Finite Group Databasebeta

← #10829271

Subgroups — #10829271

Order 768.

1336 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5507C211yesmaximal, characteristic
2C2×#4875C211yesmaximal, characteristic, complemented
3C2×#4889C211yesmaximal, characteristic, complemented
4#73934C211yesmaximal, characteristic, complemented
5C3×#1852C211yesmaximal, characteristic, complemented
6#71559C211yesmaximal, characteristic, complemented
7#70634C211yesmaximal, characteristic, complemented
8#70632C211yesmaximal, characteristic, complemented
9#69962C211yesmaximal, characteristic, complemented
10#69917C211yesmaximal, characteristic, complemented
11#69523C211yesmaximal, characteristic, complemented
12#68893C211yesmaximal, characteristic, complemented
13#68887C211yesmaximal, characteristic, complemented
14#68878C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24132—31nomaximal, Sylow
17C22×#235—21no—
18C22×C3×C4⋊C4C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×#929—21no—
21C2×C4×#67C2211yescharacteristic
22C2×#924C2211yescharacteristic
23C22×#204C2211yescharacteristic
24C2×#897C2211yescharacteristic
25C2×#896—21no—
26#5507—24no—
27#5507—24no—
28C2×#895C2211yescharacteristic
29C2×#894—21no—
30C2×#893C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#888C2211yescharacteristic
33C2×#887C2211yescharacteristic
34C2×C3×#107C2211yescharacteristic
35C2×C3×#107C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#830C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×#816C2211yescharacteristic
43C2×#815C2211yescharacteristic
44C2×Dic3⋊C8C2211yescharacteristic
45#4987C2211yescharacteristic
46#4977C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4959—21no—
53#4951—21no—
54#4889—24no—
55#4875—24no—
56#4669—21no—
57#4657—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#547—31no—
65C2×#477—31no—
66C2×#440—31no—
67#2536—31no—
68#2033—31no—
69#2033—31no—
70#2000—31no—
71#2000—31no—
72#1993—31no—
73#1955—31no—
74#1872—31no—
75#1872—31no—
76#1852—31no—
77#1852D311yescharacteristic, complemented
78#1804—31no—
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67D411yescharacteristic
83C2×#235—28no—
84C2×#235—44no—
85C2×#235—44no—
86C22×D12—21no—
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C22×Dic6—21no—
92C22×Dic6C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×#217—21no—
104C2×#217D411yescharacteristic
105#930—22no—
106#930—22no—
107#929—28no—
108C4×#67—22no—
109C4×#67—22no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4D411yescharacteristic
116C2×C4⋊Dic3—21no—
117C2×C4⋊Dic3C2311yescharacteristic
118C2×C4⋊Dic3C2311yescharacteristic
119#924—22no—
120#924—41no—
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4D411yescharacteristic
126C2×C4×Dic3—21no—
127C2×C4×Dic3C2311yescharacteristic
128C22×C3⋊C8C2311yescharacteristic
129C22×C3⋊C8C2311yescharacteristic
130C2×#204—22no—
131C2×#204—22no—
132C2×#204—22no—
133#897—22no—
134#897—41no—
135#896—28no—
136#895—22no—
137#895—22no—
138#894—28no—
139#893—22no—
140#893D414yes—
141D3×C4⋊C4—22no—
142D3×C4⋊C4—22no—
143#888—22no—
144#888D414yes—
145#887—22no—
146#887—22no—
147C3×#107—22no—
148C3×#107—22no—
149C3×C22⋊C8—22no—
150C3×#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154#830—41no—
155#821—41no—
156(C2×D3)⋊C8—22no—
157(C2×D3)⋊C8—41no—
158#816—22no—
159#815—22no—
160Dic3⋊C8—22no—
161#810—22no—
162#810—22no—
163#809—22no—
164#809—41no—
165#807—22no—
166C22×#41—61no—
167C22×SD16—31no—
168#547—64no—
169#547—64no—
170C2×C4⋊Q8—31no—
171C2×#123—61no—
172C2×#123—61no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8—61no—
176C2×#121—31no—
177C2×#121—31no—
178C2×C4×Q8—31no—
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4C2×D311yescharacteristic
183#477—64no—
184#440—64no—
185C2×#107—31no—
186C2×#107C2×D311yescharacteristic
187C2×#107C2×D311yescharacteristic
188C2×C4⋊C8—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×C22⋊C8C2×D311yescharacteristic
199C2×#97—31no—
200#398—61no—
201#394—61no—
202#388—61no—
203#388—61no—
204#382—31no—
205#380—31no—
206#380C2×D311yescharacteristic
207#340—31no—
208#340—31no—
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C23×D3C2×D411yescharacteristic
