Finite Group Databasebeta

← D3×#4816 #11867028

Subgroups — D3×#4816 #11867028

Order 1152.

1039 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#946C211yesmaximal, characteristic
2C2×D3×#216C211yesmaximal, characteristic, complemented
3C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic
4D3×#897C211yesmaximal, characteristic
5#10592515C211yesmaximal, characteristic, complemented
6C3×#4816C211yesmaximal, characteristic, complemented
7C3×D3×#103C211yesmaximal, characteristic, complemented
8#10591600C211yesmaximal, characteristic, complemented
9#10591598C211yesmaximal, characteristic, complemented
10#10590856C211yesmaximal, characteristic, complemented
11#10590849C211yesmaximal, characteristic, complemented
12D3×#816C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590524C211yesmaximal, characteristic, complemented
15#10590520C211yesmaximal, characteristic, complemented
16D3×#470—31nomaximal
17C2×#4816—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C4×D32C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64155C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3743C2211yescharacteristic
24#64106C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#897C2211yescharacteristic
30C3×D3×C4⋊C4C2211yescharacteristic
31D3×#216—24no—
32D3×(C2×D3)⋊C4—21no—
33D3×(C2×D3)⋊C4—21no—
34#63895—21no—
35#63893—21no—
36D3×C4⋊Dic3—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38#63888—21no—
39#63887—21no—
40D3×Dic3⋊C4—21no—
41#63871C2211yescharacteristic
42#63871C2211yescharacteristic
43#63857C2211yescharacteristic
44#63856C2211yescharacteristic
45C2×#3719C2211yescharacteristic, complemented
46C2×#3718C2211yescharacteristic, complemented
47C2×#3712C2211yescharacteristic
48C2×#3711C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50D3×ΓL(1,𝔽25)—24no—
51C32×#103C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59#63574C2211yescharacteristic, complemented
60#63573C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63566C2211yescharacteristic, complemented
63C2×#946—31no—
64C22×#216—31no—
65C2×D3×Q16—31no—
66C2×D3×M16—31no—
67C22×ΓL(1,𝔽25)—31no—
68D3×C22⋊Q8—31no—
69D3×C22⋊Q8—31no—
70C2×#897—31no—
71C3×#470—31no—
72C2×C3×#103—31no—
73#5189—31no—
74#5137—31no—
75C2×#816—31no—
76#5052—31no—
77#5052—31no—
78C2×#808—31no—
79#4867—31no—
80D3×#106—31no—
81#4816—31no—
82#4816—31no—
83#4816—31no—
84#4816—31no—
85#4816—31no—
86#4816—31no—
87#4816—31no—
88#4816—31no—
89#4816—31no—
90#4816—61no—
91#4816D311yescharacteristic, direct product factor
92D3×#103—31no—
93D3×#103D311yescharacteristic, complemented
94C22×D32D411yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C3×D3×Q8—22no—
99C3×D3×Q8—22no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#627—21no—
108C2×#624D411yescharacteristic
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3D411yescharacteristic
112C2×D3×Dic3D411yescharacteristic
113C4×D32—22no—
114C4×D32—22no—
115D3×Dic6—22no—
116D3×Dic6—22no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3756—22no—
120#3752—21no—
121#3752—21no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3743—22no—
127C3×#216—22no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×ΓL(1,𝔽25)—22no—
138C3×D3×C8—22no—
139#3724—21no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144#3722—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3719—22no—
149#3718—22no—
150#3712—22no—
151#3711—22no—
152D3×C3⋊C8D414yes—
153C2×#470—91noSylow
154C22×C3×Q8—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8C2×D311yescharacteristic
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×M16—31no—
162C22×C3×C8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C2×C3×C4⋊C4—31no—
166#946—31no—
167#946—31no—
168#946—31no—
169#946—31no—
170#946—31no—
171#946—61no—
172#946—61no—
173#946—61no—
174#946C2×D311yescharacteristic
175C2×#216—31no—
176C2×#216—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#216—61no—
