Finite Group Databasebeta

← #33106436

Subgroups — #33106436

Order 18688.

1106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988749C211yesmaximal, characteristic
2C2×#17988691C211yesmaximal, characteristic, complemented
3#22612936C211yesmaximal, characteristic, complemented
4#22612772C211yesmaximal, characteristic
5#22610786C211yesmaximal, characteristic, complemented
6#22610625C211yesmaximal, characteristic, complemented
7#22610561C211yesmaximal, characteristic, complemented
8#22610364C211yesmaximal, characteristic, complemented
9#22610283C211yesmaximal, characteristic, complemented
10#22610270C211yesmaximal, characteristic, complemented
11#22610197C211yesmaximal, characteristic, complemented
12#22610124C211yesmaximal, characteristic, complemented
13#103×Dic73C211yesmaximal, characteristic, complemented
14#22609712C211yesmaximal, characteristic, complemented
15C2×#417×C73C211yesmaximal, characteristic
16C22×#11924018C2211yescharacteristic
17C22×#11924016C2211yescharacteristic
18C2×#14556570C2211yescharacteristic
19C2×Q8×Dic73C2211yescharacteristic
20C2×Q8×Dic73C2211yescharacteristic
21C2×#14556556C2211yescharacteristic
22#17988749C418yescomplemented
23#17988691—24no—
24C2×#14556522C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26C2×#14556516C2211yescharacteristic
27C2×#14556516C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×#14556501C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33#17988492C2211yescharacteristic
34#17988490—21no—
35#17988490—21no—
36#17988490C2211yescharacteristic
37#17988490C2211yescharacteristic
38#17988483C2211yescharacteristic
39#17988482—21no—
40#17988468—21no—
41#17988460—21no—
42#17988447—21no—
43#17988447C2211yescharacteristic
44C4⋊C4×Dic73C2211yescharacteristic
45C4×C22⋊Dic73—21no—
46C4×C22⋊Dic73—21no—
47C4×C22⋊Dic73C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C22×#41×C73C2211yescharacteristic
55C22×M16×C73C2211yescharacteristic
56C22×C4⋊C4×C73C2211yescharacteristic
57#417×C73—24no—
58C2×#103×C73C2211yescharacteristic
59C2×#103×C73C2211yescharacteristic
60C2×#102×C73C2211yescharacteristic
61C2×#102×C73C2211yescharacteristic
62C22×Dic146C2311yescharacteristic
63C2×#11924018—22no—
64C2×#11924018—22no—
65C2×#11924018C2×C414yescomplemented
66C2×#11924016—41no—
67C2×#11924016—41no—
68C2×#11924016C2×C414yescomplemented
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556570—22no—
72#14556570C2×C414yes—
73Q8×Dic73—22no—
74Q8×Dic73—22no—
75Q8×Dic73—41no—
76Q8×Dic73—41no—
77#14556556—22no—
78#14556556—41no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73—21no—
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×#11924007—21no—
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×C22⋊Dic73—21no—
88C2×C22⋊Dic73—21no—
89C2×C22⋊Dic73—21no—
90C2×C22⋊Dic73—21no—
91C2×C22⋊Dic73—21no—
92C2×C22⋊Dic73—21no—
93C2×C22⋊Dic73D411yescharacteristic
94C2×C22⋊Dic73D411yescharacteristic
95C2×C4×Dic73—21no—
96C2×C4×Dic73—21no—
97C2×C4×Dic73—21no—
98C2×C4×Dic73—21no—
99C2×C4×Dic73C2311yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101#14556522—22no—
102#14556522—41no—
103#14556516—22no—
104#14556516—41no—
105#14556515C2×C414yescomplemented
106#14556512C2×C414yescomplemented
107C22⋊#10596831C2×C414yes—
108#14556501—22no—
109C8×Dic73—41no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498—21no—
114#14556498—21no—
115#14556498D411yescharacteristic
116#14556498D411yescharacteristic
117C2×#41×C73—22no—
118C2×#41×C73—22no—
119C2×#41×C73—22no—
120C2×#41×C73—41no—
121C2×#41×C73—41no—
122C2×#41×C73C2×C414yes—
123C22×Q8×C73C2311yescharacteristic
124C22×D4×C73—21no—
125C22×D4×C73C2311yescharacteristic
126C23×C4×C73—21no—
127C23×C4×C73—21no—
128C23×C4×C73C2311yescharacteristic
129C2×M16×C73—22no—
