Finite Group Databasebeta

← #10944296

Subgroups — #10944296

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×#5134C211yesmaximal, characteristic, complemented
3C2×#4886C211yesmaximal, characteristic, complemented
4C2×#4864C211yesmaximal, characteristic, complemented
5#74030C211yesmaximal, characteristic
6#73950C211yesmaximal, characteristic, complemented
7C3×#1809C211yesmaximal, characteristic, complemented
8#70630C211yesmaximal, characteristic, complemented
9#70578C211yesmaximal, characteristic, complemented
10#69515C211yesmaximal, characteristic, complemented
11#69514C211yesmaximal, characteristic, complemented
12#68885C211yesmaximal, characteristic, complemented
13#68884C211yesmaximal, characteristic, complemented
14#68883C211yesmaximal, characteristic, complemented
15#68882C211yesmaximal, characteristic, complemented
16#32938—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×#924C2211yescharacteristic
21C23×C3⋊C8C2211yescharacteristic
22C2×#907—24no—
23C2×#907—24no—
24C2×#907—24no—
25C22×#204C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×ΓL(1,𝔽25)C2211yescharacteristic
28C22×D3×C8C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30C2×#897C2211yescharacteristic
31C2×#897C2211yescharacteristic
32C2×#895C2211yescharacteristic
33C2×#895C2211yescharacteristic
34C2×C3×#107C2211yescharacteristic
35C2×C3×#106C2211yescharacteristic
36C3×#380C2211yescharacteristic
37C3×#380C2211yescharacteristic
38#5134—24no—
39C2×#821C2211yescharacteristic
40C2×#818C2211yescharacteristic
41C2×#816C2211yescharacteristic
42#4987C2211yescharacteristic
43#4987C2211yescharacteristic
44#4987C2211yescharacteristic
45#4987C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50#4961—21no—
51#4961—21no—
52#4960—21no—
53#4960—21no—
54#4886—24no—
55#4864—24no—
56#4673—21no—
57#4672—21no—
58#4671—21no—
59#4656—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
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#1892—31no—
78#1809—31no—
79#1809D311yescharacteristic, complemented
80#1808—31no—
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67D411yescharacteristic
84C22×#67D411yescharacteristic
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C22×D12—21no—
92C22×D12—21no—
93C22×D12D411yescharacteristic
94C22×D12C2311yescharacteristic
95C22×C4×D3C2311yescharacteristic
96C22×C4×D3C2311yescharacteristic
97C22×Dic6D411yescharacteristic
98C22×Dic6C2311yescharacteristic
99C2×C3×M16—22no—
100C2×C3×M16—22no—
101C2×C3×M16D414yescomplemented
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×#217—21no—
111#930—22no—
112#930—22no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126#924—22no—
127#924—22no—
128C2×Dic3⋊C4—21no—
129C22×C3⋊C8—22no—
130C22×C3⋊C8—22no—
131C22×C3⋊C8—22no—
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134#907—232no—
135C2×#204—22no—
136C2×#204—22no—
137C2×#204—22no—
138C2×ΓL(1,𝔽25)—22no—
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)—22no—
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)D414yescomplemented
144C2×D3×C8—22no—
145C2×D3×C8—22no—
146C2×D3×C8—22no—
147C2×D3×C8—22no—
148C2×D3×C8—22no—
149C2×D3×C8D414yescomplemented
150#897—22no—
151#897—22no—
152#897—22no—
153#897—22no—
154#895—22no—
155#895—22no—
156#895—22no—
157#895—22no—
158C3×#107—22no—
159C3×#106—22no—
160C3×#95—21no—
161C3×#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166#821—22no—
167#818—22no—
168#816—22no—
169#810—22no—
170#810—22no—
171#809—22no—
172#809—22no—
173C22×#41—31no—
174C22×SD16—31no—
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⋊Q8—31no—
187C2×#121—31no—
188C2×#121—31no—
189C2×#121—31no—
190#468—64no—
191#468—64no—
192#465—64no—
193C2×#107—31no—
194C2×#107C2×D311yescharacteristic
195C2×#106C2×D311yescharacteristic
196C2×#103—31no—
197C2×#103—31no—
198C2×#103—31no—
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#380C2×D311yescharacteristic
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
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4C2×D412yes—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4#4112yes—
237C22×C3×C4C2411yescharacteristic
238C2×#67—22no—
239C2×#67—22no—
240C2×#67—22no—
241C2×#67—22no—
242C2×#67—22no—
243C2×#67—22no—
244C2×#67—42no—
245C2×#67—81no—
246C2×#67—81no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252#235—28no—
253#235—28no—
254#235—28no—
255#235—28no—
256C2×D12—22no—
257C2×D12—22no—
258C2×D12—22no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—42no—
266C2×D12—42no—
267C2×D12—81no—
268C2×D12—81no—
269C2×D12—81no—
270C2×D12—81no—