181C2×#216—64no—
182C2×#216C2×D311yescharacteristic, complemented
183C2×(C2×D3)⋊C4—61no—
184C2×(C2×D3)⋊C4—61no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—61no—
187#924—31no—
188#924—31no—
189C2×Dic3⋊C4—61no—
190C2×#208—31no—
191C22×C3⋊C8—31no—
192D3×Q16—64no—
193D3×M16—64no—
194C2×Dic12—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—61no—
201C2×ΓL(1,𝔽25)—64no—
202C2×ΓL(1,𝔽25)C2×D311yescharacteristic
203C2×D3×C8—31no—
204C2×D3×C8C2×D311yescharacteristic
205#897—31no—
206#897—31no—
207#897—31no—
208#897—31no—
209#897—31no—
210#897—61no—
211#897—61no—
212#897—61no—
213#897C2×D311yescharacteristic
214#896—61no—
215#896—61no—
216D3×C4⋊C4—31no—
217D3×C4⋊C4—61no—
218D3×C4⋊C4—61no—
219D3×C4⋊C4C2×D311yescharacteristic
220D3×C22⋊C4—61no—
221D3×C22⋊C4—61no—
222#878—61no—
223#878—61no—
224C3×#106—31no—
225C3×#103—21no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#103C2×D311yescharacteristic, complemented
231C3×#103C2×D311yescharacteristic, complemented
232#835—31no—
233#835C2×D311yescharacteristic, complemented
234#817—31no—
235#816—31no—
236#816—31no—
237#816—31no—
238#816—31no—
239#816—61no—
240#816C2×D311yescharacteristic, complemented
241#816C2×D311yescharacteristic, complemented
242#810—31no—
243#810C2×D311yescharacteristic, complemented
244#808—31no—
245#808—31no—
246#808—31no—
247#808—31no—
248#808—31no—
249#808—61no—
250#808C2×D311yescharacteristic, complemented
251C22×C3⋊D3C2×D411yescharacteristic
252C22×C3×D3C2×D411yescharacteristic
253C22×C3×D3C2×D411yescharacteristic
254C2×D32—22no—
255C2×D32—22no—
256C2×D32—22no—
257C32×Q8—21no—
258C32×Q8—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2411yescharacteristic
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3C2×D411yescharacteristic
265C4×C3⋊D3—21no—
266C4×C3⋊D3—21no—
267#634—21no—
268#634—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—42no—
278C3×C4×D3—42no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—42no—
286#627—42no—
287#624—22no—
288D3×Dic3—22no—
289D3×Dic3—22no—
290D3×Dic3—42no—
291D3×Dic3—42no—
292C32×C8—21no—
293C3⋊(C3⋊C8)C2×D412yes—
294C3×C3⋊C8—21no—
295C3×C3⋊C8C2×D412yes—
296C22×Q16—91no—
297C22×M16—91no—
298C2×C22⋊Q8—91no—
299C2×C22⋊Q8—91no—
300#470—31no—
301#470—91no—
302#470—91no—
303#470—91no—
304#470—91no—
305#470—91no—
306#470—91no—
307#470—91no—
308C2×#106—91no—
309C2×#103—31no—
310C2×#103—91no—
311C23×D3—31no—
312C23×D3—31no—
313C2×C3×Q8—21no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×Q8—61no—
317C2×C3×Q8—62no—
318C2×C3×Q8—62no—
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×Q8C22×D311yescharacteristic
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329D3×Q8—22no—
330D3×Q8—22no—
331D3×Q8—62no—
332D3×Q8—62no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—61no—
342C2×C4×D3—62no—
343C2×C4×D3—62no—
344C2×C4×D3—62no—
345C2×C4×D3—62no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3C22×D311yescharacteristic
349C2×C4×D3C22×D311yescharacteristic
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
360C3×Q16—62no—
361C3×M16—62no—
362C2×C3×C8—21no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—62no—
366C2×C3×C8C22×D311yescharacteristic
367C2×C3×C8C22×D311yescharacteristic
368C3×C4⋊C4—21no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378#217—61no—
379#217—61no—
380#216—22no—
381#216—62no—
382#216—62no—
383#216—62no—
384#216—62no—
385#216—62no—
386#216—122no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—121no—
400(C2×D3)⋊C4—121no—
401C4⋊Dic3—21no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—121no—
412C4⋊Dic3C22×D311yescharacteristic
413C4⋊Dic3C22×D311yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4—121no—
425#208—62no—
426C2×C3⋊C8—31no—
427C2×C3⋊C8—31no—
428C2×C3⋊C8—34no—
429C2×C3⋊C8—61no—
430C2×C3⋊C8C22×D311yescharacteristic
431C2×C3⋊C8C22×D311yescharacteristic
432Dic12—62no—
433ΓL(1,𝔽25)—22no—
434ΓL(1,𝔽25)—62no—
435ΓL(1,𝔽25)—62no—
