Finite Group Databasebeta

← D3×#5190 #11874389

Subgroups — D3×#5190 #11874389

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Q16C211yesmaximal, characteristic, complemented
2D3×#947C211yesmaximal, characteristic
3D3×#944C211yesmaximal, characteristic, complemented
4C2×D3×#216C211yesmaximal, characteristic, complemented
5C2×D3×#215C211yesmaximal, characteristic
6C2×D3×#204C211yesmaximal, characteristic
7#10592889C211yesmaximal, characteristic, complemented
8C3×#5190C211yesmaximal, characteristic, complemented
9#10591629C211yesmaximal, characteristic, complemented
10#10591627C211yesmaximal, characteristic, complemented
11#10591611C211yesmaximal, characteristic, complemented
12#10591608C211yesmaximal, characteristic, complemented
13#10590899C211yesmaximal, characteristic, complemented
14#10590870C211yesmaximal, characteristic, complemented
15D3×#815C211yesmaximal, characteristic, complemented
16C2×#5190—31nomaximal
17D3×#497—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic, complemented
23#64156C2211yescharacteristic
24#64153C2211yescharacteristic, complemented
25C2×#3756C2211yescharacteristic, complemented
26C2×#3755C2211yescharacteristic
27C2×#3744C2211yescharacteristic
28C3×#947C2211yescharacteristic
29C3×#944C2211yescharacteristic, complemented
30C2×C3×#216C2211yescharacteristic, complemented
31C2×C3×#216C2211yescharacteristic, complemented
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#215C2211yescharacteristic
34C3×D3×Q16—24no—
35C2×C3×Dic12C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic
38D3×#216—24no—
39D3×#215—24no—
40D3×(C2×D3)⋊C4—22no—
41#63907—22no—
42D3×Dic3⋊C4—22no—
43C4×D3×Dic3C2211yescharacteristic
44#63873C2211yescharacteristic, complemented
45#63866C2211yescharacteristic, complemented
46#63864C2211yescharacteristic
47#63863C2211yescharacteristic
48#63839—22no—
49C2×#3719C2211yescharacteristic, complemented
50C2×#3718C2211yescharacteristic, complemented
51C2×#3717C2211yescharacteristic
52C2×#3717C2211yescharacteristic
53C2×#3716C2211yescharacteristic
54C2×#3715C2211yescharacteristic
55C2×D3×C3⋊C8C2211yescharacteristic
56D3×#204—24no—
57#63642C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59#63555C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C22×C3×Q16—31no—
62C2×#947—31no—
63C2×#944—31no—
64C22×#216—31no—
65C22×#215—31no—
66C2×D3×Q16—31no—
67C2×D3×Q16D311yescharacteristic, complemented
68C2×D3×SD16—31no—
69C2×D3×SD16—31no—
70C22×#204—31no—
71D3×C4⋊Q8—31no—
72D3×#124—31no—
73C3×#497—31no—
74#5190—31no—
75#5190—31no—
76#5190—31no—
77#5190—31no—
78#5190—31no—
79#5190—31no—
80#5190—31no—
81#5190—31no—
82#5190—31no—
83#5190—61no—
84#5190D311yescharacteristic, direct product factor
85#5167—31no—
86#5167—31no—
87C2×#815—31no—
88#5086—31no—
89#5060—31no—
90#4715—31no—
91D3×#97—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C3×D3×Q8—22no—
98C3×D3×Q8—22no—
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×#626—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3D412yes—
114D3×D12—22no—
115D3×D12—22no—
116D3×Dic6—22no—
117D3×Dic6—22no—
118C32×Q16—22no—
119C2×C32×C8C2311yescharacteristic
120#3756—22no—
121#3755—22no—
122#3752—22no—
123#3750—22no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744—22no—
127C3×#216—22no—
128C3×#216—22no—
129C3×#216—22no—
