Finite Group Databasebeta

← #11889714

Subgroups — #11889714

Order 1152.

914 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic
2#10594988C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591488C211yesmaximal, characteristic, complemented
6#10591463C211yesmaximal, characteristic, complemented
7#10591462C211yesmaximal, characteristic, complemented
8#10591441C211yesmaximal, characteristic, complemented
9#10591414C211yesmaximal, characteristic, complemented
10#10591413C211yesmaximal, characteristic, complemented
11#10591410C211yesmaximal, characteristic, complemented
12#10591405C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14#10591155C211yesmaximal, characteristic, complemented
15#10591132C211yesmaximal, characteristic, complemented
16#83498—31nomaximal
17#78763—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64133C2211yescharacteristic
23C3×#953—21no—
24C2×C3×#217—21no—
25C3×#939—21no—
26C3×#938C2211yescharacteristic
27C3×#936C2211yescharacteristic
28C3×#935—21no—
29C3×D4×Dic3C2211yescharacteristic
30C3×C4×#67C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34Dic3×#67—21no—
35#63964—21no—
36#63918C2211yescharacteristic, complemented
37#63899—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63857C2211yescharacteristic, complemented
40#63846—21no—
41#63844C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×#3711C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51#63576C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#546—31no—
62#5806D311yescharacteristic
63#5543—31no—
64#5511—31no—
65C2×C3×#102—31no—
66#5239—31no—
67#5232—31no—
68#5218—31no—
69#5218—31no—
70#5218—61no—
71C2×#832D311yescharacteristic, complemented
72#5116—31no—
73#5111—31no—
74#5055—31no—
75#5054—31no—
76#5051—31no—
77#5044—31no—
78#5042—31no—
79#5033—31no—
80#5018—31no—
81#5011—31no—
82#5007—31no—
83#4970—31no—
84#4783—31no—
85#4780—31no—
86#4774—31no—
87#4771—31no—
88#4767—31no—
89#4765—31no—
90#4759—31no—
91#4757—31no—
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—21no—
95C2×C32×D4—41no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#237—22no—
107C3×#237—41no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×D3×Dic3—21no—
112#3757—21no—
113#3754—22no—
114#3754—41no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×#217D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8—41no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3719—41no—
143#3711—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—21no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C2×D311yescharacteristic
149C2×#237C2×D311yescharacteristic
150C22×C3×C8—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×#121—31no—
155C3×#121—61no—
156C3×#120—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—61no—
161#953—21no—
162C2×#217—21no—
163C2×#216—31no—
164#939—21no—
165#938C2×D311yescharacteristic
166#936C2×D311yescharacteristic
167#935—21no—
168D4×Dic3—61no—
169D4×Dic3C2×D311yescharacteristic
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—31no—
174C2×#214—61no—
175C2×#214—61no—
176C4×#67—61no—
177C4×#67C2×D311yescharacteristic
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3C2×D311yescharacteristic
180#924—31no—
181#924—31no—
182#924—31no—
183#924—61no—
184#924—61no—
185#924C2×D311yescharacteristic
186C2×#208—31no—
187C22×C3⋊C8C2×D311yescharacteristic
188C2×Dic12—31no—
189C2×ΓL(1,𝔽25)—31no—
190#897—31no—
191#896—61no—
192D3×C4⋊C4—31no—
193#890—61no—
194#889—61no—
195#888—31no—
196#887—31no—
197#878—61no—
198#878—61no—
199#869—31no—
200C4×Dic6—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832—61no—
214#832C2×D311yescharacteristic
215#832C2×D311yescharacteristic
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#816—31no—
225#816—31no—
226#815—31no—
227Dic3⋊C8—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—42no—
241C23×C32—42no—
242C23×C32—81no—
243C23×C32C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—42no—
249C32×D4#4112yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256#634—21no—
