Finite Group Databasebeta

← #10944299

Subgroups — #10944299

Order 768.

1436 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#901C211yesmaximal, characteristic, complemented
2#82820C211yesmaximal, characteristic, complemented
3C2×#5049C211yesmaximal, characteristic, complemented
4C2×#4812C211yesmaximal, characteristic, complemented
5C2×#4807C211yesmaximal, characteristic, complemented
6#74030C211yesmaximal, characteristic
7C3×#1892C211yesmaximal, characteristic, complemented
8#71973C211yesmaximal, characteristic, complemented
9#70271C211yesmaximal, characteristic, complemented
10#70270C211yesmaximal, characteristic, complemented
11#69513C211yesmaximal, characteristic, complemented
12#68885C211yesmaximal, characteristic, complemented
13#68883C211yesmaximal, characteristic, complemented
14#68870C211yesmaximal, characteristic, complemented
15#68869C211yesmaximal, characteristic, complemented
16#32938—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C2×#901—24no—
26C2×#901—24no—
27C2×#901—24no—
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C22×D3×C8C2211yescharacteristic
31C22×D3×C8C2211yescharacteristic
32C2×#895C2211yescharacteristic
33C2×#895C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C3×#380C2211yescharacteristic
37C2×#835C2211yescharacteristic
38#5212C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41#5049—24no—
42#4991—21no—
43#4987C2211yescharacteristic
44#4987C2211yescharacteristic
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47#4979—21no—
48C2×#809C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#807C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4960—21no—
53#4960—21no—
54#4959—21no—
55#4959—21no—
56#4812—24no—
57#4807—24no—
58#4673—21no—
59#4671—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C22×#131—31no—
67C2×#468—31no—
68C2×#468—31no—
69C2×#465—31no—
70#2616—31no—
71#2615—31no—
72#1895—31no—
73#1894—31no—
74#1893—31no—
75#1893—31no—
76#1892—31no—
77#1892D311yescharacteristic, complemented
78#1809—31no—
79#1809—31no—
80#1808—31no—
81C22×C3×Q8C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C22×#67D411yescharacteristic
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C22×D12—21no—
93C22×D12—21no—
94C22×D12D411yescharacteristic
95C22×D12C2311yescharacteristic
96C22×C4×D3C2311yescharacteristic
97C22×C4×D3C2311yescharacteristic
98C22×Dic6D411yescharacteristic
99C22×C3×C8—22no—
100C22×C3×C8—22no—
101C22×C3×C8—22no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×#217—21no—
113#946—22no—
114#946—22no—
115#946—22no—
116#946—22no—
117C2×#215—22no—
118C2×#215—22no—
119C2×#215—22no—
120#930—22no—
121#930—22no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×#208—22no—
137C2×#208—22no—
138C2×#208D414yescomplemented
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141#901—232no—
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)—22no—
144C2×ΓL(1,𝔽25)—22no—
145C2×ΓL(1,𝔽25)—22no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)D414yescomplemented
148C2×D3×C8—22no—
149C2×D3×C8—22no—
150C2×D3×C8—22no—
151C2×D3×C8—22no—
152C2×D3×C8—22no—
153C2×D3×C8D414yescomplemented
154#895—22no—
155#895—22no—
156#895—22no—
157#895—22no—
158C3×#103—22no—
159C3×#103—22no—
160C3×#95—21no—
161#835—22no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167#821—22no—
168#821—22no—
169#809—22no—
170#808—22no—
171#807—22no—