436ΓL(1,𝔽25)—62no—
437ΓL(1,𝔽25)—62no—
438ΓL(1,𝔽25)—62no—
439ΓL(1,𝔽25)—122no—
440D3×C8—22no—
441D3×C8—34no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—21no—
449C2×C3×D3#12112yes—
450C2×C3×D3#13712yes—
451C2×C3×D3#13712yes—
452D32—44no—
453C32×C4—41no—
454C32×C4—41no—
455C32×C4C22×D411yescharacteristic
456C32×C4C2×#4111yescharacteristic
457C3⋊Dic3—21no—
458C3⋊Dic3—41no—
459C3⋊Dic3—41no—
460C3×Dic3—21no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C22×Q8—31no—
467C22×Q8—91no—
468C23×C4—91no—
469C2×Q16—31no—
470C2×Q16—91no—
471C2×Q16—91no—
472C2×Q16—91no—
473C2×Q16—184no—
474C2×M16—31no—
475C2×M16—91no—
476C2×M16—91no—
477C2×M16—91no—
478C2×M16—184no—
479C22×C8—31no—
480C22×C8—91no—
481C22⋊Q8—31no—
482C22⋊Q8—31no—
483C22⋊Q8—91no—
484C22⋊Q8—91no—
485C22⋊Q8—91no—
486C22⋊Q8—91no—
487C22⋊Q8—91no—
488C22⋊Q8—91no—
489C22⋊Q8—181no—
490C22⋊Q8—181no—
491C22⋊Q8—181no—
492C22⋊Q8—181no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—181no—
496C2×C4⋊C4—181no—
497C2×C22⋊C4—181no—
498C2×C22⋊C4—181no—
499#106—31no—
500#106—91no—
501#106—91no—
502#106—91no—
503#103—31no—
504#103—31no—
505#103—31no—
506#103—31no—
507#103—91no—
508#103—91no—
509#103—91no—
510#103D3211yescharacteristic, complemented
511C23×C3—31no—
512C23×C3—31no—
513C22×D3—31no—
514C22×D3—31no—
515C22×D3—61no—
516C22×D3—62no—
517C22×D3—62no—
518C22×D3—62no—
519C22×D3—62no—
520C22×D3—62no—
521C22×D3—62no—
522C22×D3D3×D411yescharacteristic
523C22×D3D3×D411yescharacteristic
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—21no—
528C3×Q8—41no—
529C3×Q8—41no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×Q8—61no—
534C3×Q8—122no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—31no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—31no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—122no—
553C2×C3×C4—122no—
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—61no—
563C2×Dic3—62no—
564C2×Dic3—62no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—121no—
570C2×Dic3—121no—
571C2×Dic3—122no—
572C2×Dic3—122no—
573C2×Dic3D3×D411yescharacteristic
574C2×Dic3D3×D411yescharacteristic
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—42no—
578C4×D3—42no—
579C4×D3—62no—
580C4×D3—62no—
581C4×D3—62no—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—61no—
585C4×D3—61no—
586C4×D3—62no—
587C4×D3—121no—
588C4×D3—121no—
589C4×D3—122no—
590C4×D3—122no—
591C4×D3#23512yes—
592C4×D3D3×D412yes—
593Dic6—21no—
594Dic6—21no—
595Dic6—21no—
596Dic6—21no—
597Dic6—42no—
598Dic6—61no—
599Dic6—61no—
600Dic6—61no—
601Dic6—61no—
602Dic6—121no—
603Dic6—121no—
604Dic6—122no—
605Dic6—122no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—32no—
609C3×C8—41no—
610C3×C8—61no—
611C3⋊C8—21no—
612C3⋊C8—32no—
613C3⋊C8—32no—
614C3⋊C8—62no—
615C3⋊C8D3×D412yes—
616C2×C32C2×#12111yescharacteristic
617C2×C32C2×#13711yescharacteristic
618C2×C32C2×#13711yescharacteristic
619C3⋊D3—41no—
620C3×D3—41no—
621C3×D3#47014yescomplemented
622C24—91no—
623C2×Q8—31no—
624C2×Q8—31no—
625C2×Q8—61no—
626C2×Q8—62no—
627C2×Q8—62no—
628C2×Q8—91no—
629C2×Q8—181no—
630C2×Q8—182no—
631C2×Q8—182no—
632C2×Q8C2×D3211yescharacteristic
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—91no—
638C22×C4—91no—
639C22×C4—91no—
640C22×C4—91no—
641C22×C4—182no—
642C22×C4—182no—
643C22×C4—181no—
644C22×C4—181no—
645Q16—62no—
646Q16—182no—
647Q16—182no—
648Q16—182no—
649M16—62no—
650M16—182no—
651M16—182no—
652M16—182no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—62no—
656C2×C8—94no—
657C2×C8—91no—
658C2×C8C2×D3211yescharacteristic
659C4⋊C4—31no—
660C4⋊C4—31no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—181no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4—181no—
671C4⋊C4—181no—
672C4⋊C4C2×D3211yescharacteristic
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22×C3—21no—
682C22×C3—32no—
683C22×C3—32no—
684C22×C3—32no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3C2×D3×D411yescharacteristic
