—
453#1876—731no—
454#1876—731no—
455#1871—731no—
456#1866—731no—
457#1866—731no—
458#1855—731no—
459#1789—731no—
460#1765—731no—
461#1764—731no—
462#1753—731no—
463C73#2146811yescharacteristic, complemented, Sylow
464C22×#41C2×D7311yescharacteristic
465C2×#135C2×D7311yescharacteristic
466C2×#135C2×D7311yescharacteristic
467#568—1464no—
468#568—1464no—
469C2×#131—731no—
470C2×#131—731no—
471C2×#131—731no—
472C2×#131—731no—
473C2×#131—731no—
474C2×#131—1461no—
475C2×#131—1461no—
476C22×M16—731no—
477C22×M16—731no—
478C22×M16—1461no—
479C22×M16—1461no—
480#525C2×D7311yescharacteristic
481#452Dic7311yescharacteristic, complemented
482#452Dic7311yescharacteristic, complemented
483#451Dic7311yescharacteristic, complemented
484#450Dic7311yescharacteristic, complemented
485#449Dic7311yescharacteristic, complemented
486#449Dic7311yescharacteristic, complemented
487#448Dic7311yescharacteristic, complemented
488#447Dic7311yescharacteristic, complemented
489#444—1464no—
490#443—1464no—
491#436—1461no—
492#436—1461no—
493#435—1461no—
494#435—1461no—
495C2×#108—731no—
496C2×#108—731no—
497#424—731no—
498C2×#104—731no—
499C2×#104—731no—
500C2×#104—731no—
501C2×#104—731no—
502C2×#104—731no—
503C2×#104—731no—
504#416C2×D7311yescharacteristic
505#416C2×D7311yescharacteristic
506#408—731no—
507#407—731no—
508C2×C22⋊C8C2×D7311yescharacteristic
509#405—731no—
510C2×#97—731no—
511C2×C4×C8—731no—
512C4×C22⋊C4—731no—
513#341—731no—
514#341—731no—
515#339—731no—
516#339—731no—
517#336—731no—
518#336—731no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41C2×Dic7311yescharacteristic
526C2×#41C2×Dic7311yescharacteristic
527C2×#41C22×D7311yescharacteristic
528C2×#41C22×D7311yescharacteristic
529C2×#41C22×D7311yescharacteristic
530C22×Q8C2×Dic7311yescharacteristic
531C22×D4—21no—
532C22×D4C2×Dic7311yescharacteristic
533C23×C4—21no—
534C23×C4C22×D7311yescharacteristic
535#135—22no—
536#135—22no—
537#135—22no—
538#135—22no—
539C2×Q16C2×Dic7311yescharacteristic
540C2×Q16C2×Dic7311yescharacteristic
541C2×SD16C2×Dic7311yescharacteristic
542C2×SD16C2×Dic7311yescharacteristic
543C2×SD16C2×Dic7311yescharacteristic
544C2×SD16C2×Dic7311yescharacteristic
545C2×D8C2×Dic7311yescharacteristic
546C2×D8C2×Dic7311yescharacteristic
547#131—734no—
548#131—734no—
549#131—1462no—
550#131—1462no—
551#131—1462no—
552#131—1462no—
553#131—1462no—
554#131—1462no—
555#131—1468no—
556#131—1468no—
557#131—1462no—
558#131—1462no—
559C2×M16—731no—
560C2×M16—731no—
561C2×M16—731no—
562C2×M16—731no—
563C2×M16—731no—
564C2×M16—731no—
565C2×M16—731no—
566C2×M16—731no—
567C2×M16—1461no—
568C2×M16—1462no—
569C2×M16—1462no—
570C2×M16—1461no—
571C2×M16—1461no—
572C2×M16—1461no—
573C2×M16—1461no—
574C2×M16—1462no—
575C2×M16—1462no—
576C2×M16—1468no—
577C2×M16—1468no—
578C2×M16—1461no—
579C22×C8—731no—
580C22×C8—731no—
581C22×C8—1461no—
582C22×C8—1461no—
583C22×C8—1461no—
584C22×C8—1461no—
585C22×C8—1461no—
586C22×C8—1461no—
587C22×C8C22×D7311yescharacteristic
588C22×C8C22×D7311yescharacteristic
589#123—21no—
590C22⋊Q8C2×Dic7311yescharacteristic
591C22⋊Q8C2×Dic7311yescharacteristic
592#121C2×Dic7311yescharacteristic
593#121C2×Dic7311yescharacteristic
594#120—21no—
