Finite Group Databasebeta

← C2×#11797972 #72227377

Subgroups — C2×#11797972 #72227377

Order 2304.

1724 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10590634C211yesmaximal, characteristic
2C2×C3×#4717C211yesmaximal, characteristic, complemented
3C2×#10592410C211yesmaximal, characteristic, complemented
4#11797972C218yesmaximal, direct product factor
5C2×#10589137C211yesmaximal, characteristic, complemented
6C2×#10589128C211yesmaximal, characteristic, complemented
7C2×#10589124C211yesmaximal, characteristic, complemented
8C2×C3×#4466C211yesmaximal, characteristic, complemented
9C2×#69091—31nomaximal
10C2×#70929—31nomaximal
11C22×#3745C2211yescharacteristic
12C2×C4×C4⋊(C3⋊D3)—21no—
13C2×C3×#904C2211yescharacteristic
14C2×C3×#901—21no—
15C2×C32×#97C2211yescharacteristic
16C2×#63648—21no—
17C2×#63644C2211yescharacteristic
18#10592410—22no—
19#10592410C2214yescomplemented
20C2×C3×#819C2211yescharacteristic
21C2×C3×#812C2211yescharacteristic
22C2×C3×#812C2211yescharacteristic
23C2×C3×#805—21no—
24C3×#4717—22no—
25C3×#4717C2214yescomplemented
26C2×#63549C412yescomplemented
27#10590634C414yescomplemented
28#10590634C2214yes—
29C2×#63546C412yescomplemented
30C3×#4466C2214yescomplemented
31#10589137C2214yescomplemented
32#10589128C2214yescomplemented
33#10589124C2214yescomplemented
34C2×C3×#444—31no—
35C2×#5193—31no—
36C2×#4908—31no—
37C2×#4717D311yescharacteristic, complemented
38C2×#4711—31no—
39C2×#4711—31no—
40C2×#4711—61no—
41C2×C3×#347—31no—
42C2×#4566—31no—
43C2×#4518—31no—
44C2×#4516—31no—
45C2×#4513—31no—
46#70929—38no—
47C2×#4495—31no—
48C2×#4494—31no—
49C2×#4466D311yescharacteristic, complemented
50#69091—38no—
51C22×C4⋊(C3⋊D3)—21no—
52C22×C4×C3⋊D3—41no—
53C2×C3×#235—21no—
54C22×C32×C8D411yescharacteristic
55C22×C32×C8C2311yescharacteristic
56C2×C32×C42D411yescharacteristic
57C2×#3752—41no—
58C2×C4⋊(C3⋊Dic3)—21no—
59C2×#3745—21no—
60C2×#3745—21no—
61C2×#3745—21no—
62C2×#3745C2×C412yes—
63C2×#3745C2×C412yes—
64C2×#3745C2312yes—
65C4×C4⋊(C3⋊D3)—24no—
66C4×C4⋊(C3⋊D3)—42no—
67C2×C3×#208—21no—
68C2×C3×Dic12C2×C411yescharacteristic, complemented
69C3×#904—21no—
70C3×#904—21no—
71C3×#904C2×C412yescomplemented
72C3×#904C2312yes—
73C2×C3×D24C2×C411yescharacteristic, complemented
74C2×C3×#204—21no—
75C3×#901—24no—
76C3×#901—42no—
77C2×C3×ΓL(1,𝔽25)—41no—
78C2×C3×D3×C8—41no—
79C32×#97D412yes—
80C32×#97C2312yes—
81#63648—24no—
82#63644—21no—
83#63644C2312yes—
84C3×#819—21no—
85C3×#819C2312yes—
86C3×#812—21no—
87C3×#812C2×C412yescomplemented
88C3×#812C2312yes—
89C3×#812C2312yes—
90C2×C3×C3⋊C16—21no—
91C2×C3×C3⋊C16C2×C412yescomplemented
92C3×#805—24no—
93#63549C2×C418yescomplemented
94#63546C2×C418yescomplemented
95C2×AGL(1,ℤ/16)—91noSylow
96C2×C3×#135—31no—
97C2×C3×#131—61no—
98C2×#904C2×D311yescharacteristic
99C22×D24—31no—
100C22×D24—31no—
