Finite Group Databasebeta

← #11909940

Subgroups — #11909940

Order 1152.

2133 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C3×#5479C211yesmaximal, characteristic
3C3×#5470C211yesmaximal, characteristic, complemented
4#10594965C212yesmaximal
5#10594960C214yesmaximal, complemented
6#10594915C212yesmaximal, complemented
7#10594853C212yesmaximal, complemented
8#10594810C212yesmaximal, complemented
9#10593945C214yesmaximal, complemented
10#10593942C212yesmaximal, complemented
11#10593904C211yesmaximal, characteristic, complemented
12#10593885C212yesmaximal, complemented
13#10593880C212yesmaximal, complemented
14#10593864C211yesmaximal, characteristic, complemented
15#10593863C211yesmaximal, characteristic, complemented
16#10593861C211yesmaximal, characteristic, complemented
17#10593853C212yesmaximal, complemented
18#86266—31nomaximal
19#86129—31nomaximal
20C22×#634C2211yescharacteristic
21C2×D3×Dic6C2212yes—
22C2×C32×C42C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2212yes—
25C2×C4×C3⋊Dic3C2212yes—
26C4×#634C2212yes—
27C4×#634C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C4×#634C2212yes—
32C3×#930C2211yescharacteristic
33C3×#929C2212yes—
34C3×C4×#67C2212yes—
35C3×#926C2212yes—
36C3×#924C2212yes—
37C3×#924C2212yes—
38C3×#924C2211yescharacteristic
39C3×#876C2212yes—
40C3×#875C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic
42C3×#872C2212yes—
43C3×#870C2211yescharacteristic
44C3×#870C2212yes—
45C3×#869C2211yescharacteristic
46C3×#869C2211yescharacteristic
47C3×C4×Dic6C2212yes—
48C3×C4×Dic6C2211yescharacteristic
49C3×C4×Dic6C2212yes—
50#63982C2214yes—
51#67⋊Dic3C2214yes—
52#63962C2214yes—
53#63957C2214yes—
54#63919C2212yes—
55#63899C2214yes—
56#63898C2212yes—
57#63896C2214yes—
58#63878C2214yes—
59#63877C2214yes—
60#63873C2212yes—
61#63872C2212yes—
62#63870C2214yes—
63#63869C2212yes—
64#63867C2214yes—
65#63866C2212yes—
66#63863C2212yes—
67#63862C2214yes—
68#63861C2214yes—
69#63859C2214yes—
70#63858C2214yes—
71#63857C2212yes—
72#63856C2212yes—
73#63847C2214yes—
74#63846C2214yes—
75#63845C2214yes—
76#63844C2212yes—
77#63843C2212yes—
78#63843C2212yes—
79#63843C2212yes—
80Dic3×Dic6C2212yes—
81#63841C2212yes—
82#63840C2214yes—
83#63838C2214yes—
84#63837C2214yes—
85C3×#533—31no—
86C3×#529—31no—
87#5732—31no—
88#5727—31no—
89#5721—31no—
90#5721—31no—
91#5701—34no—
92#5696—34no—
93#5685—32no—
94#5671—32no—
95#5650—34no—
96#5642—32no—
97#5632—32no—
98#5624—32no—
99#5622—32no—
100#5622—32no—
101#5600—32no—
102#5583—32no—
103#5572—32no—
104#5570—31no—
105#5569—32no—
106#5568—32no—
107#5567—31no—
108#5542—31no—
109#5541—32no—
110D4×Dic6—32no—
111D4×Dic6—31no—
112#5531—34no—
113#5518—32no—
114#5516—32no—
115#5479D311yescharacteristic
116#5470D311yescharacteristic, complemented
117C2×C4×Dic6—31no—
118C2×C4×Dic6—31no—
119C2×C4×Dic6—61no—
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C22×C3⋊Dic3C2312yes—
