Finite Group Databasebeta

← #10827368

Subgroups — #10827368

Order 768.

1338 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5565C211yesmaximal, characteristic, complemented
2C2×#5113C211yesmaximal, characteristic, complemented
3#82402C211yesmaximal, characteristic, complemented
4C2×#4734C211yesmaximal, characteristic, complemented
5C3×#1869C211yesmaximal, characteristic, complemented
6#71973C211yesmaximal, characteristic, complemented
7#69962C211yesmaximal, characteristic, complemented
8#69961C211yesmaximal, characteristic, complemented
9#69932C211yesmaximal, characteristic, complemented
10#69930C211yesmaximal, characteristic, complemented
11#69926C211yesmaximal, characteristic, complemented
12#68690C211yesmaximal, characteristic, complemented
13#68679C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68672C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#939—21no—
21C2×#930C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#926C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×D24C2211yescharacteristic
28C22×#204C2211yescharacteristic
29#5565—24no—
30#5565—24no—
31C2×#898—21no—
32C2×#883—21no—
33C2×#67⋊C4—21no—
34C2×C4×D12C2211yescharacteristic
35C2×#870C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39#5223—21no—
40#5212C2211yescharacteristic
41#5113—24no—
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#816C2211yescharacteristic
50#4989—21no—
51#4959—21no—
52#4956—21no—
53#4939C2211yescharacteristic
54#4929C2211yescharacteristic
55#4734—24no—
56C3×#336C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64C2×#553—31no—
65C2×#449—31no—
66C2×#416—31no—
67#2407—31no—
68#2026—31no—
69#2025—31no—
70#2000—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1877—31no—
75#1874—31no—
76#1872—31no—
77#1869D311yescharacteristic, complemented
78#1825—31no—
79C22×C3×D4D411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—41no—
92C2×#235—41no—
93C22×D12C2311yescharacteristic
94C22×D12C2311yescharacteristic
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×Dic6C2311yescharacteristic
98C22×C3×C8—22no—
99C22×C3×C8—41no—
100C22×C3×C8—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C2×C3×C4⋊C4D411yescharacteristic
108C2×C3×C22⋊C4D411yescharacteristic
109C2×C3×C22⋊C4D411yescharacteristic
110C2×C3×C42C2311yescharacteristic
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114#939—28no—
115#930—22no—
116#930—22no—
117#930—22no—
118#930—22no—
119#930—41no—
120#930D414yescomplemented
121C2×(C2×D3)⋊C4—21no—
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—
127#926—22no—
128#926D414yescomplemented
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3—22no—
131C2×C4⋊Dic3—22no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137#924—22no—
138#924—41no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×C4×Dic3—21no—
143C2×D24—22no—
144C2×D24—22no—
145C2×D24—41no—
146C2×#204—22no—
147C2×#204—22no—
148C2×#204—41no—
149#898—28no—
150#883—28no—
151#67⋊C4—28no—
152C4×D12—22no—
153C4×D12—22no—
154#870—22no—
155#870—22no—
156C3×C22⋊C8—22no—
157C3×C22⋊C8—41no—
158C3×C22⋊C8—41no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#821—22no—
163#821—22no—
164#821—22no—
165#821—41no—
166#821—41no—
167#816—22no—
168#816—22no—
169#816—22no—
170C22×#41—31no—
171C22×SD16—31no—
172C22×D8—31no—
173C23×C8C2×D311yescharacteristic
174#553—64no—
175#553—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#123—61no—
179C2×C22⋊Q8—31no—
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—31no—
183C2×#121—61no—
184C2×C4×D4—31no—
185C2×C4×D4—61no—
186C2×C4×D4C2×D311yescharacteristic
187C2×#117—31no—
188C22×C4⋊C4—31no—
189#449—64no—
190#416—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8C2×D311yescharacteristic
200C2×C22⋊C8C2×D311yescharacteristic
201C2×C22⋊C8C2×D311yescharacteristic
202#394—61no—
203#392—61no—
204#391—31no—
205#390—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336C2×D311yescharacteristic
216#336C2×D311yescharacteristic
217C24×C3C2×D411yescharacteristic
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C23×D3—21no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—41no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
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×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2411yescharacteristic
