Finite Group Databasebeta

← #11889125

Subgroups — #11889125

Order 1152.

955 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5694C211yesmaximal, characteristic, complemented
2D122C211yesmaximal, characteristic
3#10592766C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5#10590596C211yesmaximal, characteristic, complemented
6#10590596C211yesmaximal, characteristic, complemented
7#10590592C211yesmaximal, characteristic, complemented
8D3×#809C211yesmaximal, characteristic, complemented
9#10590585C211yesmaximal, characteristic, complemented
10#10590577C211yesmaximal, characteristic, complemented
11#10590425C211yesmaximal, characteristic, complemented
12#10590422C211yesmaximal, characteristic, complemented
13#10590367C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83599—31nomaximal
17#81189—31nomaximal
18C2×D3×D12—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C32×#125C2211yescharacteristic, complemented
22#64083C2211yescharacteristic
23C3×#898—21no—
24C3×#897C2211yescharacteristic, complemented
25C3×#897C2211yescharacteristic, complemented
26C3×#894—21no—
27C3×#892—21no—
28C3×#892C2211yescharacteristic, complemented
29C3×D3×C4⋊C4C2211yescharacteristic, complemented
30C3×#890—21no—
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic, complemented
34#63923—21no—
35#63923—21no—
36#63909—21no—
37#63909C2211yescharacteristic
38#63909C2211yescharacteristic
39C2×#3717C2211yescharacteristic, complemented
40C2×#3717C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63636C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47#63636C2211yescharacteristic, complemented
48#63630C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#552—31no—
62#5694D311yescharacteristic, complemented
63D4×D12—31no—
64D4×D12—31no—
65C3×#478—31no—
66#5067—31no—
67#5067—31no—
68#5067—61no—
69#5066D311yescharacteristic, complemented
70#5049—31no—
71#5048—31no—
72#5046—31no—
73#5046—31no—
74#5027—31no—
75#5026—31no—
76#5018—31no—
77#5011—31no—
78#5003—31no—
79#5001—31no—
80#4967—31no—
81C2×#809—31no—
82#4886—31no—
83#4882—31no—
84#4866—31no—
85#4864—31no—
86#4848—31no—
87#4836—31no—
88#4776—31no—
89#4776—31no—
90#4770—31no—
91D3×#102—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×D12D411yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109D3×D12—22no—
110D3×D12—22no—
111D3×D12—41no—
112D3×D12—41no—
113D3×D12—44no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C42C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3722—21no—
139#3722—21no—
140#3717—41no—
141#3717—41no—
142#3715—22no—
143#3711—41no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—61no—
152C3×#126—61no—
153C3×#125—21no—
154C3×#125—61no—
155C3×#125C2×D311yescharacteristic, complemented
156C3×#125C2×D311yescharacteristic, complemented
157C3×#123—61no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×#117—31no—
164C3×#117—61no—
165C2×C3×C4⋊C4—31no—
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—31no—
169C2×#214—31no—
170#930—31no—
171#930—31no—
172#930—61no—
173C2×#208—31no—
174C22×C3⋊C8—31no—
175C2×#204—31no—
176C2×#204—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×D3×C8—31no—
179#898—21no—
180#897C2×D311yescharacteristic, complemented
181#897C2×D311yescharacteristic, complemented
182#895—31no—
183#895—31no—
184#895—61no—
185#894—21no—
186#892—21no—
187#892C2×D311yescharacteristic, complemented
188D3×C4⋊C4C2×D311yescharacteristic, complemented
189#890—21no—
190#882—61no—
191#882—61no—
192#882—61no—
193#882—61no—
194#874—31no—
195#874—31no—
196#874—61no—
197C4×D12C2×D311yescharacteristic
198C4×D12C2×D311yescharacteristic
199C4×Dic6C2×D311yescharacteristic, complemented
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#102—31no—
204C3×#102—31no—
205#835—31no—
206#832—31no—
207#830—31no—
208#830—31no—
209#821—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213#810—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#809—61no—
227#809—61no—
228#809—61no—
229#809C2×D311yescharacteristic
230#809C2×D311yescharacteristic
231#808C2×D311yescharacteristic, complemented
232#807—31no—
233#807—31no—
234#807C2×D311yescharacteristic, complemented
235C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
236#803—31no—
237#803—31no—
238#803—61no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—42no—
260C4⋊(C3⋊D3)—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—22no—
