Finite Group Databasebeta

← #11904422

Subgroups — #11904422

Order 1152.

3291 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic, complemented
2C22×#3805C211yesmaximal, characteristic, complemented
3C2×#64095C211yesmaximal, characteristic, complemented
4C3×#5493C211yesmaximal, characteristic, complemented
5C3×#5486C211yesmaximal, characteristic, complemented
6#10595519C211yesmaximal, characteristic, complemented
7C2×#63962C211yesmaximal, characteristic, complemented
8#10595075C214yesmaximal, complemented
9#10594907C214yesmaximal, complemented
10#10594292C214yesmaximal, complemented
11#10594290C212yesmaximal, complemented
12D3×#886C212yesmaximal, complemented
13#10594081C212yesmaximal, complemented
14#10594078C212yesmaximal, complemented
15#10594077C214yesmaximal, complemented
16#86296—31nomaximal
17#85858—31nomaximal
18C22×#638C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic, complemented
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic, complemented
23#64330—28no—
24C2×#3811C2212yescomplemented
25C2×D3×#67C2212yes—
26C2×D3×#67C2212yescomplemented
27C22×#627C2211yescharacteristic, complemented
28C22×#625C2211yescharacteristic, complemented
29C2×#3805—28no—
30C2×#3805C2214yescomplemented
31C2×#3805C2214yescomplemented
32C2×#3805C2212yescomplemented
33C2×#3804C2212yes—
34C2×#3804C2212yescomplemented
35C22×D3×Dic3C2211yescharacteristic, complemented
36C22×D3×Dic3C2211yescharacteristic, complemented
37C2×C32×C22⋊C4C2211yescharacteristic, complemented
38C2×#3752C2212yescomplemented
39C2×C4⋊(C3⋊Dic3)C2212yescomplemented
40#64095C2214yescomplemented
41#64095C2212yescomplemented
42#64095C2212yescomplemented
43C2×C3×#217C2211yescharacteristic, complemented
44C3×#930C2214yescomplemented
45C3×C4×#67C2214yescomplemented
46C3×#886C2212yescomplemented
47C3×#886C2212yescomplemented
48C3×#882C2212yescomplemented
49C3×#882C2212yescomplemented
50C3×#67⋊C4C2214yescomplemented
51C3×D3×C22⋊C4C2212yescomplemented
52C3×#877C2212yescomplemented
53#63981C2212yescomplemented
54#63978C2214yescomplemented
55#63977C2212yescomplemented
56#63966C2212yescomplemented
57C2×Dic3⋊Dic3C2212yescomplemented
58#63962C2214yescomplemented
59#63962C2212yescomplemented
60#63962C2212yescomplemented
61#63962C2212yescomplemented
62C2×(C2×D3)⋊Dic3C2212yescomplemented
63#63922C2214yescomplemented
64D3×(C2×D3)⋊C4C2214yescomplemented
65#63918C2214yescomplemented
66#63908C2214yescomplemented
67#63906C2214yescomplemented
68#63895C2214yescomplemented
69#63893C2214yescomplemented
70#63893C2214yescomplemented
71Dic3×D12C2214yescomplemented
72#63891C2214yescomplemented
73#63891C2214yescomplemented
74#63890C2214yescomplemented
75D3×C4⋊Dic3C2214yescomplemented
76#63886C2214yescomplemented
77#63880C2214yescomplemented
78#63852C2214yescomplemented
79C2×#1004—31no—
80C2×#1004—31no—
81C22×#237—31no—
82C22×#237—31no—
83C3×#534—31no—
84C3×#518—31no—
85#5804—31no—