124C22×C3⋊Dic3C2312yes—
125C2×#634—24no—
126C2×#634C2312yes—
127C2×#634C2311yescharacteristic
128C2×#634C2311yescharacteristic
129C2×C3×#67C2312yes—
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3C2312yes—
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2312yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×#627C2314yes—
136C2×D3×Dic3C2314yes—
137D3×Dic6—28no—
138C32×C42C2311yescharacteristic
139C32×C42C2311yescharacteristic
140C32×C42C2311yescharacteristic
141C32×C42C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2311yescharacteristic
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2311yescharacteristic
145#3750C2312yes—
146#3750C2312yes—
147#3750C2312yes—
148#3750C2312yes—
149C4×C3⋊Dic3C2312yes—
150C4×C3⋊Dic3C2312yes—
151C4×C3⋊Dic3C2312yes—
152C4×C3⋊Dic3C2312yes—
153C3×#217C2314yes—
154C3×#217C2312yes—
155C3×(C2×D3)⋊C4C2312yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×(C2×D3)⋊C4C2312yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2312yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2312yes—
171C3×C4×Dic3C2314yes—
172C3×C4×Dic3C2312yes—
173#3724C2314yes—
174#3724C2314yes—
175#3724C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184Dic32C2314yes—
185Dic32C2314yes—
186Dic32C2314yes—
187#3523—91noSylow
188C2×D3×Q8—32no—
189C22×Dic6—31no—
190C22×Dic6—31no—
191C22×Dic6—32no—
192C22×Dic6—61no—
193C3×C4⋊Q8—31no—
194C3×C4⋊Q8—31no—
195C3×#126—32no—
196C3×#125—31no—
197C3×#125—32no—
198C3×#124—31no—
199C3×#123—32no—
200C3×C22⋊Q8—32no—
201C3×C22⋊Q8—31no—
202C3×C22⋊Q8—32no—
203C3×#121—31no—
204C3×C4×Q8—31no—
205C3×C4×Q8—32no—
206C3×C4×Q8—32no—
207C3×C4×D4—32no—
208C3×C4×D4—31no—
209C3×#117—32no—
210C3×#117—32no—
211C2×C3×C42—21no—
212C2×C3×C42C2×D311yescharacteristic
213C2×C3×C42C2×D311yescharacteristic
214#947—32no—
215#946—32no—
216Q8×Dic3—32no—
217Q8×Dic3—32no—
218Q8×Dic3—32no—
219Q8×Dic3—32no—
220#944—32no—
221#944—32no—
222#944—32no—
223#936—32no—
224#935—34no—
225D4×Dic3—34no—
226D4×Dic3—32no—
227#930C2×D311yescharacteristic
228#929C2×D312yes—
229C4×#67C2×D312yes—
230#926—32no—
231#926C2×D312yes—
232C2×C4⋊Dic3—31no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—61no—
235#924—32no—
236#924—32no—
237#924C2×D312yes—
238#924C2×D312yes—
239#924C2×D311yescharacteristic
240C2×Dic3⋊C4—32no—
241C2×Dic3⋊C4—32no—
242C2×Dic3⋊C4—62no—
243C2×C4×Dic3—32no—
244C2×C4×Dic3—32no—
245C2×C4×Dic3—62no—
246#898—34no—
247#898—34no—
248#898—34no—
249#897—32no—
250#896—34no—
251#896—34no—
252#893—32no—
253#892—32no—
254#892—34no—
255#890—34no—
256#890—32no—
257#890—32no—
258#890—34no—
259#890—32no—
260#889—34no—
261#889—34no—
262#889—34no—
263#889—34no—
264#889—34no—
265#889—34no—
266#889—34no—
267#888—32no—
268#888—32no—
269#888—34no—
270#888—34no—
271#887—32no—
272#887—32no—
273#887—32no—
274#887—34no—
275#887—34no—
276#887—32no—
277#887—34no—
278#886—34no—
