Finite Group Databasebeta

← #11889145

Subgroups — #11889145

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595297C211yesmaximal, characteristic
2#10594337C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic, complemented
4C3×#4779C211yesmaximal, characteristic, complemented
5C3×#4762C211yesmaximal, characteristic, complemented
6#10591502C211yesmaximal, characteristic, complemented
7#10591477C211yesmaximal, characteristic, complemented
8#10591467C211yesmaximal, characteristic, complemented
9#10590942C211yesmaximal, characteristic, complemented
10#10590843C211yesmaximal, characteristic, complemented
11#10590769C211yesmaximal, characteristic, complemented
12#10590737C211yesmaximal, characteristic, complemented
13#10590592C211yesmaximal, characteristic, complemented
14#10590510C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#81383—31nomaximal
17#80397—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic, complemented
22C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
23C3×#940C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic, complemented
27C3×#892C2211yescharacteristic, complemented
28C3×#887C2211yescharacteristic, complemented
29#63983—21no—
30#63981—21no—
31#63958—21no—
32#63916C2211yescharacteristic
33C4×#626C2211yescharacteristic
34#63894C2211yescharacteristic
35#63874—21no—
36#63871C2211yescharacteristic, complemented
37#63869C2211yescharacteristic, complemented
38#63867—21no—
39#63859—21no—
40#63856C2211yescharacteristic, complemented
41#63853—21no—
42C2×#3717C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63648C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#807C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5717—31no—
62#5609—31no—
63#5581—31no—
64#5529—31no—
65C3×#482—31no—
66C3×#460—31no—
67#5174—31no—
68#5171—31no—
69#5169—31no—
70#5169—31no—
71#5071—31no—
72#5042—31no—
73#5026—31no—
74#5001—31no—
75#4889—31no—
76#4882—31no—
77#4871—31no—
78#4864—31no—
79#4847—31no—
80#4836—31no—
81#4779D311yescharacteristic, complemented
82#4776—31no—
83#4774—31no—
84#4770—31no—
85D3×#102—31no—
86D3×#102—31no—
87D3×#102—61no—
88#4764—31no—
89#4762D311yescharacteristic, complemented
90#4731—31no—
91#4728—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107#3811—44no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626D411yescharacteristic
111C2×#624—21no—
112D3×D12—22no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×#217—21no—
121C3×#214—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138#3722—21no—
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143#3717—22no—
144#3711—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×D3×D4—61no—
151C2×D3×D4—61no—
152C22×D12—31no—
153C2×C3×SD16—31no—
154C2×C3×SD16—31no—
155C3×#127—31no—
156C3×#121—31no—
157C3×C4×Q8—31no—
158C3×#117—31no—
159#946—31no—
160#946—31no—
161C2×#215—31no—
162#940C2×D311yescharacteristic
163#938—31no—
164#938—61no—
165#938C2×D311yescharacteristic
166#937—61no—
167#937—61no—
168#937—61no—
169C2×#214C2×D311yescharacteristic, complemented
170C4×#67—31no—
171#924—31no—
172C2×#208—31no—
173C2×#204—31no—
174C2×#204C2×D311yescharacteristic, complemented
175C2×ΓL(1,𝔽25)—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8—61no—
179#897—31no—
180#895—31no—
181#894—61no—
182#893—31no—
183#892C2×D311yescharacteristic, complemented
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—61no—
187#890—31no—
188#889—61no—
189#887C2×D311yescharacteristic, complemented
190#884—61no—
191#883—61no—
192#882—61no—
193#879—61no—
194#876—61no—
195C4×D12—31no—
196C4×D12—31no—
197#872—61no—
198#872—61no—
199#870—31no—
200#870—61no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102C2×D311yescharacteristic, complemented
208C3×#102C2×D311yescharacteristic, complemented
209C3×C22⋊C8—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic, complemented
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8C2×D311yescharacteristic, complemented
225#818—31no—
226#817C2×D311yescharacteristic, complemented
227#815—31no—
228Dic3⋊C8C2×D311yescharacteristic, complemented
229#810—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809C2×D311yescharacteristic, complemented
236#807—31no—
237#807C2×D311yescharacteristic, complemented
238#803—31no—
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—81no—
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×D4—21no—
251C32×D4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)#4112yes—
259C4×C3⋊D3—21no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—42no—
262C3×#67—42no—
263C3×#67—42no—
264C3×#67—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×D12—21no—
272C3×D12—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277#626—22no—