86C2×#935—31no—
87#5655—34no—
88D3×#123—32no—
89#5648—32no—
90#5611—34no—
91#5610—34no—
92#5591—34no—
93#5589—32no—
94#5586—32no—
95#5555—34no—
96#5555—34no—
97#5554—34no—
98#5554—34no—
99#5526—32no—
100#5524—32no—
101#5493—31no—
102#5493—32no—
103#5493D311yescharacteristic, complemented
104C2×#886—31no—
105C2×#886—31no—
106C2×#886—31no—
107C2×#886—32no—
108C2×#886—61no—
109#5486D311yescharacteristic, complemented
110C24×C32C2311yescharacteristic
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2311yescharacteristic
115C22×D32C2312yes—
116C22×C32×C4C2312yes—
117C2×#638—24no—
118C2×#638C2312yes—
119C2×#638C2312yes—
120C22×C3⋊Dic3—24no—
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2312yes—
123C22×C3⋊Dic3C2312yes—
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2311yescharacteristic
126C2×C3×#67—24no—
127C2×C3×#67—24no—
128C2×C3×#67D418yescomplemented
129C2×C3×#67C2312yes—
130C2×C3×#67C2312yes—
131C2×C3×#67C2312yes—
132C2×C3×#67C2312yes—
133C2×C3×#67C2312yes—
134C2×C3×#67C2312yes—
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2312yes—
138C22×C3×Dic3C2311yescharacteristic
139C2×C3×D12C2314yes—
140C2×C3×C4×D3C2314yes—
141#3811—28no—
142D3×#67—28no—
143D3×#67—28no—
144C2×#627—24no—
145C2×#627C2312yes—
146C2×#627C2314yes—
147C2×#626C2312yes—
148C2×#626C2312yes—
149C2×#626C2314yes—
150C2×#625—24no—
151C2×#625C2314yes—
152C2×#625C2312yes—
153C2×#624C2312yes—
154#3805—216no—
155#3805—216no—
156#3805—28no—
157#3804—28no—
158#3804—28no—
159C2×D3×Dic3—24no—
160C2×D3×Dic3—24no—
161C2×D3×Dic3C2314yes—
162C2×D3×Dic3C2314yes—
163C2×D3×Dic3C2312yes—
164C2×D3×Dic3C2312yes—
165C32×C22⋊C4C2312yes—
166C32×C22⋊C4C2312yes—
167#3752C2314yes—
168#3752C2314yes—
169C4⋊(C3⋊Dic3)C2314yes—
170C4⋊(C3⋊Dic3)C2314yes—
171C3×#217C2312yes—
172C3×#217C2312yes—
173C3×(C2×D3)⋊C4C2314yes—
174C3×(C2×D3)⋊C4C2314yes—
175C3×(C2×D3)⋊C4C2314yes—
176C3×C4⋊Dic3C2314yes—
177C3×Dic3⋊C4C2314yes—
178C3×C4×Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182#3722C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186#3485—91noSylow
187C22×C3×D4—31no—
188C22×C3×D4—31no—
189C22×C3×D4—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—32no—
195C22×#67—32no—
196C22×#67—61no—
197C22×#67C2×D311yescharacteristic
198C22×#67C2×D311yescharacteristic
199C22×#67C2×D311yescharacteristic, complemented
200C23×Dic3—31no—
201C23×Dic3—31no—
202C23×Dic3—31no—
203C23×Dic3—31no—
204C23×Dic3—61no—
205#1004—68no—
206#1004—68no—
207C2×#237—34no—
208C2×#237—34no—
209C2×#237—34no—
210C2×#237—34no—
211C2×#237—32no—
212C2×#237—32no—
213C2×#237—32no—
214C2×#237—32no—
215C2×#237—68no—
216C2×#237—68no—
217C2×D3×D4—32no—
218C2×D3×D4—32no—
219C2×D3×D4—32no—
220C2×D3×D4—32no—
221C2×#235—32no—
222C2×#235—32no—
223C22×C4×D3—31no—
224C22×C4×D3—31no—
225C22×Dic6—31no—
226C22×Dic6—31no—
227C3×#123—32no—
228C3×#123—32no—
229C3×#121—34no—
230C3×#120—32no—
231C3×#120—32no—
232C3×C4×D4—34no—
