Finite Group Databasebeta

← D3×#4802 #11857865

Subgroups — D3×#4802 #11857865

Order 1152.

1579 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×Q8C211yesmaximal, characteristic
2C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic
3D3×#892C211yesmaximal, characteristic
4#10592501C211yesmaximal, characteristic, complemented
5C3×#4802C211yesmaximal, characteristic, complemented
6C3×D3×#103C211yesmaximal, characteristic, complemented
7#10591562C211yesmaximal, characteristic, complemented
8#10591557C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10590948C211yesmaximal, characteristic, complemented
11#10590691C211yesmaximal, characteristic, complemented
12D3×#816C211yesmaximal, characteristic, complemented
13#10590602C211yesmaximal, characteristic, complemented
14#10590600C211yesmaximal, characteristic, complemented
15D3×#810C211yesmaximal, characteristic, complemented
16D3×#419—31nomaximal
17C2×#4802—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21D32×Q8—24no—
22D32×Q8C418yescomplemented
23C2×C4×D32—21no—
24C2×C4×D32C2211yescharacteristic
25C2×#3797—21no—
26C2×#3797C2211yescharacteristic
27C2×D3×Dic6—21no—
28C2×D3×Dic6—21no—
29C2×D3×Dic6C2211yescharacteristic
30C2×D3×Dic6C2211yescharacteristic
31C2×#3743C2211yescharacteristic
32#64101C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34C2×C3×D3×C8C2211yescharacteristic
35C3×#892C2211yescharacteristic
36C3×D3×C4⋊C4C2211yescharacteristic
37D3×(C2×D3)⋊C4—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63878—21no—
40C4×D3×Dic3—21no—
41#63849C2211yescharacteristic
42#63841C2211yescharacteristic
43#63836—21no—
44C2×#3712C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C2×D3×C3⋊C8C2211yescharacteristic
47D3×ΓL(1,𝔽25)—24no—
48C32×#103C2211yescharacteristic, complemented
49#63662C2211yescharacteristic, complemented
50#63643C2211yescharacteristic, complemented
51#63637C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#63565C2211yescharacteristic, complemented
64C22×D3×Q8—31no—
65C22×D3×Q8—31no—
66C2×D3×M16—31no—
67C22×ΓL(1,𝔽25)—31no—
68D3×#117—31no—
69C2×#892—31no—
70C3×#419—31no—
71C2×C3×#103—31no—
72#5225—31no—
73C2×#835—31no—
74#5120—31no—
75C2×#816—31no—
76#5004—31no—
77C2×#810—31no—
78#4802—31no—
79#4802—31no—
80#4802—31no—
81#4802—31no—
82#4802—31no—
83#4802—31no—
84#4802—31no—
85#4802—31no—
86#4802—31no—
87#4802—31no—
88#4802—31no—
89#4802—61no—
90#4802D311yescharacteristic, direct product factor
91D3×#103—31no—
92D3×#103—31no—
93D3×#103—31no—
94D3×#103D311yescharacteristic, complemented
95C22×D32D411yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97Q8×C3⋊D3—22no—
98Q8×C3⋊D3C2×C414yescomplemented
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×#634—21no—
102C2×#634C2311yescharacteristic
103C3×D3×Q8—22no—
104C3×D3×Q8—22no—
105C3×D3×Q8C2×C414yes—
106C3×D3×Q8C2×C414yescomplemented
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6—21no—
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#627—21no—
117C2×#627—21no—
118C2×#627—21no—
119C2×#624—21no—
120C2×#624D411yescharacteristic
121C2×D3×Dic3—21no—
122C2×D3×Dic3—21no—