279#67⋊C4—34no—
280#879—34no—
281#879—34no—
282#879—34no—
283#879—34no—
284#878—34no—
285#878—34no—
286#878—34no—
287#878—34no—
288#877—34no—
289#877—34no—
290#877—34no—
291#877—34no—
292#876—34no—
293#876C2×D312yes—
294#875C2×D311yescharacteristic
295C4×D12C2×D311yescharacteristic
296#872—34no—
297#872C2×D312yes—
298#870—32no—
299#870—34no—
300#870C2×D312yes—
301#870C2×D311yescharacteristic
302#869—32no—
303#869C2×D311yescharacteristic
304#869C2×D311yescharacteristic
305C4×Dic6—32no—
306C4×Dic6—32no—
307C4×Dic6—32no—
308C4×Dic6—32no—
309C4×Dic6—31no—
310C4×Dic6—31no—
311C4×Dic6—31no—
312C4×Dic6—31no—
313C4×Dic6—31no—
314C4×Dic6—31no—
315C4×Dic6—32no—
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—32no—
319C4×Dic6—34no—
320C4×Dic6—61no—
321C4×Dic6—61no—
322C4×Dic6—62no—
323C4×Dic6—61no—
324C4×Dic6—62no—
325C4×Dic6—61no—
326C4×Dic6C2×D312yes—
327C4×Dic6C2×D311yescharacteristic
328C4×Dic6C2×D312yes—
329C23×C32C2411yescharacteristic
330C22×C3×D3C2412yes—
331C2×C32×C4—22no—
332C2×C32×C4—22no—
333C2×C32×C4—22no—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3—24no—
341C2×C3⋊Dic3—24no—
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2412yes—
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2412yes—
346#634—22no—
347#634—24no—
348#634#4114yes—
349C3×#67—24no—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2414yes—
355C3×D12—22no—
356C3×C4×D3—24no—
357C3×Dic6—24no—
358C3×Dic6—24no—
359C3×Dic6—22no—
360#627—28no—
361D3×Dic3—28no—
362#557—92no—
363#557—91no—
364#557—91no—
365#556—91no—
366#556—92no—
367#552—94no—
368#552—92no—
369D4×Q8—92no—
370D4×Q8—91no—
371#541—92no—
372#541—94no—
373#533—31no—
374#533—92no—
375#529—31no—
376#529—92no—
377#519—92no—
378C2×C4×Q8—91no—
379C2×C3×Q8—31no—
380C2×C3×Q8—32no—
381C2×C3×Q8—32no—
382C2×C3×D4—32no—
383C2×C3×D4—31no—
384C22×C3×C4—21no—
385C22×C3×C4—21no—
386C22×C3×C4—21no—
387C22×C3×C4—32no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C2×#67C22×D312yes—
395C22×Dic3—32no—
396C22×Dic3—32no—
397C22×Dic3—32no—
398C22×Dic3—32no—
399C22×Dic3—34no—
400C22×Dic3—62no—
401C22×Dic3—62no—
402D3×Q8—68no—
403C2×D12C22×D311yescharacteristic
404C2×C4×D3—34no—
405C2×C4×D3C22×D312yes—
406C2×Dic6—31no—
407C2×Dic6—31no—
408C2×Dic6—31no—
409C2×Dic6—32no—
410C2×Dic6—32no—
411C2×Dic6—31no—
412C2×Dic6—34no—
413C2×Dic6—34no—
414C2×Dic6—61no—
415C2×Dic6—62no—
416C2×Dic6—61no—
417C2×Dic6—68no—
418C2×Dic6—64no—
419C2×Dic6—64no—
420C2×Dic6—68no—
421C2×Dic6C22×D312yes—
422C2×Dic6C22×D312yes—
423C2×Dic6C22×D311yescharacteristic
424C3×C4⋊C4—31no—
425C3×C4⋊C4—32no—
426C3×C4⋊C4—32no—
427C3×C4⋊C4—31no—
428C3×C4⋊C4—32no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—32no—
431C3×C4⋊C4—32no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—32no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—32no—
436C3×C22⋊C4—32no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—32no—