233C3×C4×D4—34no—
234C3×#117—32no—
235C2×C3×C22⋊C4—21no—
236C2×C3×C22⋊C4—31no—
237C2×C3×C22⋊C4—32no—
238C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
239C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
240#953—32no—
241C2×#217—32no—
242C2×#217C2×D311yescharacteristic, complemented
243#939—34no—
244#939—34no—
245#938—34no—
246#937—32no—
247#937—34no—
248#935—32no—
249#935—32no—
250#935—34no—
251#935—32no—
252D4×Dic3—34no—
253#930—34no—
254#930—34no—
255#930—34no—
256#930C2×D314yescomplemented
257#929—32no—
258C4×#67C2×D314yescomplemented
259C2×(C2×D3)⋊C4—32no—
260C2×(C2×D3)⋊C4—32no—
261C2×(C2×D3)⋊C4—32no—
262C2×(C2×D3)⋊C4—34no—
263C2×(C2×D3)⋊C4—62no—
264C2×C4⋊Dic3—32no—
265C2×C4⋊Dic3—32no—
266C2×C4⋊Dic3—32no—
267C2×C4⋊Dic3—34no—
268C2×C4⋊Dic3—62no—
269C2×Dic3⋊C4—32no—
270#897—34no—
271#897—34no—
272#897—34no—
273#896—34no—
274#895—34no—
275#894—34no—
276D3×C4⋊C4—34no—
277#888—34no—
278#886—32no—
279#886—32no—
280#886—34no—
281#886—32no—
282#886—32no—
283#886—32no—
284#886—32no—
285#886—34no—
286#886—32no—
287#886—32no—
288#886—34no—
289#886—34no—
290#886—34no—
291#886—34no—
292#886—62no—
293#886—62no—
294#886—64no—
295#886C2×D312yescomplemented
296#886C2×D312yescomplemented
297#885—34no—
298#884—34no—
299#883—34no—
300#883—34no—
301#882—32no—
302#882—32no—
303#882—34no—
304#882C2×D312yescomplemented
305#882C2×D312yescomplemented
306#67⋊C4—34no—
307#67⋊C4C2×D314yescomplemented
308D3×C22⋊C4—34no—
309D3×C22⋊C4C2×D312yescomplemented
310#878—34no—
311#878—34no—
312#877C2×D312yescomplemented
313#875—34no—
314C4×D12—34no—
315C4×D12—34no—
316#869—34no—
317C23×C32—42no—
318C23×C32C2×D414yes—
319C23×C32C2411yescharacteristic
320C23×C32C2411yescharacteristic
321C23×C32C2411yescharacteristic
322C22×C3⋊D3—22no—
323C22×C3⋊D3—42no—
324C22×C3⋊D3C2412yes—
325C22×C3×D3—22no—
326C22×C3×D3—22no—
327C22×C3×D3—42no—
328C22×C3×D3—42no—
329C22×C3×D3—42no—
330C22×C3×D3C2×D414yes—
331C22×C3×D3C2412yes—
332C22×C3×D3C2412yes—
333C22×C3×D3C2412yes—
334C2×D32—24no—
335C2×D32—44no—
336C2×C32×C4—42no—
337C2×C32×C4C2414yes—
338#638—24no—
339#638—24no—
340C2×C3⋊Dic3—22no—
341C2×C3⋊Dic3—24no—
342C2×C3⋊Dic3—24no—
343C2×C3⋊Dic3—22no—
344C2×C3⋊Dic3—22no—
345C2×C3⋊Dic3C2412yes—
346C2×C3⋊Dic3C2412yes—
347C2×C3⋊Dic3C2412yes—
348C3×#67—24no—
349C3×#67—24no—
350C3×#67—24no—
351C3×#67—24no—
352C3×#67C2×D418yes—
353C3×#67C2×D418yes—
354C2×C3×Dic3—22no—
355C2×C3×Dic3—22no—
356C2×C3×Dic3—42no—
357C2×C3×Dic3C2×D414yes—
358C2×C3×Dic3C2414yes—
359C2×C3×Dic3C2412yes—
360C2×C3×Dic3C2412yes—
361C2×C3×Dic3C2412yes—
362C3×D12—44no—
363C3×C4×D3—44no—
364#627—24no—
365#627—28no—
366#626—24no—
367#626—24no—
368#626—44no—
369#625—28no—
370#625—24no—
371#624—24no—
372D3×Dic3—28no—
373D3×Dic3—24no—
374D3×Dic3—28no—
375D3×Dic3—24no—
376C2×H(5,𝔽2)—91no—
377C22×#41—91no—
378#547—94no—
379#547—94no—
380#546—94no—
381#546—94no—
382#536—92no—
383#534—31no—
384#534—92no—
385#534—91no—
