Finite Group Databasebeta

← #33122158

Subgroups — #33122158

Order 18688.

1068 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988884C211yesmaximal, characteristic, complemented
2C2×#17988874C211yesmaximal, characteristic, complemented
3#22612624C211yesmaximal, characteristic
4#22611266C211yesmaximal, characteristic, complemented
5#22611261C211yesmaximal, characteristic, complemented
6#22611074C211yesmaximal, characteristic, complemented
7#22611064C211yesmaximal, characteristic, complemented
8#22610889C211yesmaximal, characteristic, complemented
9#22610884C211yesmaximal, characteristic, complemented
10#22610253C211yesmaximal, characteristic
11#22610248C211yesmaximal, characteristic
12#22610130C211yesmaximal, characteristic, complemented
13#22610124C211yesmaximal, characteristic, complemented
14#22609915C211yesmaximal, characteristic, complemented
15C2×#544×C73C211yesmaximal, characteristic, complemented
16C2×#14556565C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18#17988884—24no—
19#17988874—24no—
20C2×#14556524C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×#14556522C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×C4⋊#10596831C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556511C2211yescharacteristic
29C2×#14556511C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32#17988489C2211yescharacteristic
33#17988487—21no—
34#17988485C2211yescharacteristic
35#17988477—21no—
36#17988463—21no—
37#17988458—21no—
38#17988447C2211yescharacteristic
39C4×C4⋊Dic73C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988342C2211yescharacteristic
49#17988342C2211yescharacteristic
50#544×C73—24no—
51#544×C73—24no—
52C2×C4⋊Q8×C73—21no—
53C2×C4⋊Q8×C73C2211yescharacteristic
54C2×C4⋊Q8×C73C2211yescharacteristic
55C2×#125×C73—21no—
56C2×#125×C73C2211yescharacteristic
57C2×#125×C73C2211yescharacteristic
58C2×C22⋊Q8×C73—21no—
59C2×C22⋊Q8×C73—21no—
60C2×#117×C73C2211yescharacteristic
61C2×#117×C73C2211yescharacteristic
62C22×C4⋊C4×C73C2211yescharacteristic
63C22×D292C2311yescharacteristic
64C22×C22⋊D73—21no—
65C22×C4×D73—21no—
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70#14556565—22no—
71#14556565Q814yescomplemented
72C4×D292—22no—
73C4×D292—22no—
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×#11924007—21no—
78C2×C22⋊Dic73—21no—
79C2×#11924005—21no—
80C2×#11924005—21no—
81C2×#11924005—21no—
82C2×#11924005—21no—
83C2×C4×Dic73—21no—
84#14556524—22no—
85#14556522—22no—
86#14556522—22no—
87#14556522—22no—
88C4⋊#10596831—22no—
89C4⋊#10596831—22no—
90#14556511—22no—
91#14556511—22no—
92#14556511—22no—
93#14556511—22no—
94C22⋊#10596831—22no—
95C22⋊#10596831—22no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99C22×Q8×C73—21no—
100C22×Q8×C73—21no—
101C23×C4×C73—21no—
102C23×C4×C73C2311yescharacteristic
103C4⋊Q8×C73—28no—
104C4⋊Q8×C73—22no—
105C4⋊Q8×C73—22no—
106C4⋊Q8×C73—22no—
107C4⋊Q8×C73D414yescomplemented
108#125×C73—28no—
109#125×C73—22no—
110#125×C73—22no—
111#125×C73—22no—
112#125×C73D414yescomplemented
113C22⋊Q8×C73—28no—
114C22⋊Q8×C73—28no—
115#117×C73—22no—
116#117×C73—22no—
117#117×C73—22no—
118#117×C73—22no—
119C2×C4⋊C4×C73—21no—
120C2×C4⋊C4×C73—21no—
121C2×C4⋊C4×C73—21no—
122C2×C4⋊C4×C73—21no—
123C2×C4⋊C4×C73—21no—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73—22no—
127C2×C4⋊C4×C73—22no—
128C2×C4⋊C4×C73D411yescharacteristic
129C2×C4⋊C4×C73D411yescharacteristic
130C2×C4⋊C4×C73C2311yescharacteristic
131C2×C4⋊C4×C73C2311yescharacteristic