130C2×M16×C73—22no—
131C2×M16×C73—41no—
132C22×C8×C73C2311yescharacteristic
133C22×C8×C73C2311yescharacteristic
134C2×C4⋊C4×C73—22no—
135C2×C4⋊C4×C73—21no—
136C2×C4⋊C4×C73—41no—
137C2×C4⋊C4×C73C2311yescharacteristic
138C2×C4⋊C4×C73C2311yescharacteristic
139#103×C73—22no—
140#103×C73D414yes—
141#102×C73—22no—
142#102×C73—22no—
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146C22×C412yes—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73C2×D411yescharacteristic
154C22×Dic73C2×D411yescharacteristic
155C22×Dic73C2×D411yescharacteristic
156C22×Dic73C2×D411yescharacteristic
157#11924018—28no—
158#11924016—44no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831C22×C412yes—
164C2×#10596831C22×C412yes—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—42no—
171C4⋊Dic73—42no—
172C4⋊Dic73C22×C412yes—
173#11924007—24no—
174#11924007—42no—
175#11924007—81no—
176C22⋊Dic73—24no—
177C22⋊Dic73—22no—
178C22⋊Dic73—41no—
179C22⋊Dic73—42no—
180C22⋊Dic73—42no—
181C22⋊Dic73—81no—
182C22⋊Dic73—81no—
183C22⋊Dic73—81no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—42no—
189C4×Dic73—42no—
190C4×Dic73—42no—
191C4×Dic73—81no—
192C24×C73—21no—
193C24×C73C2×D411yescharacteristic
194#41×C73—28no—
195#41×C73—44no—
196#41×C73—44no—
197#41×C73—44no—
198C2×Q8×C73—21no—
199C2×Q8×C73—21no—
200C2×Q8×C73—21no—
201C2×Q8×C73C22×C412yes—
202C2×Q8×C73C2×D412yes—
203C2×Q8×C73#4112yes—
204C2×D4×C73—24no—
205C2×D4×C73—21no—
206C2×D4×C73—21no—
207C2×D4×C73—21no—
208C2×D4×C73—21no—
209C2×D4×C73—21no—
210C2×D4×C73—42no—
211C2×D4×C73—42no—
212C2×D4×C73C22×C412yes—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—24no—
220C22×C4×C73—21no—
221C22×C4×C73—42no—
222C22×C4×C73—42no—
223C22×C4×C73—42no—
224C22×C4×C73—42no—
225C22×C4×C73—81no—
226C22×C4×C73C22×C412yes—
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73#4112yes—
229C22×C4×C73C2411yescharacteristic
230M16×C73—44no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73C2×D412yes—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—42no—
241C4⋊C4×C73C2×D412yes—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—22no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73C4×D412yes—
256C23×C73C22×D411yescharacteristic
257Q8×C73—22no—
258Q8×C73—22no—
259Q8×C73—22no—
260Q8×C73C4×D414yes—
261D4×C73—22no—
262D4×C73—22no—
263D4×C73—48no—
264D4×C73—41no—
265D4×C73—41no—
266C2×C4×C73—22no—
267C2×C4×C73—21no—
268C2×C4×C73—22no—
269C2×C4×C73—21no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—48no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—84no—
283C2×C4×C73C4×D412yes—
284C2×C4×C73C23×C411yescharacteristic
285C2×C4×C73C22×D411yescharacteristic
286C2×C4×C73C2×#4111yescharacteristic
287C2×C4×C73C2×#4111yescharacteristic
288C2×C4×C73H(5,𝔽2)11yescharacteristic
289C2×C4×C73H(5,𝔽2)11yescharacteristic
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—22no—
293C2×Dic73—22no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—21no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73#13712yes—
314Dic146—22no—
315Dic146—22no—
316Dic146—41no—
317Dic146—41no—
318C8×C73—22no—
319C8×C73—41no—
320#10596831—22no—
321#10596831—22no—
322C22×C73—22no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—42no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—81no—
333C22×C73—81no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73C2×C4×D411yescharacteristic
337C22×C73D4211yescharacteristic
338C22×C73#54611yescharacteristic
339C22×C73C2×#13711yescharacteristic
340C22×C73#57511yescharacteristic
341C22×C73#57711yescharacteristic
342C22×C73#57711yescharacteristic
343C4×C73—22no—
344C4×C73—24no—
345C4×C73—42no—
346C4×C73—81no—
347C4×C73C2×C4×D411yescharacteristic
348C4×C73#51811yescharacteristic
349C4×C73#54611yescharacteristic