101C22×D24—61no—
102C2×#901—21no—
103C2×C4×D12—62no—
104C2×C4×D12—61no—
105C2×C4×D12—61no—
106C2×C3×M32—31no—
107C2×C3×M32—31no—
108C3×#444—34no—
109C3×#444—62no—
110C2×C3×#108—31no—
111C2×C3×#104—61no—
112C2×C3×#97—21no—
113C2×C3×#97C2×D311yescharacteristic
114C2×C3×#97C2×D311yescharacteristic
115#5193—34no—
116#5193—34no—
117C2×#828—32no—
118C2×#826—32no—
119C2×#821—62no—
120C2×#821—61no—
121C2×#821—61no—
122C2×#819C2×D311yescharacteristic
123C2×#817—31no—
124C2×#817—31no—
125C2×#817—61no—
126C2×#812C2×D311yescharacteristic
127C2×#812C2×D311yescharacteristic
128C2×#805—21no—
129#4908—34no—
130#4908—34no—
131C2×#800—32no—
132C2×D48—32no—
133#4717—22no—
134#4717C2×D314yescomplemented
135#4711—34no—
136#4711—34no—
137#4711—64no—
138#4711—64no—
139#4711—62no—
140#4711—62no—
141C3×#347—34no—
142#4566—34no—
143#4518—34no—
144#4516—34no—
145#4513—34no—
146#4495—34no—
147#4494—34no—
148#4466C2×D314yescomplemented
149C23×C3⋊D3—41no—
150C22×C32×C4—21no—
151C22×C32×C4C2×D411yescharacteristic
152C22×C3⋊Dic3—41no—
153C2×C4⋊(C3⋊D3)—22no—
154C2×C4⋊(C3⋊D3)—22no—
155C2×C4⋊(C3⋊D3)—22no—
156C2×C4⋊(C3⋊D3)—41no—
157C2×C4⋊(C3⋊D3)—41no—
158C2×C4⋊(C3⋊D3)—41no—
159C2×C4×C3⋊D3—44no—
160C2×C4×C3⋊D3—84no—
161C2×C3×#67—41no—
162C3×#235—22no—
163C3×#235—22no—
164C3×#235—41no—
165C3×#235—41no—
166C2×C3×D12—21no—
167C2×C3×C4×D3—41no—
168C2×C3×Dic6—21no—
169C2×C32×C8—21no—
170C2×C32×C8—21no—
171C2×C32×C8C22×C411yescharacteristic
172C2×C32×C8C22×C411yescharacteristic
173C2×C32×C8C2×D412yes—
174C2×C32×C8C2×D411yescharacteristic
175C2×C32×C8#4111yescharacteristic
176C2×C32×C8#4111yescharacteristic
177C2×C32×C8C2411yescharacteristic
178C32×C42—21no—
179C32×C42C2×D412yes—
180#3752—44no—
181C4⋊(C3⋊Dic3)—22no—
182C4⋊(C3⋊Dic3)—41no—
183#3745—22no—
184#3745—22no—
185#3745—22no—
186#3745C22×C414yes—
187C3×#208—22no—
188C3×#208—41no—
189C2×C3×C3⋊C8—41no—
190C3×Dic12—21no—
191C3×Dic12C22×C412yescomplemented
192C3×D24—21no—
193C3×D24C22×C412yescomplemented
194C3×#204—22no—
195C3×#204—22no—
196C3×ΓL(1,𝔽25)—44no—
197C3×D3×C8—44no—
198C3×C3⋊C16—22no—
199C3×C3⋊C16C22×C414yescomplemented
200C2×#509—91no—
201C2×#444—31no—
202C2×#442—91no—
203AGL(1,ℤ/16)—98no—
204C2×#365—91no—
205C2×#361—91no—
206C2×#360—91no—
207C2×#347—31no—
208C2×C3×#41—61no—
209C2×#235—21no—
210C22×D12—62no—
211C22×D12—61no—
212C22×D12—61no—
213C22×C4×D3—122no—
214C22×C4×D3—121no—
215C22×C4×D3—121no—
216C3×#135—32no—
217C3×#135—32no—
218C3×#135—61no—
219C3×#135—61no—
220C2×C3×Q16—31no—
221C2×C3×SD16—61no—
222C2×C3×D8—31no—
223C3×#131—64no—
224C3×#131—122no—
225C2×C3×M16—61no—
226C2×C3×M16—121no—
227C22×C3×C8—21no—
228C22×C3×C8—21no—
229C22×C3×C8—121no—
230C22×C3×C8D1211yescharacteristic
231C22×C3×C8#6711yescharacteristic
232C22×C3×C8C22×D311yescharacteristic
233C22×C3×C8C22×D311yescharacteristic
234C2×C3×C42—21no—