132C2×C4⋊C4×C73C2311yescharacteristic
133C2×C4⋊C4×C73C2311yescharacteristic
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73D411yescharacteristic
136C2×C22⋊C4×C73D411yescharacteristic
137C2×C42×C73—21no—
138C2×C42×C73C2311yescharacteristic
139C2×C42×C73C2311yescharacteristic
140C23×D73—21no—
141C2×D292—21no—
142C2×D292—21no—
143C2×D292—21no—
144C2×D292—21no—
145C2×D292—21no—
146C2×D292C2×Q812yes—
147C2×C22⋊D73—24no—
148C2×C22⋊D73—81no—
149C2×C22⋊D73—81no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C2×C4×D73—42no—
154C2×C4×D73—81no—
155C2×C4×D73—81no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73C2×Q812yes—
174#11924007—81no—
175C22⋊Dic73—81no—
176#11924005—24no—
177#11924005—42no—
178#11924005—81no—
179#11924005—81no—
180C4×Dic73—81no—
181C24×C73C2×D411yescharacteristic
182C2×Q8×C73—24no—
183C2×Q8×C73—24no—
184C2×Q8×C73—81no—
185C2×Q8×C73—81no—
186C2×Q8×C73—81no—
187C2×Q8×C73—81no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—24no—
197C22×C4×C73—81no—
198C22×C4×C73—81no—
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×Q812yes—
205C22×C4×C73#4112yes—
206C22×C4×C73C2411yescharacteristic
207C4⋊C4×C73—24no—
208C4⋊C4×C73—24no—
209C4⋊C4×C73—24no—
210C4⋊C4×C73—24no—
211C4⋊C4×C73—24no—
212C4⋊C4×C73—24no—
213C4⋊C4×C73—24no—
214C4⋊C4×C73—22no—
215C4⋊C4×C73—22no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73C2×D412yes—
221C4⋊C4×C73C2×D412yes—
222C4⋊C4×C73C2×D412yes—
223C4⋊C4×C73C2×D412yes—
224C22⋊C4×C73—24no—
225C22⋊C4×C73—22no—
226C22⋊C4×C73—22no—
227C42×C73—24no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73C2×D412yes—
231C42×C73C2×D412yes—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73C22⋊Q812yes—
239C23×C73C22×D411yescharacteristic
240C22×D73—22no—
241C22×D73—41no—
242C22×D73—41no—
243C22×D73—41no—
244C22×D73—41no—
245C22×D73—41no—
246C22×D73—41no—
247Q8×C73—84no—
248Q8×C73—84no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—21no—
260C2×C4×C73—22no—
261C2×C4×C73—21no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—84no—
278C2×C4×C73#12012yes—
279C2×C4×C73#12012yes—
280C2×C4×C73C22⋊Q812yes—
281C2×C4×C73C22×D411yescharacteristic
282C2×C4×C73C22×D411yescharacteristic
283C2×C4×C73C22×Q811yescharacteristic
284C2×C4×C73C2×#4111yescharacteristic
285C2×C4×C732−1+411yescharacteristic
286C2×C4×C732−1+411yescharacteristic
287C22⋊D73—84no—
288C2×Dic73—22no—
289C2×Dic73—41no—
290C2×Dic73—41no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297D292—22no—
298D292—22no—
299D292—41no—
300D292—41no—
301C4×D73—84no—
302#10596831—41no—
303#10596831—41no—
304#10596831—41no—
305#10596831—41no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—41no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73—41no—
313C22×C73C2×#12011yescharacteristic
314C22×C73C2×C22⋊Q811yescharacteristic
315C22×C73#53611yescharacteristic
316C22×C73#57611yescharacteristic
317C22×C73#57711yescharacteristic
318C22×C73#57711yescharacteristic
319C22×C73#57711yescharacteristic
320C2×D73—42no—
321C2×D73—42no—
322C2×D73—42no—
323C2×D73—81no—
324C2×D73—81no—
325C2×D73—81no—
326C2×D73—81no—
327C4×C73—22no—
328C4×C73—22no—
329C4×C73—22no—
330C4×C73—41no—
331C4×C73—42no—
332C4×C73—41no—
333C4×C73—42no—
334C4×C73—42no—
335C4×C73—42no—
336C4×C73#54811yescharacteristic
337C4×C73#54811yescharacteristic
338C4×C73D4×Q811yescharacteristic
339C4×C73D4×Q811yescharacteristic
340Dic73—42no—
341Dic73—81no—
342Dic73—81no—
343#24309—731nomaximal, Sylow
344C2×C73—42no—
345C2×C73#240911yescharacteristic
