Finite Group Databasebeta

← #10944304

Subgroups — #10944304

Order 768.

1494 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#901C211yesmaximal, characteristic, complemented
2#82709C211yesmaximal, characteristic, complemented
3C2×#5039C211yesmaximal, characteristic, complemented
4C2×#4782C211yesmaximal, characteristic, complemented
5C2×#4775C211yesmaximal, characteristic, complemented
6#74030C211yesmaximal, characteristic, complemented
7C3×#1893C211yesmaximal, characteristic, complemented
8#71973C211yesmaximal, characteristic, complemented
9#70203C211yesmaximal, characteristic, complemented
10#70202C211yesmaximal, characteristic, complemented
11#69513C211yesmaximal, characteristic, complemented
12#68885C211yesmaximal, characteristic, complemented
13#68883C211yesmaximal, characteristic, complemented
14#68870C211yesmaximal, characteristic, complemented
15#68868C211yesmaximal, characteristic, complemented
16#32939—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C22×#213C2211yescharacteristic
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×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C3×#380C2211yescharacteristic
37#5223—21no—
38#5223—21no—
39C2×#832C2211yescharacteristic
40#5212C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43#5039—24no—
44#4987C2211yescharacteristic
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47#4987C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#808C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4960—21no—
53#4960—21no—
54#4960—21no—
55#4947—21no—
56#4782—24no—
57#4775—24no—
58#4673—21no—
59#4671—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C22×#131—31no—
67C2×#469—31no—
68C2×#469—31no—
69C2×#466—31no—
70#2615—31no—
71#2615—31no—
72#1895—31no—
73#1895—31no—
74#1893—31no—
75#1893—31no—
76#1893—31no—
77#1893D311yescharacteristic, complemented
78#1809—31no—
79#1809—31no—
80#1807—31no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
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×D12—21no—
96C22×D12—21no—
97C22×D12D411yescharacteristic
98C22×D12C2311yescharacteristic
99C22×C4×D3C2311yescharacteristic
100C22×C4×D3C2311yescharacteristic
101C22×Dic6D411yescharacteristic
102C22×C3×C8—22no—
103C22×C3×C8—22no—
104C22×C3×C8—22no—
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×#121—22no—
108C3×#121—22no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117#938—22no—
118#938—22no—
119#938—22no—
120#938—22no—
121C2×#213—22no—
122C2×#213—22no—
123C2×#213—22no—
124#930—22no—
125#930—22no—
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×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
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×#102—22no—
159C3×#102—22no—
160C3×#95—21no—
161#832—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#808—22no—
172#807—22no—
173C22×#41—31no—
174C22×D8—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×#121—31no—
185C2×#121—31no—
186C2×#121—31no—
187C2×#121—31no—
188C2×#121—31no—
189C2×#121C2×D311yescharacteristic
190#469—64no—
191#469—64no—
192#466—64no—
193C2×#107—31no—
194C2×#106—31no—
195C2×#106—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×#102C2×D311yescharacteristic
201C2×#102C2×D311yescharacteristic
202#393—61no—
203#393—61no—
204#392—61no—
205#392—61no—
206#392—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×C3—21no—
223C24×C3C2×D411yescharacteristic
224C23×D3—21no—
225C23×D3C2×D411yescharacteristic
226C23×D3C2×D411yescharacteristic
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—42no—
234C2×C3×D4—81no—
235C2×C3×D4—81no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D412yes—
245C22×C3×C4#4112yes—
246C22×C3×C4C2411yescharacteristic
247C2×#67—22no—
248C2×#67—22no—
249C2×#67—22no—
250C2×#67—22no—
251C2×#67—22no—
252C2×#67—22no—
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—42no—
256C2×#67—81no—
257C2×#67—81no—
258C2×#67—81no—
259C2×#67—81no—
260C2×#67—81no—
261C2×#67—81no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267#235—28no—
268#235—28no—
269#235—28no—
270#235—28no—
271C2×D12—22no—
272C2×D12—22no—
273C2×D12—22no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—42no—
281C2×D12—42no—