257#634—21no—
258C3×#67—22no—
259C3×#67—42no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3—81no—
267C2×C3×Dic3—81no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#627—81no—
276D3×Dic3—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—31no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—31no—
296C24×C3—21no—
297C24×C3—21no—
298C24×C3—41no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—22no—
303C2×C3×D4—22no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—41no—
310C2×C3×D4—42no—
311C2×C3×D4—41no—
312C2×C3×D4—41no—
313C2×C3×D4—42no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C22×D311yescharacteristic
319C2×C3×D4C22×D311yescharacteristic
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—21no—
328C2×#67—21no—
329C2×#67#6711yescharacteristic
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—61no—
334#237—22no—
335#237—41no—
336C2×C4×D3—61no—
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—61no—
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—31no—
361#217—21no—
362#217—21no—
363#217—21no—
364#217—21no—
365#217—21no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—121no—
370#217#6711yescharacteristic
371#216—121no—
372#214—62no—
373#214—62no—
374#214—122no—
375#214—121no—
376#214—121no—
377#214—122no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4#6711yescharacteristic
380C4⋊Dic3—21no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
399Dic3⋊C4#6711yescharacteristic
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3C22×D311yescharacteristic
403#208—121no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—41no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413Dic12—121no—
414ΓL(1,𝔽25)—121no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—84no—
424C22×C32#13712yes—
425C22×C32C22×D411yescharacteristic
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C32×C4—21no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—31no—
442C22×D4D3211yescharacteristic
443C2×Q16—91no—
444C2×SD16—91no—
445C2×SD16—91no—
446C2×M16—91no—
447C22×C8—31no—
448C4⋊Q8—91no—
449#125—181no—
450#124—31no—
451#123—61no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455C22⋊Q8—181no—
456C22⋊Q8—181no—
457#121—31no—
458#121—61no—
459#120—61no—
460C4×Q8—91no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—181no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—91no—
466C2×C22⋊C4—61no—
467#107—91no—
468#107—91no—
469#107—91no—
470C4⋊C8—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481C22⋊C8—91no—
482C22⋊C8—91no—
483#97—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—44no—
495C23×C3—42no—
496C23×C3—42no—
497C23×C3—82no—
498C23×C3—81no—
499C23×C3—81no—
500C23×C3—82no—
501C23×C3D3×D411yescharacteristic
502C23×C3C2×#6711yescharacteristic
503C22×D3C2×#6711yescharacteristic
504C3×Q8—61no—
505C3×Q8—61no—
506C3×D4—22no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—22no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—42no—
517C3×D4—42no—
518C3×D4—44no—
519C3×D4—62no—
520C3×D4—122no—
521C3×D4—241no—
522C3×D4#23512yes—
523C3×D4#23712yes—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—122no—
542C2×C3×C4—241no—
543C2×C3×C4—241no—
544C2×C3×C4D3×D411yescharacteristic
545C2×C3×C4C2×#6711yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548#67—22no—
549#67—42no—
550#67—81no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—42no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—81no—
561C2×Dic3—81no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—241no—
565C2×Dic3C2×#6711yescharacteristic
566C2×Dic3C2×#6711yescharacteristic
567C2×Dic3C2×#6711yescharacteristic
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—241no—
571Dic6—21no—
572Dic6—21no—
573Dic6—61no—
574Dic6—61no—
575Dic6—61no—
576Dic6—61no—
577Dic6—121no—
578Dic6—121no—
579Dic6—241no—
580Dic6—241no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—61no—
589C3⋊C8—121no—
590C3⋊C8—121no—
591C2×C32—22no—
592C2×C32—42no—
593C2×C32—81no—