386#525—92no—
387C2×#123—92no—
388C2×#123—91no—
389C2×#123—91no—
390#518—31no—
391C24×C3—21no—
392C24×C3—31no—
393C24×C3—31no—
394C24×C3—31no—
395C24×C3C22×D311yescharacteristic
396C24×C3C22×D311yescharacteristic
397C23×D3—31no—
398C23×D3—31no—
399C23×D3—32no—
400C23×D3—32no—
401C23×D3—61no—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C23×D3C22×D311yescharacteristic
405C2×C3×D4—38no—
406C2×C3×D4—32no—
407C2×C3×D4—32no—
408C2×C3×D4—32no—
409C2×C3×D4—32no—
410C2×C3×D4—32no—
411C2×C3×D4—32no—
412C2×C3×D4—34no—
413C2×C3×D4—64no—
414C2×C3×D4—64no—
415C22×C3×C4—22no—
416C22×C3×C4—31no—
417C22×C3×C4—31no—
418C22×C3×C4—31no—
419C22×C3×C4—32no—
420C22×C3×C4—34no—
421C22×C3×C4C22×D312yes—
422C22×C3×C4C22×D312yes—
423C2×#67—24no—
424C2×#67—24no—
425C2×#67—32no—
426C2×#67—32no—
427C2×#67—32no—
428C2×#67—32no—
429C2×#67—34no—
430C2×#67—32no—
431C2×#67—34no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—32no—
435C2×#67—34no—
436C2×#67—62no—
437C2×#67—62no—
438C2×#67—68no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—68no—
444C2×#67—124no—
445C2×#67D1218yescomplemented
446C2×#67C22×D312yes—
447C2×#67C22×D312yes—
448C2×#67C22×D312yes—
449C2×#67C22×D312yes—
450C2×#67C22×D312yes—
451C2×#67C22×D312yes—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—32no—
455C22×Dic3—31no—
456C22×Dic3—32no—
457C22×Dic3—32no—
458C22×Dic3—31no—
459C22×Dic3—31no—
460C22×Dic3—31no—
461C22×Dic3—32no—
462C22×Dic3—32no—
463C22×Dic3—34no—
464C22×Dic3—32no—
465C22×Dic3—34no—
466C22×Dic3—62no—
467C22×Dic3—61no—
468C22×Dic3—61no—
469C22×Dic3—61no—
470C22×Dic3—62no—
471C22×Dic3—64no—
472C22×Dic3—64no—
473C22×Dic3—64no—
474C22×Dic3—64no—
475C22×Dic3—124no—
476C22×Dic3C22×D311yescharacteristic
477C22×Dic3C22×D311yescharacteristic
478C22×Dic3C22×D312yes—
479C22×Dic3C22×D311yescharacteristic
480#237—68no—
481#237—616no—
482#237—616no—
483#237—68no—
484#237—616no—
485#237—616no—
486#237—68no—
487#237—68no—
488D3×D4—68no—
489D3×D4—68no—
490D3×D4—68no—
491D3×D4—68no—
492#235—68no—
493#235—68no—
494C2×D12—32no—
495C2×D12—32no—
496C2×D12—34no—
497C2×D12C22×D314yes—
498C2×C4×D3—34no—
499C2×C4×D3—32no—
500C2×C4×D3—34no—
501C2×C4×D3—32no—
502C2×C4×D3—32no—
503C2×C4×D3—32no—
504C2×C4×D3—64no—
505C2×C4×D3—64no—
506C2×C4×D3C22×D314yes—
507C2×Dic6—32no—
508C2×Dic6—34no—
509C2×Dic6—32no—
510C2×Dic6—34no—
511C2×Dic6—64no—
512C2×Dic6—64no—
513C3×C4⋊C4—34no—
514C3×C4⋊C4—34no—
515C3×C22⋊C4—22no—
516C3×C22⋊C4—22no—
517C3×C22⋊C4—32no—
518C3×C22⋊C4—32no—
519C3×C22⋊C4—34no—
520C3×C22⋊C4—34no—
521C3×C22⋊C4—34no—
522C3×C22⋊C4C22×D312yes—
523C3×C22⋊C4C22×D312yes—
524C3×C22⋊C4C22×D312yes—
525C3×C22⋊C4C22×D312yes—
526C3×C42—34no—
527#217—34no—
528#217—34no—
529#217—34no—
530#217C22×D312yes—
531#217C22×D312yes—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—34no—
534(C2×D3)⋊C4—34no—
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—34no—
540(C2×D3)⋊C4—34no—
