Finite Group Databasebeta

← #33103299

Subgroups — #33103299

Order 18688.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988592C211yesmaximal, characteristic
2#22612814C211yesmaximal, characteristic, complemented
3#22610631C211yesmaximal, characteristic, complemented
4#22610617C211yesmaximal, characteristic, complemented
5#22610555C211yesmaximal, characteristic, complemented
6#22610548C211yesmaximal, characteristic, complemented
7#22610192C211yesmaximal, characteristic, complemented
8#22610178C211yesmaximal, characteristic, complemented
9#22610023C211yesmaximal, characteristic, complemented
10#22609962C211yesmaximal, characteristic, complemented
11#22609862C211yesmaximal, characteristic
12#22609756C211yesmaximal, characteristic, complemented
13C4×#14556512C211yesmaximal, characteristic, complemented
14#22609715C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C2×#14556550C2211yescharacteristic
18C2×#14556524C2211yescharacteristic, complemented
19C2×#14556522C2211yescharacteristic, complemented
20#17988592C418yescomplemented
21C2×#14556512C2211yescharacteristic
22C2×#14556512C2211yescharacteristic
23C2×#14556512C2211yescharacteristic
24C2×#14556512C2211yescharacteristic
25C2×#14556512C2211yescharacteristic
26C2×#14556512C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×#14556502C2211yescharacteristic, complemented
31C2×C4×#10596831C2211yescharacteristic, complemented
32#17988485C2211yescharacteristic, complemented
33#17988485C2211yescharacteristic, complemented
34#17988475—21no—
35#17988475—21no—
36#17988451—21no—
37#17988447C2211yescharacteristic
38C4×C4⋊Dic73C2211yescharacteristic, complemented
39C4×C4⋊Dic73C2211yescharacteristic, complemented
40#17988432—21no—
41#17988349C2211yescharacteristic, complemented
42#17988349C2211yescharacteristic, complemented
43#17988349C2211yescharacteristic, complemented
44#17988349C2211yescharacteristic, complemented
45#17988349C2211yescharacteristic, complemented
46#17988349C2211yescharacteristic, complemented
47#17988342C2211yescharacteristic, complemented
48#17988342C2211yescharacteristic, complemented
49C23×D4×C73C2211yescharacteristic
50C2×C4×D4×C73C2211yescharacteristic
51C2×C4×D4×C73C2211yescharacteristic
52C22×C22⋊C4×C73—21no—
53#390×C73C2211yescharacteristic
54#390×C73C2211yescharacteristic
55#386×C73—21no—
56#386×C73—21no—
57#380×C73C2211yescharacteristic
58#379×C73—21no—
59C4×C22⋊C4×C73C2211yescharacteristic
60C2×#11924012—41no—
61C2×#11924012—41no—
62C2×#11924012C2×C414yescomplemented
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67#14556550—22no—
68#14556550C2×C414yescomplemented
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×C22⋊Dic73—21no—
76C2×C22⋊Dic73—21no—
77C2×C4×Dic73—21no—
78C2×C4×Dic73—21no—
79C2×C4×Dic73—21no—
80#14556524—41no—
81#14556522—41no—
82#14556512—22no—
83#14556512—22no—
84#14556512—41no—
85#14556512—41no—
86#14556512C2×C414yes—
87#14556512C2×C414yes—
88#14556512C2×C414yescomplemented
89#14556512C2×C414yescomplemented
90C22⋊#10596831—22no—
91#14556502—41no—
92C4×#10596831—41no—
93#14556498—21no—
94#14556498—21no—
95#14556498—21no—
96#14556498—21no—
97#14556498—21no—
98C25×C73—21no—
99C22×D4×C73—22no—
100C22×D4×C73—22no—
101C22×D4×C73—21no—
102C22×D4×C73—22no—
103C22×D4×C73—41no—
104C22×D4×C73—41no—
105C22×D4×C73C2×C414yes—
106C22×D4×C73C2311yescharacteristic
107C22×D4×C73C2311yescharacteristic
108C23×C4×C73—21no—
109C23×C4×C73—21no—
110C23×C4×C73C2311yescharacteristic
111C4×D4×C73—22no—
112C4×D4×C73—22no—
113C4×D4×C73—41no—
114C4×D4×C73—41no—
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—44no—
125C2×C22⋊C4×C73D411yescharacteristic