594C2×C32#54611yescharacteristic
595C2×C32C2×#13711yescharacteristic
596C2×C32#57611yescharacteristic
597C3×D3—41no—
598C24—21no—
599#41—62no—
600#41—121no—
601C2×Q8—31no—
602C2×Q8—91no—
603C2×Q8—181no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—31no—
607C2×D4—41no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4C2×D3211yescharacteristic
611C2×D4C2×D3211yescharacteristic
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—181no—
617C22×C4C2×D3211yescharacteristic
618Q16—361no—
619SD16—182no—
620SD16—361no—
621M16—361no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—91no—
625C2×C8—91no—
626C2×C8—121no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—181no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—22no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—84no—
680C22×C3—84no—
681C22×C3—88no—
682C22×C3#91512yes—
683C22×C3#95112yes—
684C22×C3C2×D3×D411yescharacteristic
685C22×C3C22×#6711yescharacteristic
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—41no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4C2×#23511yescharacteristic
702C3×C4C2×#23711yescharacteristic
703C3×C4#100411yescharacteristic
704C3×C4#100411yescharacteristic
705Dic3—21no—
706Dic3—21no—
707Dic3—21no—
708Dic3—41no—
709Dic3—41no—
710Dic3—41no—
711Dic3—41no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—241no—
717Dic3—241no—
718C32#331411yescharacteristic, complemented, Sylow
719C23—21no—
720C23—21no—
721C23—31no—
722C23—42no—
723C23—42no—
724C23—81no—
725C23D3×#6711yescharacteristic
726Q8—61no—
727Q8—61no—
728Q8—181no—
729Q8—181no—
730Q8—721no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—42no—
735D4—62no—
736D4—122no—
737D4—241no—
738D4#380412yes—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—122no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—241no—
754C2×C4—241no—
755C2×C4—721no—
756C2×C4D3×#6711yescharacteristic
757C2×C4C22×D3211yescharacteristic
758C8—61no—
759C8—61no—
760C8—181no—
761C8—181no—
762C2×C3—22no—
763C2×C3—22no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—42no—
768C2×C3—42no—
769C2×C3—42no—
770C2×C3—82no—
771C2×C3—82no—
772C2×C3—81no—
773C2×C3—81no—
774C2×C3—121no—
775C2×C3#549011yescharacteristic
776C2×C3#575711yescharacteristic
777C2×C3C2×#91511yescharacteristic
778C2×C3#580611yescharacteristic
779C2×C3C2×#95111yescharacteristic
780C2×C3#583511yescharacteristic
781D3—41no—
782C22—21no—
783C22—21no—
784C22—22no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—61no—
791C22—61no—
792C22—61no—
793C22—84no—
794C22#6392912yes—
795C22C2×D3×#6711yescharacteristic
796C4—21no—
797C4—61no—
798C4—61no—
799C4—61no—
800C4—121no—
801C4—121no—
802C4—121no—
803C4—121no—
804C4—361no—
805C4—361no—
806C4C2×#380411yescharacteristic
807C4#6433011yescharacteristic
808C3—21no—
809C3#7876311yescharacteristic, complemented
810C3#8349811yescharacteristic, complemented
811C2—22no—
812C2—42no—
813C2—81no—
814C2—121no—
815C2#1059509611yescharacteristic
816C2C2×#6392911yescharacteristic
817C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC22×D4D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594988C2semidirect
3. #10592917C2semidirect
4. C2×C3×#832C2semidirect
5. #10591488C2semidirect
6. #10591463C2semidirect
7. #10591462C2semidirect
8. #10591441C2semidirect
9. #10591414C2semidirect
10. #10591413C2semidirect
11. #10591410C2semidirect
12. #10591405C2semidirect
13. #10591187C2semidirect
14. #10591155C2semidirect
15. #10591132C2semidirect
36. #63918C22semidirect
38. D3×C4⋊Dic3C22semidirect
39. #63857C22semidirect
41. #63844C22semidirect
42. C2×#3719C22semidirect
43. C2×#3711C22semidirect
51. #63576C22semidirect
52. #63576C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
71. C2×#832D3semidirect
718. C32#3314semidirect
809. C3#78763semidirect
810. C3#83498semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
#105949882
#105929172
C2×C3×#8322
#105914882
#105914632
#105914622
#105914412
#105914142
#105914132
#105914102
#105914052
#105911872
#105911552
#105911322
#834983
#787633