541(C2×D3)⋊C4—64no—
542(C2×D3)⋊C4—64no—
543(C2×D3)⋊C4C22×D314yes—
544(C2×D3)⋊C4C22×D314yes—
545(C2×D3)⋊C4C22×D314yes—
546C4⋊Dic3—34no—
547C4⋊Dic3—34no—
548C4⋊Dic3—34no—
549C4⋊Dic3—34no—
550C4⋊Dic3—34no—
551C4⋊Dic3—34no—
552C4⋊Dic3—34no—
553C4⋊Dic3—64no—
554C4⋊Dic3—64no—
555C4⋊Dic3C22×D314yes—
556Dic3⋊C4—34no—
557Dic3⋊C4—34no—
558Dic3⋊C4—34no—
559Dic3⋊C4C22×D314yes—
560C4×Dic3C22×D314yes—
561C22×C32—22no—
562C22×C32—22no—
563C22×C32—22no—
564C22×C32—44no—
565C22×C32C22×D412yes—
566C22×C32C22×D412yes—
567C22×C32C22×D412yes—
568C22×C32C2511yescharacteristic
569C2×C3⋊D3—22no—
570C2×C3⋊D3—24no—
571C2×C3⋊D3—82no—
572C2×C3×D3—24no—
573C2×C3×D3—22no—
574C2×C3×D3—22no—
575C2×C3×D3—24no—
576C2×C3×D3—24no—
577C2×C3×D3—44no—
578C2×C3×D3—44no—
579C2×C3×D3—82no—
580C2×C3×D3C22×D414yes—
581D32—84no—
582C32×C4—24no—
583C3⋊Dic3—22no—
584C3⋊Dic3—22no—
585C3⋊Dic3—22no—
586C3×Dic3—22no—
587C3×Dic3—22no—
588C3×Dic3—24no—
589C3×Dic3C22×D414yes—
590H(5,𝔽2)—188no—
591C2×#41—92no—
592C2×#41—92no—
593C2×#41—94no—
594C2×#41—94no—
595C2×#41—92no—
596C2×#41—188no—
597C22×Q8—91no—
598C22×D4—31no—
599C22×D4—31no—
600C22×D4—31no—
601C22×D4—92no—
602C22×D4—92no—
603C22×D4—92no—
604C22×D4—91no—
605C22×D4—91no—
606C23×C4—91no—
607C23×C4—91no—
608C23×C4—91no—
609C4⋊Q8—94no—
610#124—94no—
611#123—32no—
612#123—32no—
613#123—94no—
614#123—94no—
615#123—94no—
616#123—92no—
617#123—92no—
618#123—92no—
619#123—94no—
620#123—92no—
621#123—92no—
622#123—92no—
623#123—94no—
624C22⋊Q8—94no—
625C22⋊Q8—94no—
626C22⋊Q8—94no—
627#121—34no—
628#121—94no—
629#121—94no—
630#121—94no—
631#121—94no—
632#120—32no—
633#120—32no—
634#120—92no—
635#120—94no—
636#120—92no—
637C4×D4—34no—
638C4×D4—34no—
639C4×D4—94no—
640C4×D4—94no—
641#117—32no—
642C2×C4⋊C4—94no—
643C2×C4⋊C4—92no—
644C2×C4⋊C4—92no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—32no—
647C2×C22⋊C4—94no—
648C2×C22⋊C4—92no—
649C2×C22⋊C4—92no—
650C2×C22⋊C4D3211yescharacteristic, complemented
651C23×C3—21no—
652C23×C3—21no—
653C23×C3—21no—
654C23×C3—24no—
655C23×C3—32no—
656C23×C3—34no—
657C23×C3—32no—
658C23×C3—32no—
659C23×C3—42no—
660C23×C3—42no—
661C23×C3—44no—
662C23×C3—62no—
663C23×C3—62no—
664C23×C3—122no—
665C23×C3—122no—
666C23×C3—122no—
667C23×C3C2×D1214yes—
668C23×C3D3×D414yes—
669C23×C3C23×D311yescharacteristic
670C23×C3C23×D311yescharacteristic
671C23×C3C23×D311yescharacteristic
672C23×C3C23×D311yescharacteristic
673C23×C3C23×D311yescharacteristic
674C23×C3C23×D311yescharacteristic
675C22×D3—22no—
676C22×D3—22no—
677C22×D3—32no—
678C22×D3—32no—
679C22×D3—42no—
680C22×D3—42no—
681C22×D3—42no—
682C22×D3—62no—
683C22×D3—64no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—64no—
687C22×D3—122no—
688C22×D3—124no—
689C22×D3—124no—
690C22×D3—122no—
691C22×D3—122no—
692C22×D3—124no—
693C22×D3C2×D1214yes—
694C22×D3C23×D312yes—
695C22×D3C23×D312yes—
696C22×D3C23×D312yes—
697C3×D4—38no—
698C3×D4—38no—
699C3×D4—64no—