123C2×D3×Dic3—21no—
124C2×D3×Dic3D411yescharacteristic
125C2×D3×Dic3D411yescharacteristic
126C4×D32—28no—
127C4×D32C2×C414yes—
128C4×D32D414yes—
129#3797—22no—
130#3797—28no—
131#3797C2×C414yescomplemented
132D3×Dic6—22no—
133D3×Dic6—22no—
134D3×Dic6—28no—
135D3×Dic6—28no—
136D3×Dic6C2×C414yes—
137D3×Dic6C2×C414yescomplemented
138C2×C32×C8C2311yescharacteristic
139C32×C4⋊C4C2311yescharacteristic
140#3752—21no—
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4×C3⋊Dic3—21no—
143C2×C3⋊(C3⋊C8)C2311yescharacteristic
144#3743—22no—
145C3×(C2×D3)⋊C4—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×ΓL(1,𝔽25)—22no—
153C3×D3×C8—22no—
154Dic3⋊Dic3—21no—
155#3722—21no—
156(C2×D3)⋊Dic3—21no—
157Dic32—21no—
158Dic32—21no—
159#3712—22no—
160#3711—22no—
161D3×C3⋊C8—22no—
162C2×#419—91noSylow
163C22×C3×Q8—31no—
164C22×C3×Q8—31no—
165C2×D3×Q8—31no—
166C2×D3×Q8—31no—
167C2×D3×Q8—38no—
168C2×D3×Q8—38no—
169C2×D3×Q8—31no—
170C2×D3×Q8—31no—
171C2×D3×Q8—31no—
172C2×D3×Q8—31no—
173C2×D3×Q8—61no—
174C2×D3×Q8—61no—
175C2×D3×Q8—61no—
176C2×D3×Q8—61no—
177C2×D3×Q8—61no—
178C2×D3×Q8—64no—
179C2×D3×Q8—64no—
180C2×D3×Q8C2×D311yescharacteristic
181C2×D3×Q8C2×D311yescharacteristic
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—61no—
185C22×C4×D3—61no—
186C22×Dic6—31no—
187C22×Dic6—31no—
188C22×Dic6—61no—
189C22×Dic6—61no—
190C2×C3×M16—31no—
191C22×C3×C8—31no—
192C3×#117—31no—
193C2×C3×C4⋊C4—31no—
194C2×(C2×D3)⋊C4—61no—
195#926—31no—
196C2×C4⋊Dic3—31no—
197C2×C4×Dic3—61no—
198C2×#208—31no—
199C22×C3⋊C8—31no—
200D3×M16—64no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)—61no—
207C2×ΓL(1,𝔽25)—64no—
208C2×ΓL(1,𝔽25)C2×D311yescharacteristic
209C2×D3×C8—31no—
210C2×D3×C8C2×D311yescharacteristic
211#892—31no—
212#892—31no—
213#892—31no—
214#892—31no—
215#892—31no—
216#892—61no—
217#892—61no—
218#892—61no—
219#892C2×D311yescharacteristic
220D3×C4⋊C4—31no—
221D3×C4⋊C4C2×D311yescharacteristic
222D3×C22⋊C4—61no—
223#877—61no—
224#872—61no—
225C42×D3—61no—
226C3×#103—21no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#103—31no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#103C2×D311yescharacteristic, complemented
234C3×#103C2×D311yescharacteristic, complemented
235#835—31no—
236#835—31no—
237#835—31no—
238#835—31no—
239#835—31no—
240#835—31no—
241#835—61no—
242#835C2×D311yescharacteristic, complemented
243#835C2×D311yescharacteristic, complemented
244#816—31no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—31no—
249#816—31no—
250#816—61no—
251#816C2×D311yescharacteristic, complemented
252#816C2×D311yescharacteristic, complemented
253#810—31no—
254#810—31no—
255#810—31no—
256#810—31no—
257#810—31no—
258#810—31no—
259#810—61no—
260#810C2×D311yescharacteristic, complemented
261#810C2×D311yescharacteristic, complemented
262C22×C3⋊D3C2×D411yescharacteristic
263C22×C3×D3C2×D411yescharacteristic
264C22×C3×D3C2×D411yescharacteristic
265C2×D32—22no—
266C2×D32—22no—
267C2×D32C22⋊C414yes—
268C32×Q8—21no—
269C32×Q8C22×C412yes—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2411yescharacteristic
