Finite Group Databasebeta

← #10944290

Subgroups — #10944290

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×#907C211yesmaximal, characteristic, complemented
2C2×C3×#468C211yesmaximal, characteristic, complemented
3C2×#5174C211yesmaximal, characteristic, complemented
4C2×#5171C211yesmaximal, characteristic, complemented
5#82820C211yesmaximal, characteristic, complemented
6#82709C211yesmaximal, characteristic
7#71988C211yesmaximal, characteristic, complemented
8#71696C211yesmaximal, characteristic, complemented
9#71681C211yesmaximal, characteristic, complemented
10#70631C211yesmaximal, characteristic, complemented
11#70630C211yesmaximal, characteristic, complemented
12#70271C211yesmaximal, characteristic, complemented
13#70270C211yesmaximal, characteristic, complemented
14#70203C211yesmaximal, characteristic, complemented
15#70202C211yesmaximal, characteristic, complemented
16#32938—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C23×C3⋊C8C2211yescharacteristic
27C2×#907—24no—
28C2×#907—24no—
29C2×#907—24no—
30C22×ΓL(1,𝔽25)C2211yescharacteristic
31C22×ΓL(1,𝔽25)C2211yescharacteristic
32C22×D3×C8C2211yescharacteristic
33C22×D3×C8C2211yescharacteristic
34C3×#468—24no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40#5223—21no—
41#5223—21no—
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44#5212C2211yescharacteristic
45#5212C2211yescharacteristic
46#5174—24no—
47#5171—24no—
48C2×#818C2211yescharacteristic
49C2×#817C2211yescharacteristic
50#4991—21no—
51#4987C2211yescharacteristic
52#4987C2211yescharacteristic
53#4987C2211yescharacteristic
54#4987C2211yescharacteristic
55#4979—21no—
56#4960—21no—
57#4959—21no—
58#4959—21no—
59#4947—21no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C22×#131—31no—
67C2×#468—31no—
68C2×#468D311yescharacteristic, complemented
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#1892—31no—
78#1809—31no—
79#1809—31no—
80#1808—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C22×#67D411yescharacteristic
88C22×#67D411yescharacteristic
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—22no—
94C2×#235—22no—
95C22×D12D411yescharacteristic
96C22×C4×D3C2311yescharacteristic
97C22×C4×D3C2311yescharacteristic
98C22×Dic6D411yescharacteristic
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×M16—22no—
103C2×C3×M16—22no—
104C2×C3×M16D414yescomplemented
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×#121—22no—
110C3×#121—22no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#217—21no—
120#946—22no—
121#946—22no—
122#946—22no—
123#946—22no—
124#938—22no—
125#938—22no—
126#938—22no—
127#938—22no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C22×C3⋊C8—22no—
141C22×C3⋊C8—22no—
142C22×C3⋊C8—22no—
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145#907—232no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)—22no—
148C2×ΓL(1,𝔽25)—22no—
149C2×ΓL(1,𝔽25)—22no—
150C2×ΓL(1,𝔽25)—22no—
151C2×ΓL(1,𝔽25)D414yescomplemented
152C2×D3×C8—22no—
153C2×D3×C8—22no—
154C2×D3×C8—22no—
155C2×D3×C8—22no—
156C2×D3×C8—22no—
157C2×D3×C8D414yescomplemented
158C3×#107—22no—
159C3×#103—22no—
160C3×#102—22no—
161#835—22no—
162#835—22no—
163#832—22no—
164#832—22no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#818—22no—
172#817—22no—
173C22×#41—31no—
174C22×SD16C2×D311yescharacteristic
175C2×#131—64no—
176C2×#131—64no—
177C2×#131—64no—
178C22×M16—31no—
179C22×M16—31no—
180C22×M16C2×D311yescharacteristic
181C23×C8—31no—
182C23×C8—31no—
183C23×C8—31no—
184C2×C22⋊Q8—31no—
185C2×C22⋊Q8—31no—
186C2×C22⋊Q8C2×D311yescharacteristic
187C2×#121—31no—
188C2×#121—31no—
189C2×#121C2×D311yescharacteristic
190#468—24no—
191#468—64no—
192#465—64no—
193C2×#107—31no—
194C2×#107C2×D311yescharacteristic
195C2×#106—31no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#103C2×D311yescharacteristic
199C2×#102—31no—
200C2×#102—31no—
201C2×#102C2×D311yescharacteristic
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#380—31no—
216#340—31no—
217#340—31no—
218#340—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222C24×C3—21no—
223C24×C3C2×D411yescharacteristic