235C2×C3×C42D1211yescharacteristic
236C2×C3×C42#6711yescharacteristic
237C2×(C2×D3)⋊C4—122no—
238C2×(C2×D3)⋊C4—121no—
239C2×(C2×D3)⋊C4—121no—
240C2×C4⋊Dic3—62no—
241C2×C4⋊Dic3—61no—
242C2×C4⋊Dic3—61no—
243C2×#208—21no—
244C2×Dic12C4×D311yescharacteristic, complemented
245#904—21no—
246#904—21no—
247#904C4×D312yescomplemented
248#904C22×D312yes—
249C2×D24—32no—
250C2×D24—32no—
251C2×D24—32no—
252C2×D24—32no—
253C2×D24—32no—
254C2×D24—32no—
255C2×D24—62no—
256C2×D24—62no—
257C2×D24—62no—
258C2×D24—62no—
259C2×D24—62no—
260C2×D24—62no—
261C2×D24—61no—
262C2×D24—61no—
263C2×D24—61no—
264C2×D24—61no—
265C2×D24—61no—
266C2×D24—61no—
267C2×D24C4×D311yescharacteristic, complemented
268C2×#204—21no—
269#901—24no—
270#901—42no—
271C2×ΓL(1,𝔽25)—41no—
272C2×D3×C8—41no—
273C4×D12—68no—
274C4×D12—64no—
275C4×D12—64no—
276C4×D12—124no—
277C4×D12—122no—
278C4×D12—122no—
279C3×M32—32no—
280C3×M32—32no—
281C3×M32—32no—
282C3×M32—61no—
283C2×C3×C16—32no—
284C2×C3×C16—61no—
285C3×#108—32no—
286C3×#108—61no—
287C3×#104—64no—
288C3×#97—22no—
289C3×#97—22no—
290C3×#97D1212yes—
291C3×#97#6712yes—
292C3×#97C22×D312yes—
293C3×#97C22×D312yes—
294#828—38no—
295#826—38no—
296#821—68no—
297#821—64no—
298#821—64no—
299#819—21no—
300#819C22×D312yes—
301#817—32no—
302#817—32no—
303#817—62no—
304#817—62no—
305#817—61no—
306#817—61no—
307#812—21no—
308#812C4×D312yescomplemented
309#812C22×D312yes—
310#812C22×D312yes—
311C2×C3⋊C16—21no—
312C2×C3⋊C16C4×D312yescomplemented
313#805—24no—
314#800—38no—
315D48—38no—
316C23×C32AGL(1,ℤ/8)11yescharacteristic
317C22×C3⋊D3—42no—
318C22×C3⋊D3—42no—
319C22×C3⋊D3—42no—
320C22×C3⋊D3—82no—
321C22×C3⋊D3—82no—
322C22×C3×D3—41no—
323C2×C32×C4—22no—
324C2×C32×C4—42no—
325C2×C32×C4C4×D411yescharacteristic
326C2×C32×C4C4×D411yescharacteristic
327C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
328C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
329C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
330C2×C32×C4C22×D411yescharacteristic
331C2×C3⋊Dic3—42no—
332C2×C3⋊Dic3—82no—
333C4⋊(C3⋊D3)—24no—
334C4⋊(C3⋊D3)—42no—
335C4⋊(C3⋊D3)—42no—
336C4⋊(C3⋊D3)—42no—
337C4×C3⋊D3—88no—
338C3×#67—42no—
339C3×#67—42no—
340C2×C3×Dic3—41no—
341C3×D12—22no—
342C3×D12—41no—
343C3×C4×D3—42no—
344C3×C4×D3—42no—
345C3×Dic6—22no—
346C3×Dic6—41no—
347C32×C8—22no—
348C32×C8C4×D411yescharacteristic
349C32×C8C4×D411yescharacteristic
350C32×C8C23×C411yescharacteristic
351C32×C8C2×#4111yescharacteristic
352C3×C3⋊C8—42no—
353C2×#135—31no—
354C22×D8—91no—
355C2×#131—61no—
356C2×C4×D4—181no—
357#509—94no—
358#509—94no—
359C2×SD32—92no—
360C2×D16—92no—
361C2×M32—31no—
362C2×M32—31no—
363#444—34no—
364#444—62no—
365#442—94no—
366#442—182no—
367C2×#108—31no—
368C2×#106—91no—
369C2×#104—61no—
370C2×#102—181no—
371C2×#97D3211yescharacteristic
372#365—94no—