439C3×C22⋊C4—32no—
440C3×C22⋊C4—32no—
441C3×C22⋊C4—32no—
442C3×C42—21no—
443C3×C42—21no—
444C3×C42—21no—
445C3×C42—21no—
446C3×C42—32no—
447C3×C42—34no—
448C3×C42C22×D311yescharacteristic
449C3×C42C22×D311yescharacteristic
450C3×C42C22×D311yescharacteristic
451C3×C42C22×D311yescharacteristic
452C3×C42C22×D311yescharacteristic
453C3×C42C22×D311yescharacteristic
454C3×C42C22×D311yescharacteristic
455C3×C42C22×D311yescharacteristic
456#217—34no—
457#217—34no—
458#217—34no—
459#217C22×D312yes—
460#217C22×D314yes—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4C22×D312yes—
465(C2×D3)⋊C4C22×D312yes—
466(C2×D3)⋊C4C22×D312yes—
467(C2×D3)⋊C4C22×D312yes—
468C4⋊Dic3—31no—
469C4⋊Dic3—31no—
470C4⋊Dic3—32no—
471C4⋊Dic3—32no—
472C4⋊Dic3—31no—
473C4⋊Dic3—31no—
474C4⋊Dic3—34no—
475C4⋊Dic3—34no—
476C4⋊Dic3—34no—
477C4⋊Dic3—34no—
478C4⋊Dic3—34no—
479C4⋊Dic3—61no—
480C4⋊Dic3—61no—
481C4⋊Dic3—62no—
482C4⋊Dic3C22×D312yes—
483C4⋊Dic3C22×D312yes—
484C4⋊Dic3C22×D311yescharacteristic
485C4⋊Dic3C22×D312yes—
486C4⋊Dic3C22×D312yes—
487C4⋊Dic3C22×D311yescharacteristic
488Dic3⋊C4—32no—
489Dic3⋊C4—32no—
490Dic3⋊C4—32no—
491Dic3⋊C4—32no—
492Dic3⋊C4—32no—
493Dic3⋊C4—32no—
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—62no—
508Dic3⋊C4—62no—
509Dic3⋊C4—62no—
510Dic3⋊C4—62no—
511Dic3⋊C4C22×D312yes—
512Dic3⋊C4C22×D314yes—
513Dic3⋊C4C22×D314yes—
514Dic3⋊C4C22×D312yes—
515Dic3⋊C4C22×D312yes—
516Dic3⋊C4C22×D312yes—
517C4×Dic3—32no—
518C4×Dic3—32no—
519C4×Dic3—32no—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—34no—
526C4×Dic3—34no—
527C4×Dic3—34no—
528C4×Dic3—34no—
529C4×Dic3—34no—
530C4×Dic3—34no—
531C4×Dic3—62no—
532C4×Dic3—62no—
533C4×Dic3—62no—
534C4×Dic3—62no—
535C4×Dic3C22×D314yes—
536C4×Dic3C22×D312yes—
537C22×C32—21no—
538C22×C32—21no—
539C22×C322−1+412yes—
540C22×C32C2511yescharacteristic
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C32×C4—21no—
545C32×C4—21no—
546C32×C4—21no—
547C32×C4—21no—
548C32×C4C2×#4112yes—
549C32×C42−1+412yes—
550C3⋊Dic3—22no—
551C3⋊Dic3—22no—
552C3⋊Dic3—22no—
553C3⋊Dic3C2×#4114yes—
554C3×Dic3—24no—
555C3×Dic3—22no—
556C3×Dic3—24no—
557C3×Dic3—22no—
558C3×Dic3—22no—
559C22×Q8—92no—
560C22×Q8—91no—
561C4⋊Q8—31no—
562C4⋊Q8—31no—
563C4⋊Q8—92no—
564C4⋊Q8—92no—
565C4⋊Q8—94no—
566C4⋊Q8—92no—
567#126—32no—
568#126—94no—
569#126—94no—
570#126—94no—
571#126—94no—
572#125—31no—
573#125—32no—
574#125—94no—
575#125—92no—
576#125—92no—
577#125—94no—
578#125—94no—
579#125—94no—
580#125—94no—
581#124—31no—
582#124—92no—
583#123—32no—
584#123—94no—
585C22⋊Q8—31no—
586C22⋊Q8—32no—
587C22⋊Q8—32no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—92no—
592C22⋊Q8—92no—
593#121—31no—
594C4×Q8—32no—
595C4×Q8—31no—
596C4×Q8—32no—
597C4×Q8—92no—
598C4×Q8—94no—
599C4×Q8—92no—
600C4×Q8—94no—
601C4×Q8—92no—
602C4×Q8—92no—
603C4×Q8—92no—
604C4×Q8—91no—
605C4×Q8—92no—
606C4×Q8—91no—
