Finite Group Databasebeta

← #33106305

Subgroups — #33106305

Order 18688.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988699C211yesmaximal, characteristic, complemented
2C22×#14556512C211yesmaximal, characteristic, complemented
3#22612951C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic73C211yesmaximal, characteristic, complemented
5#22610808C211yesmaximal, characteristic, complemented
6#22610630C211yesmaximal, characteristic, complemented
7#22610560C211yesmaximal, characteristic, complemented
8#22610360C211yesmaximal, characteristic, complemented
9#22610281C211yesmaximal, characteristic, complemented
10#22610281C211yesmaximal, characteristic, complemented
11#22610194C211yesmaximal, characteristic, complemented
12#22610126C211yesmaximal, characteristic, complemented
13#22609758C211yesmaximal, characteristic, complemented
14#22609710C211yesmaximal, characteristic, complemented
15C2×#447×C73C211yesmaximal, characteristic
16C23×#10596831C2211yescharacteristic
17C2×D4×Dic73—21no—
18C2×D4×Dic73C2211yescharacteristic
19C2×D4×Dic73C2211yescharacteristic
20C2×D4×Dic73C2211yescharacteristic, complemented
21C22×C4⋊Dic73C2211yescharacteristic
22C22×C22⋊Dic73—21no—
23#17988699—24no—
24C2×#14556523C2211yescharacteristic, complemented
25C2×#14556523C2211yescharacteristic, complemented
26C2×#14556512—24no—
27C2×#14556512C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556512C2211yescharacteristic, complemented
32C2×#14556512C2211yescharacteristic, complemented
33C2×#14556501C2211yescharacteristic, complemented
34C2×#14556501C2211yescharacteristic, complemented
35#17988490C2211yescharacteristic
36#17988490C2211yescharacteristic
37#17988490C2211yescharacteristic, complemented
38#17988486C2211yescharacteristic, complemented
39#17988480—21no—
40#17988467—21no—
41#17988467—21no—
42#17988467—21no—
43#17988462—21no—
44#17988447C2211yescharacteristic
45#17988443—21no—
46C4⋊C4×Dic73C2211yescharacteristic, complemented
47C4×C22⋊Dic73C2211yescharacteristic
48#17988350C2211yescharacteristic, complemented
49#17988350C2211yescharacteristic, complemented
50#17988349C2211yescharacteristic, complemented
51#17988349C2211yescharacteristic, complemented
52#17988341C2211yescharacteristic, complemented
53#17988341C2211yescharacteristic, complemented
54C23×D4×C73C2211yescharacteristic
55C22×D8×C73C2211yescharacteristic
56C22×D8×C73C2211yescharacteristic
57C2×#121×C73C2211yescharacteristic
58#447×C73C418yescomplemented
59C2×#102×C73C2211yescharacteristic
60C2×#102×C73C2211yescharacteristic
61C2×C22⋊C8×C73C2211yescharacteristic
62C23×Dic73—21no—
63C23×Dic73—21no—
64C23×Dic73—21no—
65C23×Dic73—21no—
66C22×#10596831—22no—
67C22×#10596831—22no—
68C22×#10596831—41no—
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71D4×Dic73—22no—
72D4×Dic73—22no—
73D4×Dic73—22no—
74D4×Dic73—41no—
75D4×Dic73—41no—
76D4×Dic73—41no—
77D4×Dic73—44no—
78C2×C4⋊Dic73—22no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73—21no—