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3C2×D411yescharacteristic
276C4×C3⋊D3—24no—
277C4×C3⋊D3C22×C412yes—
278C4×C3⋊D3C2×D412yes—
279#634—21no—
280#634—24no—
281#634C22×C412yes—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×C4×D3—24no—
289C3×C4×D3—24no—
290C3×C4×D3—42no—
291C3×C4×D3C22×C412yes—
292C3×C4×D3C22×C412yes—
293C3×C4×D3C2×D412yes—
294C3×C4×D3C2×D412yes—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—24no—
298C3×Dic6—24no—
299C3×Dic6C22×C412yes—
300C3×Dic6C22×C412yes—
301#627—24no—
302#627—24no—
303#627—24no—
304#624—24no—
305#624C22⋊C414yes—
306D3×Dic3—24no—
307D3×Dic3—24no—
308D3×Dic3—42no—
309D3×Dic3C22⋊C414yes—
310D3×Dic3C22⋊C414yes—
311C32×C8—21no—
312C3⋊(C3⋊C8)—21no—
313C3×C3⋊C8—21no—
314C3×C3⋊C8—21no—
315C23×Q8—91no—
316C22×M16—91no—
317C2×#117—91no—
318#419—31no—
319#419—91no—
320#419—91no—
321#419—91no—
322#419—91no—
323#419—91no—
324#419—91no—
325#419—91no—
326C2×#103—31no—
327C2×#103—91no—
328C2×#103—91no—
329C2×#103—91no—
330C23×D3—31no—
331C23×D3—31no—
332C2×C3×Q8—21no—
333C2×C3×Q8—34no—
334C2×C3×Q8—34no—
335C2×C3×Q8—31no—
336C2×C3×Q8—31no—
337C2×C3×Q8—61no—
338C2×C3×Q8—61no—
339C2×C3×Q8—62no—
340C2×C3×Q8—62no—
341C2×C3×Q8C22×D311yescharacteristic
342C2×C3×Q8C22×D311yescharacteristic
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353D3×Q8—22no—
354D3×Q8—22no—
355D3×Q8—34no—
356D3×Q8—34no—
357D3×Q8—34no—
358D3×Q8—34no—
359D3×Q8—34no—
360D3×Q8—34no—
361D3×Q8—64no—
362D3×Q8—62no—
363D3×Q8—62no—
364D3×Q8—68no—
365D3×Q8—68no—
366D3×Q8—68no—
367D3×Q8—68no—
368D3×Q8—62no—
369D3×Q8—62no—
370D3×Q8—62no—
371D3×Q8—62no—
372D3×Q8—122no—
373D3×Q8C4×D314yes—
374D3×Q8C4×D314yescomplemented
375C2×C4×D3—21no—
376C2×C4×D3—21no—
377C2×C4×D3—21no—
378C2×C4×D3—31no—
379C2×C4×D3—31no—
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—31no—
384C2×C4×D3—34no—
385C2×C4×D3—34no—
386C2×C4×D3—34no—
387C2×C4×D3—34no—
388C2×C4×D3—61no—
389C2×C4×D3—68no—
390C2×C4×D3—68no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3—61no—
394C2×C4×D3—61no—
395C2×C4×D3—61no—
396C2×C4×D3—61no—
397C2×C4×D3—61no—
398C2×C4×D3—121no—
399C2×C4×D3C22×D311yescharacteristic
400C2×C4×D3C22×D311yescharacteristic
401C2×Dic6—21no—
402C2×Dic6—21no—
403C2×Dic6—31no—
404C2×Dic6—31no—
405C2×Dic6—34no—
406C2×Dic6—34no—
407C2×Dic6—61no—
408C2×Dic6—68no—
409C2×Dic6—68no—
410C2×Dic6—62no—
411C2×Dic6—62no—
412C2×Dic6—61no—
413C2×Dic6—61no—
414C2×Dic6—61no—
415C2×Dic6—61no—
416C2×Dic6—61no—
417C2×Dic6—61no—
418C2×Dic6—61no—
419C2×Dic6—61no—
420C2×Dic6—121no—
421C2×Dic6C22×D311yescharacteristic
422C2×Dic6C22×D311yescharacteristic
423C3×M16—62no—
424C2×C3×C8—21no—
425C2×C3×C8—31no—
426C2×C3×C8—31no—
427C2×C3×C8—62no—
428C2×C3×C8C22×D311yescharacteristic
429C2×C3×C8C22×D311yescharacteristic
430C3×C4⋊C4—21no—
431C3×C4⋊C4—31no—
432C3×C4⋊C4—31no—
433C3×C4⋊C4—61no—
434C3×C4⋊C4C22×D311yescharacteristic
435C3×C4⋊C4C22×D311yescharacteristic
436C3×C22⋊C4—61no—
437C3×C42—61no—
438#217—61no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—121no—
446C4⋊Dic3—31no—
447C4⋊Dic3—31no—
448C4⋊Dic3—61no—
449C4⋊Dic3—61no—
450C4⋊Dic3C22×D311yescharacteristic