350C4×C73#55111yescharacteristic
351Dic73—22no—
352Dic73—42no—
353Dic73—42no—
354Dic73—41no—
355Dic73—41no—
356Dic73—41no—
357Dic73—81no—
358Dic73—81no—
359#22867—731nomaximal, Sylow
360C2×C73—42no—
361C2×C73—82no—
362C2×C73#235811yescharacteristic
363C2×C73C4×#13711yescharacteristic
364C2×C73#295211yescharacteristic
365C2×C73#327511yescharacteristic
366C2×C73#327811yescharacteristic
367C2×C73#331611yescharacteristic
368C2×C73#331711yescharacteristic
369C2×#452—731no—
370C2×#441—731no—
371C2×#417D7311yescharacteristic
372#2360—731no—
373#2341—731no—
374#1968—731no—
375#1936—731no—
376#1926—731no—
377#1894—731no—
378#1880—731no—
379#1878—731no—
380#1865—731no—
381#1853—731no—
382C4×#103—731no—
383#1753—731no—
384C73#2286711yescharacteristic, complemented, Sylow
385C22×#41C2×D7311yescharacteristic
386C22×Q16—731no—
387C22×SD16—731no—
388C22×M16C2×D7311yescharacteristic
389C2×C22⋊Q8—731no—
390C2×C4×Q8—731no—
391C2×C4×Q8—731no—
392C2×C4×Q8—731no—
393C22×C4⋊C4C2×D7311yescharacteristic
394#452—738no—
395#441—1464no—
396C2×#106—731no—
397C2×#106—731no—
398#417—24no—
399C2×#103—731no—
400C2×#103—731no—
401C2×#103—731no—
402C2×#103C2×D7311yescharacteristic
403C2×#103C2×D7311yescharacteristic
404C2×#102—731no—
405C2×#102C2×D7311yescharacteristic
406C2×#102C2×D7311yescharacteristic
407C2×C22⋊C8—731no—
408C2×#97—731no—
409C2×C4×C8—731no—
410#391—731no—
411#390—731no—
412#390—731no—
413#390—1461no—
414#390—1461no—
415#389—731no—
416#389—1461no—
417#387—1461no—
418#385—1461no—
419#380—731no—
420#380—1461no—
421C4×C4⋊C4—731no—
422C4×C22⋊C4—731no—
423C4×C22⋊C4—1461no—
424C4×C22⋊C4—1461no—
425#340—731no—
426#340—731no—
427#340—731no—
428#340—731no—
429#336—731no—
430#336—731no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41C4×D7314yes—
437C22×Q8—731no—
438C22×Q8C22×D7311yescharacteristic
439C22×D4—21no—
440C22×D4C22×D7311yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C22×D7311yescharacteristic
444C2×Q16—734no—
445C2×Q16—1462no—
446C2×Q16—1462no—
447C2×SD16—2921no—
448C2×SD16—2921no—
449C2×SD16—734no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—41no—
453C22×C8—731no—
454C22×C8—731no—
455C22×C8C22×D7311yescharacteristic
456C22×C8C22×D7311yescharacteristic
457C22⋊Q8—734no—
458C22⋊Q8—1462no—
459C4×Q8—2921no—
460C4×Q8—2921no—
461C4×Q8—2921no—
462C4×Q8—1462no—
463C4×Q8—1462no—
464C4×Q8—1462no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—731no—
469C2×C4⋊C4—731no—
470C2×C4⋊C4—731no—
471C2×C4⋊C4—1461no—
472C2×C4⋊C4—1461no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4—1461no—
475C2×C4⋊C4—1461no—
476C2×C4⋊C4C22×D7311yescharacteristic
477C2×C4⋊C4C22×D7311yescharacteristic
478C2×C22⋊C4—731no—
479C2×C22⋊C4—731no—
480C2×C22⋊C4—1461no—
481C2×C22⋊C4—1461no—
482C2×C22⋊C4—1461no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4—1461no—
485C2×C22⋊C4—1461no—
486C2×C42—731no—
487C2×C42—731no—
488C2×C42—1461no—
489C2×C42—1461no—
490C2×C42—1461no—
491C2×C42—1461no—
492#106—2921no—
493#106—1462no—
494#103—22no—
495#103—2921no—
496#103—734no—
497#103—1462no—
498#103C22⋊D7314yes—
499#102—22no—
500#102—22no—
501#102—734no—
502C22⋊C8—734no—
503#97—1462no—
504C4×C8—2921no—
505#95—731no—
506#95—731no—
507#95—1461no—
508#95—1461no—
509#95—1461no—
510#95—1461no—
511#95—1461no—
512C24—21no—
513C24D4×D7311yescharacteristic
514#41—28no—
515#41—44no—
516#41—44no—
517#41—44no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—732no—
522C2×Q8—1461no—
523C2×Q8—1461no—
524C2×Q8—1461no—
525C2×Q8—1461no—
526C2×Q8—1461no—
527C2×Q8C2×C4×D7312yes—
528C2×Q8C2×C22⋊D7312yes—
529C2×Q8#1192402812yes—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4C2×C4×D7312yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4—731no—
553C22×C4—731no—
554C22×C4—731no—
555C22×C4—731no—