346C2×C73#301011yescharacteristic
347C2×C73#301211yescharacteristic
348C2×C73#308111yescharacteristic
349C2×C73#308411yescharacteristic
350C2×C73#324111yescharacteristic
351C2×C73#324411yescharacteristic
352D73—82no—
353C2×#544D7311yescharacteristic, complemented
354C2×#478—731no—
355C2×#476—731no—
356#2324—731no—
357#2059—731no—
358#2058—731no—
359#2025—731no—
360#2023—731no—
361#1989—731no—
362#1988—731no—
363#1875—731no—
364#1874—731no—
365#1854—731no—
366#1853—731no—
367#1798—731no—
368C73#2430911yescharacteristic, complemented, Sylow
369#544—24no—
370#544—24no—
371C2×C4⋊Q8—21no—
372C2×C4⋊Q8C2×D7311yescharacteristic
373C2×C4⋊Q8C2×D7311yescharacteristic
374C2×#125—21no—
375C2×#125C2×D7311yescharacteristic
376C2×#125C2×D7311yescharacteristic
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8—21no—
379C2×#121—731no—
380C2×C4×D4—731no—
381C2×#117C2×D7311yescharacteristic
382C2×#117C2×D7311yescharacteristic
383C22×C4⋊C4C2×D7311yescharacteristic
384#478—1464no—
385#476—1464no—
386C2×#107—731no—
387C2×#106—731no—
388C2×#106—731no—
389C2×#106—731no—
390C2×C4⋊C8—731no—
391C2×C4⋊C8—731no—
392C2×#102—731no—
393C2×#102—731no—
394C2×#102—731no—
395C2×#102—731no—
396C2×C22⋊C8—731no—
397C2×C22⋊C8—731no—
398#390—731no—
399#390—1461no—
400#389—731no—
401#388—1461no—
402#386—1461no—
403#385—1461no—
404#380—731no—
405C4×C4⋊C4—731no—
406#340—731no—
407#340—731no—
408#340—731no—
409#340—731no—
410#340—731no—
411#340—731no—
412#340—731no—
413#340—731no—
414#336—731no—
415#336—731no—
416C22×Q8—21no—
417C22×Q8—21no—
418C22×D4—731no—
419C22×D4—1461no—
420C23×C4—21no—
421C23×C4—1461no—
422C23×C4C22×D7311yescharacteristic
423C22×C8—731no—
424C22×C8—731no—
425C22×C8—731no—
426C22×C8—731no—
427C4⋊Q8—28no—
428C4⋊Q8—22no—
429C4⋊Q8—22no—
430C4⋊Q8—22no—
431C4⋊Q8C22⋊D7314yescomplemented
432#125—28no—
433#125—22no—
434#125—22no—
435#125—22no—
436#125C22⋊D7314yescomplemented
437C22⋊Q8—28no—
438C22⋊Q8—28no—
439#121—734no—
440#121—1462no—
441C4×D4—1462no—
442C4×D4—1462no—
443#117—22no—
444#117—22no—
445#117—22no—
446#117—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—731no—
457C2×C4⋊C4—731no—
458C2×C4⋊C4—731no—
459C2×C4⋊C4—1461no—
460C2×C4⋊C4C22⋊D7311yescharacteristic
461C2×C4⋊C4C22⋊D7311yescharacteristic
462C2×C4⋊C4C22×D7311yescharacteristic
463C2×C4⋊C4C22×D7311yescharacteristic
464C2×C4⋊C4C22×D7311yescharacteristic
465C2×C4⋊C4C22×D7311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—1461no—
468C2×C22⋊C4—1461no—
469C2×C22⋊C4—1461no—
470C2×C22⋊C4—1461no—
471C2×C22⋊C4—1461no—
472C2×C22⋊C4C22⋊D7311yescharacteristic
473C2×C22⋊C4C22⋊D7311yescharacteristic
474C2×C42—21no—
475C2×C42—1461no—
476C2×C42C22×D7311yescharacteristic
477C2×C42C22×D7311yescharacteristic
478#107—1462no—
479#106—1462no—
480#106—1462no—
481#106—1462no—
482C4⋊C8—1462no—
483C4⋊C8—1462no—
484#102—1462no—
485#102—1462no—
486#102—1462no—
487#102—1462no—
488C22⋊C8—1462no—
489C22⋊C8—1462no—
490#95—1461no—
491#95—1461no—
492#95—1461no—
493C24—1461no—
494C24C2×C22⋊D7311yescharacteristic
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—81no—
498C2×Q8—81no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×D4—5841no—
502C2×D4—5841no—
503C2×D4—732no—
504C2×D4—1464no—
505C2×D4—1461no—
506C2×D4—1461no—
507C2×D4—1461no—
508C2×D4—1461no—
509C2×D4—1461no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—2922no—
522C22×C4—5841no—
523C22×C4—5841no—
524C22×C4—1461no—
525C22×C4—1461no—
526C22×C4—1461no—
527C22×C4C2×C22⋊D7311yescharacteristic
528C22×C4C2×C22⋊D7311yescharacteristic