373#361—94no—
374#360—94no—
375#347—34no—
376C23×D3—122no—
377C23×D3—121no—
378C23×D3—121no—
379C3×#41—62no—
380C3×#41—62no—
381C3×#41—121no—
382C3×#41—121no—
383C2×C3×Q8—61no—
384C2×C3×D4—61no—
385C2×C3×D4—121no—
386C22×C3×C4—22no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—121no—
391C22×C3×C4C2×D1211yescharacteristic
392C22×C3×C4C2×#6711yescharacteristic
393C2×#67—41no—
394C22×Dic3—122no—
395C22×Dic3—121no—
396C22×Dic3—121no—
397#235—22no—
398#235—22no—
399#235—41no—
400#235—41no—
401C2×D12—21no—
402C2×D12—64no—
403C2×D12—64no—
404C2×D12—64no—
405C2×D12—62no—
406C2×D12—62no—
407C2×D12—62no—
408C2×D12—62no—
409C2×D12—62no—
410C2×D12—62no—
411C2×D12—122no—
412C2×D12—122no—
413C2×D12—122no—
414C2×D12—121no—
415C2×D12—121no—
416C2×D12—121no—
417C2×D12—121no—
418C2×D12—121no—
419C2×D12—121no—
420C2×C4×D3—41no—
421C2×C4×D3—128no—
422C2×C4×D3—124no—
423C2×C4×D3—124no—
424C2×C4×D3—248no—
425C2×C4×D3—244no—
426C2×C4×D3—244no—
427C2×Dic6—21no—
428C3×Q16—32no—
429C3×Q16—61no—
430C3×SD16—62no—
431C3×SD16—62no—
432C3×D8—32no—
433C3×D8—61no—
434C3×M16—62no—
435C3×M16—124no—
436C3×M16—121no—
437C2×C3×C8—21no—
438C2×C3×C8—21no—
439C2×C3×C8—21no—
440C2×C3×C8—21no—
441C2×C3×C8—21no—
442C2×C3×C8—21no—
443C2×C3×C8—21no—
444C2×C3×C8—21no—
445C2×C3×C8—21no—
446C2×C3×C8—21no—
447C2×C3×C8—22no—
448C2×C3×C8—41no—
449C2×C3×C8—41no—
450C2×C3×C8—124no—
451C2×C3×C8—121no—
452C2×C3×C8C2×C4×D311yescharacteristic
453C2×C3×C8C2×C4×D311yescharacteristic
454C2×C3×C8C2×C4×D311yescharacteristic
455C2×C3×C8C2×C4×D311yescharacteristic
456C2×C3×C8C2×D1212yes—
457C2×C3×C8C2×D1211yescharacteristic
458C2×C3×C8#23511yescharacteristic
459C2×C3×C8#23511yescharacteristic
460C2×C3×C8#23511yescharacteristic
461C2×C3×C8#23511yescharacteristic
462C2×C3×C8C2×#6712yes—
463C2×C3×C8C2×#6711yescharacteristic
464C2×C3×C8C23×D311yescharacteristic
465C2×C3×C8C23×D311yescharacteristic
466C3×C42—22no—
467C3×C42—21no—
468C3×C42—21no—
469C3×C42—22no—
470C3×C42C2×D1212yes—
471C3×C42C2×#6712yes—
472(C2×D3)⋊C4—128no—
473(C2×D3)⋊C4—124no—
474(C2×D3)⋊C4—124no—
475C4⋊Dic3—64no—
476C4⋊Dic3—62no—
477C4⋊Dic3—62no—
478C4⋊Dic3—122no—
479C4⋊Dic3—121no—
480C4⋊Dic3—121no—
481#208—22no—
482#208—41no—
483C2×C3⋊C8—41no—
484Dic12—21no—
485Dic12C2×C4×D312yescomplemented
486D24—21no—
487D24—34no—
488D24—34no—
489D24—64no—
490D24—64no—
491D24—64no—
492D24—64no—
493D24—62no—
494D24—62no—
495D24—62no—
496D24—62no—
497D24—62no—
498D24—62no—
499D24C2×C4×D312yescomplemented
500#204—22no—
501#204—22no—
502ΓL(1,𝔽25)—44no—
503D3×C8—44no—
504C3×C16—34no—
505C3×C16—62no—
506C3⋊C16—22no—
507C3⋊C16C2×C4×D314yescomplemented
508C22×C32—22no—
509C22×C32#44211yescharacteristic
510C22×C32#44211yescharacteristic
511C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
512C2×C3⋊D3—44no—
513C2×C3⋊D3—82no—
514C2×C3⋊D3—82no—