556C22×C4—1461no—
557C22×C4—1461no—
558C22×C4—1461no—
559C22×C4—1461no—
560C22×C4C2×C4×D7312yes—
561C22×C4D4×D7311yescharacteristic
562C22×C4#1192402712yes—
563C22×C4C23×D7311yescharacteristic
564Q16—1468no—
565SD16—2924no—
566M16—44no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—732no—
573C2×C8—732no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8C2×C22⋊D7312yes—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—42no—
583C4⋊C4—2922no—
584C4⋊C4—2922no—
585C4⋊C4—2922no—
586C4⋊C4—5841no—
587C4⋊C4—732no—
588C4⋊C4—1461no—
589C4⋊C4—1461no—
590C4⋊C4—1461no—
591C4⋊C4—1461no—
592C4⋊C4—1464no—
593C4⋊C4—1461no—
594C4⋊C4C2×C22⋊D7312yes—
595C22⋊C4—2922no—
596C22⋊C4—2922no—
597C22⋊C4—2921no—
598C22⋊C4—5841no—
599C22⋊C4—5841no—
600C22⋊C4—5841no—
601C22⋊C4—1462no—
602C22⋊C4—1464no—
603C42—2922no—
604C42—2922no—
605C42—2922no—
606C42—5841no—
607C42—1461no—
608C42—1461no—
609C42—1461no—
610C42—1461no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23#1455655112yes—
625C23C2×D4×D7311yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—2921no—
630Q8—2921no—
631Q8—1462no—
632Q8—1462no—
633Q8C4×C22⋊D7314yes—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—48no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—84no—
656C2×C4—2921no—
657C2×C4—2921no—
658C2×C4—2921no—
659C2×C4—2921no—
660C2×C4—2921no—
661C2×C4—2921no—
662C2×C4—2921no—
663C2×C4—2921no—
664C2×C4—2921no—
665C2×C4—2921no—
666C2×C4—732no—
667C2×C4—1461no—
668C2×C4—1461no—
669C2×C4—1461no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1461no—
675C2×C4—1461no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4—1461no—
679C2×C4—1461no—
680C2×C4#1455655112yes—
681C2×C4C22×C4×D7311yescharacteristic
682C2×C4C22×C22⋊D7311yescharacteristic
683C2×C4C2×#1192402711yescharacteristic
684C2×C4C2×#1192402811yescharacteristic
685C2×C4#1455663611yescharacteristic
686C2×C4#1455663611yescharacteristic
687C8—22no—
688C8—41no—
689C8—1462no—
690C8—1462no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22C2×#1455655111yescharacteristic
706C22D4×C22⋊D7311yescharacteristic
707C22#1798922711yescharacteristic
708C22#137×D7311yescharacteristic
709C22#1798938311yescharacteristic
710C22#1798939611yescharacteristic
711C22#1798939711yescharacteristic
712C4—22no—
713C4—24no—
714C4—42no—
715C4—81no—
716C4—2921no—
717C4—2921no—
718C4—2921no—
719C4—2922no—
720C4—2922no—
721C4—5841no—
722C4—5841no—
723C4—1462no—
724C4C2×C4×C22⋊D7311yescharacteristic
725C4#1798906011yescharacteristic
726C4#1798923111yescharacteristic
727C4#1798926311yescharacteristic
728C2—42no—
729C2—82no—
730C2#2261291011yescharacteristic
731C2#2261875511yescharacteristic
732C2#2261881011yescharacteristic
733C2#2262156211yescharacteristic
734C2#2262159111yescharacteristic
735C2#2262204311yescharacteristic
736C2#2262205811yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#417×C73C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#417D73
hypocenterC73#22867
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#17988691C2semidirect
3. #22612936C2semidirect
5. #22610786C2semidirect
6. #22610625C2semidirect
7. #22610561C2semidirect
8. #22610364C2semidirect
9. #22610283C2semidirect
10. #22610270C2semidirect
11. #22610197C2semidirect
12. #22610124C2semidirect
13. #103×Dic73C2semidirect
14. #22609712C2semidirect
22. #17988749C4semidirect
65. C2×#11924018C2×C4semidirect
68. C2×#11924016C2×C4semidirect
105. #14556515C2×C4semidirect
106. #14556512C2×C4semidirect
384. C73#22867semidirect

Maximal subgroups

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

subgroupindex
C2×#179887492
C2×#179886912
#226129362
#226127722
#226107862
#226106252
#226105612
#226103642
#226102832
#226102702
#226101972
#226101242
#103×Dic732
#226097122
C2×#417×C732
#2286773