172#807—22no—
173C22×#41—31no—
174C22×SD16—31no—
175C2×#131—64no—
176C2×#131—64no—
177C2×#131—64no—
178C22×M16—31no—
179C22×M16—31no—
180C22×M16—31no—
181C23×C8—31no—
182C23×C8—31no—
183C23×C8C2×D311yescharacteristic
184C2×C22⋊Q8—31no—
185C2×C22⋊Q8—31no—
186C2×C22⋊Q8C2×D311yescharacteristic
187C2×#121—31no—
188C2×#121—31no—
189C2×#121—31no—
190#468—64no—
191#468—64no—
192#465—64no—
193C2×#107—31no—
194C2×#107—31no—
195C2×#106—31no—
196C2×#103—31no—
197C2×#103C2×D311yescharacteristic
198C2×#103C2×D311yescharacteristic
199C2×#102—31no—
200C2×#102—31no—
201C2×#102—31no—
202#395—61no—
203#394—61no—
204#394—61no—
205#394—61no—
206#393—61no—
207#392—61no—
208#392—61no—
209#392—61no—
210#380—31no—
211#380—31no—
212#380—31no—
213#380—31no—
214#380—31no—
215#380C2×D311yescharacteristic
216#340—31no—
217#340—31no—
218#340—31no—
219#340—31no—
220#340C2×D311yescharacteristic
221#340C2×D311yescharacteristic
222C24×C3C2×D411yescharacteristic
223C23×D3—21no—
224C23×D3C2×D411yescharacteristic
225C23×D3C2×D411yescharacteristic
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D412yes—
242C22×C3×C4#4112yes—
243C22×C3×C4C2411yescharacteristic
244C2×#67—22no—
245C2×#67—22no—
246C2×#67—22no—
247C2×#67—22no—
248C2×#67—22no—
249C2×#67—22no—
250C2×#67—42no—
251C2×#67—81no—
252C2×#67—81no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258#235—28no—
259#235—28no—
260#235—28no—
261#235—28no—
262C2×D12—22no—
263C2×D12—22no—
264C2×D12—22no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—42no—
272C2×D12—42no—
273C2×D12—81no—
274C2×D12—81no—
275C2×D12—81no—
276C2×D12—81no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3C2×D412yes—
286C2×C4×D3C2×D412yes—
287C2×C4×D3#4112yes—
288C2×C4×D3#4112yes—
289C2×Dic6—22no—
290C2×Dic6—22no—
291C2×Dic6—22no—
292C2×C3×C8—28no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8C2×D412yes—
298C2×C3×C8C2×D412yes—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—42no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—81no—
308#217—81no—
309#215—44no—
310(C2×D3)⋊C4—42no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—42no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—81no—
316(C2×D3)⋊C4—81no—
317(C2×D3)⋊C4—81no—
318(C2×D3)⋊C4—81no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3—21no—
325Dic3⋊C4—42no—
326Dic3⋊C4—42no—
327#208—28no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8C2×D412yes—
331C2×C3⋊C8C2×D412yes—
332C2×C3⋊C8C2×D412yes—
333C2×C3⋊C8C2×D412yes—
334ΓL(1,𝔽25)—28no—
335ΓL(1,𝔽25)—28no—
336D3×C8—28no—
337D3×C8—28no—
338C2×#41—62no—
339C2×#41—62no—
340C2×#41—62no—
341C2×#41—62no—
342C2×#41—62no—
343C2×#41—62no—
344C22×Q8—31no—
345C22×Q8C22×D311yescharacteristic
346C22×D4—31no—
347C22×D4—31no—
348C22×D4—31no—
349C22×D4—31no—
350C22×D4—61no—
351C22×D4—61no—
352C22×D4—61no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4C22×D311yescharacteristic
356C2×SD16—62no—
357C2×SD16—62no—
358C2×SD16—62no—
359#131—632no—
360C2×M16—34no—
361C2×M16—34no—
362C2×M16—62no—
363C2×M16—62no—
364C2×M16—62no—
365C2×M16—62no—
366C2×M16—62no—
367C2×M16—62no—
368C2×M16—62no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—31no—
373C22×C8—31no—
374C22×C8—34no—
375C22×C8—62no—
376C22×C8—62no—
377C22×C8—62no—
378C22×C8—62no—
379C22×C8—62no—
380C22×C8C22×D311yescharacteristic
381C22×C8C22×D311yescharacteristic
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—62no—