278#626—42no—
279#626—42no—
280#624—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—31no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—31no—
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—
304C23×D3—121no—
305C2×C3×Q8—31no—
306C2×C3×D4—21no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C22×D311yescharacteristic
313C22×C3×C4—31no—
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—21no—
317C2×#67—31no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—121no—
323D3×D4—62no—
324D3×D4—62no—
325D3×D4—62no—
326D3×D4—64no—
327D3×D4—121no—
328D3×D4—121no—
329D3×D4—121no—
330D3×D4—122no—
331D3×D4—124no—
332D3×D4—124no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—61no—
337C2×D12—62no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—121no—
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—121no—
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6C22×D311yescharacteristic
352C3×SD16—121no—
353C3×SD16—121no—
354C2×C3×C8—21no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C3×C4⋊C4—21no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368C3×C42—61no—
369C3×C42—61no—
370#217—21no—
371#217—31no—
372#217—61no—
373#217—61no—
374#215—62no—
375#214—41no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—121no—
405C4×Dic3—21no—
406C4×Dic3—21no—
407C4×Dic3C22×D311yescharacteristic
408#208—121no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414#204—41no—
415#204—62no—
416ΓL(1,𝔽25)—121no—
417D3×C8—121no—
418D3×C8—121no—
419D3×C8—122no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32C22×D411yescharacteristic
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—22no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—84no—
430C2×C3⋊D3AGL(1,ℤ/8)12yes—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437D32—84no—
438C32×C4—41no—
439C32×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—21no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C22×D4—91no—
450C22×D4—91no—
451C22×D4—181no—
452C2×SD16—31no—
453C2×SD16—31no—
454C2×SD16—91no—
455C2×M16—91no—
456C22×C8—91no—
457#127—31no—
458#126—181no—
459#125—91no—
460#125—181no—
461#123—181no—
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464#121—31no—
465#121—91no—
466#121—181no—
467#120—181no—
468#120—181no—
469C4×Q8—31no—
470C4×D4—91no—
471C4×D4—91no—
472#117—31no—
473#117—181no—
474C2×C4⋊C4—91no—
475#107—31no—
476#107—91no—
477#106—31no—
478C4⋊C8—31no—
479#103—91no—
480#102—31no—
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102D3211yescharacteristic, complemented
489C22⋊C8—31no—
490C22⋊C8—91no—
491#97—91no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—41no—
496C23×C3—61no—
497C22×D3—21no—
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—121no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—124no—
513C22×D3—242no—
514C22×D3—241no—
515C22×D3—241no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—242no—
519C22×D3D3×D411yescharacteristic
520C3×Q8—61no—
521C3×Q8—61no—
522C3×D4—22no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—41no—
528C3×D4—61no—
529C3×D4—61no—
530C3×D4—122no—
531C3×D4—122no—
532C3×D4—241no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—41no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547#67—42no—
548#67—42no—
549#67—62no—
550#67—81no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—124no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—121no—
565C2×Dic3D3×D411yescharacteristic
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568D12—21no—
569D12—21no—
570D12—32no—
571D12—32no—
572D12—62no—
573D12—62no—
574D12—61no—
575D12—61no—
576D12—121no—
577D12—122no—
578D12—122no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—62no—
582C4×D3—62no—
583C4×D3—61no—
584C4×D3—61no—
585C4×D3—61no—
586C4×D3—61no—
587C4×D3—122no—
588C4×D3—122no—
589C4×D3—122no—
590C4×D3—122no—
591C4×D3—242no—
592Dic6—21no—
593Dic6—21no—
594C3×C8—21no—
595C3×C8—21no—
596C3×C8—41no—
597C3×C8—61no—
598C3×C8—61no—
599C3⋊C8—21no—
600C3⋊C8—21no—
601C3⋊C8—61no—
602C3⋊C8—61no—
603C3⋊C8—121no—
604C2×C32—81no—
605C2×C32#54611yescharacteristic
606C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
607C2×C32#57711yescharacteristic
608C3⋊D3—22no—
609C3⋊D3—42no—
610C3×D3—41no—
611C3×D3—81no—
612C24—181no—
613C24—181no—
614C2×Q8—31no—
615C2×D4—31no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—91no—
620C2×D4—91no—
621C2×D4—181no—
622C2×D4—182no—
623C2×D4—181no—
624C2×D4—181no—
625C2×D4—182no—
626C2×D4—361no—
627C2×D4—361no—
628C2×D4—364no—
629C2×D4C2×D3211yescharacteristic
630C22×C4—31no—
631C22×C4—91no—
632C22×C4—181no—
633C22×C4—181no—
634SD16—121no—
635SD16—121no—
636SD16—182no—
637M16—361no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—91no—