81C2×C4⋊Dic73—41no—
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×C22⋊Dic73—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⋊Dic73—21no—
94C2×C22⋊Dic73—21no—
95C2×C22⋊Dic73—21no—
96C2×C22⋊Dic73—44no—
97C2×C22⋊Dic73D411yescharacteristic
98C2×C22⋊Dic73D411yescharacteristic
99C2×C4×Dic73—21no—
100C2×C4×Dic73C2311yescharacteristic
101C2×C4×Dic73C2311yescharacteristic
102#14556523—22no—
103#14556523—41no—
104#14556512—22no—
105#14556512—22no—
106#14556512—22no—
107#14556512—22no—
108#14556512—41no—
109#14556512D414yescomplemented
110#14556501—22no—
111#14556501—41no—
112#14556498—21no—
113#14556498—21no—
114#14556498—21no—
115#14556498D411yescharacteristic
116#14556498D411yescharacteristic
117C25×C73—21no—
118C22×D4×C73—22no—
119C22×D4×C73—22no—
120C22×D4×C73—21no—
121C22×D4×C73—21no—
122C22×D4×C73—22no—
123C22×D4×C73—41no—
124C22×D4×C73—41no—
125C22×D4×C73C2×C414yescomplemented
126C22×D4×C73C2311yescharacteristic
127C22×D4×C73C2311yescharacteristic
128C22×D4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C2×D8×C73—22no—
131C2×D8×C73—22no—
132C2×D8×C73—41no—
133C2×D8×C73—41no—
134C2×D8×C73C2×C414yescomplemented
135C2×D8×C73C2×C414yescomplemented
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138#121×C73—22no—
139#121×C73C2×C414yescomplemented
140C2×C4⋊C4×C73C2311yescharacteristic
141C2×C22⋊C4×C73—21no—
142#102×C73C2×C414yescomplemented
143#102×C73C2×C414yescomplemented
144C22⋊C8×C73C2×C414yescomplemented
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—42no—
150C22×Dic73—42no—
151C22×Dic73—42no—
152C22×Dic73—42no—
153C22×Dic73—42no—
154C22×Dic73—42no—
155C22×Dic73—42no—
156C22×Dic73—42no—
157C22×Dic73—81no—
158C22×Dic73—81no—
159C22×Dic73—81no—
160C22×Dic73—81no—
161C22×Dic73C2×D411yescharacteristic
162C22×Dic73C2×D411yescharacteristic
163C22×Dic73C2×D411yescharacteristic
164C22×Dic73C2×D411yescharacteristic
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—44no—
171C2×#10596831C2×D412yes—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73—21no—
177C4⋊Dic73—21no—
178C4⋊Dic73—21no—
179C4⋊Dic73—42no—
180C4⋊Dic73—42no—
181C4⋊Dic73C2×D412yes—
182C22⋊Dic73—22no—
183C22⋊Dic73—22no—
184C22⋊Dic73—42no—
185C22⋊Dic73—42no—
186C22⋊Dic73—42no—
187C22⋊Dic73—42no—
188C22⋊Dic73—42no—
189C22⋊Dic73—42no—
190C22⋊Dic73—42no—
191C22⋊Dic73—81no—
192C22⋊Dic73—81no—
193C22⋊Dic73—81no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73—42no—
199C24×C73—21no—
200C24×C73—21no—
201C24×C73—21no—
202C24×C73—24no—
203C24×C73—42no—
204C24×C73—42no—
205C24×C73—42no—
206C24×C73—42no—
207C24×C73—81no—
208C24×C73—81no—
209C24×C73C2×D411yescharacteristic
210C2×D4×C73—28no—
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—21no—
219C2×D4×C73—21no—
220C2×D4×C73—21no—
221C2×D4×C73—21no—
222C2×D4×C73—21no—
223C2×D4×C73—21no—
224C2×D4×C73—21no—
225C2×D4×C73—21no—
226C2×D4×C73—44no—
227C2×D4×C73—44no—
228C2×D4×C73—44no—
229C2×D4×C73—42no—
230C2×D4×C73—42no—
231C2×D4×C73—42no—