216C22×C3×C4—24no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—42no—
228C22×C3×C4—42no—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2411yescharacteristic
231C2×#67—22no—
232C2×#67—22no—
233C2×#67—24no—
234C2×#67—22no—
235C2×#67—42no—
236C2×#67—42no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3C2×D411yescharacteristic
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243#235—432no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—24no—
249C2×D12—21no—
250C2×D12—42no—
251C2×D12—42no—
252C2×D12C2×D412yes—
253C2×C4×D3—24no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—24no—
261C2×C4×D3—42no—
262C2×C4×D3—42no—
263C2×C4×D3—42no—
264C2×C4×D3—42no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—24no—
271C2×Dic6—42no—
272C2×Dic6—42no—
273C2×Dic6#4112yescomplemented
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8#4112yescomplemented
280C3×C4⋊C4—24no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4C2×D412yes—
288C3×C4⋊C4C2×D412yes—
289C3×C22⋊C4—42no—
290#217—22no—
291#217—42no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—42no—
302C4⋊Dic3C2×D412yes—
303Dic3⋊C4—24no—
304Dic3⋊C4—24no—
305Dic3⋊C4—22no—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308C4×Dic3—42no—
309C4×Dic3C2×D412yes—
310C4×Dic3C2×D412yes—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317#204—28no—
318C2×#41—68no—
319C2×#41—124no—
320C2×#41—124no—
321C22×Q8—31no—
322C22×Q8—61no—
323C22×D4—31no—
324C22×D4—31no—
325C22×D4—61no—
326C22×D4—61no—
327C23×C4—21no—
328C23×C4—31no—
329C23×C4—61no—
330C23×C4—61no—
331C23×C4C22×D311yescharacteristic
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—62no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8C22×D311yescharacteristic
338C22×C8C22×D311yescharacteristic
339C4⋊Q8—34no—
340C4⋊Q8—62no—
341#123—68no—
342#123—68no—
343C22⋊Q8—68no—
344C22⋊Q8—62no—
345C22⋊Q8—62no—
346C22⋊Q8—121no—
347C22⋊Q8—121no—
348#121—62no—
349#121—62no—
350#121—62no—
351#121—62no—
352C4×Q8—62no—
353C4×Q8—62no—
354C4×D4—34no—
355C4×D4—62no—
356C4×D4—62no—
357C4×D4—62no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—62no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C4⋊C4C22×D311yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C42—31no—
385C2×C42—61no—
386#107—22no—
387#107—22no—
388#107—62no—
389C4⋊C8—62no—
390#103—62no—
391#103—62no—
392#103—62no—
393#102—62no—
394#102—121no—
395#102—121no—
396C22⋊C8—22no—
397C22⋊C8—62no—
398C22⋊C8—121no—
399C22⋊C8—121no—
400#97—62no—
401#95—21no—
402#95—61no—
403#95—61no—
404#95—61no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3AGL(1,ℤ/8)12yes—
412C23×C3C22×D411yescharacteristic
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—22no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3AGL(1,ℤ/8)12yes—
427C2×C3×C4—21no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—48no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C42−1+411yescharacteristic
453#67—28no—
454#67—48no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3#12012yes—
472C2×Dic3#12012yes—
473D12—22no—
474D12—22no—
475D12—48no—
476D12—41no—
477D12—41no—
478C4×D3—48no—
479C4×D3—48no—
480C4×D3—41no—
481C4×D3—41no—
482C4×D3—41no—
483C4×D3—41no—
484Dic6—22no—
485Dic6—22no—
486Dic6—48no—
487Dic6—41no—
488Dic6—41no—
489C3×C8—22no—
490C3×C8—41no—
491C3⋊C8—41no—
492C3⋊C8—41no—
493C24—31no—
494C24—61no—
495C24D3×D411yescharacteristic
496#41—1232no—
497C2×Q8—32no—
498C2×Q8—64no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—122no—
505C2×Q8—122no—
506C2×D4—32no—
507C2×D4—64no—
508C2×D4—62no—
509C2×D4—62no—
510C2×D4—62no—
511C2×D4—64no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—122no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4—122no—
521C22×C4—24no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—64no—
538C22×C4—64no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—122no—
549C22×C4—122no—
550C22×C4—122no—
551C22×C4—122no—
552C22×C4D3×D411yescharacteristic
553C22×C4C23×D311yescharacteristic
554SD16—68no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8—61no—
564C2×C8—61no—
565C2×C8—61no—
566C2×C8#23512yescomplemented
567C4⋊C4—24no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—32no—