641C2×C8—361no—
642C2×C8C2×D3211yescharacteristic
643C4⋊C4—31no—
644C4⋊C4—31no—
645C4⋊C4—61no—
646C4⋊C4—91no—
647C4⋊C4—91no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4C2×D3211yescharacteristic
654C22⋊C4—61no—
655C22⋊C4—61no—
656C22⋊C4—91no—
657C22⋊C4—91no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C42—31no—
663C42—61no—
664C42—61no—
665C22×C3—21no—
666C22×C3—42no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C2×D3×D411yescharacteristic
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—32no—
687C2×D3—32no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—62no—
699C2×D3—62no—
700C2×D3—122no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—244no—
708C2×D3—244no—
709C2×D3—244no—
710C2×D3—248no—
711C2×D3—244no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—61no—
719C3×C4—81no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4#100411yescharacteristic
724C3×C4D3×#4111yescharacteristic
725C3×C4D3×#4111yescharacteristic
726C3×C4#100911yescharacteristic
727Dic3—21no—
728Dic3—21no—
729Dic3—21no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—62no—
734Dic3—61no—
735Dic3—61no—
736Dic3—121no—
737Dic3—121no—
738Dic3—241no—
739C32#331011yescharacteristic, complemented, Sylow
740C23—21no—
741C23—31no—
742C23—61no—
743C23—91no—
744C23—181no—
745C23—362no—
746C23—362no—
747C23—362no—
748C23—362no—
749C23—721no—
750C23—721no—
751Q8—61no—
752Q8—61no—
753D4—21no—
754D4—21no—
755D4—61no—
756D4—61no—
757D4—92no—
758D4—122no—
759D4—122no—
760D4—182no—
761D4—181no—
762D4—241no—
763D4—362no—
764D4—362no—
765D4—362no—
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—91no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—362no—
780C2×C4—362no—
781C2×C4C22×D3211yescharacteristic
782C8—21no—
783C8—61no—
784C8—61no—
785C8—181no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—82no—
790C2×C3—81no—
791C2×C3—81no—
792C2×C3—121no—
793C2×C3—241no—
794C2×C3#561211yescharacteristic
795C2×C3#565411yescharacteristic
796C2×C3#576211yescharacteristic
797C2×C3#577011yescharacteristic
798C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
799C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
800D3—41no—
801D3—64no—
802D3—62no—
803D3—62no—
804D3—81no—
805D3—122no—
806D3—122no—
807D3—242no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—92no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—181no—
819C22—181no—
820C22—182no—
821C22—361no—
822C22—361no—
823C22—724no—
824C22—724no—
825C22D32×D411yescharacteristic
826C4—41no—
827C4—61no—
828C4—61no—
829C4—61no—
830C4—121no—
831C4—121no—
832C4—121no—
833C4—181no—
834C4—361no—
835C4#6430611yescharacteristic
836C4#6431411yescharacteristic
837C3—21no—
838C3#8039711yescharacteristic, complemented
839C3#8138311yescharacteristic, complemented
840C2—81no—
841C2—121no—
842C2—182no—
843C2—241no—
844C2—362no—
845C2#1059427911yescharacteristic
846C2#1059472611yescharacteristic
847C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595297C2
hypercenter#102D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594337C2semidirect
3. C3⋊D3×#102C2semidirect
4. C3×#4779C2semidirect
5. C3×#4762C2semidirect
6. #10591502C2semidirect
7. #10591477C2semidirect
8. #10591467C2semidirect
9. #10590942C2semidirect
10. #10590843C2semidirect
11. #10590769C2semidirect
12. #10590737C2semidirect
13. #10590592C2semidirect
14. #10590510C2semidirect
15. #10590457C2semidirect
21. C2×C8×C3⋊D3C22semidirect
22. C4⋊C4×C3⋊D3C22semidirect
25. C2×C3×#214C22semidirect
26. C2×C3×#204C22semidirect
27. C3×#892C22semidirect
28. C3×#887C22semidirect
36. #63871C22semidirect
37. #63869C22semidirect
40. #63856C22semidirect
43. C2×#3711C22semidirect
44. C32×#102C22semidirect
45. #63659C22semidirect
48. C3×#832C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×#817C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#807C22semidirect
54. #63575C22semidirect
55. #63565C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. #63554C22semidirect
81. #4779D3semidirect
89. #4762D3semidirect
169. C2×#214C2×D3semidirect
174. C2×#204C2×D3semidirect
183. #892C2×D3semidirect
189. #887C2×D3semidirect
207. C3×#102C2×D3semidirect
208. C3×#102C2×D3semidirect
216. #832C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
226. #817C2×D3semidirect
228. Dic3⋊C8C2×D3semidirect
235. #809C2×D3semidirect
237. #807C2×D3semidirect
488. #102D32semidirect
739. C32#3310semidirect
838. C3#80397semidirect
839. C3#81383semidirect

Maximal subgroups

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

subgroupindex
#105952972
#105943372
C3⋊D3×#1022
C3×#47792
C3×#47622
#105915022
#105914772
#105914672
#105909422
#105908432
#105907692
#105907372
#105905922
#105905102
#105904572
#813833
#803973