130C3×#215—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×Dic12—22no—
137C3×#204—22no—
138C3×D3×C8D414yes—
139#3724—22no—
140Dic3⋊Dic3—22no—
141#3722—22no—
142(C2×D3)⋊Dic3—22no—
143Dic32D412yes—
144#3719—22no—
145#3718—22no—
146#3717—22no—
147#3717—22no—
148#3716—22no—
149#3715—22no—
150D3×C3⋊C8D414yes—
151C2×#497—91noSylow
152C22×C3×Q8—31no—
153C22×C3×Q8—31no—
154C2×D3×Q8—31no—
155C2×D3×Q8C2×D311yescharacteristic
156C2×D3×Q8C2×D311yescharacteristic
157C2×D3×D4—31no—
158C22×D12—31no—
159C22×Dic6—31no—
160C2×C3×Q16—21no—
161C2×C3×Q16—31no—
162C2×C3×Q16—31no—
163C2×C3×Q16—31no—
164C2×C3×Q16—31no—
165C2×C3×Q16—64no—
166C2×C3×Q16C2×D311yescharacteristic, complemented
167C2×C3×Q16C2×D311yescharacteristic, complemented
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C22×C3×C8—31no—
171C3×C4⋊Q8—31no—
172C3×#124—31no—
173#947—31no—
174#947—31no—
175#947—31no—
176#947—31no—
177#947—61no—
178#947—62no—
179#947C2×D311yescharacteristic
180#944—31no—
181#944—31no—
182#944—31no—
183#944—31no—
184#944—31no—
185#944—61no—
186#944—62no—
187#944C2×D311yescharacteristic, complemented
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—31no—
191C2×#216—31no—
192C2×#216—31no—
193C2×#216—61no—
194C2×#216—64no—
195C2×#216C2×D311yescharacteristic, complemented
196C2×#216C2×D311yescharacteristic, complemented
197C2×#216C2×D311yescharacteristic, complemented
198C2×#215—31no—
199C2×#215—31no—
200C2×#215—31no—
201C2×#215—31no—
202C2×#215—31no—
203C2×#215—61no—
204C2×#215—64no—
205C2×#215C2×D311yescharacteristic
206#936—31no—
207C2×#214—31no—
208C2×#214—31no—
209C2×(C2×D3)⋊C4—62no—
210C2×Dic3⋊C4—62no—
211C2×C4×Dic3—31no—
212C22×C3⋊C8—31no—
213D3×Q16—24no—
214D3×Q16—64no—
215D3×SD16—64no—
216D3×SD16—64no—
217C2×Dic12—31no—
218C2×Dic12C2×D311yescharacteristic, complemented
219C2×#204—31no—
220C2×#204—31no—
221C2×#204—31no—
222C2×#204—31no—
223C2×#204—31no—
224C2×#204—61no—
225C2×#204—64no—
226C2×#204C2×D311yescharacteristic
227C2×D3×C8—31no—
228C2×D3×C8C2×D311yescharacteristic
229D3×C4⋊C4—62no—
230#888—62no—
231#885—62no—
232D3×C22⋊C4—62no—
233#875—31no—
234C42×D3—31no—
235#869—31no—
236C3×#97—31no—
237#815—31no—
238#815—31no—
239#815—31no—
240#815—31no—
241#815—31no—
242#815—61no—
243#815C2×D311yescharacteristic, complemented
244#803—31no—
245C22×C3⋊D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3C2×D411yescharacteristic
248C2×D32—42no—
249C2×D32—44no—
250C32×Q8—21no—
251C32×Q8—21no—
252C32×Q8—21no—
253C32×Q8—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2411yescharacteristic
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3C2×D412yes—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261#634—21no—
262#634—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D412yes—
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×C4×D3C2×D412yes—
273C3×C4×D3C2×D412yes—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×Dic6—21no—
280C3×Dic6—42no—
281C3×Dic6—42no—
282#627—42no—
283#626—42no—
284D3×Dic3—24no—
285D3×Dic3—42no—
286C32×C8C2×D412yes—
287C3⋊(C3⋊C8)C2×D412yes—
288C3×C3⋊C8C2×D412yes—
289C3×C3⋊C8C2×D412yes—
290C22×Q16—31no—
291C22×Q16—91no—
292C22×SD16—91no—
293C22×SD16—91no—
294C2×C4⋊Q8—91no—
295C2×#124—91no—
296#497—31no—
297#497—91no—
298#497—91no—
299#497—91no—
300#497—91no—
301#497—91no—
302#497—91no—
303#497—91no—
304C2×#97—91no—