385C22⋊Q8—62no—
386C22⋊Q8—62no—
387C22⋊Q8—62no—
388#121—62no—
389#121—62no—
390#121—62no—
391#121—62no—
392#121—62no—
393#121—62no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C4⋊C4C22×D311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C22⋊C4—61no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415#107—62no—
416#107—62no—
417#106—62no—
418#103—22no—
419#103—22no—
420#103—62no—
421#102—62no—
422#102—62no—
423#102—62no—
424#95—21no—
425#95—61no—
426#95—61no—
427#95—61no—
428#95—61no—
429#95—61no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3#12112yes—
437C23×C3C22×D411yescharacteristic
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C22×D3#12112yes—
458C22×D3#12112yes—
459C3×Q8—41no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×Q8—41no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4#12112yes—
482C2×C3×C4C22×D411yescharacteristic
483C2×C3×C4C22×D411yescharacteristic
484C2×C3×C4C22×D411yescharacteristic
485C2×C3×C4C2×#4111yescharacteristic
486C2×C3×C4C2×#4111yescharacteristic
487C2×C3×C4C2×#4111yescharacteristic
488#67—28no—
489#67—28no—
490#67—84no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3#12112yes—
505C2×Dic3#12112yes—
506D12—28no—
507D12—41no—
508D12—41no—
509D12—41no—
510D12—41no—
511D12—84no—
512D12—84no—
513C4×D3—22no—
514C4×D3—22no—
515C4×D3—22no—
516C4×D3—22no—
517C4×D3—22no—
518C4×D3—22no—
519C4×D3—22no—
520C4×D3—22no—
521Dic6—28no—
522C3×C8—22no—
523C3×C8—22no—
524C3⋊C8—22no—
525C3⋊C8#12014yes—
526C24—31no—
527C24—31no—
528C24—61no—
529C24D3×D411yescharacteristic
530#41—68no—
531#41—68no—
532#41—68no—
533#41—68no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—62no—
541C2×Q8—62no—
542C2×Q8—62no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—62no—
547C2×D4—62no—
548C2×D4—62no—
549C2×D4—62no—
550C2×D4—62no—
551C2×D4—62no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—122no—
561C2×D4—241no—
562C2×D4—241no—
563C2×D4—241no—
564C2×D4—241no—
565C2×D4—241no—
566C2×D4—241no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—32no—
578C22×C4—32no—
579C22×C4—32no—
580C22×C4—32no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4#23512yes—
593C22×C4D3×D411yescharacteristic
594C22×C4D3×D412yes—
595C22×C4C23×D311yescharacteristic
596SD16—124no—
597M16—68no—
598M16—68no—
599M16—68no—
600C2×C8—28no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—32no—
606C2×C8—32no—
607C2×C8—32no—
608C2×C8—32no—
609C2×C8—68no—
610C2×C8—68no—
611C2×C8—61no—
612C2×C8—61no—
613C2×C8D3×D412yes—
614C2×C8D3×D412yes—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—42no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—122no—
629C4⋊C4—122no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—122no—
635C22⋊C4—122no—
636C22⋊C4—122no—
637C22⋊C4—241no—
638C22⋊C4—241no—
639C22⋊C4—241no—
640C22⋊C4—241no—
641C22⋊C4—241no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3C2×#12111yescharacteristic
650C22×C3C2×#12111yescharacteristic
651C22×C3C2×#12111yescharacteristic
652C22×C3#57611yescharacteristic
653C22×C3#57711yescharacteristic
654C22×C3#57711yescharacteristic
655C22×C3#57811yescharacteristic
656C2×D3—22no—
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—22no—
660C2×D3—22no—
661C2×D3—22no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C2×D3—81no—
675C2×D3—81no—
676C2×D3—81no—