515C2×C3⋊D3—84no—
516C2×C3⋊D3—84no—
517C2×C3×D3—42no—
518C2×C3×D3—82no—
519C32×C4—42no—
520C32×C4#44211yescharacteristic
521C32×C4#44211yescharacteristic
522C32×C4C2×C4×D411yescharacteristic
523C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
524C3⋊Dic3—82no—
525C3×Dic3—42no—
526C2×#41—61no—
527C22×D4—181no—
528C23×C4—361no—
529#135—32no—
530#135—32no—
531#135—61no—
532#135—61no—
533C2×Q16—31no—
534C2×SD16—61no—
535C2×D8—31no—
536C2×D8—92no—
537C2×D8—92no—
538C2×D8—92no—
539C2×D8—181no—
540C2×D8—181no—
541C2×D8—181no—
542#131—64no—
543#131—122no—
544C2×M16—61no—
545C2×M16—121no—
546C22×C8—121no—
547C22×C8#62611yescharacteristic
548C22×C8C2×D3211yescharacteristic
549C4×D4—184no—
550C4×D4—362no—
551C2×C4⋊C4—181no—
552C2×C22⋊C4—361no—
553C2×C42#62611yescharacteristic
554SD32—98no—
555D16—98no—
556M32—32no—
557M32—32no—
558M32—32no—
559M32—61no—
560C2×C16—32no—
561C2×C16—61no—
562#108—32no—
563#108—61no—
564#106—92no—
565#106—181no—
566#104—64no—
567#102—184no—
568#97#62612yes—
569#97C2×D3212yes—
570C23×C3—21no—
571C23×C3—121no—
572C23×C3#90811yescharacteristic
573C23×C3#94911yescharacteristic
574C22×D3—41no—
575C22×D3—124no—
576C22×D3—124no—
577C22×D3—124no—
578C22×D3—122no—
579C22×D3—122no—
580C22×D3—122no—
581C22×D3—122no—
582C22×D3—122no—
583C22×D3—122no—
584C22×D3—244no—
585C22×D3—242no—
586C22×D3—242no—
587C22×D3—244no—
588C22×D3—242no—
589C22×D3—242no—
590C3×Q8—62no—
591C3×Q8—121no—
592C3×D4—62no—
593C3×D4—122no—
594C3×D4—122no—
595C3×D4—121no—
596C2×C3×C4—24no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—44no—
606C2×C3×C4—42no—
607C2×C3×C4—42no—
608C2×C3×C4—121no—
609C2×C3×C4—122no—
610C2×C3×C4—122no—
611C2×C3×C4C4×D1211yescharacteristic
612C2×C3×C4C4×D1211yescharacteristic
613C2×C3×C4#90811yescharacteristic
614C2×C3×C4#90811yescharacteristic
615C2×C3×C4#90811yescharacteristic
616C2×C3×C4C4×#6711yescharacteristic
617C2×C3×C4C4×#6711yescharacteristic
618C2×C3×C4#93211yescharacteristic
619C2×C3×C4#93211yescharacteristic
620C2×C3×C4#94911yescharacteristic
621C2×C3×C4C22×D1211yescharacteristic
622C2×C3×C4C22×#6711yescharacteristic
623#67—42no—
624#67—42no—
625C2×Dic3—41no—
626C2×Dic3—124no—
627C2×Dic3—122no—
628C2×Dic3—122no—
629C2×Dic3—244no—
630C2×Dic3—242no—
631C2×Dic3—242no—
632D12—22no—
633D12—41no—
634D12—68no—
635D12—64no—
636D12—64no—
637D12—124no—
638D12—124no—
639D12—124no—
640D12—122no—
641D12—122no—
642D12—122no—
643D12—122no—
644D12—122no—
645D12—122no—
646C4×D3—42no—
647C4×D3—42no—
648C4×D3—2416no—
649C4×D3—248no—
650C4×D3—248no—
651Dic6—22no—
652Dic6—41no—
653C3×C8—22no—
654C3×C8—22no—
655C3×C8—21no—
656C3×C8—21no—
657C3×C8—21no—
658C3×C8—21no—
659C3×C8—42no—
660C3×C8—122no—
661C3×C8C4×D1211yescharacteristic
662C3×C8C4×D1211yescharacteristic
663C3×C8C4×#6711yescharacteristic
664C3×C8C4×#6711yescharacteristic