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—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—42no—
239C2×C3×D4—81no—
240C2×C3×D4—81no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D412yes—
250C22×C3×C4#4112yes—
251C22×C3×C4C2411yescharacteristic
252C2×#67—22no—
253C2×#67—22no—
254C2×#67—22no—
255C2×#67—22no—
256C2×#67—22no—
257C2×#67—22no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—81no—
261C2×#67—81no—
262C2×#67—81no—
263C2×#67—81no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3C2×D411yescharacteristic
269C22×Dic3C2×D411yescharacteristic
270#235—28no—
271#235—28no—
272#235—28no—
273#235—28no—
274C2×D12—22no—
275C2×D12—22no—
276C2×D12—22no—
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—
292C3×SD16—44no—
293C3×M16—28no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8C2×D412yes—
297C2×C3×C8C2×D412yes—
298C2×C3×C8C2×D412yes—
299C2×C3×C8C2×D412yes—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—42no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—42no—
307#217—42no—
308#217—42no—
309#217—81no—
310#217—81no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—81no—
314(C2×D3)⋊C4—81no—
315(C2×D3)⋊C4—81no—
316(C2×D3)⋊C4—81no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3—21no—
325Dic3⋊C4—42no—
326Dic3⋊C4—42no—
327C2×C3⋊C8—28no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
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—21no—
347C22×D4—31no—
348C22×D4—31no—
349C22×D4—31no—
350C22×D4—61no—
351C22×D4—61no—
352C22×D4C22×D311yescharacteristic
353C23×C4—31no—
354C23×C4—31no—
355C23×C4C22×D311yescharacteristic
356C2×SD16—22no—
357C2×SD16—22no—
358C2×SD16—22no—
359#131—632no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—34no—
363C2×M16—62no—
364C2×M16—62no—
365C2×M16—62no—
366C2×M16—62no—
367C2×M16—62no—
368C2×M16#6714yescomplemented
369C22×C8—31no—
370C22×C8—31no—
371C22×C8—34no—
372C22×C8—62no—
373C22×C8—62no—
374C22×C8—62no—
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—22no—
389#121—22no—
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—31no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4—61no—
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—22no—
416#107—62no—
417#106—62no—
418#103—22no—
419#103—62no—
420#103—62no—
421#102—22no—
422#102—62no—
423#102—62no—
424#95—61no—
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—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3#12112yes—
444C23×C3C22×D411yescharacteristic
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3#12112yes—
458C22×D3#12112yes—
459C3×Q8—41no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×D4—41no—
464C3×D4—41no—
465C3×D4—41no—
466C3×D4—41no—
467C3×D4—84no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
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—41no—
482C2×C3×C4—41no—
483C2×C3×C4#12112yes—
484C2×C3×C4C22×D411yescharacteristic
485C2×C3×C4C22×D411yescharacteristic
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4C2×#4111yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×C3×C4C2×#4111yescharacteristic
490#67—28no—
491#67—28no—
492#67—84no—
493#67—84no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3#12112yes—
511C2×Dic3#12112yes—
512D12—28no—
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#12014yes—
524C3⋊C8—22no—
525C3⋊C8—22no—
526C24—21no—
527C24—31no—
528C24—31no—
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—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—42no—
550C2×D4—62no—
551C2×D4—62no—
552C2×D4—62no—
553C2×D4—62no—
554C2×D4—62no—
555C2×D4—62no—
556C2×D4—62no—
557C2×D4—62no—
558C2×D4—62no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—122no—
562C2×D4—122no—
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—31no—
575C22×C4—31no—
576C22×C4—32no—
577C22×C4—32no—
578C22×C4—32no—
579C22×C4—32no—
580C22×C4—61no—
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×C4D3×D411yescharacteristic
593C22×C4#23712yes—
594C22×C4C2×#6712yes—
595C22×C4C23×D311yescharacteristic
596SD16—44no—
597M16—28no—
598M16—68no—
599M16—68no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—32no—
603C2×C8—32no—
604C2×C8—68no—