232C2×D4×C73—42no—
233C2×D4×C73C22×C412yes—
234C2×D4×C73C22×C412yes—
235C2×D4×C73C22×C412yes—
236C2×D4×C73C2×D412yes—
237C2×D4×C73#4112yes—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73C22×C412yes—
244C22×C4×C73C2×D411yescharacteristic
245C22×C4×C73#4112yes—
246C22×C4×C73C2411yescharacteristic
247D8×C73—28no—
248D8×C73—44no—
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C2×C8×C73—21no—
252C2×C8×C73—21no—
253C2×C8×C73C22×C412yes—
254C2×C8×C73C22×C412yes—
255C4⋊C4×C73—21no—
256C4⋊C4×C73C22×C412yes—
257C22⋊C4×C73—24no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—22no—
263C23×C73—22no—
264C23×C73—22no—
265C23×C73—22no—
266C23×C73—22no—
267C23×C73—48no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—48no—
285C23×C73—84no—
286C23×C73—84no—
287C23×C73—84no—
288C23×C73—84no—
289C23×C73—84no—
290C23×C73C4×D412yes—
291C23×C73AGL(1,ℤ/8)12yes—
292C23×C73AGL(1,ℤ/8)12yes—
293C23×C73C22×D411yescharacteristic
294D4×C73—22no—
295D4×C73—22no—
296D4×C73—22no—
297D4×C73—22no—
298D4×C73—22no—
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—48no—
302D4×C73—48no—
303D4×C73—41no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73C4×D414yescomplemented
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73C4×D412yes—
318C2×C4×C73C23×C411yescharacteristic
319C2×C4×C73C22×D411yescharacteristic
320C2×C4×C73C2×#4111yescharacteristic
321C2×C4×C73C2×#4111yescharacteristic
322C2×C4×C73H(5,𝔽2)11yescharacteristic
323C2×C4×C73H(5,𝔽2)11yescharacteristic
324C2×Dic73—21no—
325C2×Dic73—21no—
326C2×Dic73—22no—
327C2×Dic73—21no—
328C2×Dic73—21no—
329C2×Dic73—21no—
330C2×Dic73—21no—
331C2×Dic73—21no—
332C2×Dic73—21no—
333C2×Dic73—21no—
334C2×Dic73—21no—
335C2×Dic73—21no—
336C2×Dic73—21no—
337C2×Dic73—41no—
338C2×Dic73—41no—
339C2×Dic73—41no—
340C2×Dic73—41no—
341C2×Dic73—41no—
342C2×Dic73—41no—
343C2×Dic73—41no—
344C2×Dic73—41no—
345C2×Dic73—41no—
346C2×Dic73—41no—
347C2×Dic73—41no—
348C2×Dic73—84no—
349C2×Dic73—84no—
350C2×Dic73—84no—
351C2×Dic73—84no—
352C8×C73—22no—
353C8×C73—22no—
354#10596831—22no—
355#10596831—41no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—22no—
360C22×C73—22no—
361C22×C73—22no—
362C22×C73—24no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73—42no—
366C22×C73—42no—
367C22×C73—42no—
368C22×C73—42no—
369C22×C73—42no—
370C22×C73—42no—
371C22×C73—42no—
372C22×C73—42no—
373C22×C73—42no—
374C22×C73—42no—
375C22×C73—816no—
376C22×C73—81no—
377C22×C73—81no—
378C22×C73—81no—
379C22×C73—81no—
380C22×C73—81no—
381C22×C73—81no—
382C22×C73—81no—
383C22×C73—81no—
384C22×C73#44214yescomplemented
385C22×C73C2×C4×D411yescharacteristic
386C22×C73D4211yescharacteristic
387C22×C73#54611yescharacteristic
388C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C73#57611yescharacteristic
391C22×C73#57711yescharacteristic
392C4×C73—22no—
393C4×C73—42no—
394C4×C73C2×C4×D411yescharacteristic
395C4×C73#51811yescharacteristic
396C4×C73#54611yescharacteristic