241C2×#67—24no—
242C2×#67—24no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—81no—
251C2×#67—81no—
252C2×#67—81no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—24no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—81no—
261C22×Dic3—81no—
262#235—28no—
263#235—44no—
264#235—44no—
265#235—44no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12C2×D412yes—
277C2×D12#4112yes—
278C2×C4×D3—24no—
279C2×C4×D3—42no—
280C2×C4×D3—42no—
281C2×C4×D3—42no—
282C2×C4×D3—81no—
283C2×C4×D3—81no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6#4112yes—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—44no—
303C3×C4⋊C4—22no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—22no—
306C3×C42—21no—
307C3×C42—21no—
308#217—24no—
309#217—42no—
310#217—81no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—42no—
316(C2×D3)⋊C4—81no—
317C4⋊Dic3—24no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3—21no—
325C4⋊Dic3C2×D412yes—
326C4⋊Dic3C2×D412yes—
327C4⋊Dic3C2×D412yes—
328Dic3⋊C4—24no—
329Dic3⋊C4—24no—
330Dic3⋊C4—42no—
331C4×Dic3—24no—
332D24—44no—
333#204—44no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—121no—
339C2×#41—121no—
340C22×Q8—31no—
341C22×D4—31no—
342C22×D4—31no—
343C22×D4—61no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4—61no—
347C22×D4D1211yescharacteristic
348C23×C4—61no—
349C23×C4—61no—
350C23×C4—61no—
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×D8—62no—
357C2×D8—62no—
358C2×D8—121no—
359C22×C8—22no—
360C22×C8—41no—
361C22×C8—41no—
362C22×C8C22×D311yescharacteristic
363C22×C8C22×D311yescharacteristic
364C22×C8C22×D311yescharacteristic
365C22×C8C22×D311yescharacteristic
366#126—68no—
367#125—62no—
368#125—62no—
369#123—68no—
370C22⋊Q8—62no—
371C22⋊Q8—121no—
372#121—34no—
373#121—62no—
374#121—62no—
375#121—68no—
376#121—62no—
377#121—62no—
378#121—121no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—62no—
382C4×D4—62no—
383C4×D4—68no—
384#117—34no—
385#117—62no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4D1211yescharacteristic
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4D1211yescharacteristic
408C2×C22⋊C4D1211yescharacteristic
409C2×C42—61no—
410C2×C42C22×D311yescharacteristic
411#103—62no—
412#103—62no—
413#103—62no—
414#102—62no—
415#102—62no—
416#102—62no—
417#102—121no—
418#102—121no—
419C22⋊C8—22no—
420C22⋊C8—41no—
421C22⋊C8—41no—
422#95—61no—
423#95—61no—
424#95—61no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3#12012yes—
438C23×C3#13512yes—
439C23×C3C22×D411yescharacteristic
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C3×D4—44no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4#12012yes—
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479C2×C3×C4H(5,𝔽2)11yescharacteristic
480C2×C3×C4H(5,𝔽2)11yescharacteristic
481#67—48no—
482#67—48no—
483#67—84no—
484#67—84no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—41no—
490C2×Dic3—41no—
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—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—84no—
504D12—22no—
505D12—22no—
506D12—22no—
507D12—22no—
508D12—41no—
509D12—41no—
510D12—41no—
511D12—41no—
512C4×D3—48no—
513C4×D3—84no—
514Dic6—22no—
515Dic6—22no—
516Dic6—41no—
517Dic6—41no—
518C3×C8—41no—
519C3×C8—41no—
520C3×C8—41no—
521C3×C8—41no—
522C24—61no—
523C24—61no—
524C24C2×D1211yescharacteristic
525C24C2×D1211yescharacteristic
526#41—68no—
527#41—124no—
528#41—124no—
529#41—124no—
530C2×Q8—32no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—32no—
539C2×D4—32no—
540C2×D4—41no—
541C2×D4—64no—
542C2×D4—64no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4—122no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—241no—
561C2×D4—241no—
562C2×D4—241no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—64no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—64no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—122no—
582C22×C4—122no—
583C22×C4—122no—
584C22×C4—241no—
585C22×C4—241no—
586C22×C4—241no—
587C22×C4—241no—
588C22×C4C2×D1211yescharacteristic
589C22×C4C2×D1211yescharacteristic
590C22×C4C2×D1211yescharacteristic
591C22×C4C2×D1211yescharacteristic
592C22×C4D3×D412yes—
593C22×C4D3×D412yes—
594C22×C4C23×D311yescharacteristic
595SD16—124no—
