Finite Group Databasebeta

← #10823163

Subgroups — #10823163

Order 768.

1458 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#916C211yesmaximal, characteristic
2C2×#4839C211yesmaximal, characteristic, complemented
3C2×#4803C211yesmaximal, characteristic, complemented
4C2×#4771C211yesmaximal, characteristic, complemented
5#76482C211yesmaximal, characteristic, complemented
6#76294C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8#72051C211yesmaximal, characteristic, complemented
9#70482C211yesmaximal, characteristic, complemented
10#70285C211yesmaximal, characteristic, complemented
11#70212C211yesmaximal, characteristic, complemented
12#69681C211yesmaximal, characteristic, complemented
13#69650C211yesmaximal, characteristic, complemented
14D3×#340C211yesmaximal, characteristic, complemented
15#68863C211yesmaximal, characteristic, complemented
16#23543—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×#237C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#916—24no—
23C2×#916—24no—
24C2×#916—24no—
25C22×#204C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28C2×D3×C4⋊C4C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×#872C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C3×#391C2211yescharacteristic
35C3×#390C2211yescharacteristic
36#5229C2211yescharacteristic
37C2×#835C2211yescharacteristic
38#5221C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#816C2211yescharacteristic
42C2×Dic3⋊C8C2211yescharacteristic
43C2×Dic3⋊C8C2211yescharacteristic
44#4988C2211yescharacteristic
45#4973C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#809C2211yescharacteristic
48#4956—21no—
49#4956—21no—
50#4942—21no—
51#4942—21no—
52#4939C2211yescharacteristic
53#4929C2211yescharacteristic
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55#4839—24no—
56#4803—24no—
57#4771—24no—
58#4667—21no—
59#4667—21no—
60#4665—21no—
61#4665—21no—
62C3×#340C2211yescharacteristic
63#4551C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C22×#135—31no—
67C2×#424—31no—
68C2×#417—31no—
69C2×#417—31no—
70#2311—31no—
71#2311—31no—
72#2056—31no—
73#2056—31no—
74#2055—31no—
75#2055—31no—
76#2055—31no—
77#2055D311yescharacteristic, complemented
78#2054—31no—
79#2054—31no—
80C2×#340—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×#67—21no—
84C23×Dic3—21no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239D414yes—
91C2×#237—22no—
92C2×#237—22no—
93C2×#237—22no—
94C2×#237—22no—
95C2×#237—22no—
96C2×#237D414yes—
97C22×D12—21no—
98C22×D12C2311yescharacteristic
99C22×C4×D3—21no—
100C22×C4×D3—21no—
101C22×C4×D3—21no—
102C22×C4×D3C2311yescharacteristic
103C22×Dic6C2311yescharacteristic
104C2×C3×SD16—22no—
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C42C2311yescharacteristic
114C2×#217—21no—
115C2×#217—21no—
116C2×#216—22no—
117C2×#216—22no—
118C2×#216—22no—
119C2×#213—22no—
120C2×#213—22no—
121C2×#213—22no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×(C2×D3)⋊C4D411yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4D411yescharacteristic
133C2×Dic3⋊C4D411yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137#916—232no—
138C2×#204—22no—
139C2×#204—22no—
140C2×#204—22no—
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)—22no—
144C2×D3×C8—22no—
145C2×D3×C8—22no—
146C2×D3×C8D414yes—
147D3×C4⋊C4—22no—
148D3×C4⋊C4—22no—
149D3×C4⋊C4—22no—
150D3×C4⋊C4—22no—
151#872—22no—
152#872—22no—
153C3×C4⋊C8—22no—
154C3×#103—22no—
155C3×#102—22no—
156C3×#95—21no—
157C3×#95—21no—