700C3×D4—64no—
701C3×D4—64no—
702C3×D4—64no—
703C3×D4—124no—
704C2×C3×C4—24no—
705C2×C3×C4—34no—
706C2×C3×C4—32no—
707C2×C3×C4—32no—
708C2×C3×C4—32no—
709C2×C3×C4—34no—
710C2×C3×C4—42no—
711C2×C3×C4—42no—
712C2×C3×C4—44no—
713C2×C3×C4—62no—
714C2×C3×C4—62no—
715C2×C3×C4—124no—
716C2×C3×C4—122no—
717C2×C3×C4C23×D314yes—
718C2×C3×C4C23×D314yes—
719#67—24no—
720#67—24no—
721#67—24no—
722#67—24no—
723#67—64no—
724#67—64no—
725#67—68no—
726#67—64no—
727#67—64no—
728#67—64no—
729#67—64no—
730#67—64no—
731#67—68no—
732#67—64no—
733#67—124no—
734#67—124no—
735#67—124no—
736#67C2×D1218yes—
737#67C2×D1218yes—
738C2×Dic3—22no—
739C2×Dic3—22no—
740C2×Dic3—32no—
741C2×Dic3—32no—
742C2×Dic3—32no—
743C2×Dic3—32no—
744C2×Dic3—32no—
745C2×Dic3—32no—
746C2×Dic3—42no—
747C2×Dic3—62no—
748C2×Dic3—62no—
749C2×Dic3—62no—
750C2×Dic3—68no—
751C2×Dic3—64no—
752C2×Dic3—62no—
753C2×Dic3—62no—
754C2×Dic3—64no—
755C2×Dic3—64no—
756C2×Dic3—62no—
757C2×Dic3—62no—
758C2×Dic3—62no—
759C2×Dic3—64no—
760C2×Dic3—64no—
761C2×Dic3—62no—
762C2×Dic3—68no—
763C2×Dic3—64no—
764C2×Dic3—122no—
765C2×Dic3—122no—
766C2×Dic3—124no—
767C2×Dic3—124no—
768C2×Dic3—122no—
769C2×Dic3C2×D1214yes—
770C2×Dic3C23×D314yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774D12—44no—
775D12—64no—
776D12—64no—
777D12—124no—
778C4×D3—44no—
779C4×D3—64no—
780C4×D3—68no—
781C4×D3—64no—
782C4×D3—68no—
783C4×D3—64no—
784C4×D3—64no—
785Dic6—68no—
786Dic6—64no—
787Dic6—68no—
788Dic6—64no—
789C2×C32—22no—
790C2×C32—22no—
791C2×C32—22no—
792C2×C32C23×D411yescharacteristic
793C2×C32#58512yes—
794C3⋊D3—42no—
795C3×D3—24no—
796C3×D3—42no—
797C3×D3—42no—
798C24—31no—
799C24—31no—
800C24—31no—
801C24—92no—
802C24—91no—
803C24C2×D3211yescharacteristic
804#41—188no—
805#41—188no—
806#41—1816no—
807#41—1816no—
808#41—188no—
809C2×Q8—94no—
810C2×Q8—92no—
811C2×Q8—184no—
812C2×D4—32no—
813C2×D4—32no—
814C2×D4—38no—
815C2×D4—32no—
816C2×D4—32no—
817C2×D4—32no—
818C2×D4—32no—
819C2×D4—34no—
820C2×D4—64no—
821C2×D4—64no—
822C2×D4—92no—
823C2×D4—92no—
824C2×D4—94no—
825C2×D4—94no—
826C2×D4—92no—
827C2×D4—92no—
828C2×D4—92no—
829C2×D4—188no—
830C2×D4—188no—
831C2×D4—188no—
832C2×D4—184no—
833C2×D4—184no—
834C22×C4—31no—
835C22×C4—31no—
836C22×C4—31no—
837C22×C4—32no—
838C22×C4—34no—
839C22×C4—92no—
840C22×C4—94no—
841C22×C4—92no—
842C22×C4—94no—
843C22×C4—92no—
844C22×C4—92no—
845C22×C4—92no—
846C22×C4—91no—
847C22×C4—91no—
848C22×C4—91no—
849C22×C4—184no—
850C22×C4—184no—
851C22×C4—184no—
852C22×C4C2×D3212yes—
853C4⋊C4—34no—
854C4⋊C4—34no—
855C4⋊C4—94no—
856C4⋊C4—94no—
857C4⋊C4—94no—
858C4⋊C4—94no—
859C4⋊C4—94no—
860C22⋊C4—32no—
861C22⋊C4—32no—
862C22⋊C4—34no—
863C22⋊C4—34no—
864C22⋊C4—34no—
865C22⋊C4—94no—
866C22⋊C4—94no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4C2×D3212yes—
872C22⋊C4C2×D3212yes—
873C42—34no—
874C22×C3—24no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—21no—
885C22×C3—34no—