596D8—124no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—44no—
610C4⋊C4—22no—
611C4⋊C4—32no—
612C4⋊C4—32no—
613C4⋊C4—32no—
614C4⋊C4—64no—
615C4⋊C4—64no—
616C4⋊C4—64no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—122no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—64no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—64no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—241no—
635C22⋊C4—241no—
636C42—21no—
637C42—21no—
638C42—64no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3C2×#12011yescharacteristic
654C22×C3#54611yescharacteristic
655C22×C3#54611yescharacteristic
656C22×C3C2×#13511yescharacteristic
657C22×C3#57511yescharacteristic
658C22×C3#57611yescharacteristic
659C22×C3#57711yescharacteristic
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—42no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—81no—
667C2×D3—81no—
668C2×D3—81no—
669C2×D3—81no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C3×C4—22no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4#52511yescharacteristic
679C3×C4#53511yescharacteristic
680C3×C4#54611yescharacteristic
681C3×C4#54611yescharacteristic
682Dic3—42no—
683Dic3—42no—
684Dic3—42no—
685Dic3—42no—
686Dic3—81no—
687Dic3—81no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—62no—
701C23—62no—
702C23—121no—
703C23—121no—
704C23—121no—
705C23—121no—
706C23—121no—
707C23—121no—
708C23—121no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23#88212yes—
715C23#90412yes—
716C23C22×D1211yescharacteristic
717Q8—62no—
718Q8—62no—
719Q8—121no—
720Q8—121no—
721D4—44no—
722D4—62no—
723D4—62no—
724D4—62no—
725D4—62no—
726D4—128no—
727D4—128no—
728D4—121no—
729D4—121no—
730D4—121no—
731D4—121no—
732D4—244no—
733D4—244no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—128no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—121no—
763C2×C4—121no—
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—244no—
773C2×C4—244no—
774C2×C4#88212yes—
775C2×C4C2×D3×D411yescharacteristic
776C2×C4C2×D3×D411yescharacteristic
777C2×C4#100411yescharacteristic
778C2×C4#100411yescharacteristic
779C2×C4D3×#4111yescharacteristic
780C2×C4D3×#4111yescharacteristic
781C8—41no—
782C8—41no—
783C8—41no—
784C8—41no—
785C2×C3—42no—
786C2×C3—42no—
787C2×C3#240411yescharacteristic
788C2×C3#300211yescharacteristic
789C2×C3#301211yescharacteristic
790C2×C3#329711yescharacteristic
791C2×C3#330111yescharacteristic
792C2×C3#330711yescharacteristic
793C2×C3#330911yescharacteristic
794D3—82no—
795D3—82no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—122no—
811C22—122no—
812C22—122no—
813C22—122no—
814C22—122no—
815C22—122no—
816C22—241no—
817C22—241no—
818C22—241no—
819C22—241no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22C2×#88211yescharacteristic
825C22#555411yescharacteristic
826C22#555411yescharacteristic
827C22C2×#90411yescharacteristic
828C22#574811yescharacteristic
829C22#575111yescharacteristic
830C22#575211yescharacteristic
831C4—22no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—122no—
836C4—122no—
837C4—122no—
838C4—122no—
839C4—241no—
840C4—241no—
841C4#559211yescharacteristic
842C4#561011yescharacteristic
843C4#561011yescharacteristic
844C4#565611yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—42no—
847C2—42no—
848C2—242no—
849C2—242no—
850C2#7488511yescharacteristic
851C2#7861011yescharacteristic
852C2#7867211yescharacteristic
853C2#7944111yescharacteristic
854C2#7945011yescharacteristic
855C2#7950011yescharacteristic
856C2#7951011yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1869C2
socleC23×C3C22×D4
hypercenter#1869D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#5565C2semidirect
2. C2×#5113C2semidirect
3. #82402C2semidirect
4. C2×#4734C2semidirect
5. C3×#1869C2semidirect
6. #71973C2semidirect
7. #69962C2semidirect
8. #69961C2semidirect
9. #69932C2semidirect
10. #69930C2semidirect
11. #69926C2semidirect
12. #68690C2semidirect
13. #68679C2semidirect
14. #68673C2semidirect
15. #68672C2semidirect
77. #1869D3semidirect
120. #930D4semidirect
128. #926D4semidirect
845. C3#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#55652
C2×#51132
#824022
C2×#47342
C3×#18692
#719732
#699622
#699612
#699322
#699302
#699262
#686902
#686792
#686732
#686722
#239623