677C3×C4—22no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4C2×#12011yescharacteristic
683C3×C4#52511yescharacteristic
684C3×C4#52511yescharacteristic
685C3×C4#52511yescharacteristic
686Dic3—22no—
687Dic3—22no—
688Dic3—81no—
689Dic3—81no—
690Dic3—81no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—32no—
698C23—32no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—61no—
708C23—61no—
709C23—61no—
710C23—61no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23—121no—
716C23—121no—
717C23—121no—
718C23#88412yes—
719C23C2×D3×D411yescharacteristic
720Q8—41no—
721Q8—41no—
722Q8—41no—
723Q8—41no—
724Q8—68no—
725D4—68no—
726D4—68no—
727D4—68no—
728D4—121no—
729D4—121no—
730D4—121no—
731D4—121no—
732D4—244no—
733D4—244no—
734D4—244no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—32no—
742C2×C4—32no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4—121no—
775C2×C4—121no—
776C2×C4#88412yes—
777C2×C4C2×#23511yescharacteristic
778C2×C4C2×D3×D411yescharacteristic
779C2×C4C2×D3×D411yescharacteristic
780C2×C4C2×D3×D411yescharacteristic
781C2×C4D3×#4111yescharacteristic
782C2×C4D3×#4111yescharacteristic
783C8—22no—
784C8—22no—
785C8—34no—
786C8—62no—
787C2×C3—42no—
788C2×C3#284711yescharacteristic
789C2×C3#305711yescharacteristic
790C2×C3#306111yescharacteristic
791C2×C3#306211yescharacteristic
792C2×C3#306211yescharacteristic
793C2×C3#306311yescharacteristic
794C2×C3#306311yescharacteristic
795D3—42no—
796D3—42no—
797D3—161no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—62no—
806C22—62no—
807C22—62no—
808C22—62no—
809C22—62no—
810C22—62no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—241no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22—241no—
825C22—241no—
826C22C2×#88411yescharacteristic
827C22D3×#12111yescharacteristic
828C22D3×#12111yescharacteristic
829C22#576211yescharacteristic
830C22#576611yescharacteristic
831C22#576911yescharacteristic
832C22#577011yescharacteristic
833C4—22no—
834C4—62no—
835C4—62no—
836C4—81no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4—241no—
841C4—241no—
842C4—241no—
843C4#554711yescharacteristic
844C4#554711yescharacteristic
845C4D3×#12011yescharacteristic
846C4#565611yescharacteristic
847C3#3293811yescharacteristic, complemented, Sylow
848C2—42no—
849C2—122no—
850C2—122no—
851C2—481no—
852C2#7493511yescharacteristic
853C2#7880011yescharacteristic
854C2#7884011yescharacteristic
855C2#8065911yescharacteristic
856C2#8066111yescharacteristic
857C2#8076111yescharacteristic
858C2#8076211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1892C2
socleC23×C3C22×D4
prime radical#74030C2
hypercenter#1892D3
hypocenterC3#32938
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
1. C22×#901C2semidirect
2. #82820C2semidirect
3. C2×#5049C2semidirect
4. C2×#4812C2semidirect
5. C2×#4807C2semidirect
7. C3×#1892C2semidirect
8. #71973C2semidirect
9. #70271C2semidirect
10. #70270C2semidirect
11. #69513C2semidirect
12. #68885C2semidirect
13. #68883C2semidirect
14. #68870C2semidirect
15. #68869C2semidirect
77. #1892D3semidirect
138. C2×#208D4semidirect
147. C2×ΓL(1,𝔽25)D4semidirect
153. C2×D3×C8D4semidirect
847. C3#32938semidirect

Maximal subgroups

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

subgroupindex
C22×#9012
#828202
C2×#50492
C2×#48122
C2×#48072
#740302
C3×#18922
#719732
#702712
#702702
#695132
#688852
#688832
#688702
#688692
#329383