886C22×C3—42no—
887C22×C3—42no—
888C22×C3—44no—
889C22×C3—44no—
890C22×C3—48no—
891C22×C3—64no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—64no—
895C22×C3—64no—
896C22×C3—124no—
897C22×C3—124no—
898C22×C3—242no—
899C22×C3C22×D1212yes—
900C22×C3C22×D1212yes—
901C22×C3C22×D1212yes—
902C22×C3C2×D3×D412yes—
903C22×C3C2×D3×D412yes—
904C22×C3C2×D3×D412yes—
905C22×C3C24×D311yescharacteristic
906C22×C3C24×D311yescharacteristic
907C2×D3—24no—
908C2×D3—22no—
909C2×D3—22no—
910C2×D3—24no—
911C2×D3—24no—
912C2×D3—44no—
913C2×D3—44no—
914C2×D3—62no—
915C2×D3—62no—
916C2×D3—64no—
917C2×D3—64no—
918C2×D3—82no—
919C2×D3—122no—
920C2×D3—124no—
921C2×D3—244no—
922C2×D3—244no—
923C2×D3—242no—
924C2×D3—242no—
925C2×D3—244no—
926C2×D3C22×D1214yes—
927C3×C4—24no—
928C3×C4—24no—
929C3×C4—34no—
930C3×C4—44no—
931C3×C4—62no—
932C3×C4—62no—
933C3×C4—64no—
934Dic3—22no—
935Dic3—22no—
936Dic3—24no—
937Dic3—62no—
938Dic3—62no—
939Dic3—62no—
940Dic3—62no—
941Dic3—62no—
942Dic3—62no—
943Dic3—122no—
944Dic3—122no—
945Dic3—122no—
946Dic3C22×D1214yes—
947C32#348511yescharacteristic, complemented, Sylow
948C23—32no—
949C23—34no—
950C23—32no—
951C23—32no—
952C23—42no—
953C23—62no—
954C23—62no—
955C23—92no—
956C23—122no—
957C23—122no—
958C23—122no—
959C23—184no—
960C23—182no—
961C23—362no—
962C23—364no—
963C23D3×D1214yes—
964C23C22×D3211yescharacteristic
965C23C22×D3211yescharacteristic
966C23C22×D3211yescharacteristic
967Q8—188no—
968Q8—184no—
969D4—38no—
970D4—38no—
971D4—64no—
972D4—64no—
973D4—64no—
974D4—64no—
975D4—124no—
976D4—184no—
977D4—184no—
978D4—184no—
979D4—188no—
980D4—184no—
981D4—184no—
982D4—364no—
983C2×C4—34no—
984C2×C4—32no—
985C2×C4—34no—
986C2×C4—32no—
987C2×C4—32no—
988C2×C4—42no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—92no—
992C2×C4—92no—
993C2×C4—92no—
994C2×C4—124no—
995C2×C4—122no—
996C2×C4—184no—
997C2×C4—188no—
998C2×C4—184no—
999C2×C4—188no—
1000C2×C4—184no—
1001C2×C4—182no—
1002C2×C4—182no—
1003C2×C4—184no—
1004C2×C4—184no—
1005C2×C4—182no—
1006C2×C4C22×D3214yes—
1007C2×C3—24no—
1008C2×C3—22no—
1009C2×C3—22no—
1010C2×C3—22no—
1011C2×C3—22no—
1012C2×C3—22no—
1013C2×C3—22no—
1014C2×C3—21no—
1015C2×C3—22no—
1016C2×C3—42no—
1017C2×C3—42no—
1018C2×C3—64no—
1019C2×C3—122no—
1020C2×C3—122no—
1021C2×C3C23×D1211yescharacteristic
1022C2×C3C22×D3×D411yescharacteristic
1023C2×C3#596612yes—
1024C2×C3#596612yes—
1025D3—24no—
1026D3—42no—
1027D3—42no—
1028D3—122no—
1029D3—122no—
1030D3—242no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—34no—
1035C22—44no—
1036C22—64no—
1037C22—62no—
1038C22—62no—
1039C22—64no—
1040C22—64no—
1041C22—124no—
1042C22—124no—
1043C22—182no—
1044C22—184no—
1045C22—242no—
1046C22—722no—
1047C22—724no—
1048C22C2×D3×D1212yes—
1049C22C2×D3×D1212yes—
1050C22C2×D3×D1212yes—
1051C22C23×D3211yescharacteristic
1052C4—24no—
1053C4—34no—
1054C4—62no—
1055C4—62no—
1056C4—64no—
1057C4—182no—