282C2×D12—81no—
283C2×D12—81no—
284C2×D12—81no—
285C2×D12—81no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3C2×D412yes—
295C2×C4×D3C2×D412yes—
296C2×C4×D3#4112yes—
297C2×C4×D3#4112yes—
298C2×Dic6—22no—
299C2×Dic6—22no—
300C2×Dic6—22no—
301C2×C3×C8—28no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8C2×D412yes—
307C2×C3×C8C2×D412yes—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—81no—
316#217—42no—
317#217—42no—
318#217—81no—
319#213—44no—
320(C2×D3)⋊C4—42no—
321(C2×D3)⋊C4—42no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—81no—
324(C2×D3)⋊C4—81no—
325(C2×D3)⋊C4—81no—
326(C2×D3)⋊C4—81no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333#208—28no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8C2×D412yes—
337C2×C3⋊C8C2×D412yes—
338C2×C3⋊C8C2×D412yes—
339C2×C3⋊C8C2×D412yes—
340ΓL(1,𝔽25)—28no—
341ΓL(1,𝔽25)—28no—
342D3×C8—28no—
343D3×C8—28no—
344C2×#41—62no—
345C2×#41—62no—
346C2×#41—62no—
347C2×#41—62no—
348C2×#41—62no—
349C2×#41—62no—
350C22×Q8—31no—
351C22×D4—21no—
352C22×D4—31no—
353C22×D4—31no—
354C22×D4—31no—
355C22×D4—31no—
356C22×D4—61no—
357C22×D4—61no—
358C22×D4—61no—
359C22×D4—61no—
360C22×D4—61no—
361C22×D4C22×D311yescharacteristic
362C23×C4—31no—
363C23×C4—31no—
364C23×C4C22×D311yescharacteristic
365C2×D8—62no—
366C2×D8—62no—
367C2×D8—62no—
368#131—632no—
369C2×M16—34no—
370C2×M16—34no—
371C2×M16—62no—
372C2×M16—62no—
373C2×M16—62no—
374C2×M16—62no—
375C2×M16—62no—
376C2×M16—62no—
377C2×M16—62no—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—31no—
382C22×C8—31no—
383C22×C8—34no—
384C22×C8—62no—
385C22×C8—62no—
386C22×C8—62no—
387C22×C8—62no—
388C22×C8—62no—
389C22×C8C22×D311yescharacteristic
390C22×C8C22×D311yescharacteristic
391#121—22no—
392#121—22no—
393#121—62no—
394#121—62no—
395#121—62no—
396#121—62no—
397#121—62no—
398#121—62no—
399#121—62no—
400#121—62no—
401#121—62no—
402#121—62no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421#107—62no—
422#106—62no—
423#106—62no—
424#102—22no—
425#102—22no—
426#102—62no—
427#102—62no—
428#102—62no—
429#102—62no—
430#95—21no—
431#95—61no—
432#95—61no—
433#95—61no—
434#95—61no—
435#95—61no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3#12112yes—
450C23×C3C22×D411yescharacteristic
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3#12112yes—
471C22×D3#12112yes—
472C3×D4—41no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—41no—
476C3×D4—84no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4#12112yes—
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499#67—28no—
500#67—28no—
501#67—84no—
502#67—84no—
503#67—84no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3#12112yes—
518C2×Dic3#12112yes—
519D12—28no—
520D12—41no—
521D12—41no—
522D12—41no—
523D12—41no—
524D12—84no—
525D12—84no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—22no—
529C4×D3—22no—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—22no—
534Dic6—28no—
535C3×C8—22no—
536C3×C8—22no—
537C3⋊C8—22no—
538C3⋊C8#12014yes—
539C24—21no—
540C24—31no—
541C24—31no—
542C24—61no—
543C24D3×D411yescharacteristic
544#41—68no—
545#41—68no—
546#41—68no—
547#41—68no—
548C2×Q8—62no—
549C2×Q8—62no—
550C2×Q8—62no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—62no—
559C2×D4—62no—
560C2×D4—62no—
561C2×D4—62no—
562C2×D4—62no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4—62no—
566C2×D4—62no—
567C2×D4—61no—
568C2×D4—61no—
569C2×D4—61no—
570C2×D4—61no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—122no—
576C2×D4—122no—
577C2×D4—122no—
578C2×D4—122no—
579C2×D4—122no—
580C2×D4—241no—
581C2×D4—241no—
582C2×D4—241no—
583C2×D4—241no—
584C2×D4—241no—
585C2×D4—241no—
586C2×D4—241no—
587C2×D4—241no—
588C2×D4—241no—
589C2×D4—241no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4#23512yes—
615C22×C4D3×D411yescharacteristic
616C22×C4D3×D412yes—
617C22×C4C23×D311yescharacteristic
618D8—124no—
619M16—68no—
620M16—68no—
621M16—68no—
622C2×C8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—32no—
628C2×C8—32no—
629C2×C8—32no—
630C2×C8—32no—
631C2×C8—68no—
632C2×C8—68no—
633C2×C8—61no—
634C2×C8—61no—
635C2×C8D3×D412yes—
636C2×C8D3×D412yes—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C22⋊C4—42no—