305C23×D3—61no—
306C23×D3—61no—
307C2×C3×Q8—21no—
308C2×C3×Q8—21no—
309C2×C3×Q8—31no—
310C2×C3×Q8—31no—
311C2×C3×Q8—31no—
312C2×C3×Q8—61no—
313C2×C3×Q8—61no—
314C2×C3×Q8—62no—
315C2×C3×Q8—62no—
316C2×C3×Q8—62no—
317C2×C3×Q8—62no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×Q8C22×D311yescharacteristic
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×D4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C2×#67—61no—
327C22×Dic3—32no—
328C22×Dic3—61no—
329D3×Q8—22no—
330D3×Q8—22no—
331D3×Q8—22no—
332D3×Q8—22no—
333D3×Q8—62no—
334D3×Q8—62no—
335D3×D4—62no—
336D3×D4—62no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—62no—
341C2×D12—62no—
342C2×D12—61no—
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—21no—
345C2×C4×D3—21no—
346C2×C4×D3—32no—
347C2×C4×D3—61no—
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—21no—
350C2×Dic6—21no—
351C2×Dic6—31no—
352C2×Dic6—31no—
353C2×Dic6—61no—
354C2×Dic6—62no—
355C2×Dic6—62no—
356C2×Dic6—61no—
357C2×Dic6—61no—
358C2×Dic6C22×D311yescharacteristic
359C2×Dic6C22×D311yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C3×Q16—22no—
362C3×Q16—22no—
363C3×Q16—42no—
364C3×Q16—62no—
365C3×Q16—62no—
366C3×Q16—62no—
367C3×Q16—62no—
368C3×SD16—62no—
369C3×SD16—62no—
370C2×C3×C8—21no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C2×C3×C8—34no—
374C2×C3×C8C22×D311yescharacteristic
375C2×C3×C8C22×D311yescharacteristic
376C3×C4⋊C4—62no—
377C3×C22⋊C4—62no—
378C3×C42—31no—
379#217—62no—
380#216—22no—
381#216—22no—
382#216—22no—
383#216—62no—
384#216—62no—
385#216—62no—
386#216—62no—
387#216—62no—
388#216—122no—
389#215—22no—
390#215—62no—
391#215—62no—
392#215—62no—
393#215—62no—
394#215—62no—
395#215—122no—
396#214—62no—
397#214—62no—
398(C2×D3)⋊C4—22no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—122no—
405C4⋊Dic3—62no—
406Dic3⋊C4—22no—
407Dic3⋊C4—62no—
408Dic3⋊C4—62no—
409Dic3⋊C4—62no—
410Dic3⋊C4—62no—
411Dic3⋊C4—62no—
412Dic3⋊C4—122no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—32no—
416C4×Dic3—32no—
417C4×Dic3—61no—
418C4×Dic3C22×D311yescharacteristic
419C2×C3⋊C8—31no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—34no—
422C2×C3⋊C8—61no—
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425Dic12—22no—
426Dic12—62no—
427#204—22no—
428#204—62no—
429#204—62no—
430#204—62no—
431#204—62no—
432#204—62no—
433#204—122no—
434D3×C8—34no—
435D3×C8#6714yes—
436C22×C32C22×D411yescharacteristic
437C2×C3⋊D3—41no—
438C2×C3⋊D3—42no—
439C2×C3×D3—41no—
440C2×C3×D3—42no—
441C2×C3×D3#12712yes—
442C2×C3×D3#13714yes—
443D32—84no—
444C32×C4—41no—
445C32×C4—41no—
446C32×C4C22×D411yescharacteristic
447C32×C4C22×D411yescharacteristic
448C3⋊Dic3—22no—
449C3⋊Dic3—41no—
450C3×Dic3—22no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3#12712yes—
455C22×Q8—31no—
456C22×Q8—31no—
457C22×Q8—91no—
458C22×D4—91no—
459C2×Q16—31no—
460C2×Q16—31no—
461C2×Q16—31no—
462C2×Q16—31no—
463C2×Q16—64no—
464C2×Q16—91no—
465C2×Q16—91no—
466C2×Q16—91no—
467C2×Q16—184no—
468C2×Q16D3211yescharacteristic, complemented
469C2×SD16—31no—
470C2×SD16—31no—
471C2×SD16—91no—
472C2×SD16—91no—
473C2×SD16—91no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—184no—
478C2×SD16—184no—
479C22×C8—31no—
480C22×C8—91no—
481C4⋊Q8—31no—
482C4⋊Q8—91no—
483C4⋊Q8—91no—
484C4⋊Q8—91no—
485C4⋊Q8—182no—
486#124—31no—