397C4×C73#55111yescharacteristic
398Dic73—41no—
399Dic73—42no—
400Dic73—41no—
401Dic73—41no—
402Dic73—41no—
403Dic73—81no—
404Dic73—81no—
405Dic73—81no—
406#22858—731nomaximal, Sylow
407C2×C73—24no—
408C2×C73—44no—
409C2×C73—82no—
410C2×C73—82no—
411C2×C73#235811yescharacteristic
412C2×C73C2×#44211yescharacteristic
413C2×C73#294611yescharacteristic
414C2×C73#326411yescharacteristic
415C2×C73#326511yescharacteristic
416C2×C73#330611yescharacteristic
417C2×C73#331811yescharacteristic
418C2×#447D7311yescharacteristic
419C2×#442—731no—
420C22×#102—731no—
421#2361—731no—
422D4×C22⋊C4—731no—
423#1972—731no—
424#1936—731no—
425#1926—731no—
426#1893—731no—
427#1879—731no—
428#1879—731no—
429#1864—731no—
430#1853—731no—
431#1762—731no—
432#1752—731no—
433C73#2285811yescharacteristic, complemented, Sylow
434C23×D4C2×D7311yescharacteristic
435C22×D8C2×D7311yescharacteristic
436C22×D8C2×D7311yescharacteristic
437C23×C8—731no—
438C2×#121C2×D7311yescharacteristic
439C2×C4×D4—731no—
440C2×C4×D4—731no—
441C2×C4×D4—731no—
442C2×C4×D4—1461no—
443C22×C4⋊C4—731no—
444C22×C22⋊C4—1461no—
445#447Dic7318yescomplemented
446#442—1464no—
447C2×#106—731no—
448C2×#106—731no—
449C2×#102—731no—
450C2×#102—731no—
451C2×#102—731no—
452C2×#102—731no—
453C2×#102—731no—
454C2×#102—731no—
455C2×#102—1464no—
456C2×#102C2×D7311yescharacteristic
457C2×#102C2×D7311yescharacteristic
458C2×C22⋊C8C2×D7311yescharacteristic
459C2×#97—731no—
460C2×#97—731no—
461#390—731no—
462#390—731no—
463#390—731no—
464#389—731no—
465#388—1461no—
466#386—1461no—
467#386—1461no—
468#386—1461no—
469#385—1461no—
470#380—731no—
471#379—1461no—
472C4×C4⋊C4—731no—
473C4×C22⋊C4—731no—
474#340—731no—
475#340—731no—
476#340—731no—
477#340—731no—
478#336—731no—
479#336—731no—
480C25—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—22no—
486C22×D4—41no—
487C22×D4—41no—
488C22×D4C2×Dic7314yescomplemented
489C22×D4C22×D7311yescharacteristic
490C22×D4C22×D7311yescharacteristic
491C22×D4C22×D7311yescharacteristic
492C23×C4—1461no—
493C23×C4—1461no—
494C23×C4—1461no—
495C23×C4—1461no—
496C23×C4C22×D7311yescharacteristic
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—41no—
500C2×D8—41no—
501C2×D8C2×Dic7314yescomplemented
502C2×D8C2×Dic7314yescomplemented
503C22×C8—2921no—
504C22×C8—731no—
505C22×C8—731no—
506C22×C8—1462no—
507C22×C8—1462no—
508C22×C8C22×D7311yescharacteristic
509C22×C8C22×D7311yescharacteristic
510#121—22no—
511#121C2×Dic7314yescomplemented
512C4×D4—2924no—
513C4×D4—2921no—
514C4×D4—2921no—
515C4×D4—2921no—
516C4×D4—1462no—
517C4×D4—1462no—
518C4×D4—1462no—
519C2×C4⋊C4—2921no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1462no—
527C2×C4⋊C4C22×D7311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—2924no—
530C2×C22⋊C4—731no—
531C2×C22⋊C4—731no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C22⋊C4—1461no—
537C2×C22⋊C4—1461no—
538C2×C22⋊C4—1461no—
539C2×C22⋊C4—1461no—
540C2×C22⋊C4—1461no—
541C2×C22⋊C4—1461no—
542C2×C42—731no—