1058C4—182no—
1059C4—182no—
1060C3—21no—
1061C3#8585811yescharacteristic, complemented
1062C3#8629611yescharacteristic, complemented
1063C2—22no—
1064C2—22no—
1065C2—22no—
1066C2—64no—
1067C2—122no—
1068C2—122no—
1069C2—362no—
1070C2C22×D3×D1211yescharacteristic
1071C2#1059667912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64330C2semidirect
2. C22×#3805C2semidirect
3. C2×#64095C2semidirect
4. C3×#5493C2semidirect
5. C3×#5486C2semidirect
6. #10595519C2semidirect
7. C2×#63962C2semidirect
8. #10595075C2semidirect
9. #10594907C2semidirect
10. #10594292C2semidirect
11. #10594290C2semidirect
12. D3×#886C2semidirect
13. #10594081C2semidirect
14. #10594078C2semidirect
15. #10594077C2semidirect
19. C23×C3⋊Dic3C22semidirect
22. C22×C3×#67C22semidirect
24. C2×#3811C22semidirect
26. C2×D3×#67C22semidirect
27. C22×#627C22semidirect
28. C22×#625C22semidirect
30. C2×#3805C22semidirect
31. C2×#3805C22semidirect
32. C2×#3805C22semidirect
34. C2×#3804C22semidirect
35. C22×D3×Dic3C22semidirect
36. C22×D3×Dic3C22semidirect
37. C2×C32×C22⋊C4C22semidirect
38. C2×#3752C22semidirect
39. C2×C4⋊(C3⋊Dic3)C22semidirect
40. #64095C22semidirect
41. #64095C22semidirect
42. #64095C22semidirect
43. C2×C3×#217C22semidirect
44. C3×#930C22semidirect
45. C3×C4×#67C22semidirect
46. C3×#886C22semidirect
47. C3×#886C22semidirect
48. C3×#882C22semidirect
49. C3×#882C22semidirect
50. C3×#67⋊C4C22semidirect
51. C3×D3×C22⋊C4C22semidirect
52. C3×#877C22semidirect
53. #63981C22semidirect
54. #63978C22semidirect
55. #63977C22semidirect
56. #63966C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. #63962C22semidirect
59. #63962C22semidirect
60. #63962C22semidirect
61. #63962C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63922C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63918C22semidirect
66. #63908C22semidirect
67. #63906C22semidirect
68. #63895C22semidirect
69. #63893C22semidirect
70. #63893C22semidirect
71. Dic3×D12C22semidirect
72. #63891C22semidirect
73. #63891C22semidirect
74. #63890C22semidirect
75. D3×C4⋊Dic3C22semidirect
76. #63886C22semidirect
77. #63880C22semidirect
78. #63852C22semidirect
103. #5493D3semidirect
109. #5486D3semidirect
128. C2×C3×#67D4semidirect
199. C22×#67C2×D3semidirect
238. C2×C3×C22⋊C4C2×D3semidirect
239. C2×C3×C22⋊C4C2×D3semidirect
242. C2×#217C2×D3semidirect
256. #930C2×D3semidirect
258. C4×#67C2×D3semidirect
295. #886C2×D3semidirect
296. #886C2×D3semidirect
304. #882C2×D3semidirect
305. #882C2×D3semidirect
307. #67⋊C4C2×D3semidirect
309. D3×C22⋊C4C2×D3semidirect
312. #877C2×D3semidirect
445. C2×#67D12semidirect
650. C2×C22⋊C4D32semidirect
947. C32#3485semidirect
1061. C3#85858semidirect
1062. C3#86296semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
C22×#38052
C2×#640952
C3×#54932
C3×#54862
#105955192
C2×#639622
#105950752
#105949072
#105942922
#105942902
D3×#8862
#105940812
#105940782
#105940772
#862963
#858583