595C4×D4—21no—
596C4×D4—21no—
597#117C22×D7311yescharacteristic
598C2×C22⋊C4—1461no—
599C2×C42—731no—
600C2×C42—731no—
601#108—1462no—
602#108—1462no—
603C4⋊C8—1461no—
604C4⋊C8—1461no—
605#104—1462no—
606#104—1462no—
607#104—1462no—
608#104—1462no—
609#104—1462no—
610#104—1462no—
611#103C2×Dic7311yescharacteristic
612#103C2×Dic7311yescharacteristic
613#103C2×Dic7311yescharacteristic
614#103C2×Dic7311yescharacteristic
615#102C2×Dic7311yescharacteristic
616#102C2×Dic7311yescharacteristic
617#102C2×Dic7311yescharacteristic
618#102C2×Dic7311yescharacteristic
619C22⋊C8—1461no—
620C22⋊C8—1461no—
621C22⋊C8—1461no—
622C22⋊C8—1461no—
623C22⋊C8C2×Dic7311yescharacteristic
624C22⋊C8C2×Dic7311yescharacteristic
625C22⋊C8C2×Dic7311yescharacteristic
626C22⋊C8C2×Dic7311yescharacteristic
627#97—1461no—
628#97—1462no—
629C4×C8—1461no—
630C4×C8—1462no—
631#95—1461no—
632C24—21no—
633C24#1192402711yescharacteristic
634#41—24no—
635#41—24no—
636#41—24no—
637#41—24no—
638#41—22no—
639#41—22no—
640#41—22no—
641#41—22no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—21no—
647#41—21no—
648#41—21no—
649#41—21no—
650#41D4×D7312yes—
651#41D4×D7312yes—
652#41#1192402712yes—
653#41#1192402712yes—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8C22×Dic7311yescharacteristic
658C2×Q8C22×Dic7311yescharacteristic
659C2×Q8C22×Dic7311yescharacteristic
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4C22×Dic7311yescharacteristic
673C2×D4C22×Dic7311yescharacteristic
674C2×D4C22×Dic7311yescharacteristic
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—1461no—
688C22×C4—1461no—
689C22×C4C22×Dic7311yescharacteristic
690C22×C4C22×Dic7311yescharacteristic
691C22×C4D4×D7311yescharacteristic
692C22×C4D4×D7311yescharacteristic
693C22×C4#1192402711yescharacteristic
694C22×C4C23×D7311yescharacteristic
695Q16—22no—
696Q16—22no—
697SD16—22no—
698SD16—22no—
699SD16—22no—
700SD16—22no—
701D8—22no—
702D8—22no—
703M16—2922no—
704M16—732no—
705M16—732no—
706M16—1461no—
707M16—1461no—
708M16—1461no—
709M16—1461no—
710M16—1462no—
711M16—1462no—
712M16—1462no—
713M16—1462no—
714M16—1464no—
715M16—1464no—
716M16—1464no—
717M16—1464no—
718M16—1464no—
719M16—1461no—
720M16—1461no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—2922no—
726C2×C8—732no—
727C2×C8—732no—
728C2×C8—731no—
729C2×C8—731no—
730C2×C8—731no—
731C2×C8—731no—
732C2×C8—1461no—
733C2×C8—1461no—
734C2×C8—1464no—
735C2×C8—1464no—
736C2×C8—1464no—
737C2×C8—1464no—
738C2×C8—1464no—
739C2×C8—1461no—
740C2×C8—1461no—
741C2×C8—1461no—
742C2×C8—1461no—
743C2×C8C22×Dic7311yescharacteristic
744C2×C8C22×Dic7311yescharacteristic
745C2×C8C22×Dic7311yescharacteristic
746C2×C8C22×Dic7311yescharacteristic
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4C22×Dic7311yescharacteristic
750C4⋊C4C22×Dic7311yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—2922no—
757C42—21no—
758C42—1461no—
759C42—1461no—
760C42—1461no—
761C42—1461no—
762C23—24no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—41no—
769C23—41no—
770C23—81no—
771C23—81no—
772C23D4×Dic7311yescharacteristic
773C23D4×Dic7311yescharacteristic
774C23C2×#1192402711yescharacteristic
775Q8—24no—
776Q8—21no—
777Q8—21no—
778Q8—21no—