158#835—22no—
159#832—22no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166#821—22no—
167#816—22no—
168Dic3⋊C8—22no—
169Dic3⋊C8—22no—
170#810—22no—
171#809—22no—
172C4⋊(C3⋊C8)—22no—
173C22×#41—31no—
174C22×#41—31no—
175C2×#135—64no—
176C2×#135—64no—
177C2×#135—64no—
178C22×Q16—31no—
179C22×SD16—31no—
180C22×SD16C2×D311yescharacteristic
181C22×D8—31no—
182C22×M16—31no—
183C23×C8—31no—
184C2×#117—31no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187#424—64no—
188C2×C4⋊C8—31no—
189C2×C4⋊C8—31no—
190C2×C4⋊C8—31no—
191C2×C4⋊C8C2×D311yescharacteristic
192#417—64no—
193#417—64no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103C2×D311yescharacteristic
198C2×#102—31no—
199C2×#102—31no—
200C2×#102—31no—
201C2×#102C2×D311yescharacteristic
202#391—31no—
203#391—31no—
204#391—31no—
205#391C2×D311yescharacteristic
206#390—31no—
207#390—31no—
208#390—31no—
209#390C2×D311yescharacteristic
210#386—61no—
211#386—61no—
212#386—61no—
213#386—61no—
214#380—61no—
215#380—61no—
216#380—61no—
217#380—61no—
218#340—31no—
219#340—31no—
220#340—31no—
221#340C2×D311yescharacteristic
222C24×C3—21no—
223C23×D3—21no—
224C23×D3C2×D411yescharacteristic
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8C2×D412yes—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4C2×D412yes—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C2×#67—24no—
244C2×#67—42no—
245C2×#67—42no—
246C22×Dic3—21no—
247C22×Dic3—24no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—42no—
251C22×Dic3—42no—
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255#239—28no—
256#239—28no—
257#239—44no—
258#239—44no—
259#237—28no—
260#237—28no—
261#237—44no—
262#237—44no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—24no—
268C2×D12—21no—
269C2×D12—42no—
270C2×D12—42no—
271C2×D12C2×D412yes—
272C2×C4×D3—24no—
273C2×C4×D3—42no—
274C2×C4×D3—42no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C2×C4×D3—81no—
278C2×C4×D3—81no—
279C2×C4×D3—81no—
280C2×C4×D3—81no—
281C2×C4×D3C2×D412yes—
282C2×C4×D3C2×D412yes—
283C2×C4×D3C2×D412yes—
284C2×C4×D3#4112yes—
285C2×C4×D3#4112yes—
286C2×C4×D3#4112yes—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C2×Dic6C2×D412yes—
293C3×SD16—28no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8C2×D412yes—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C22⋊C4—81no—
305C3×C22⋊C4—81no—
306C3×C42—21no—
307C3×C42—21no—
308#217—81no—
309#217—81no—
310#216—28no—
311#213—28no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4—22no—
314(C2×D3)⋊C4—81no—
315(C2×D3)⋊C4—81no—
316(C2×D3)⋊C4—81no—
317(C2×D3)⋊C4—81no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322Dic3⋊C4—22no—
323Dic3⋊C4—22no—
324Dic3⋊C4—42no—
325Dic3⋊C4—42no—
326C4×Dic3—21no—
327C4×Dic3—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8C2×D412yes—
334#204—28no—
335ΓL(1,𝔽25)—44no—
336D3×C8—28no—
337C2×#41—34no—
338C2×#41—34no—
339C2×#41—62no—
340C2×#41—62no—
341C2×#41—62no—
342C2×#41—62no—
343C2×#41—62no—
344C2×#41—62no—
345C2×#41—62no—
346C2×#41—62no—
347C2×#41—62no—
348C2×#41—62no—
349C22×Q8—31no—
350C22×Q8C22×D311yescharacteristic
351C22×D4—31no—
352C22×D4—61no—
353C22×D4—61no—
354C22×D4C22×D311yescharacteristic
355C23×C4—31no—
356C23×C4—61no—
357C23×C4—61no—
358C23×C4—61no—
359C23×C4—61no—
360#135—632no—
361C2×Q16—62no—
362C2×Q16—62no—
363C2×Q16—62no—
364C2×SD16—22no—
365C2×SD16—22no—
366C2×SD16—22no—
367C2×SD16—62no—
368C2×SD16—62no—
369C2×SD16—62no—
370C2×D8—62no—
371C2×D8—62no—
372C2×D8—62no—
373C2×M16—62no—