487#124—91no—
488#124—91no—
489#124—91no—
490#124—182no—
491C2×C4⋊C4—182no—
492C2×C22⋊C4—182no—
493C2×C42—91no—
494#97—31no—
495#97—91no—
496#97—91no—
497#97—91no—
498C23×C3—31no—
499C23×C3—61no—
500C22×D3—21no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—121no—
504C22×D3—122no—
505C22×D3—124no—
506C22×D3—124no—
507C22×D3—122no—
508C22×D3D3×D411yescharacteristic
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—21no—
517C3×Q8—41no—
518C3×Q8—41no—
519C3×Q8—41no—
520C3×Q8—41no—
521C3×Q8—61no—
522C3×Q8—61no—
523C3×Q8—61no—
524C3×Q8—61no—
525C3×Q8—61no—
526C3×Q8—61no—
527C3×Q8—122no—
528C3×Q8—122no—
529C3×D4—61no—
530C3×D4—61no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—31no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—32no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—122no—
546C2×C3×C4—122no—
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549#67—122no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—62no—
556C2×Dic3—64no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—122no—
561C2×Dic3D3×D412yes—
562C2×Dic3D3×D411yescharacteristic
563D12—21no—
564D12—21no—
565D12—61no—
566D12—61no—
567D12—61no—
568D12—61no—
569D12—121no—
570D12—121no—
571D12—122no—
572C4×D3—42no—
573C4×D3—42no—
574C4×D3—64no—
575C4×D3—122no—
576C4×D3D3×D412yes—
577C4×D3C2×#6712yes—
578Dic6—21no—
579Dic6—21no—
580Dic6—21no—
581Dic6—21no—
582Dic6—21no—
583Dic6—21no—
584Dic6—42no—
585Dic6—42no—
586Dic6—61no—
587Dic6—61no—
588Dic6—61no—
589Dic6—61no—
590Dic6—121no—
591Dic6—121no—
592Dic6—122no—
593Dic6—122no—
594C3×C8—22no—
595C3×C8—32no—
596C3×C8—32no—
597C3×C8D3×D412yes—
598C3×C8C2×#6712yes—
599C3⋊C8—32no—
600C3⋊C8—32no—
601C3⋊C8—62no—
602C3⋊C8D3×D412yes—
603C3⋊C8C2×#6712yes—
604C2×C32C2×#12711yescharacteristic
605C2×C32C2×#13712yes—
606C3⋊D3—81no—
607C3×D3—81no—
608C3×D3#49714yescomplemented
609C24—181no—
610C2×Q8—31no—
611C2×Q8—31no—
612C2×Q8—31no—
613C2×Q8—61no—
614C2×Q8—61no—
615C2×Q8—62no—
616C2×Q8—62no—
617C2×Q8—62no—
618C2×Q8—62no—
619C2×Q8—91no—
620C2×Q8—181no—
621C2×Q8—182no—
622C2×Q8—182no—
623C2×Q8C2×D3211yescharacteristic
624C2×Q8C2×D3211yescharacteristic
625C2×D4—31no—
626C2×D4—91no—
627C2×D4—182no—
628C2×D4—182no—
629C2×D4—181no—
630C22×C4—31no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—92no—
634C22×C4—181no—
635Q16—22no—
636Q16—62no—
637Q16—62no—
638Q16—62no—
639Q16—62no—
640Q16—182no—
641Q16—182no—
642Q16—182no—
643SD16—62no—
644SD16—62no—
645SD16—182no—
646SD16—182no—
647SD16—182no—
648SD16—182no—
649SD16—182no—
650SD16—182no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—34no—
654C2×C8—94no—
655C2×C8—91no—
656C2×C8C2×D3211yescharacteristic
657C4⋊C4—62no—
658C4⋊C4—182no—
659C4⋊C4—182no—
660C4⋊C4—182no—
661C22⋊C4—62no—
662C22⋊C4—182no—
663C22⋊C4—182no—
664C22⋊C4—182no—
665C42—31no—
666C42—92no—
667C42—91no—
668C22×C3—21no—
669C22×C3—32no—
670C22×C3—34no—
671C22×C3—122no—
672C22×C3—121no—
673C22×C3C2×D3×D411yescharacteristic
674C22×C3C2×D3×D411yescharacteristic
675C2×D3—41no—
676C2×D3—42no—
677C2×D3—121no—
678C2×D3—122no—
679C2×D3—122no—
680C2×D3—121no—
681C2×D3—241no—
682C2×D3—242no—
683C2×D3—244no—
684C2×D3—244no—
685C2×D3#91814yes—
686C2×D3#94012yes—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—32no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—62no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C2×D3×D411yescharacteristic