779Q8—21no—
780Q8D4×Dic7312yes—
781Q8D4×Dic7312yes—
782D4—24no—
783D4—24no—
784D4—24no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—41no—
794D4—41no—
795D4—81no—
796D4—81no—
797D4D4×Dic7312yes—
798D4D4×Dic7312yes—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—2921no—
824C2×C4—2921no—
825C2×C4—2921no—
826C2×C4—2921no—
827C2×C4—2921no—
828C2×C4—1462no—
829C2×C4D4×Dic7311yescharacteristic
830C2×C4D4×Dic7311yescharacteristic
831C2×C4C23×Dic7311yescharacteristic
832C2×C4C2×D4×D7311yescharacteristic
833C2×C4C2×D4×D7311yescharacteristic
834C2×C4C2×D4×D7311yescharacteristic
835C2×C4C2×#1192402711yescharacteristic
836C2×C4C2×#1192402711yescharacteristic
837C8—21no—
838C8—21no—
839C8—21no—
840C8—21no—
841C8—2921no—
842C8—2921no—
843C8—732no—
844C8—732no—
845C8—1461no—
846C8—1461no—
847C8—1462no—
848C8—1462no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—22no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—84no—
869C22C2×D4×Dic7311yescharacteristic
870C22#1798909311yescharacteristic
871C22#1798909311yescharacteristic
872C4—21no—
873C4—22no—
874C4—22no—
875C4—21no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—2922no—
880C4—5841no—
881C4C2×D4×Dic7311yescharacteristic
882C4C2×D4×Dic7311yescharacteristic
883C4#120×D7311yescharacteristic
884C4#1798909311yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—42no—
890C2—42no—
891C2—81no—
892C2#120×Dic7311yescharacteristic
893C2#2261884111yescharacteristic
894C2#2261884811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
Fitting, prime radicalC73×#3002C2
socleC22×C73C2×C4×D4
cosocleC22×C4×C73C24
hypercenter#3002D73
hypocenterC73#21468
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#17989354C2semidirect
2. C2×#17988709C2semidirect
3. C2×#17988704C2semidirect
4. #22618635C2semidirect
5. #22610260C2semidirect
6. #22610260C2semidirect
7. #22610234C2semidirect
8. #22610208C2semidirect
9. #22610208C2semidirect
10. #22610138C2semidirect
11. #22609875C2semidirect
12. #22609778C2semidirect
13. #22609771C2semidirect
14. #22609717C2semidirect
24. C2×#14556598C22semidirect
35. C2×#14556527C22semidirect
36. C2×#14556527C22semidirect
37. #17988614C22semidirect
42. C2×#14556518C22semidirect
43. C2×#14556518C22semidirect
44. #17988554C22semidirect
46. #17988543C22semidirect
47. C2×#14556501C22semidirect
48. C2×C8×Dic73C22semidirect
50. #17988352C22semidirect
51. #17988352C22semidirect
52. #17988346C22semidirect
53. #17988346C22semidirect
54. #17988341C22semidirect
55. #17988341C22semidirect
60. #452×C73C4semidirect
61. #452×C73C4semidirect
62. #451×C73C4semidirect
63. #450×C73C4semidirect
64. #449×C73C4semidirect
65. #449×C73C4semidirect
66. #448×C73C4semidirect
67. #447×C73C4semidirect
81. #14556598D4semidirect
82. #14556598D4semidirect
463. C73#21468semidirect
481. #452Dic73semidirect
482. #452Dic73semidirect
483. #451Dic73semidirect
484. #450Dic73semidirect
485. #449Dic73semidirect
486. #449Dic73semidirect
487. #448Dic73semidirect
488. #447Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179893542
C2×#179887092
C2×#179887042
#226186352
#226102602
#226102342
#226102082
#226101382
#226098752
#226097782
#226097712
#226097172
C73×#30022
#2146873