126C2×C22⋊C4×C73D411yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C2×C42×C73C2311yescharacteristic
129#95×C73—21no—
130#95×C73D411yescharacteristic
131#95×C73D411yescharacteristic
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136#11924012—44no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831C22×C412yes—
148C2×#10596831C22×C412yes—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73C22×C412yes—
156C4⋊Dic73C22×C412yes—
157#11924007—81no—
158#11924007—81no—
159C22⋊Dic73—24no—
160C22⋊Dic73—81no—
161C4×Dic73—24no—
162C4×Dic73—42no—
163C4×Dic73—42no—
164C24×C73—21no—
165C24×C73—21no—
166C24×C73—24no—
167C24×C73—42no—
168C24×C73—42no—
169C24×C73—42no—
170C24×C73—42no—
171C24×C73—81no—
172C24×C73—81no—
173C24×C73C2×D411yescharacteristic
174C2×D4×C73—28no—
175C2×D4×C73—24no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—44no—
185C2×D4×C73—44no—
186C2×D4×C73—44no—
187C2×D4×C73—42no—
188C2×D4×C73—42no—
189C2×D4×C73C22×C412yes—
190C2×D4×C73C22×C412yes—
191C2×D4×C73#4112yes—
192C2×D4×C73#4112yes—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—42no—
200C22×C4×C73—42no—
201C22×C4×C73—42no—
202C22×C4×C73—42no—
203C22×C4×C73—81no—
204C22×C4×C73—81no—
205C22×C4×C73C22×C412yes—
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73#4112yes—
212C22×C4×C73C2411yescharacteristic
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C22⋊C4×C73—22no—
218C22⋊C4×C73—41no—
219C22⋊C4×C73—42no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—42no—
224C22⋊C4×C73—81no—
225C22⋊C4×C73—81no—
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C23×C73—22no—
231C23×C73—22no—
232C23×C73—22no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—22no—
240C23×C73—48no—
241C23×C73—48no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—84no—
253C23×C73—84no—
254C23×C73—84no—
255C23×C73—84no—
256C23×C73—84no—
257C23×C73C4×D412yes—
258C23×C73C22×D411yescharacteristic
259D4×C73—22no—
260D4×C73—22no—
261D4×C73—22no—
262D4×C73—22no—
263D4×C73—22no—
264D4×C73—48no—
265D4×C73—41no—
266D4×C73—41no—
267D4×C73#11714yes—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—84no—
292C2×C4×C73—84no—
293C2×C4×C73C4×D412yes—
294C2×C4×C73AGL(1,ℤ/8)12yes—
295C2×C4×C73C23×C411yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×C4×C73C2×#4111yescharacteristic
298C2×C4×C73C2×#4111yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C2×Dic73—22no—
302C2×Dic73—22no—
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—
313#10596831—22no—
314#10596831—22no—
315#10596831—41no—
316#10596831—41no—
317C22×C73—22no—
318C22×C73—24no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—42no—
322C22×C73—42no—
323C22×C73—42no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—42no—
327C22×C73—41no—
328C22×C73—42no—
329C22×C73—42no—
330C22×C73—41no—
331C22×C73—42no—
332C22×C73—42no—
333C22×C73—42no—
334C22×C73—816no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73—81no—
338C22×C73—81no—
339C22×C73C2×C4×D411yescharacteristic
340C22×C73#54611yescharacteristic
341C22×C73#54611yescharacteristic
342C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C73#57511yescharacteristic
344C22×C73#57611yescharacteristic
345C22×C73#57711yescharacteristic
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—41no—
351C4×C73—81no—
352C4×C73—81no—
353C4×C73C2×#11711yescharacteristic
354C4×C73#51811yescharacteristic
355C4×C73#55111yescharacteristic
356C4×C73#55111yescharacteristic
357Dic73—42no—
358Dic73—42no—
359Dic73—81no—
360Dic73—81no—
361#22584—731nomaximal, Sylow
362C2×C73—42no—
363C2×C73—44no—
364C2×C73—82no—
365C2×C73#234211yescharacteristic