607C4×Q8—91no—
608C4×Q8—92no—
609C4×Q8—91no—
610C4×D4—32no—
611C4×D4—31no—
612C4×D4—94no—
613C4×D4—92no—
614#117—32no—
615#117—32no—
616#117—94no—
617#117—94no—
618#117—94no—
619#117—92no—
620C2×C4⋊C4—92no—
621C2×C4⋊C4—91no—
622C2×C42—92no—
623C2×C42D3211yescharacteristic
624C23×C3—21no—
625C23×C3—32no—
626C23×C3C23×D311yescharacteristic
627C23×C3C23×D311yescharacteristic
628C22×D3C23×D312yes—
629C3×Q8—64no—
630C3×Q8—62no—
631C3×Q8—64no—
632C3×D4—64no—
633C3×D4—62no—
634C2×C3×C4—24no—
635C2×C3×C4—24no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—34no—
652C2×C3×C4—34no—
653C2×C3×C4—42no—
654C2×C3×C4—64no—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667#67—24no—
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—62no—
677C2×Dic3—62no—
678C2×Dic3—62no—
679C2×Dic3—62no—
680C2×Dic3—68no—
681C2×Dic3—64no—
682C2×Dic3—64no—
683C2×Dic3—68no—
684C2×Dic3—64no—
685C2×Dic3—64no—
686C2×Dic3—124no—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D314yes—
689C2×Dic3C23×D312yes—
690C2×Dic3C23×D312yes—
691C2×Dic3C23×D314yes—
692D12—22no—
693C4×D3—24no—
694C4×D3—68no—
695Dic6—24no—
696Dic6—24no—
697Dic6—22no—
698Dic6—34no—
699Dic6—34no—
700Dic6—64no—
701Dic6—68no—
702Dic6—68no—
703Dic6—64no—
704Dic6—64no—
705Dic6—68no—
706Dic6—64no—
707Dic6—62no—
708Dic6—62no—
709C2×C32—22no—
710C2×C32C22×#4111yescharacteristic
711C2×C32C2×2−1+411yescharacteristic
712C2×C32C2×2−1+411yescharacteristic
713C3×D3—42no—
714C2×Q8—31no—
715C2×Q8—32no—
716C2×Q8—32no—
717C2×Q8—94no—
718C2×Q8—91no—
719C2×Q8—92no—
720C2×Q8—91no—
721C2×Q8—184no—
722C2×Q8—188no—
723C2×D4—32no—
724C2×D4—31no—
725C22×C4—32no—
726C22×C4—94no—
727C22×C4—92no—
728C22×C4—92no—
729C22×C4C2×D3211yescharacteristic
730C22×C4C2×D3211yescharacteristic
731C22×C4C2×D3211yescharacteristic
732C4⋊C4—32no—
733C4⋊C4—32no—
734C4⋊C4—32no—
735C4⋊C4—32no—
736C4⋊C4—32no—
737C4⋊C4—34no—
738C4⋊C4—31no—
739C4⋊C4—32no—
740C4⋊C4—32no—
741C4⋊C4—31no—
742C4⋊C4—34no—
743C4⋊C4—32no—
744C4⋊C4—94no—
745C4⋊C4—94no—
746C4⋊C4—94no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—92no—
753C4⋊C4—91no—
754C4⋊C4—92no—
755C4⋊C4—91no—
756C4⋊C4—92no—
757C4⋊C4—92no—
758C4⋊C4—92no—
759C22⋊C4—34no—
760C22⋊C4—32no—
761C22⋊C4—32no—
762C22⋊C4—32no—
763C22⋊C4—32no—
764C22⋊C4—32no—
765C22⋊C4—94no—
766C22⋊C4—94no—
767C22⋊C4—94no—
768C42—34no—
769C42—32no—
770C42—94no—
771C42—94no—
772C42—94no—
773C42—92no—
774C42—92no—
775C42—92no—
776C42—92no—
777C42C2×D3211yescharacteristic
778C42C2×D3211yescharacteristic
779C42C2×D3211yescharacteristic
780C42C2×D3211yescharacteristic
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—22no—
788C22×C3—21no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3#100712yes—
793C22×C3#101012yes—
794C22×C3C24×D311yescharacteristic
795C22×C3C24×D311yescharacteristic
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—21no—
805C3×C4—21no—
806C3×C4—21no—