650C22⋊C4—81no—
651C22⋊C4—122no—
652C22⋊C4—122no—
653C22⋊C4—122no—
654C22⋊C4—122no—
655C22⋊C4—122no—
656C22⋊C4—241no—
657C22⋊C4—241no—
658C22⋊C4—241no—
659C22⋊C4—241no—
660C22⋊C4—241no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3C2×#12111yescharacteristic
676C22×C3C2×#12111yescharacteristic
677C22×C3C2×#12111yescharacteristic
678C22×C3#57611yescharacteristic
679C22×C3#57611yescharacteristic
680C22×C3#57711yescharacteristic
681C22×C3#57711yescharacteristic
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—81no—
697C2×D3—81no—
698C2×D3—81no—
699C2×D3—81no—
700C2×D3—81no—
701C2×D3—81no—
702C2×D3—81no—
703C3×C4—22no—
704C3×C4—81no—
705C3×C4—81no—
706C3×C4—81no—
707C3×C4C2×#12011yescharacteristic
708C3×C4#52511yescharacteristic
709C3×C4#52511yescharacteristic
710C3×C4#52511yescharacteristic
711Dic3—22no—
712Dic3—22no—
713Dic3—81no—
714Dic3—81no—
715Dic3—81no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—32no—
723C23—32no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—61no—
732C23—61no—
733C23—61no—
734C23—61no—
735C23—61no—
736C23—61no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—121no—
744C23—121no—
745C23—121no—
746C23—121no—
747C23—121no—
748C23—121no—
749C23—121no—
750C23#88412yes—
751C23C2×D3×D411yescharacteristic
752Q8—68no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—68no—
758D4—68no—
759D4—68no—
760D4—84no—
761D4—121no—
762D4—121no—
763D4—121no—
764D4—121no—
765D4—244no—
766D4—244no—
767D4—244no—
768D4—244no—
769D4—244no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—121no—
802C2×C4—121no—
803C2×C4—121no—
804C2×C4—121no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4#88412yes—
809C2×C4C2×#23511yescharacteristic
810C2×C4C2×D3×D411yescharacteristic
811C2×C4C2×D3×D411yescharacteristic
812C2×C4C2×D3×D411yescharacteristic
813C2×C4D3×#4111yescharacteristic
814C2×C4D3×#4111yescharacteristic
815C8—22no—
816C8—22no—
817C8—34no—
818C8—62no—
819C2×C3—42no—
820C2×C3—161no—
821C2×C3#284711yescharacteristic
822C2×C3#305811yescharacteristic
823C2×C3#306011yescharacteristic
824C2×C3#306211yescharacteristic
825C2×C3#306211yescharacteristic
826C2×C3#306211yescharacteristic
827C2×C3#306211yescharacteristic
828D3—42no—
829D3—42no—
830D3—161no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—62no—
839C22—62no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—121no—
852C22—121no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—241no—
860C22—241no—
861C22—241no—
862C22—241no—
863C22—241no—
864C22—241no—
865C22—241no—
866C22C2×#88411yescharacteristic
867C22D3×#12111yescharacteristic
868C22D3×#12111yescharacteristic
869C22#575711yescharacteristic
870C22#576211yescharacteristic
871C22#576911yescharacteristic
872C22#577011yescharacteristic
873C4—22no—
874C4—62no—
875C4—62no—
876C4—81no—
877C4—81no—
878C4—81no—
879C4—241no—
880C4—241no—
881C4—241no—
882C4#554711yescharacteristic
883C4#554711yescharacteristic
884C4D3×#12011yescharacteristic
885C4#565611yescharacteristic
886C3#3293911yescharacteristic, complemented, Sylow
887C2—42no—
888C2—122no—
889C2—122no—
890C2—161no—
891C2—481no—
892C2#7493511yescharacteristic
893C2#7875211yescharacteristic
894C2#7884011yescharacteristic
895C2#8066011yescharacteristic
896C2#8066111yescharacteristic
897C2#8071611yescharacteristic
898C2#8071811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1893C2
socleC23×C3C22×D4
hypercenter#1893D3
hypocenterC3#32939
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
1. C22×#901C2semidirect
2. #82709C2semidirect
3. C2×#5039C2semidirect
4. C2×#4782C2semidirect
5. C2×#4775C2semidirect
6. #74030C2semidirect
7. C3×#1893C2semidirect
8. #71973C2semidirect
9. #70203C2semidirect
10. #70202C2semidirect
11. #69513C2semidirect
12. #68885C2semidirect
13. #68883C2semidirect
14. #68870C2semidirect
15. #68868C2semidirect
77. #1893D3semidirect
138. C2×#208D4semidirect
147. C2×ΓL(1,𝔽25)D4semidirect
153. C2×D3×C8D4semidirect
886. C3#32939semidirect

Maximal subgroups

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

subgroupindex
C22×#9012
#827092
C2×#50392
C2×#47822
C2×#47752
#740302
C3×#18932
#719732
#702032
#702022
#695132
#688852
#688832
#688702
#688682
#329393