Finite Group Databasebeta

← #11824572

Subgroups — #11824572

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1095 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63971C211yesmaximal, characteristic, complemented
2C2×#63971C211yesmaximal, characteristic, complemented
3C2×#63909C211yesmaximal, characteristic, complemented
4C2×#63880C211yesmaximal, characteristic, complemented
5#10592659C211yesmaximal, characteristic, complemented
6C3×#4956C211yesmaximal, characteristic, complemented
7C3×#4951C211yesmaximal, characteristic, complemented
8#10591722C211yesmaximal, characteristic, complemented
9#10591712C211yesmaximal, characteristic, complemented
10#10591380C211yesmaximal, characteristic, complemented
11#10591364C211yesmaximal, characteristic, complemented
12D3×C3⋊#95C211yesmaximal, characteristic, complemented
13#10591345C211yesmaximal, characteristic, complemented
14#10591216C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#75882—31nomaximal
17#74752—31nomaximal
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37#63971—24no—
38#63971—24no—
39C2×#3724C2211yescharacteristic
40C2×#3724C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47#63909—24no—
48#63880—24no—
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#939—31no—
58C2×#939—31no—
59C2×#930—31no—
60C2×#895—31no—
61C2×#884—31no—
62C2×#884—31no—
63C2×#67⋊C4—31no—
64C2×C4×D12—31no—
65C3×#388—31no—
66C3×#386—31no—
67C2×C3⋊#95—31no—
68#4982—31no—
69#4961—31no—
70#4960—31no—
71#4960—31no—
72#4960—61no—
73#4959—31no—
74#4958—31no—
75#4956—31no—
76#4956—31no—
77#4956D311yescharacteristic, complemented
78#4951D311yescharacteristic, complemented
79#4940—31no—
80#4675—31no—
81#4675—31no—
82#4669—31no—
83#4665—31no—
84#4665—31no—
85#4665—31no—
86D3×#95—31no—
87#4657—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—41no—
98C2×#638—41no—
99C2×#638—41no—
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—22no—
104C2×C4⋊(C3⋊D3)—41no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—41no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—22no—
121C2×#626—22no—
122C2×#626—22no—
123C2×#626D414yescomplemented
124C2×#624—22no—
125C2×#624—41no—
126C2×#624—41no—
127C2×D3×Dic3—22no—
128C2×D3×Dic3—22no—
129C2×D3×Dic3—41no—
130C2×D3×Dic3—41no—
131C2×D3×Dic3—41no—
132C2×D3×Dic3D414yescomplemented
133C32×C22⋊C4—22no—
134#3752—22no—
135#3752—22no—
136C3×#217—22no—
137C3×#217—22no—
138C3×#217—41no—
139C3×(C2×D3)⋊C4—22no—
140C3×C4⋊Dic3—22no—
141C3×C4×Dic3—22no—
142#3724—22no—
143#3724—22no—
144Dic3⋊Dic3—22no—
145#3722—22no—
146#3722—22no—
147#3722—22no—
148#3722—22no—
149#3722—41no—
150#2543—91noSylow
151C22×C3×D4—31no—
152C23×C3×C4—31no—
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—61no—
160C22×#67—61no—
161C22×#67C2×D311yescharacteristic
162C23×Dic3—31no—
163C23×Dic3—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—31no—
167C22×D12—31no—
168C22×D12—61no—
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3C2×D311yescharacteristic
174C2×C3×C4⋊C4—31no—
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4C2×D311yescharacteristic
181C2×C3×C22⋊C4C2×D311yescharacteristic
182C2×C3×C42—31no—
183C2×#217C2×D311yescharacteristic
184C2×#217C2×D311yescharacteristic
185C2×#217C2×D311yescharacteristic
186#939—64no—
187#939—64no—
188#930—64no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3C2×D311yescharacteristic
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×C4×Dic3C2×D311yescharacteristic
214#895—64no—
215#884—64no—
216#884—64no—
217#67⋊C4—64no—
218C4×D12—64no—
219C3×#95—31no—
220C3×#95—31no—
221C3×#95—31no—
222C3×#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—61no—
232C3⋊#95C2×D311yescharacteristic
233C3⋊#95C2×D311yescharacteristic
234C3⋊#95C2×D311yescharacteristic
235C3⋊#95C2×D311yescharacteristic
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32C2411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C2×D412yes—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3C2×D412yes—
263C22×C3×D3C2×D412yes—
264C22×C3×D3#4112yes—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4#4112yes—
271#638—44no—
272#638—44no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3C2×D412yes—
278C2×C3⋊Dic3#4112yes—
279C4⋊(C3⋊D3)—44no—
280C3×#67—44no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3C2×D412yes—
301C2×C3×Dic3C2×D412yes—
302C3×C4×D3—44no—
303#626—28no—
304#626—44no—
305#624—44no—
306D3×Dic3—44no—
307D3×Dic3—44no—
308C2×#121—91no—
309C2×#121—91no—
310C2×#121—91no—
311C2×C4×D4—91no—
312#398—91no—
313#397—91no—
314#394—91no—
315#392—91no—
316#388—31no—
317#388—91no—
318#386—31no—
319#386—91no—
320#386—91no—
321#386—91no—