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—
292C3×M16—28no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8C2×D412yes—
296C2×C3×C8C2×D412yes—
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—21no—
306C3×C4⋊C4—21no—
307C3×C22⋊C4—81no—
308C3×C22⋊C4—81no—
309#217—42no—
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—42no—
324C4⋊Dic3—42no—
325Dic3⋊C4—42no—
326C2×C3⋊C8—28no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8C2×D412yes—
332C2×C3⋊C8C2×D412yes—
333#204—44no—
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—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—22no—
361C2×M16—22no—
362C2×M16—34no—
363C2×M16—62no—
364C2×M16—62no—
365C2×M16—62no—
366C2×M16—62no—
367C2×M16—62no—
368C2×M16D1214yescomplemented
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—62no—
383C22⋊Q8—62no—
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—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4C22×D311yescharacteristic
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—22no—
416#107—62no—
417#106—22no—
418#103—62no—
419#103—62no—
420#103—62no—
421#102—62no—
422#102—62no—
423#102—62no—
424#95—21no—
425#95—21no—
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—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
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#12112yes—
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4C2×#4111yescharacteristic
483C2×C3×C4C2×#4111yescharacteristic
484#67—28no—
485#67—28no—
486#67—84no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3#12112yes—
501C2×Dic3#12112yes—
502D12—28no—
503D12—41no—
504D12—41no—
505D12—41no—
506D12—41no—
507D12—84no—
508D12—84no—
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#12014yes—
524C3⋊C8—22no—
525C3⋊C8—22no—
526C24—31no—
527C24—31no—
528C24—61no—
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—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×C4C2×D1212yes—
593C22×C4D3×D411yescharacteristic
594C22×C4#23912yes—
595C22×C4C23×D311yescharacteristic
596SD16—124no—
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×C8C2×D1212yes—
612C2×C8C2×D1212yes—
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—21no—
622C4⋊C4—21no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—122no—
628C4⋊C4—122no—
629C4⋊C4—122no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—122no—
635C22⋊C4—122no—
636C22⋊C4—122no—
637C22⋊C4—122no—
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#89512yes—
719C23C2×D3×D411yescharacteristic
720Q8—68no—
721Q8—121no—
722Q8—121no—
723Q8—121no—
724Q8—121no—
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#89512yes—
777C2×C4C22×D1211yescharacteristic
778C2×C4C2×D3×D411yescharacteristic
779C2×C4C2×D3×D411yescharacteristic
780C2×C4C2×#23911yescharacteristic
781C2×C4D3×#4111yescharacteristic
782C2×C4D3×#4111yescharacteristic
783C8—22no—
784C8—62no—
785C8—62no—
786C8#88214yes—
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×#89511yescharacteristic
827C22D3×#12111yescharacteristic
828C22D3×#12111yescharacteristic
829C22#577411yescharacteristic
830C22#577511yescharacteristic
831C22#577811yescharacteristic
832C22#577911yescharacteristic
833C4—22no—
834C4—62no—
835C4—62no—
836C4—81no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4—241no—
841C4—241no—
842C4—241no—
843C4C2×#88211yescharacteristic
844C4#552411yescharacteristic
845C4#562711yescharacteristic
846C4#562711yescharacteristic
847C3#3293811yescharacteristic, complemented, Sylow
848C2—42no—
849C2—122no—
850C2—122no—
851C2—481no—
852C2#7404811yescharacteristic
853C2#7921311yescharacteristic
854C2#7921411yescharacteristic
855C2#8080711yescharacteristic
856C2#8080811yescharacteristic
857C2#8086711yescharacteristic
858C2#8090711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1809C2
socleC23×C3C22×D4
prime radical#74030C2
hypercenter#1809D3
hypocenterC3#32938
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
1. C22×#907C2semidirect
2. C2×#5134C2semidirect
3. C2×#4886C2semidirect
4. C2×#4864C2semidirect
6. #73950C2semidirect
7. C3×#1809C2semidirect
8. #70630C2semidirect
9. #70578C2semidirect
10. #69515C2semidirect
11. #69514C2semidirect
12. #68885C2semidirect
13. #68884C2semidirect
14. #68883C2semidirect
15. #68882C2semidirect
79. #1809D3semidirect
101. C2×C3×M16D4semidirect
143. C2×ΓL(1,𝔽25)D4semidirect
149. C2×D3×C8D4semidirect
368. C2×M16D12semidirect
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×#51342
C2×#48862
C2×#48642
#740302
#739502
C3×#18092
#706302
#705782
#695152
#695142
#688852
#688842
#688832
#688822
#329383