366C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
367C2×C73#294611yescharacteristic
368C2×C73#331011yescharacteristic
369C2×C73#331911yescharacteristic
370C2×C73#332311yescharacteristic
371C2×C73#332511yescharacteristic
372C2×#418—731no—
373#2346—731no—
374D4×C22⋊C4D7311yescharacteristic
375#1936—731no—
376#1934—731no—
377#1926—731no—
378#1925—731no—
379#1864—731no—
380#1862—731no—
381#1825—731no—
382#1809—731no—
383#1786—731no—
384#1762—731no—
385C4×#102—731no—
386#1753—731no—
387C73#2258411yescharacteristic, complemented, Sylow
388C23×D4C2×D7311yescharacteristic
389C22×M16—731no—
390C2×C4×D4C2×D7311yescharacteristic
391C2×C4×D4C2×D7311yescharacteristic
392C2×#117—731no—
393C22×C22⋊C4—21no—
394C2×#107—731no—
395C2×#106—731no—
396#418—738no—
397C2×#102—731no—
398C2×#102—731no—
399C2×#102—731no—
400C2×#102—731no—
401C2×#102—731no—
402C2×#102—731no—
403C2×#102—731no—
404C2×#102—731no—
405C2×C22⋊C8—731no—
406C2×#97—731no—
407C2×C4×C8—731no—
408#390C2×D7311yescharacteristic
409#390C2×D7311yescharacteristic
410#389—731no—
411#389—731no—
412#388—1461no—
413#388—1461no—
414#386—21no—
415#386—21no—
416#382—1461no—
417#380—731no—
418#380C2×D7311yescharacteristic
419#379—21no—
420C4×C4⋊C4—731no—
421C4×C4⋊C4—731no—
422C4×C22⋊C4C2×D7311yescharacteristic
423#376—1461no—
424#340—731no—
425#340—731no—
426#340—731no—
427#340—731no—
428#340—731no—
429#340—731no—
430#336—731no—
431#336—731no—
432C25—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—22no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4C4×D7314yes—
440C22×D4C22×D7311yescharacteristic
441C22×D4C22×D7311yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C22×D7311yescharacteristic
445C2×M16—2921no—
446C2×M16—2921no—
447C2×M16—734no—
448C22×C8—731no—
449C22×C8—731no—
450C22×C8—731no—
451C22×C8—731no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—41no—
456#117—734no—
457#117—1462no—
458C2×C4⋊C4—731no—
459C2×C4⋊C4—731no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—1461no—
463C2×C4⋊C4—1461no—
464C2×C4⋊C4C22×D7311yescharacteristic
465C2×C4⋊C4C22×D7311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—44no—
474C2×C22⋊C4—1461no—
475C2×C22⋊C4—1461no—
476C2×C22⋊C4C22⋊D7311yescharacteristic
477C2×C22⋊C4C22⋊D7311yescharacteristic
478C2×C42—1461no—
479C2×C42—1461no—
480C2×C42—1461no—
481C2×C42C22×D7311yescharacteristic
482C2×C42C22×D7311yescharacteristic
483#107—2921no—
484#106—2921no—
485#102—2921no—
486#102—2921no—
487#102—734no—
488#102—734no—
489#102—734no—
490#102—734no—
491#102—1462no—
492#102—1462no—
493C22⋊C8—1462no—
494#97—2921no—
495C4×C8—2921no—
496#95—21no—
497#95—1461no—
498#95—1461no—
499#95—1461no—
500#95—1461no—
501#95—1461no—
502#95C22⋊D7311yescharacteristic
503#95C22⋊D7311yescharacteristic
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24C2×C22⋊D7311yescharacteristic
514C2×D4—28no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4C2×C4×D7312yes—
530C2×D4C2×C4×D7312yes—
531C2×D4#1192402712yes—
532C2×D4#1192402712yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—1461no—
546C22×C4—1461no—
547C22×C4—1461no—
548C22×C4—1461no—
549C22×C4C2×C4×D7312yes—
550C22×C4C2×C22⋊D7311yescharacteristic
551C22×C4C2×C22⋊D7311yescharacteristic
552C22×C4C2×C22⋊D7311yescharacteristic
553C22×C4C2×C22⋊D7311yescharacteristic
554C22×C4C2×C22⋊D7311yescharacteristic
555C22×C4#1192402812yes—
556C22×C4C23×D7311yescharacteristic
557M16—2924no—
558C2×C8—732no—
559C2×C8—732no—
560C2×C8—1461no—
561C2×C8—1461no—
562C2×C8—1461no—
563C2×C8—1461no—
564C2×C8—1461no—
565C2×C8—1461no—
566C2×C8—1461no—
567C2×C8—1461no—
568C2×C8—1461no—