701C3×C4C2×D3×D411yescharacteristic
702C3×C4C2×D3×D411yescharacteristic
703C3×C4C22×#6711yescharacteristic
704Dic3—22no—
705Dic3—41no—
706Dic3—41no—
707Dic3—41no—
708Dic3—62no—
709Dic3—62no—
710Dic3—122no—
711Dic3—121no—
712Dic3—121no—
713Dic3—241no—
714Dic3#94012yes—
715C32C2×#49711yescharacteristic, complemented, Sylow
716C23—31no—
717C23—61no—
718C23—181no—
719C23—362no—
720C23—364no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—61no—
726Q8—61no—
727Q8—61no—
728Q8—61no—
729Q8—61no—
730Q8—61no—
731Q8—122no—
732Q8—122no—
733Q8—181no—
734Q8—181no—
735Q8—362no—
736D4—61no—
737D4—61no—
738D4—181no—
739D4—181no—
740D4—362no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—31no—
744C2×C4—32no—
745C2×C4—32no—
746C2×C4—32no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—92no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—184no—
754C2×C4—181no—
755C2×C4—362no—
756C2×C4C22×D3211yescharacteristic
757C8—32no—
758C8—32no—
759C8—92no—
760C8D3×#6712yes—
761C2×C3—22no—
762C2×C3—21no—
763C2×C3—34no—
764C2×C3—241no—
765C2×C3D3×#12711yescharacteristic
766C2×C3C2×#91812yes—
767C2×C3D3×#13712yes—
768C2×C3C2×#94011yescharacteristic
769D3—81no—
770D3—241no—
771D3—241no—
772D3—481no—
773D3#519014yesdirect product factor
774C22—34no—
775C22—32no—
776C22—122no—
777C22—121no—
778C22—362no—
779C22—361no—
780C22—724no—
781C22D32×D411yescharacteristic
782C4—32no—
783C4—41no—
784C4—41no—
785C4—62no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—182no—
790C4—361no—
791C4D32×D411yescharacteristic
792C4C2×D3×#6711yescharacteristic
793C3—21no—
794C3D3×#49711yescharacteristic, complemented
795C3C2×#519011yescharacteristic, complemented
796C2—34no—
797C2—241no—
798C2—721no—
799C2D3×#91812yes—
800C2D3×#94011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC2×Q16D32
hypocenterC32C2×#497
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Q16C2semidirect
3. D3×#944C2semidirect
4. C2×D3×#216C2semidirect
7. #10592889C2semidirect
8. C3×#5190C2semidirect
9. #10591629C2semidirect
10. #10591627C2semidirect
11. #10591611C2semidirect
12. #10591608C2semidirect
13. #10590899C2semidirect
14. #10590870C2semidirect
15. D3×#815C2semidirect
22. C2×C32×Q16C22semidirect
24. #64153C22semidirect
25. C2×#3756C22semidirect
29. C3×#944C22semidirect
30. C2×C3×#216C22semidirect
31. C2×C3×#216C22semidirect
32. C2×C3×#216C22semidirect
35. C2×C3×Dic12C22semidirect
44. #63873C22semidirect
45. #63866C22semidirect
49. C2×#3719C22semidirect
50. C2×#3718C22semidirect
57. #63642C22semidirect
58. C3×#815C22semidirect
59. #63555C22semidirect
60. #63554C22semidirect
67. C2×D3×Q16D3semidirect
84. #5190D3direct (N × H)
166. C2×C3×Q16C2×D3semidirect
167. C2×C3×Q16C2×D3semidirect
187. #944C2×D3semidirect
195. C2×#216C2×D3semidirect
196. C2×#216C2×D3semidirect
197. C2×#216C2×D3semidirect
218. C2×Dic12C2×D3semidirect
243. #815C2×D3semidirect
468. C2×Q16D32semidirect
608. C3×D3#497semidirect
715. C32C2×#497semidirect
773. D3#5190direct (N × H)
794. C3D3×#497semidirect
795. C3C2×#5190semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
D3×#9472
D3×#9442
C2×D3×#2162
C2×D3×#2152
C2×D3×#2042
#105928892
C3×#51902
#105916292
#105916272
#105916112
#105916082
#105908992
#105908702
D3×#8152
C2×#51903
D3×#4973