451C4⋊Dic3C22×D311yescharacteristic
452Dic3⋊C4—21no—
453Dic3⋊C4—61no—
454C4×Dic3—21no—
455C4×Dic3—61no—
456C4×Dic3—61no—
457C4×Dic3—61no—
458C4×Dic3—61no—
459C4×Dic3—61no—
460C4×Dic3—61no—
461C4×Dic3—121no—
462#208—62no—
463C2×C3⋊C8—31no—
464C2×C3⋊C8—31no—
465C2×C3⋊C8—61no—
466C2×C3⋊C8—62no—
467C2×C3⋊C8C22×D311yescharacteristic
468C2×C3⋊C8C22×D311yescharacteristic
469ΓL(1,𝔽25)—22no—
470ΓL(1,𝔽25)—62no—
471ΓL(1,𝔽25)—62no—
472ΓL(1,𝔽25)—62no—
473ΓL(1,𝔽25)—62no—
474ΓL(1,𝔽25)—62no—
475ΓL(1,𝔽25)—122no—
476D3×C8—22no—
477D3×C8—62no—
478C22×C32C22×D411yescharacteristic
479C2×C3⋊D3—21no—
480C2×C3⋊D3—21no—
481C2×C3⋊D3C2×C22⋊C412yes—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3C2×C22⋊C412yes—
485C2×C3×D3C2×C22⋊C412yes—
486C2×C3×D3#13712yes—
487C2×C3×D3#13712yes—
488D32—28no—
489C32×C4—22no—
490C32×C4—41no—
491C32×C4C23×C411yescharacteristic
492C32×C4C22×D411yescharacteristic
493C3⋊Dic3—22no—
494C3⋊Dic3—41no—
495C3⋊Dic3C2×C22⋊C412yes—
496C3×Dic3—22no—
497C3×Dic3—22no—
498C3×Dic3—41no—
499C3×Dic3—41no—
500C3×Dic3C2×C22⋊C412yes—
501C3×Dic3C2×C22⋊C412yes—
502C22×Q8—31no—
503C22×Q8—31no—
504C22×Q8—91no—
505C22×Q8—91no—
506C22×Q8—91no—
507C22×Q8—98no—
508C22×Q8—91no—
509C22×Q8—181no—
510C22×Q8—181no—
511C22×Q8—181no—
512C22×Q8—184no—
513C23×C4—91no—
514C23×C4—181no—
515C2×M16—31no—
516C2×M16—91no—
517C2×M16—91no—
518C2×M16—91no—
519C2×M16—184no—
520C22×C8—31no—
521C22×C8—91no—
522#117—31no—
523#117—91no—
524#117—91no—
525#117—91no—
526#117—181no—
527#117—181no—
528C2×C4⋊C4—31no—
529C2×C4⋊C4—91no—
530C2×C22⋊C4—181no—
531C2×C42—181no—
532#103—31no—
533#103—31no—
534#103—31no—
535#103—31no—
536#103—31no—
537#103—31no—
538#103—91no—
539#103—91no—
540#103—91no—
541#103—91no—
542#103—91no—
543#103—91no—
544#103—91no—
545#103—91no—
546#103—91no—
547#103D3211yescharacteristic, complemented
548C23×C3—31no—
549C23×C3—31no—
550C22×D3—31no—
551C22×D3—31no—
552C22×D3—34no—
553C22×D3—34no—
554C22×D3—61no—
555C22×D3—62no—
556C22×D3—62no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3D3×D411yescharacteristic
560C22×D3D3×D411yescharacteristic
561C3×Q8—21no—
562C3×Q8—21no—
563C3×Q8—22no—
564C3×Q8—32no—
565C3×Q8—32no—
566C3×Q8—41no—
567C3×Q8—64no—
568C3×Q8—64no—
569C3×Q8—61no—
570C3×Q8—61no—
571C3×Q8C2×C4×D312yes—
572C3×Q8C2×C4×D312yes—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—64no—
587C2×C3×C4—64no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—122no—
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—31no—
600C2×Dic3—31no—
601C2×Dic3—34no—
602C2×Dic3—34no—
603C2×Dic3—61no—
604C2×Dic3—64no—
605C2×Dic3—64no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—121no—
611C2×Dic3—121no—
612C2×Dic3—122no—
613C2×Dic3D3×D411yescharacteristic
614C2×Dic3D3×D411yescharacteristic
615C4×D3—24no—
616C4×D3—24no—
617C4×D3—34no—
618C4×D3—34no—
619C4×D3—32no—
620C4×D3—32no—
621C4×D3—32no—
622C4×D3—32no—
623C4×D3—34no—
624C4×D3—34no—
625C4×D3—42no—
626C4×D3—62no—
627C4×D3—62no—
628C4×D3—64no—
629C4×D3—64no—
630C4×D3—64no—
631C4×D3—64no—
632C4×D3—64no—
633C4×D3—64no—
634C4×D3—124no—
635C4×D3—122no—
636C4×D3C2×C4×D312yes—
637C4×D3C2×C4×D312yes—