569C2×C8—1461no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—5841no—
575C4⋊C4—5841no—
576C4⋊C4—732no—
577C4⋊C4—732no—
578C4⋊C4—1461no—
579C4⋊C4—1461no—
580C4⋊C4—1461no—
581C4⋊C4—1461no—
582C4⋊C4—1461no—
583C4⋊C4—1461no—
584C22⋊C4—22no—
585C22⋊C4—41no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C22⋊C4—5841no—
594C22⋊C4—1464no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—2922no—
600C42—2922no—
601C42—1464no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—22no—
606C23—22no—
607C23—21no—
608C23—21no—
609C23—22no—
610C23—21no—
611C23—22no—
612C23—48no—
613C23—48no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23C4×C22⋊D7312yes—
630C23C22×C22⋊D7311yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#1455654714yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—2921no—
666C2×C4—2921no—
667C2×C4—2921no—
668C2×C4—2921no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—1462no—
676C2×C4—1462no—
677C2×C4C4×C22⋊D7312yes—
678C2×C4#1455661712yes—
679C2×C4C22×C4×D7311yescharacteristic
680C2×C4C2×#1192402711yescharacteristic
681C2×C4C2×#1192402711yescharacteristic
682C2×C4C2×#1192402811yescharacteristic
683C2×C4#1455663611yescharacteristic
684C2×C4#1455663611yescharacteristic
685C8—2921no—
686C8—2921no—
687C8—1462no—
688C8—1462no—
689C22—22no—
690C22—24no—
691C22—22no—
692C22—22no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—42no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×C4×C22⋊D7311yescharacteristic
712C22#1798923111yescharacteristic
713C22#1798923111yescharacteristic
714C22C2×#1455661711yescharacteristic
715C22#1798938511yescharacteristic
716C22#1798939011yescharacteristic
717C22#1798939811yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—2922no—
726C4—2922no—
727C4—5841no—
728C4—5841no—
729C4C2×#1455654711yescharacteristic
730C4#1798906011yescharacteristic
731C4#1798926311yescharacteristic
732C4#1798926311yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2#2261277611yescharacteristic
737C2C4×#1455661711yescharacteristic
738C2#2261876311yescharacteristic
739C2#2262195211yescharacteristic
740C2#2262208711yescharacteristic
741C2#2262214711yescharacteristic
742C2#2262217311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingD4×C22⋊C4×C73C2
socleC23×C73C22×D4
prime radicalC23×D4×C73C22
cosocleC22×C4×C73C24
hypercenterD4×C22⋊C4D73
hypocenterC73#22584
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #22612814C2semidirect
3. #22610631C2semidirect
4. #22610617C2semidirect
5. #22610555C2semidirect
6. #22610548C2semidirect
7. #22610192C2semidirect
8. #22610178C2semidirect
9. #22610023C2semidirect
10. #22609962C2semidirect
12. #22609756C2semidirect
13. C4×#14556512C2semidirect
14. #22609715C2semidirect
18. C2×#14556524C22semidirect
19. C2×#14556522C22semidirect
20. #17988592C4semidirect
30. C2×#14556502C22semidirect
31. C2×C4×#10596831C22semidirect
32. #17988485C22semidirect
33. #17988485C22semidirect
38. C4×C4⋊Dic73C22semidirect
39. C4×C4⋊Dic73C22semidirect
41. #17988349C22semidirect
42. #17988349C22semidirect
43. #17988349C22semidirect
44. #17988349C22semidirect
45. #17988349C22semidirect
46. #17988349C22semidirect
47. #17988342C22semidirect
48. #17988342C22semidirect
62. C2×#11924012C2×C4semidirect
68. #14556550C2×C4semidirect
88. #14556512C2×C4semidirect
89. #14556512C2×C4semidirect
387. C73#22584semidirect

Maximal subgroups

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

subgroupindex
C2×#179885922
#226128142
#226106312
#226106172
#226105552
#226105482
#226101922
#226101782
#226100232
#226099622
#226098622
#226097562
C4×#145565122
#226097152
D4×C22⋊C4×C732
#2258473