807C3×C4—21no—
808C3×C4—21no—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—41no—
812C3×C4—41no—
813C3×C4—62no—
814C3×C4—62no—
815C3×C4—64no—
816C3×C4—64no—
817C3×C4—62no—
818C3×C4D3×#4112yes—
819C3×C4D3×#4112yes—
820C3×C4#101012yes—
821C3×C4#101012yes—
822Dic3—24no—
823Dic3—22no—
824Dic3—22no—
825Dic3—24no—
826Dic3—22no—
827Dic3—34no—
828Dic3—34no—
829Dic3—64no—
830Dic3—64no—
831Dic3—62no—
832Dic3—62no—
833Dic3—62no—
834Dic3—62no—
835Dic3—62no—
836Dic3—62no—
837Dic3—122no—
838Dic3—122no—
839C32#352311yescharacteristic, complemented, Sylow
840C23—32no—
841C23C22×D3211yescharacteristic
842Q8—62no—
843Q8—64no—
844Q8—64no—
845Q8—94no—
846Q8—184no—
847Q8—188no—
848Q8—182no—
849D4—64no—
850D4—62no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—32no—
855C2×C4—34no—
856C2×C4—32no—
857C2×C4—34no—
858C2×C4—32no—
859C2×C4—64no—
860C2×C4—92no—
861C2×C4—92no—
862C2×C4—92no—
863C2×C4—92no—
864C2×C4—188no—
865C2×C4—184no—
866C2×C4—184no—
867C2×C4C22×D3211yescharacteristic
868C2×C4C22×D3211yescharacteristic
869C2×C4C22×D3211yescharacteristic
870C2×C4C22×D3211yescharacteristic
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3211yescharacteristic
873C2×C3—24no—
874C2×C3—22no—
875C2×C3—22no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—122no—
880C2×C3C2×#100711yescharacteristic
881C2×C3C2×D3×#4111yescharacteristic
882C2×C3C2×D3×#4111yescharacteristic
883C2×C3C2×#101011yescharacteristic
884C2×C3C2×#101011yescharacteristic
885C2×C3C2×#101011yescharacteristic
886D3—42no—
887C22—21no—
888C22—21no—
889C22—62no—
890C22—62no—
891C22—62no—
892C22#6429712yes—
893C22C23×D3211yescharacteristic
894C4—21no—
895C4—21no—
896C4—21no—
897C4—21no—
898C4—62no—
899C4—62no—
900C4—64no—
901C4—62no—
902C4—64no—
903C4—94no—
904C4—182no—
905C4—182no—
906C4—182no—
907C4#6429812yes—
908C4#6430612yes—
909C3—21no—
910C3#8612911yescharacteristic, complemented
911C3#8626611yescharacteristic, complemented
912C2—22no—
913C2—122no—
914C2C2×#6429711yescharacteristic
915C2C2×#6429811yescharacteristic
916C2C2×#6430611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
prime radicalC3×#930C22
hypercenterC2×C42D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
3. C3×#5470C2semidirect
5. #10594960C2semidirect
6. #10594915C2semidirect
7. #10594853C2semidirect
8. #10594810C2semidirect
9. #10593945C2semidirect
10. #10593942C2semidirect
11. #10593904C2semidirect
12. #10593885C2semidirect
13. #10593880C2semidirect
14. #10593864C2semidirect
15. #10593863C2semidirect
16. #10593861C2semidirect
17. #10593853C2semidirect
116. #5470D3semidirect
839. C32#3523semidirect
910. C3#86129semidirect
911. C3#86266semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×#54792
C3×#54702
#105949652
#105949602
#105949152
#105948532
#105948102
#105939452
#105939422
#105939042
#105938852
#105938802
#105938642
#105938632
#105938612
#105938532
#862663
#861293