638C4×D3D3×D412yes—
639C4×D3D3×D412yes—
640Dic6—21no—
641Dic6—21no—
642Dic6—24no—
643Dic6—24no—
644Dic6—32no—
645Dic6—32no—
646Dic6—62no—
647Dic6—64no—
648Dic6—64no—
649Dic6—64no—
650Dic6—64no—
651Dic6—64no—
652Dic6—64no—
653Dic6—61no—
654Dic6—61no—
655Dic6—64no—
656Dic6—64no—
657Dic6—124no—
658Dic6—121no—
659Dic6C2×C4×D312yes—
660Dic6C2×C4×D312yes—
661C3×C8—21no—
662C3×C8—21no—
663C3×C8—41no—
664C3×C8—61no—
665C3×C8—61no—
666C3⋊C8—21no—
667C3⋊C8—21no—
668C3⋊C8—61no—
669C3⋊C8—61no—
670C3⋊C8—121no—
671C2×C32C22×C22⋊C411yescharacteristic
672C2×C32C2×#13711yescharacteristic
673C2×C32C2×#13711yescharacteristic
674C3⋊D3—22no—
675C3×D3—22no—
676C3×D3#41914yescomplemented
677C24—91no—
678C2×Q8—34no—
679C2×Q8—34no—
680C2×Q8—31no—
681C2×Q8—31no—
682C2×Q8—61no—
683C2×Q8—61no—
684C2×Q8—62no—
685C2×Q8—62no—
686C2×Q8—94no—
687C2×Q8—94no—
688C2×Q8—94no—
689C2×Q8—94no—
690C2×Q8—91no—
691C2×Q8—181no—
692C2×Q8—181no—
693C2×Q8—181no—
694C2×Q8—182no—
695C2×Q8—182no—
696C2×Q8—181no—
697C2×Q8—188no—
698C2×Q8—188no—
699C2×Q8—182no—
700C2×Q8—188no—
701C2×Q8—182no—
702C2×Q8C2×D3211yescharacteristic
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—91no—
709C22×C4—94no—
710C22×C4—94no—
711C22×C4—91no—
712C22×C4—91no—
713C22×C4—91no—
714C22×C4—181no—
715C22×C4—188no—
716C22×C4—181no—
717C22×C4—181no—
718C22×C4—181no—
719C22×C4—181no—
720M16—62no—
721M16—182no—
722M16—182no—
723M16—182no—
724C2×C8—31no—
725C2×C8—31no—
726C2×C8—62no—
727C2×C8—91no—
728C2×C8—182no—
729C2×C8C2×D3211yescharacteristic
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—61no—
733C4⋊C4—91no—
734C4⋊C4—181no—
735C4⋊C4C2×D3211yescharacteristic
736C22⋊C4—61no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C42—61no—
741C42—181no—
742C42—181no—
743C42—181no—
744C22×C3—21no—
745C22×C3—32no—
746C22×C3—32no—
747C22×C3—32no—
748C22×C3—32no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—32no—
756C2×D3—32no—
757C2×D3—62no—
758C2×D3—68no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—68no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3D3×C22⋊C412yes—
767C2×D3D3×C22⋊C412yes—
768C2×D3#91512yes—
769C2×D3#91812yes—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—32no—
775C3×C4—32no—
776C3×C4—42no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—62no—
780C3×C4—62no—
781C3×C4—81no—
782C3×C4—121no—
783C3×C4—121no—
784C3×C4C22×C4×D311yescharacteristic
785C3×C4C22×C4×D311yescharacteristic
786C3×C4C2×D3×D411yescharacteristic
787C3×C4C2×D3×D411yescharacteristic
788Dic3—22no—
789Dic3—22no—
790Dic3—32no—
791Dic3—32no—
792Dic3—41no—
793Dic3—41no—
794Dic3—62no—
795Dic3—62no—
796Dic3—62no—
797Dic3—122no—
798Dic3—121no—
799Dic3—121no—
800Dic3—241no—
801Dic3D3×C22⋊C412yes—
802Dic3D3×C22⋊C412yes—
803C32C2×#41911yescharacteristic, complemented, Sylow
804C23—31no—
805C23—31no—
806C23—94no—
807C23—91no—
808C23—182no—
809C23—182no—
810Q8—21no—
811Q8—32no—
812Q8—32no—
813Q8—64no—
814Q8—64no—
815Q8—61no—
816Q8—61no—
817Q8—92no—
818Q8—184no—
819Q8—184no—
820Q8—184no—
821Q8—184no—
822Q8—181no—
823Q8C4×D3212yes—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—31no—