575C4⋊C4—62no—
576C4⋊C4—64no—
577C4⋊C4—64no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—122no—
582C4⋊C4—122no—
583C4⋊C4—122no—
584C4⋊C4D3×D412yes—
585C4⋊C4D3×D412yes—
586C22⋊C4—42no—
587C22⋊C4—62no—
588C22⋊C4—64no—
589C22⋊C4—64no—
590C22⋊C4—64no—
591C22⋊C4—62no—
592C22⋊C4—122no—
593C22⋊C4—122no—
594C22⋊C4—122no—
595C42—32no—
596C42—32no—
597C42—122no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3C2×#12011yescharacteristic
606C22×C3#54611yescharacteristic
607C22×C3#54711yescharacteristic
608C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
609C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
610C22×C3#57811yescharacteristic
611C22×C3#57811yescharacteristic
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—42no—
622C2×D3—81no—
623C2×D3—81no—
624C2×D3—81no—
625C2×D3—81no—
626C3×C4—41no—
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—81no—
630C3×C4—81no—
631C3×C4#52511yescharacteristic
632C3×C4#53711yescharacteristic
633C3×C4#54811yescharacteristic
634C3×C4#55011yescharacteristic
635Dic3—22no—
636Dic3—22no—
637Dic3—42no—
638Dic3—41no—
639Dic3—42no—
640Dic3—81no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—32no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—62no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23#91112yes—
662C23C2×D3×D411yescharacteristic
663Q8—62no—
664Q8—62no—
665Q8—128no—
666Q8—121no—
667Q8—121no—
668D4—68no—
669D4—62no—
670D4—62no—
671D4—128no—
672D4—128no—
673D4—121no—
674D4—121no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—48no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—62no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—62no—
706C2×C4—128no—
707C2×C4—128no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4C2×#23511yescharacteristic
720C2×C4C2×D3×D411yescharacteristic
721C2×C4C2×D3×D411yescharacteristic
722C2×C4#100711yescharacteristic
723C2×C4D3×#4111yescharacteristic
724C2×C4#100911yescharacteristic
725C8—22no—
726C8—41no—
727C8—121no—
728C8—121no—
729C2×C3—42no—
730C2×C3#240711yescharacteristic
731C2×C3#300311yescharacteristic
732C2×C3#301111yescharacteristic
733C2×C3#330811yescharacteristic
734C2×C3#330811yescharacteristic
735C2×C3#334311yescharacteristic
736C2×C3#334311yescharacteristic
737D3—42no—
738D3—82no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—62no—
747C22—62no—
748C22—62no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—122no—
754C22—122no—
755C22—122no—
756C22—241no—
757C22—241no—
758C22—241no—
759C22—241no—
760C22#550711yescharacteristic
761C22D3×#12011yescharacteristic
762C22#565411yescharacteristic
763C22C2×#91111yescharacteristic
764C22#576611yescharacteristic
765C22D3×AGL(1,ℤ/8)11yescharacteristic
766C22#577911yescharacteristic
767C4—42no—
768C4—42no—
769C4—41no—
770C4—62no—
771C4—62no—
772C4—81no—
773C4—81no—
774C4—122no—
775C4—121no—
776C4—122no—
777C4—241no—
778C4#554711yescharacteristic
779C4#555311yescharacteristic
780C4#562911yescharacteristic
781C4#563311yescharacteristic
782C3#2413211yescharacteristic, complemented, Sylow
783C2—42no—
784C2—122no—
785C2—242no—
786C2#7440411yescharacteristic
787C2#7915811yescharacteristic
788C2#7922311yescharacteristic
789C2#8000211yescharacteristic
790C2#8018511yescharacteristic
791C2#8130611yescharacteristic
792C2#8147311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1852C2
socleC23×C3C22×D4
prime radicalC2×#5507C2
hypercenter#1852D3
hypocenterC3#24132
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#4875C2semidirect
3. C2×#4889C2semidirect
4. #73934C2semidirect
5. C3×#1852C2semidirect
6. #71559C2semidirect
7. #70634C2semidirect
8. #70632C2semidirect
9. #69962C2semidirect
10. #69917C2semidirect
11. #69523C2semidirect
12. #68893C2semidirect
13. #68887C2semidirect
14. #68878C2semidirect
15. #68806C2semidirect
77. #1852D3semidirect
273. C2×Dic6#41semidirect
279. C2×C3×C8#41semidirect
566. C2×C8#235semidirect
782. C3#24132semidirect

Maximal subgroups

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

subgroupindex
C2×#55072
C2×#48752
C2×#48892
#739342
C3×#18522
#715592
#706342
#706322
#699622
#699172
#695232
#688932
#688872
#688782
#688062
#241323