Finite Group Databasebeta

← #10944293

Subgroups — #10944293

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#82709C211yesmaximal, characteristic
3C2×#5042C211yesmaximal, characteristic, complemented
4C2×#4780C211yesmaximal, characteristic, complemented
5C2×#4778C211yesmaximal, characteristic, complemented
6#73950C211yesmaximal, characteristic, complemented
7C3×#1893C211yesmaximal, characteristic, complemented
8#71972C211yesmaximal, characteristic, complemented
9#70203C211yesmaximal, characteristic, complemented
10#70202C211yesmaximal, characteristic, complemented
11#69513C211yesmaximal, characteristic, complemented
12#68884C211yesmaximal, characteristic, complemented
13#68882C211yesmaximal, characteristic, complemented
14#68870C211yesmaximal, characteristic, complemented
15#68869C211yesmaximal, characteristic, complemented
16#32938—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C22×#214C2211yescharacteristic
23C2×#924C2211yescharacteristic
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×#897C2211yescharacteristic
33C2×#897C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C3×#380C2211yescharacteristic
37#5223—21no—
38#5223—21no—
39C2×#832C2211yescharacteristic
40#5212C2211yescharacteristic
41C2×#816C2211yescharacteristic
42C2×#816C2211yescharacteristic
43#5042—24no—
44#4987C2211yescharacteristic
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47#4987C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#807C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4961—21no—
53#4961—21no—
54#4960—21no—
55#4947—21no—
56#4780—24no—
57#4778—24no—
58#4672—21no—
59#4656—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#1893D311yescharacteristic, complemented
76#1892—31no—
77#1892—31no—
78#1809—31no—
79#1809—31no—
80#1808—31no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C22×#67D411yescharacteristic
87C22×#67D411yescharacteristic
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—22no—
94C22×D12D411yescharacteristic
95C22×C4×D3C2311yescharacteristic
96C22×C4×D3C2311yescharacteristic
97C22×Dic6D411yescharacteristic
98C22×Dic6C2311yescharacteristic
99C22×C3×C8—22no—
100C22×C3×C8—22no—
101C22×C3×C8—22no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×#121—22no—
105C3×#121—22no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115#938—22no—
116#938—22no—
117#938—22no—
118#938—22no—
119C2×#214—22no—
120C2×#214—22no—
121C2×#214—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×C4⋊Dic3—21no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133#924—22no—
134#924—22no—
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#897—22no—
155#897—22no—
156#897—22no—
157#897—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#816—22no—
168#816—22no—
169#810—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⋊Q8—31no—
187C2×#121—31no—
188C2×#121—31no—
189C2×#121C2×D311yescharacteristic
190#468—64no—
191#468—64no—
192#465—64no—
193C2×#107—31no—
194C2×#107—31no—
195C2×#106—31no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#103—31no—
199C2×#102—31no—
200C2×#102C2×D311yescharacteristic
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#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×D3C2×D411yescharacteristic
225C23×D3C2×D411yescharacteristic
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—42no—
233C2×C3×D4—81no—
234C2×C3×D4—81no—
235C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
243C22×C3×C4C2×D412yes—
244C22×C3×C4#4112yes—
245C22×C3×C4C2411yescharacteristic
246C2×#67—22no—
247C2×#67—22no—
248C2×#67—22no—
249C2×#67—22no—
250C2×#67—22no—
251C2×#67—22no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—81no—
255C2×#67—81no—
256C2×#67—81no—
257C2×#67—81no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264#235—28no—
265#235—28no—
266#235—28no—
267#235—28no—
268C2×D12—22no—
269C2×D12—22no—
270C2×D12—22no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3C2×D412yes—
280C2×C4×D3C2×D412yes—
281C2×C4×D3#4112yes—
282C2×C4×D3#4112yes—
283C2×Dic6—22no—
284C2×Dic6—22no—
285C2×Dic6—22no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—21no—
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×C22⋊C4—42no—
306C3×C22⋊C4—81no—
307#217—42no—
308#217—42no—
309#217—42no—
310#217—81no—
311#214—44no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—42no—
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—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3—42no—
325C4⋊Dic3—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×Q8—31no—
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—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—62no—
383C22⋊Q8—62no—
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—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—61no—
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—62no—
419#103—62no—
420#103—62no—
421#102—22no—
422#102—22no—
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—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×D4—41no—
460C3×D4—41no—
461C3×D4—41no—
462C3×D4—41no—
463C3×D4—84no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
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#12112yes—
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C22×D411yescharacteristic
482C2×C3×C4C22×D411yescharacteristic
483C2×C3×C4C2×#4111yescharacteristic
484C2×C3×C4C2×#4111yescharacteristic
485C2×C3×C4C2×#4111yescharacteristic
486#67—28no—
487#67—28no—
488#67—84no—
489#67—84no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—41no—
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—41no—
505C2×Dic3—41no—
506C2×Dic3#12112yes—
507C2×Dic3#12112yes—
508D12—28no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—22no—
515C4×D3—22no—
516C4×D3—22no—
517Dic6—28no—
518Dic6—41no—
519Dic6—41no—
520Dic6—41no—
521Dic6—41no—
522C3×C8—22no—
523C3×C8—22no—
524C3⋊C8—22no—
525C3⋊C8#12014yes—
526C24—21no—
527C24—31no—
528C24—31no—
529C24D3×D411yescharacteristic
530#41—68no—
531#41—68no—
532#41—68no—
533#41—68no—
534C2×Q8—62no—
535C2×Q8—62no—
536C2×Q8—62no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—61no—
542C2×Q8—61no—
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×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—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—122no—
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×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#88412yes—
719C23C2×D3×D411yescharacteristic
720Q8—68no—
721Q8—121no—
722Q8—121no—
723Q8—121no—
724Q8—121no—
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#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—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—
826C22C2×#88411yescharacteristic
827C22D3×#12111yescharacteristic
828C22D3×#12111yescharacteristic
829C22#575711yescharacteristic
830C22#576211yescharacteristic
831C22#577011yescharacteristic
832C22#577111yescharacteristic
833C4—22no—
834C4—62no—
835C4—62no—
836C4—81no—
837C4—81no—
838C4—81no—
839C4—241no—
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—161no—
852C2#7493511yescharacteristic
853C2#7875211yescharacteristic
854C2#7884111yescharacteristic
855C2#8065911yescharacteristic
856C2#8066211yescharacteristic
857C2#8071711yescharacteristic
858C2#8071811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1893C2
socleC23×C3C22×D4
prime radical#82709C2
hypercenter#1893D3
hypocenterC3#32938
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
3. C2×#5042C2semidirect
4. C2×#4780C2semidirect
5. C2×#4778C2semidirect
6. #73950C2semidirect
7. C3×#1893C2semidirect
8. #71972C2semidirect
9. #70203C2semidirect
10. #70202C2semidirect
11. #69513C2semidirect
12. #68884C2semidirect
13. #68882C2semidirect
14. #68870C2semidirect
15. #68869C2semidirect
75. #1893D3semidirect
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
#827092
C2×#50422
C2×#47802
C2×#47782
#739502
C3×#18932
#719722
#702032
#702022
#695132
#688842
#688822
#688702
#688692
#329383