374C2×M16—62no—
375C2×M16—62no—
376C22×C8—31no—
377C22×C8—34no—
378C22×C8—31no—
379C22×C8—62no—
380C22×C8—62no—
381C22×C8C22×D311yescharacteristic
382C22×C8C22×D311yescharacteristic
383#117—62no—
384#117—62no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—62no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C42—31no—
408C2×C42C22×D311yescharacteristic
409C4⋊C8—22no—
410C4⋊C8—62no—
411C4⋊C8—62no—
412C4⋊C8—62no—
413#103—22no—
414#103—62no—
415#103—62no—
416#103—62no—
417#102—22no—
418#102—62no—
419#102—62no—
420#102—62no—
421#95—21no—
422#95—21no—
423#95—61no—
424#95—61no—
425#95—61no—
426#95—61no—
427#95—61no—
428#95—61no—
429C23×C3—22no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3C22×D411yescharacteristic
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—22no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3#12112yes—
449C22×D3#12112yes—
450C22×D3#12112yes—
451C3×Q8—22no—
452C3×Q8—22no—
453C3×Q8—41no—
454C3×Q8—41no—
455C3×D4—22no—
456C3×D4—22no—
457C3×D4—41no—
458C3×D4—41no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480#67—48no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—48no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3#12112yes—
498C2×Dic3#12112yes—
499C2×Dic3#12112yes—
500D12—22no—
501D12—22no—
502D12—48no—
503D12—41no—
504D12—41no—
505C4×D3—48no—
506C4×D3—84no—
507C4×D3—84no—
508C4×D3#12014yes—
509C4×D3#12314yes—
510C4×D3#12314yes—
511C4×D3#12414yes—
512Dic6—22no—
513Dic6—22no—
514Dic6—41no—
515Dic6—41no—
516C3×C8—22no—
517C3×C8—41no—
518C3⋊C8—22no—
519C3⋊C8—41no—
520C24—21no—
521C24—31no—
522C24—61no—
523#41—68no—
524#41—68no—
525#41—68no—
526#41—68no—
527#41—124no—
528#41—124no—
529#41—124no—
530#41—124no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—32no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—61no—
542C2×Q8D3×D412yes—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—32no—
549C2×D4—64no—
550C2×D4—64no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4D3×D412yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—31no—
565C22×C4—32no—
566C22×C4—32no—
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—64no—
574C22×C4—64no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—122no—
579C22×C4—122no—
580C22×C4—122no—
581C22×C4—122no—
582C22×C4—122no—
583C22×C4—122no—
584C22×C4—241no—
585C22×C4—241no—
586C22×C4—241no—
587C22×C4—241no—
588C22×C4D3×D411yescharacteristic
589C22×C4D3×D411yescharacteristic
590C22×C4C23×D311yescharacteristic
591Q16—68no—
592SD16—28no—
593SD16—68no—
594D8—68no—
595M16—124no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—32no—
602C2×C8—68no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8D3×D412yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—62no—
614C4⋊C4—62no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—122no—
620C4⋊C4—122no—
621C22⋊C4—62no—
622C22⋊C4—62no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—241no—
626C22⋊C4—241no—
627C22⋊C4—241no—
628C22⋊C4—241no—
629C22⋊C4—241no—
630C22⋊C4—241no—
631C42—21no—
632C42—21no—
633C42—61no—
634C42—61no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3C2×#12111yescharacteristic
643C22×C3C2×#12111yescharacteristic
644C22×C3C2×#12111yescharacteristic
645C22×C3#57611yescharacteristic
646C22×C3#57711yescharacteristic
647C22×C3#57711yescharacteristic
648C22×C3#57811yescharacteristic
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—42no—
658C2×D3—81no—
659C2×D3—81no—
660C2×D3—81no—
661C2×D3—81no—