529C22×C4C2×C22⋊D7311yescharacteristic
530C22×C4C2×C22⋊D7311yescharacteristic
531C22×C4C2×C22⋊D7311yescharacteristic
532C22×C4Q8×D7312yes—
533C22×C4#1192402912yes—
534C22×C4C23×D7311yescharacteristic
535C2×C8—1461no—
536C2×C8—1461no—
537C2×C8—1461no—
538C2×C8—1461no—
539C2×C8—1461no—
540C2×C8—1461no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—5841no—
561C4⋊C4—732no—
562C4⋊C4—1461no—
563C4⋊C4—1461no—
564C4⋊C4—1461no—
565C4⋊C4—1461no—
566C4⋊C4—1461no—
567C4⋊C4C2×C22⋊D7312yes—
568C4⋊C4C2×C22⋊D7312yes—
569C4⋊C4C2×C22⋊D7312yes—
570C4⋊C4C2×C22⋊D7312yes—
571C22⋊C4—24no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—2922no—
575C22⋊C4—5841no—
576C22⋊C4—5841no—
577C22⋊C4—5841no—
578C22⋊C4—1464no—
579C42—24no—
580C42—21no—
581C42—21no—
582C42—5841no—
583C42C2×C22⋊D7312yes—
584C42C2×C22⋊D7312yes—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—2921no—
592C23—2921no—
593C23—2921no—
594C23—2921no—
595C23—2921no—
596C23—2921no—
597C23—1462no—
598C23#1455656712yes—
599C23C22×C22⋊D7311yescharacteristic
600Q8—84no—
601Q8—84no—
602D4—2921no—
603D4—2921no—
604D4—5844no—
605D4—1462no—
606D4—1462no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—2921no—
637C2×C4—2921no—
638C2×C4—2921no—
639C2×C4—2921no—
640C2×C4—2921no—
641C2×C4—2921no—
642C2×C4—2921no—
643C2×C4—2921no—
644C2×C4—5844no—
645C2×C4—1462no—
646C2×C4#1455656012yes—
647C2×C4#1455656012yes—
648C2×C4#1455656712yes—
649C2×C4C22×C22⋊D7311yescharacteristic
650C2×C4C22×C22⋊D7311yescharacteristic
651C2×C4C2×Q8×D7311yescharacteristic
652C2×C4C2×#1192402911yescharacteristic
653C2×C4#1455663911yescharacteristic
654C2×C4#1455663911yescharacteristic
655C8—2921no—
656C8—2921no—
657C8—2921no—
658C8—2921no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—2922no—
667C22—2922no—
668C22—2922no—
669C22—5841no—
670C22—5841no—
671C22—5841no—
672C22—5841no—
673C22C2×#1455656011yescharacteristic
674C22C2×#1455656711yescharacteristic
675C22#1798916111yescharacteristic
676C22#1798939011yescharacteristic
677C22#1798939511yescharacteristic
678C22#1798939511yescharacteristic
679C22#1798939811yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—2922no—
690C4—5841no—
691C4—5841no—
692C4#1798924811yescharacteristic
693C4#1798924811yescharacteristic
694C4Q8×C22⋊D7311yescharacteristic
695C4Q8×C22⋊D7311yescharacteristic
696C2—42no—
697C2—5842no—
698C2#2261329011yescharacteristic
699C2#2261921711yescharacteristic
700C2#2261923511yescharacteristic
701C2#2261975611yescharacteristic
702C2#2261978911yescharacteristic
703C2#2262118411yescharacteristic
704C2#2262122911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#544×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
hypercenterC2×#544D73
hypocenterC73#24309
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×#17988884C2semidirect
2. C2×#17988874C2semidirect
4. #22611266C2semidirect
5. #22611261C2semidirect
6. #22611074C2semidirect
7. #22611064C2semidirect
8. #22610889C2semidirect
9. #22610884C2semidirect
12. #22610130C2semidirect
13. #22610124C2semidirect
14. #22609915C2semidirect
15. C2×#544×C73C2semidirect
71. #14556565Q8semidirect
107. C4⋊Q8×C73D4semidirect
112. #125×C73D4semidirect
353. C2×#544D73semidirect
368. C73#24309semidirect
431. C4⋊Q8C22⋊D73semidirect
436. #125C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179888842
C2×#179888742
#226126242
#226112662
#226112612
#226110742
#226110642
#226108892
#226108842
#226102532
#226102482
#226101302
#226101242
#226099152
C2×#544×C732
#2430973