267C3×D12—21no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—42no—
274C3×C4×D3—42no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277#626—42no—
278#626—42no—
279#626—42no—
280#626—42no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—31no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—31no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315D3×D4—62no—
316D3×D4—62no—
317D3×D4—121no—
318D3×D4—121no—
319D3×D4—124no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—62no—
327C2×D12—62no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—121no—
337C2×D12—121no—
338C2×D12—121no—
339C2×D12—121no—
340C2×D12—124no—
341C2×D12#6711yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3C22×D311yescharacteristic
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6C22×D311yescharacteristic
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—41no—
360C3×C4⋊C4—41no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C22⋊C4—31no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—21no—
376C3×C42—61no—
377C3×C42—61no—
378C3×C42C22×D311yescharacteristic
379C3×C42C22×D311yescharacteristic
380#215—62no—
381#215—121no—
382#215—121no—
383#214—62no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4#6711yescharacteristic
393(C2×D3)⋊C4#6711yescharacteristic
394C4⋊Dic3—21no—
395C4⋊Dic3—21no—
396C4⋊Dic3#6711yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403#208—121no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—121no—
414#204—121no—
415ΓL(1,𝔽25)—121no—
416D3×C8—121no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3AGL(1,ℤ/8)12yes—
433D32—84no—
434D32—84no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4—41no—
438C32×C4—41no—
439C32×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—91no—
447C22×D4—91no—
448C22×D4—181no—
449C2×SD16—91no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×M16—91no—
453C22×C8—91no—
454#127—91no—
455#126—61no—
456#125—61no—
457#125D3211yescharacteristic, complemented
458#123—61no—
459C22⋊Q8—31no—
460C22⋊Q8—31no—
461#121—91no—
462#121—91no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—31no—
467C4×D4—31no—
468C4×D4—31no—
469#117—31no—
470#117—61no—
471C2×C4⋊C4—31no—
472#107—31no—
473#107—91no—
474#106—31no—
475C4⋊C8—31no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486C22⋊C8—91no—
487C22⋊C8—91no—
488#97—91no—
489C23×C3—31no—
490C23×C3—31no—
491C23×C3—61no—
492C22×D3—21no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—121no—
498C22×D3—121no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—241no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3C2×#6711yescharacteristic
512C22×D3C2×#6711yescharacteristic
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—32no—
516C3×D4—62no—
517C3×D4—61no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—122no—
537C2×C3×C4—122no—
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4C2×#6711yescharacteristic
541C2×C3×C4C2×#6711yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3C2×#6711yescharacteristic
552C2×Dic3C2×#6711yescharacteristic
553D12—22no—
554D12—21no—
555D12—61no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—121no—
564D12—121no—
565D12—121no—
566D12—121no—
567D12—122no—
568D12—122no—
569D12—122no—
570D12—122no—
571D12—122no—
572D12—122no—
573D12—242no—
574D12—241no—
575D12—241no—
576D12—242no—
577D12#23912yes—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—42no—
583C4×D3—42no—
584Dic6—21no—
585Dic6—21no—
586C3×C8—61no—
587C3×C8—61no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—121no—
595C3⋊C8—121no—
596C2×C32#54611yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C2×C32#57711yescharacteristic
599C3⋊D3—81no—
600C3⋊D3—81no—
601C3×D3—22no—
602C3×D3—41no—
603C3×D3—42no—
604C24—181no—
605C24—181no—
606C2×Q8—31no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—91no—
610C2×D4—91no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4—182no—
614C2×D4—182no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—361no—
620C2×D4—361no—
621C2×D4—364no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—61no—
625C22×C4—61no—
626SD16—182no—
627SD16—361no—
628SD16—361no—
629M16—361no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—91no—
634C2×C8—361no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4C2×D3211yescharacteristic