605C2×C8—68no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—61no—
610C2×C8—68no—
611C2×C8D3×D412yes—
612C2×C8D3×D412yes—
613C2×C8C2×#6712yes—
614C2×C8C2×#6712yes—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—42no—
620C4⋊C4—61no—
621C4⋊C4—61no—
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—42no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—122no—
635C22⋊C4—122no—
636C22⋊C4—241no—
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×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3C2×#12111yescharacteristic
657C22×C3C2×#12111yescharacteristic
658C22×C3C2×#12111yescharacteristic
659C22×C3#57611yescharacteristic
660C22×C3#57711yescharacteristic
661C22×C3#57711yescharacteristic
662C22×C3#57811yescharacteristic
663C2×D3—22no—
664C2×D3—22no—
665C2×D3—22no—
666C2×D3—22no—
667C2×D3—22no—
668C2×D3—22no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C3×C4—22no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4C2×#12011yescharacteristic
682C3×C4#52511yescharacteristic
683C3×C4#52511yescharacteristic
684C3×C4#52511yescharacteristic
685Dic3—22no—
686Dic3—22no—
687Dic3—81no—
688Dic3—81no—
689Dic3—81no—
690Dic3—81no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—32no—
698C23—32no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—61no—
707C23—61no—
708C23—61no—
709C23—61no—
710C23—61no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23#93812yes—
719C23C2×D3×D411yescharacteristic
720Q8—41no—
721Q8—41no—
722Q8—41no—
723Q8—41no—
724Q8—68no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—68no—
730D4—68no—
731D4—68no—
732D4—84no—
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—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—121no—
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#93812yes—
777C2×C4C2×D3×D411yescharacteristic
778C2×C4C2×D3×D411yescharacteristic
779C2×C4C2×#23711yescharacteristic
780C2×C4D3×#4111yescharacteristic
781C2×C4D3×#4111yescharacteristic
782C2×C4C22×#6711yescharacteristic
783C8—22no—
784C8—62no—
785C8—62no—
786C8#93714yes—
787C2×C3—42no—
788C2×C3—161no—
789C2×C3#284711yescharacteristic
790C2×C3#305711yescharacteristic
791C2×C3#306111yescharacteristic
792C2×C3#306211yescharacteristic
793C2×C3#306211yescharacteristic
794C2×C3#306311yescharacteristic
795C2×C3#306311yescharacteristic
796D3—42no—
797D3—42no—
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—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22D3×#12111yescharacteristic
827C22D3×#12111yescharacteristic
828C22#577411yescharacteristic
829C22#577511yescharacteristic
830C22#577811yescharacteristic
831C22#577911yescharacteristic
832C22C2×#93811yescharacteristic
833C4—22no—
834C4—62no—
835C4—62no—
836C4—81no—
837C4—81no—
838C4—81no—
839C4—241no—
840C4—241no—
841C4—241no—
842C4—241no—
843C4#560611yescharacteristic
844C4#560611yescharacteristic
845C4C2×#93711yescharacteristic
846C4#582811yescharacteristic
847C3#3293811yescharacteristic, complemented, Sylow
848C2—42no—
849C2—122no—
850C2—122no—
851C2—161no—
852C2#8080711yescharacteristic
853C2#8080811yescharacteristic
854C2#8080911yescharacteristic
855C2#8081011yescharacteristic
856C2#8272311yescharacteristic
857C2#8395111yescharacteristic
858C2#8398611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#468C2
socleC23×C3C22×D4
prime radical#82709C2
hypercenterC2×#468D3
hypocenterC3#32938
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C22×#907C2semidirect
2. C2×C3×#468C2semidirect
3. C2×#5174C2semidirect
4. C2×#5171C2semidirect
5. #82820C2semidirect
7. #71988C2semidirect
8. #71696C2semidirect
9. #71681C2semidirect
10. #70631C2semidirect
11. #70630C2semidirect
12. #70271C2semidirect
13. #70270C2semidirect
14. #70203C2semidirect
15. #70202C2semidirect
68. C2×#468D3semidirect
104. C2×C3×M16D4semidirect
151. C2×ΓL(1,𝔽25)D4semidirect
157. C2×D3×C8D4semidirect
368. C2×M16#67semidirect
847. C3#32938semidirect

Maximal subgroups

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

subgroupindex
C22×#9072
C2×C3×#4682
C2×#51742
C2×#51712
#828202
#827092
#719882
#716962
#716812
#706312
#706302
#702712
#702702
#702032
#702022
#329383