689C22×C3C2×D3×D411yescharacteristic
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—124no—
703C2×D3—124no—
704C2×D3#88412yes—
705C2×D3#91512yes—
706C2×D3#91812yes—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—32no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—61no—
715C3×C4—81no—
716C3×C4—81no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4C2×#23511yescharacteristic
722C3×C4C2×D3×D411yescharacteristic
723C3×C4C2×D3×D411yescharacteristic
724C3×C4D3×#4111yescharacteristic
725Dic3—21no—
726Dic3—41no—
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—61no—
731Dic3—61no—
732Dic3—121no—
733Dic3—121no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—241no—
738Dic3—241no—
739Dic3#88412yes—
740C32C2×#47011yescharacteristic, complemented, Sylow
741C23—31no—
742C23—31no—
743C23—91no—
744C23—182no—
745C23—182no—
746C23—182no—
747Q8—21no—
748Q8—21no—
749Q8—61no—
750Q8—61no—
751Q8—61no—
752Q8—61no—
753Q8—122no—
754Q8—181no—
755Q8—181no—
756Q8—362no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—31no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—31no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—91no—
770C2×C4—122no—
771C2×C4—122no—
772C2×C4—182no—
773C2×C4—182no—
774C2×C4—182no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—362no—
780C2×C4—362no—
781C2×C4C22×D3211yescharacteristic
782C8—21no—
783C8—32no—
784C8—61no—
785C8—92no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—34no—
790C2×C3—121no—
791C2×C3C2×#88411yescharacteristic
792C2×C3D3×#12111yescharacteristic
793C2×C3C2×#91511yescharacteristic
794C2×C3C2×#91811yescharacteristic
795C2×C3D3×#13711yescharacteristic
796C2×C3D3×#13711yescharacteristic
797D3—41no—
798D3—121no—
799D3—121no—
800D3—241no—
801D3#481614yesdirect product factor
802C22—32no—
803C22—32no—
804C22—32no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—181no—
809C22—181no—
810C22—181no—
811C22—364no—
812C22D32×D411yescharacteristic
813C4—32no—
814C4—41no—
815C4—41no—
816C4—61no—
817C4—121no—
818C4—121no—
819C4—121no—
820C4—121no—
821C4—181no—
822C4—361no—
823C4—361no—
824C4D3×#23511yescharacteristic
825C4D32×D411yescharacteristic
826C3—21no—
827C3C2×#481611yescharacteristic, complemented
828C3D3×#47011yescharacteristic, complemented
829C2—34no—
830C2—121no—
831C2—361no—
832C2D3×#88411yescharacteristic
833C2D3×#91511yescharacteristic
834C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#103D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×D3×#216C2semidirect
5. #10592515C2semidirect
6. C3×#4816C2semidirect
7. C3×D3×#103C2semidirect
8. #10591600C2semidirect
9. #10591598C2semidirect
10. #10590856C2semidirect
11. #10590849C2semidirect
12. D3×#816C2semidirect
13. D3×#808C2semidirect
14. #10590524C2semidirect
15. #10590520C2semidirect
22. C2×#3756C22semidirect
26. C2×C3×#216C22semidirect
45. C2×#3719C22semidirect
46. C2×#3718C22semidirect
51. C32×#103C22semidirect
52. #63643C22semidirect
53. #63635C22semidirect
54. C3×#835C22semidirect
55. C3×#816C22semidirect
56. C3×#816C22semidirect
57. C3×#810C22semidirect
58. C3×#808C22semidirect
59. #63574C22semidirect
60. #63573C22semidirect
61. #63567C22semidirect
62. #63566C22semidirect
91. #4816D3direct (N × H)
93. D3×#103D3semidirect
182. C2×#216C2×D3semidirect
230. C3×#103C2×D3semidirect
231. C3×#103C2×D3semidirect
233. #835C2×D3semidirect
240. #816C2×D3semidirect
241. #816C2×D3semidirect
243. #810C2×D3semidirect
250. #808C2×D3semidirect
510. #103D32semidirect
621. C3×D3#470semidirect
740. C32C2×#470semidirect
801. D3#4816direct (N × H)
827. C3C2×#4816semidirect
828. C3D3×#470semidirect

Maximal subgroups

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

subgroupindex
D3×#9462
C2×D3×#2162
C2×D3×ΓL(1,𝔽25)2
D3×#8972
#105925152
C3×#48162
C3×D3×#1032
#105916002
#105915982
#105908562
#105908492
D3×#8162
D3×#8082
#105905242
#105905202
D3×#4703
C2×#48163