645C4⋊C4C2×D3211yescharacteristic
646C22⋊C4—31no—
647C22⋊C4—31no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C42—61no—
655C42—61no—
656C42C2×D3211yescharacteristic
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—62no—
664C22×C3—61no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C22×#6711yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—22no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—241no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3—241no—
693C2×D3—241no—
694C2×D3—241no—
695C2×D3—244no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3—244no—
699C2×D3#94912yes—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—81no—
715C3×C4—81no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4C2×#23911yescharacteristic
720C3×C4D3×#4111yescharacteristic
721C3×C4#100911yescharacteristic
722C3×C4#100911yescharacteristic
723Dic3—21no—
724Dic3—21no—
725Dic3—41no—
726Dic3—41no—
727Dic3—41no—
728C32#331011yescharacteristic, complemented, Sylow
729C23—31no—
730C23—31no—
731C23—61no—
732C23—181no—
733C23—181no—
734C23—362no—
735C23—362no—
736C23—362no—
737C23—362no—
738C23—721no—
739C23—721no—
740Q8—61no—
741Q8—61no—
742D4—32no—
743D4—62no—
744D4—61no—
745D4—181no—
746D4—181no—
747D4—181no—
748D4—181no—
749D4—362no—
750D4—362no—
751D4—362no—
752D4—362no—
753D4—362no—
754D4—721no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4D3×#6711yescharacteristic
769C2×C4D3×#6711yescharacteristic
770C2×C4C22×D3211yescharacteristic
771C8—61no—
772C8—61no—
773C8—181no—
774C8—181no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—62no—
779C2×C3—121no—
780C2×C3—122no—
781C2×C3#563011yescharacteristic
782C2×C3#577011yescharacteristic
783C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
784C2×C3C2×#94911yescharacteristic
785C2×C3#582911yescharacteristic
786C2×C3#583711yescharacteristic
787D3—22no—
788D3—42no—
789D3—41no—
790D3—241no—
791D3—241no—
792D3—241no—
793D3—241no—
794D3—481no—
795D3—481no—
796C22—32no—
797C22—61no—
798C22—61no—
799C22—61no—
800C22—62no—
801C22—61no—
802C22—61no—
803C22—121no—
804C22—121no—
805C22—361no—
806C22—361no—
807C22—361no—
808C22—361no—
809C22—361no—
810C22—361no—
811C22—724no—
812C22—724no—
813C22C2×D3×#6711yescharacteristic
814C4—21no—
815C4—21no—
816C4—41no—
817C4—41no—
818C4—61no—
819C4—61no—
820C4—121no—
821C4—121no—
822C4—121no—
823C4D3×#23911yescharacteristic
824C4#6432011yescharacteristic
825C3—21no—
826C3#8118911yescharacteristic, complemented
827C3#8359911yescharacteristic, complemented
828C2—62no—
829C2—121no—
830C2—122no—
831C2—721no—
832C2—721no—
833C2#1059542711yescharacteristic
834C2D3×#94911yescharacteristic
835C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalD122C2
hypercenter#125D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×#5694C2semidirect
3. #10592766C2semidirect
4. C3×#5066C2semidirect
5. #10590596C2semidirect
6. #10590596C2semidirect
7. #10590592C2semidirect
8. D3×#809C2semidirect
9. #10590585C2semidirect
10. #10590577C2semidirect
11. #10590425C2semidirect
12. #10590422C2semidirect
13. #10590367C2semidirect
14. #10590358C2semidirect
15. #10590330C2semidirect
21. C32×#125C22semidirect
24. C3×#897C22semidirect
25. C3×#897C22semidirect
28. C3×#892C22semidirect
29. C3×D3×C4⋊C4C22semidirect
33. C3×C4×Dic6C22semidirect
39. C2×#3717C22semidirect
40. C2×#3717C22semidirect
42. C2×#3711C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63636C22semidirect
45. #63636C22semidirect
46. #63636C22semidirect
47. #63636C22semidirect
48. #63630C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. C3×C4⋊(C3⋊C8)C22semidirect
54. #63576C22semidirect
55. #63565C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #5694D3semidirect
69. #5066D3semidirect
155. C3×#125C2×D3semidirect
156. C3×#125C2×D3semidirect
180. #897C2×D3semidirect
181. #897C2×D3semidirect
187. #892C2×D3semidirect
188. D3×C4⋊C4C2×D3semidirect
199. C4×Dic6C2×D3semidirect
231. #808C2×D3semidirect
234. #807C2×D3semidirect
235. C4⋊(C3⋊C8)C2×D3semidirect
457. #125D32semidirect
728. C32#3310semidirect
826. C3#81189semidirect
827. C3#83599semidirect

Maximal subgroups

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

subgroupindex
C3×#56942
D1222
#105927662
C3×#50662
#105905962
#105905922
D3×#8092
#105905852
#105905772
#105904252
#105904222
#105903672
#105903582
#105903302
#835993
#811893