543C2×C42—731no—
544C2×C42—1461no—
545#106—2921no—
546#106—1462no—
547#102—2921no—
548#102—734no—
549#102—1462no—
550#102—1462no—
551#102—1462no—
552#102—1462no—
553#102C2×Dic7314yescomplemented
554#102C2×Dic7314yescomplemented
555C22⋊C8C2×Dic7314yescomplemented
556#97—2921no—
557#97—1462no—
558#95—731no—
559#95—731no—
560#95—1461no—
561#95—1461no—
562#95—1461no—
563C24—21no—
564C24—21no—
565C24—21no—
566C24—24no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—81no—
572C24—81no—
573C24D4×D7311yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4C22×Dic7312yes—
598C2×D4C22×Dic7312yes—
599C2×D4C22×Dic7312yes—
600C2×D4D4×D7312yes—
601C2×D4#1192402712yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—2922no—
608C22×C4—2922no—
609C22×C4—2922no—
610C22×C4—2922no—
611C22×C4—2922no—
612C22×C4—2922no—
613C22×C4—2922no—
614C22×C4—2922no—
615C22×C4—5841no—
616C22×C4—5841no—
617C22×C4—5841no—
618C22×C4—5841no—
619C22×C4—731no—
620C22×C4—731no—
621C22×C4—731no—
622C22×C4—731no—
623C22×C4—1461no—
624C22×C4—1461no—
625C22×C4—1461no—
626C22×C4—1461no—
627C22×C4C22×Dic7312yes—
628C22×C4D4×D7311yescharacteristic
629C22×C4#1192402712yes—
630C22×C4C23×D7311yescharacteristic
631D8—28no—
632D8—44no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—2924no—
638C2×C8—732no—
639C2×C8—1461no—
640C2×C8—1461no—
641C2×C8—1461no—
642C2×C8—1461no—
643C2×C8—1461no—
644C2×C8C22×Dic7312yes—
645C2×C8C22×Dic7312yes—
646C4⋊C4—21no—
647C4⋊C4—2922no—
648C4⋊C4—2922no—
649C4⋊C4—732no—
650C4⋊C4—1461no—
651C4⋊C4—1461no—
652C4⋊C4—1461no—
653C4⋊C4—1461no—
654C4⋊C4—1461no—
655C4⋊C4—1461no—
656C4⋊C4—1461no—
657C4⋊C4C22×Dic7312yes—
658C22⋊C4—24no—
659C22⋊C4—2922no—
660C22⋊C4—2922no—
661C22⋊C4—2922no—
662C22⋊C4—2922no—
663C22⋊C4—2922no—
664C22⋊C4—2922no—
665C22⋊C4—2922no—
666C22⋊C4—5841no—
667C22⋊C4—5841no—
668C22⋊C4—5841no—
669C22⋊C4—1462no—
670C22⋊C4—1462no—
671C42—2922no—
672C42—1461no—
673C42—1461no—
674C42—1461no—
675C42—1461no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—48no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—84no—
708C23D4×Dic7312yes—
709C23#1455661512yes—
710C23#1455661512yes—
711C23C2×D4×D7311yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4D4×Dic7314yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—2921no—
736C2×C4—2921no—
737C2×C4—2921no—
738C2×C4—2921no—
739C2×C4—2921no—
740C2×C4—2921no—
741C2×C4—2921no—
742C2×C4—2921no—
743C2×C4—2921no—
744C2×C4—2921no—
745C2×C4—2921no—
746C2×C4—5844no—
747C2×C4—5844no—
748C2×C4—5844no—
749C2×C4—5844no—
750C2×C4—1461no—
751C2×C4—1461no—
752C2×C4—1461no—
753C2×C4—1461no—
754C2×C4—1461no—
755C2×C4—1461no—
756C2×C4—1462no—
757C2×C4—1461no—
758C2×C4—1461no—
759C2×C4—1461no—
760C2×C4—1461no—
761C2×C4—1461no—
762C2×C4—1461no—
763C2×C4D4×Dic7312yes—
764C2×C4C23×Dic7311yescharacteristic
765C2×C4C2×D4×D7311yescharacteristic
766C2×C4C2×#1192402711yescharacteristic
767C2×C4C2×#1192402711yescharacteristic
768C2×C4#1455663611yescharacteristic