827C2×C4—31no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—64no—
833C2×C4—64no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—94no—
839C2×C4—94no—
840C2×C4—94no—
841C2×C4—91no—
842C2×C4—92no—
843C2×C4—92no—
844C2×C4—122no—
845C2×C4—184no—
846C2×C4—184no—
847C2×C4—184no—
848C2×C4—184no—
849C2×C4—181no—
850C2×C4—181no—
851C2×C4—362no—
852C2×C4C22×D3211yescharacteristic
853C8—21no—
854C8—61no—
855C8—61no—
856C8—181no—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—34no—
861C2×C3—62no—
862C2×C3C2×D3×C22⋊C411yescharacteristic
863C2×C3C2×D3×C22⋊C411yescharacteristic
864C2×C3C2×#91511yescharacteristic
865C2×C3C2×#91811yescharacteristic
866C2×C3D3×#13711yescharacteristic
867C2×C3D3×#13711yescharacteristic
868D3—22no—
869D3—62no—
870D3—62no—
871D3—122no—
872D3#480214yesdirect product factor
873C22—32no—
874C22—32no—
875C22—32no—
876C22—32no—
877C22—61no—
878C22—61no—
879C22—92no—
880C22—188no—
881C22—181no—
882C22—181no—
883C22D32×D411yescharacteristic
884C4—22no—
885C4—32no—
886C4—32no—
887C4—41no—
888C4—62no—
889C4—62no—
890C4—92no—
891C4—121no—
892C4—121no—
893C4—182no—
894C4—361no—
895C4C2×C4×D3211yescharacteristic
896C4D32×D411yescharacteristic
897C3—21no—
898C3C2×#480211yescharacteristic, complemented
899C3D3×#41911yescharacteristic, complemented
900C2—34no—
901C2—62no—
902C2—182no—
903C2D32×C22⋊C411yescharacteristic
904C2D3×#91511yescharacteristic
905C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×D32D4
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C2×#419
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
4. #10592501C2semidirect
5. C3×#4802C2semidirect
6. C3×D3×#103C2semidirect
7. #10591562C2semidirect
8. #10591557C2semidirect
9. D3×#835C2semidirect
10. #10590948C2semidirect
11. #10590691C2semidirect
12. D3×#816C2semidirect
13. #10590602C2semidirect
14. #10590600C2semidirect
15. D3×#810C2semidirect
22. D32×Q8C4semidirect
48. C32×#103C22semidirect
49. #63662C22semidirect
50. #63643C22semidirect
51. #63637C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#816C22semidirect
55. C3×#816C22semidirect
56. C3×#810C22semidirect
57. C3×#810C22semidirect
58. #63567C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63566C22semidirect
62. #63565C22semidirect
63. #63565C22semidirect
90. #4802D3direct (N × H)
94. D3×#103D3semidirect
98. Q8×C3⋊D3C2×C4semidirect
106. C3×D3×Q8C2×C4semidirect
131. #3797C2×C4semidirect
137. D3×Dic6C2×C4semidirect
233. C3×#103C2×D3semidirect
234. C3×#103C2×D3semidirect
242. #835C2×D3semidirect
243. #835C2×D3semidirect
251. #816C2×D3semidirect
252. #816C2×D3semidirect
260. #810C2×D3semidirect
261. #810C2×D3semidirect
374. D3×Q8C4×D3semidirect
547. #103D32semidirect
676. C3×D3#419semidirect
803. C32C2×#419semidirect
872. D3#4802direct (N × H)
898. C3C2×#4802semidirect
899. C3D3×#419semidirect

Maximal subgroups

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

subgroupindex
C2×D32×Q82
C2×D3×ΓL(1,𝔽25)2
D3×#8922
#105925012
C3×#48022
C3×D3×#1032
#105915622
#105915572
D3×#8352
#105909482
#105906912
D3×#8162
#105906022
#105906002
D3×#8102
D3×#4193
C2×#48023