662C2×D3#39414yes—
663C3×C4—42no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—81no—
667C3×C4—81no—
668C3×C4C2×#12011yescharacteristic
669C3×C4C2×#12311yescharacteristic
670C3×C4C2×#12311yescharacteristic
671C3×C4C2×#12411yescharacteristic
672Dic3—42no—
673Dic3—41no—
674Dic3—41no—
675Dic3—81no—
676Dic3—81no—
677Dic3#39414yes—
678C23—22no—
679C23—32no—
680C23—32no—
681C23—32no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—61no—
692C23—62no—
693C23—121no—
694C23—121no—
695C23—121no—
696C23—121no—
697C23—121no—
698C23—121no—
699C23C2×D3×D411yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—41no—
703Q8—41no—
704Q8—62no—
705Q8—62no—
706Q8—121no—
707Q8—121no—
708D4—22no—
709D4—22no—
710D4—41no—
711D4—41no—
712D4—62no—
713D4—62no—
714D4—128no—
715D4—128no—
716D4—121no—
717D4—121no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—34no—
729C2×C4—34no—
730C2×C4—34no—
731C2×C4—34no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—62no—
747C2×C4—128no—
748C2×C4—128no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—244no—
758C2×C4—244no—
759C2×C4C2×D3×D411yescharacteristic
760C2×C4C2×D3×D411yescharacteristic
761C2×C4C2×D3×D411yescharacteristic
762C2×C4D3×#4111yescharacteristic
763C2×C4D3×#4111yescharacteristic
764C2×C4D3×#4111yescharacteristic
765C8—22no—
766C8—41no—
767C8—62no—
768C8—121no—
769C2×C3—82no—
770C2×C3C2×#39411yescharacteristic
771C2×C3#304511yescharacteristic
772C2×C3#304511yescharacteristic
773C2×C3#304611yescharacteristic
774C2×C3#304611yescharacteristic
775C2×C3#306011yescharacteristic
776C2×C3#306111yescharacteristic
777D3—24no—
778D3—82no—
779C22—34no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—62no—
784C22—62no—
785C22—62no—
786C22—62no—
787C22—62no—
788C22—62no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—122no—
794C22—122no—
795C22—122no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22D3×#12111yescharacteristic
801C22D3×#12111yescharacteristic
802C22D3×#12111yescharacteristic
803C22#576211yescharacteristic
804C22#577011yescharacteristic
805C22#577411yescharacteristic
806C22#577911yescharacteristic
807C4—34no—
808C4—41no—
809C4—42no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—121no—
814C4—122no—
815C4—121no—
816C4—241no—
817C4—241no—
818C4D3×#12011yescharacteristic
819C4D3×#12311yescharacteristic
820C4D3×#12311yescharacteristic
821C4D3×#12411yescharacteristic
822C3#2354311yescharacteristic, complemented, Sylow
823C2—64no—
824C2—82no—
825C2—242no—
826C2D3×#39411yescharacteristic
827C2#8038611yescharacteristic
828C2#8043111yescharacteristic
829C2#8053811yescharacteristic
830C2#8060311yescharacteristic
831C2#8066011yescharacteristic
832C2#8080811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2055C2
socleC23×C3C22×D4
prime radicalC22×#916C2
hypercenter#2055D3
hypocenterC3#23543
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. C2×#4839C2semidirect
3. C2×#4803C2semidirect
4. C2×#4771C2semidirect
5. #76482C2semidirect
6. #76294C2semidirect
7. C3×#2055C2semidirect
8. #72051C2semidirect
9. #70482C2semidirect
10. #70285C2semidirect
11. #70212C2semidirect
12. #69681C2semidirect
13. #69650C2semidirect
14. D3×#340C2semidirect
15. #68863C2semidirect
77. #2055D3semidirect
822. C3#23543semidirect

Maximal subgroups

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

subgroupindex
C22×#9162
C2×#48392
C2×#48032
C2×#47712
#764822
#762942
C3×#20552
#720512
#704822
#702852
#702122
#696812
#696502
D3×#3402
#688632
#235433