769C2×C4#1455663611yescharacteristic
770C8—22no—
771C8—22no—
772C8—2921no—
773C8—1462no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—816no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22#1798869914yescomplemented
803C22C2×D4×Dic7311yescharacteristic
804C22#1798921911yescharacteristic
805C22#1798922411yescharacteristic
806C22C2×#1455661511yescharacteristic
807C22C2×#1455661511yescharacteristic
808C22#1798939111yescharacteristic
809C22#1798939711yescharacteristic
810C4—22no—
811C4—42no—
812C4—2921no—
813C4—2921no—
814C4—2922no—
815C4—2921no—
816C4—2921no—
817C4—5841no—
818C4—5841no—
819C4—5841no—
820C4C2×D4×Dic7311yescharacteristic
821C4#1798906211yescharacteristic
822C4#1798922411yescharacteristic
823C4#1798926811yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—82no—
828C2#2261291511yescharacteristic
829C2C2×#1798869911yescharacteristic
830C2#2261876411yescharacteristic
831C2#2262140411yescharacteristic
832C2#2262143011yescharacteristic
833C2#2262189611yescharacteristic
834C2#2262207611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
Fitting, prime radicalC2×#447×C73C2
socleC23×C73C22×D4
cosocleC22×C4×C73C24
hypercenterC2×#447D73
hypocenterC73#22858
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#17988699C2semidirect
2. C22×#14556512C2semidirect
3. #22612951C2semidirect
4. D4×C22⋊Dic73C2semidirect
5. #22610808C2semidirect
6. #22610630C2semidirect
7. #22610560C2semidirect
8. #22610360C2semidirect
9. #22610281C2semidirect
10. #22610281C2semidirect
11. #22610194C2semidirect
12. #22610126C2semidirect
13. #22609758C2semidirect
14. #22609710C2semidirect
20. C2×D4×Dic73C22semidirect
24. C2×#14556523C22semidirect
25. C2×#14556523C22semidirect
31. C2×#14556512C22semidirect
32. C2×#14556512C22semidirect
33. C2×#14556501C22semidirect
34. C2×#14556501C22semidirect
37. #17988490C22semidirect
38. #17988486C22semidirect
46. C4⋊C4×Dic73C22semidirect
48. #17988350C22semidirect
49. #17988350C22semidirect
50. #17988349C22semidirect
51. #17988349C22semidirect
52. #17988341C22semidirect
53. #17988341C22semidirect
58. #447×C73C4semidirect
109. #14556512D4semidirect
125. C22×D4×C73C2×C4semidirect
134. C2×D8×C73C2×C4semidirect
135. C2×D8×C73C2×C4semidirect
139. #121×C73C2×C4semidirect
142. #102×C73C2×C4semidirect
143. #102×C73C2×C4semidirect
144. C22⋊C8×C73C2×C4semidirect
307. D4×C73C4×D4semidirect
384. C22×C73#442semidirect
433. C73#22858semidirect
445. #447Dic73semidirect
488. C22×D4C2×Dic73semidirect
501. C2×D8C2×Dic73semidirect
502. C2×D8C2×Dic73semidirect
511. #121C2×Dic73semidirect
553. #102C2×Dic73semidirect
554. #102C2×Dic73semidirect
555. C22⋊C8C2×Dic73semidirect
725. D4D4×Dic73semidirect
802. C22#17988699semidirect

Maximal subgroups

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

subgroupindex
C2×#179886992
C22×#145565122
#226129512
D4×C22⋊Dic732
#226108082
#226106302
#226105602
#226103602
#226102812
#226101942
#226101262
#226097582
#226097102
C2×#447×C732
#2285873