665C3×C8C22×C4×D311yescharacteristic
666C3×C8C22×C4×D311yescharacteristic
667C3×C8C2×#23511yescharacteristic
668C3×C8C2×#23511yescharacteristic
669C3⋊C8—42no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32AGL(1,ℤ/16)12yescomplemented
673C2×C32C2×#44211yescharacteristic
674C3⋊D3—84no—
675C3×D3—82no—
676C24—361no—
677#41—62no—
678#41—62no—
679#41—121no—
680#41—121no—
681C2×Q8—61no—
682C2×D4—61no—
683C2×D4—121no—
684C2×D4—182no—
685C2×D4—182no—
686C2×D4—182no—
687C2×D4—361no—
688C2×D4—361no—
689C2×D4—361no—
690C22×C4—21no—
691C22×C4—121no—
692C22×C4—364no—
693C22×C4—361no—
694C22×C4—724no—
695C22×C4C2×#62611yescharacteristic
696Q16—32no—
697Q16—61no—
698SD16—62no—
699SD16—62no—
700D8—32no—
701D8—61no—
702D8—94no—
703D8—182no—
704D8—182no—
705D8—182no—
706M16—62no—
707M16—124no—
708M16—121no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—124no—
712C2×C8—121no—
713C2×C8#379811yescharacteristic
714C2×C8#379811yescharacteristic
715C2×C8C4×D3211yescharacteristic
716C2×C8C4×D3211yescharacteristic
717C2×C8C2×#62612yes—
718C2×C8C2×#62611yescharacteristic
719C2×C8C22×D3211yescharacteristic
720C4⋊C4—182no—
721C4⋊C4—361no—
722C22⋊C4—364no—
723C42—21no—
724C42C2×#62612yes—
725C16—34no—
726C16—62no—
727C22×C3—24no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—122no—
734C22×C3—242no—
735C22×C3#471111yescharacteristic
736C22×C3#471111yescharacteristic
737C22×C3#501411yescharacteristic
738C22×C3#501411yescharacteristic
739C22×C3C2×#90811yescharacteristic
740C22×C3C2×#94911yescharacteristic
741C2×D3—42no—
742C2×D3—82no—
743C2×D3—128no—
744C2×D3—124no—
745C2×D3—124no—
746C2×D3—244no—
747C2×D3—242no—
748C2×D3—242no—
749C2×D3—244no—
750C2×D3—248no—
751C2×D3—242no—
752C2×D3—244no—
753C2×D3—242no—
754C2×D3—244no—
755C2×D3—248no—
756C2×D3—244no—
757C2×D3—244no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—44no—
763C3×C4—42no—
764C3×C4—42no—
765C3×C4—122no—
766C3×C4#471111yescharacteristic
767C3×C4#471111yescharacteristic
768C3×C4#501411yescharacteristic
769C3×C4#501411yescharacteristic
770C3×C4C2×C4×D1211yescharacteristic
771C3×C4C2×#90811yescharacteristic
772C3×C4C2×C4×#6711yescharacteristic
773C3×C4C2×#93211yescharacteristic
774Dic3—42no—
775Dic3—244no—
776Dic3—242no—
777Dic3—242no—
778C32C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
779C23—121no—
780C23—362no—
781C23—362no—
782C23—362no—
783C23—722no—
784C23—722no—
785C23#6382511yescharacteristic
786Q8—62no—
787Q8—121no—
788D4—62no—
789D4—122no—
790D4—122no—
791D4—121no—
792D4—184no—
793D4—362no—
794D4—362no—
795D4—362no—
796C2×C4—22no—
797C2×C4—42no—
798C2×C4—121no—
799C2×C4—122no—
800C2×C4—122no—
801C2×C4—362no—
802C2×C4—728no—
803C2×C4—722no—
804C2×C4#6382511yescharacteristic
805C2×C4#6383011yescharacteristic
806C2×C4#6383011yescharacteristic
807C2×C4C4×#62611yescharacteristic
808C2×C4C4×#62611yescharacteristic
809C2×C4C22×#62611yescharacteristic
810C8—22no—
811C8—122no—
812C8C4×#62611yescharacteristic
813C8C4×#62611yescharacteristic
814C8C2×#379811yescharacteristic
815C8C2×C4×D3211yescharacteristic
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—22no—
824C2×C3—242no—
825C2×C3#6909112yescomplemented
826C2×C3#7092912yescomplemented
827C2×C3C2×#471111yescharacteristic
828C2×C3C2×#501411yescharacteristic
829D3—82no—
830D3—248no—
831D3—244no—
832D3—244no—
833C22—22no—
834C22—122no—
835C22—242no—
836C22—364no—
837C22—722no—
838C22—722no—
839C22—724no—
840C22—724no—
841C22#1059034611yescharacteristic
842C22#1059034611yescharacteristic
843C22C2×#6382511yescharacteristic
844C4—42no—
845C4—122no—
846C4—722no—
847C4#1059034611yescharacteristic
848C4#1059034611yescharacteristic
849C4C2×#6383011yescharacteristic
850C4C2×C4×#62611yescharacteristic
851C3—21no—
852C3C2×#7092911yescharacteristic, complemented
853C3C2×#6909111yescharacteristic, complemented
854C2—21no—
855C2—21no—
856C2—242no—
857C2—724no—
858C2#1179797212yesdirect product factor
859C2C2×#1059034611yescharacteristic
subgroupG/H
centerC22#10590346
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×#97C22
socleC22×C32#442
prime radicalC2×#10590634C2
cosocleC2×C32×C8C24
hypercenterC2×#97D32
hypocenterC32C2×AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4717C2semidirect
3. C2×#10592410C2semidirect
4. #11797972C2direct (N × H)
5. C2×#10589137C2semidirect
6. C2×#10589128C2semidirect
7. C2×#10589124C2semidirect
8. C2×C3×#4466C2semidirect
19. #10592410C22semidirect
25. C3×#4717C22semidirect
26. C2×#63549C4semidirect
27. #10590634C4semidirect
29. C2×#63546C4semidirect
30. C3×#4466C22semidirect
31. #10589137C22semidirect
32. #10589128C22semidirect
33. #10589124C22semidirect
37. C2×#4717D3semidirect
49. C2×#4466D3semidirect
68. C2×C3×Dic12C2×C4semidirect
71. C3×#904C2×C4semidirect
73. C2×C3×D24C2×C4semidirect
87. C3×#812C2×C4semidirect
91. C2×C3×C3⋊C16C2×C4semidirect
93. #63549C2×C4semidirect
94. #63546C2×C4semidirect
134. #4717C2×D3semidirect
148. #4466C2×D3semidirect
191. C3×Dic12C22×C4semidirect
193. C3×D24C22×C4semidirect
199. C3×C3⋊C16C22×C4semidirect
244. C2×Dic12C4×D3semidirect
247. #904C4×D3semidirect
267. C2×D24C4×D3semidirect
308. #812C4×D3semidirect
312. C2×C3⋊C16C4×D3semidirect
485. Dic12C2×C4×D3semidirect
499. D24C2×C4×D3semidirect
507. C3⋊C16C2×C4×D3semidirect
672. C2×C32AGL(1,ℤ/16)semidirect
778. C32C2×AGL(1,ℤ/16)semidirect
825. C2×C3#69091semidirect
826. C2×C3#70929semidirect
852. C3C2×#70929semidirect
853. C3C2×#69091semidirect
858. C2#11797972direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#105906342
C2×C3×#47172
C2×#105924102
#117979722
C2×#105891372
C2×#105891282
C2×#105891242
C2×C3×#44662
C2×#690913
C2×#709293