322C2×#95—91no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3C22×D311yescharacteristic
326C24×C3C22×D311yescharacteristic
327C23×D3—31no—
328C23×D3—31no—
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—61no—
332C23×D3—61no—
333C23×D3C22×D311yescharacteristic
334C2×C3×D4—62no—
335C2×C3×D4—62no—
336C2×C3×D4—62no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—62no—
347C22×C3×C4—62no—
348C22×C3×C4—121no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—22no—
354C2×#67—22no—
355C2×#67—22no—
356C2×#67—34no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—62no—
361C2×#67—62no—
362C2×#67—62no—
363C2×#67—62no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—122no—
369C2×#67—122no—
370C2×#67—122no—
371C2×#67—121no—
372C2×#67—121no—
373C2×#67—121no—
374C2×#67—121no—
375C2×#67—121no—
376C2×#67—121no—
377C2×#67—122no—
378C2×#67—122no—
379C2×#67—122no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—34no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—62no—
388C22×Dic3—62no—
389C22×Dic3—121no—
390C22×Dic3—121no—
391C22×Dic3—121no—
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C2×D12—34no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—62no—
404C2×D12—62no—
405C2×D12—62no—
406C2×D12—62no—
407C2×D12—62no—
408C2×D12—62no—
409C2×D12—122no—
410C2×D12—122no—
411C2×D12—121no—
412C2×D12—121no—
413C2×D12—122no—
414C2×C4×D3—22no—
415C2×C4×D3—22no—
416C2×C4×D3—34no—
417C2×C4×D3—41no—
418C2×C4×D3—62no—
419C2×C4×D3—62no—
420C2×C4×D3—62no—
421C2×C4×D3—62no—
422C2×C4×D3—121no—
423C2×C4×D3—121no—
424C2×C4×D3—121no—
425C2×C4×D3—121no—
426C2×C4×D3—121no—
427C2×C4×D3—121no—
428C2×C4×D3—121no—
429C3×C4⋊C4—62no—
430C3×C22⋊C4—22no—
431C3×C22⋊C4—22no—
432C3×C22⋊C4—42no—
433C3×C22⋊C4—62no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—62no—
436C3×C22⋊C4—121no—
437C3×C42—62no—
438#217—22no—
439#217—22no—
440#217—41no—
441(C2×D3)⋊C4—22no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—122no—
455(C2×D3)⋊C4—122no—
456(C2×D3)⋊C4—121no—
457(C2×D3)⋊C4—121no—
458C4⋊Dic3—22no—
459C4⋊Dic3—62no—
460Dic3⋊C4—62no—
461Dic3⋊C4—62no—
462Dic3⋊C4—62no—
463Dic3⋊C4—62no—
464Dic3⋊C4—62no—
465C4×Dic3—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32C22×D411yescharacteristic
474C22×C32C22×D411yescharacteristic
475C22×C32C2×#4111yescharacteristic
476C22×C32C2×#4111yescharacteristic
477C22×C32C2×#4111yescharacteristic
478C22×C32H(5,𝔽2)11yescharacteristic
479C22×C32H(5,𝔽2)11yescharacteristic
480C2×C3⋊D3—22no—
481C2×C3⋊D3—22no—
482C2×C3⋊D3—22no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3—41no—
490C2×C3⋊D3—41no—
491C2×C3⋊D3—41no—
492C2×C3⋊D3—41no—
493C2×C3⋊D3—41no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3#12114yes—
501C32×C4—22no—
502C32×C4—41no—
503C3⋊Dic3—22no—
504C3⋊Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C3×Dic3—41no—
512C22×D4—31no—
513C22×D4—91no—
514C22×D4—91no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—91no—
518C23×C4—31no—
519C23×C4—91no—
520C23×C4—91no—
521C23×C4—91no—
522#121—184no—
523#121—184no—
524#121—184no—
525C4×D4—184no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4D3211yescharacteristic
542C2×C42—31no—
543#95—31no—
544#95—31no—
545#95—31no—
546#95—31no—
547#95—91no—
548#95—91no—
549#95—91no—
550#95—91no—
551C23×C3—22no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—32no—
568C23×C3—32no—
569C23×C3—32no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3C23×D311yescharacteristic
581C23×C3C23×D311yescharacteristic
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—32no—
587C22×D3—32no—
588C22×D3—62no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—62no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—121no—
617C22×D3—121no—
618C22×D3—121no—
619C22×D3—121no—
620C22×D3—121no—
621C22×D3—121no—
622C22×D3—121no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—121no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3#23512yes—
629C22×D3D3×D412yes—
630C22×D3D3×D412yes—
631C3×D4—124no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—22no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—124no—
670C2×C3×C4#23512yes—
671C2×C3×C4#23712yes—
672#67—44no—
673#67—68no—
674#67—124no—
675#67—124no—
676#67—124no—
677#67—124no—
678#67—124no—
679#67—128no—
680#67—128no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—32no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—32no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—124no—
719C2×Dic3—124no—
720C2×Dic3D3×D412yes—
721C2×Dic3D3×D412yes—
722D12—68no—
723D12—124no—
724D12—124no—
725D12—128no—
726D12—124no—
727C4×D3—44no—
728C4×D3—124no—
729C4×D3—124no—
730C4×D3—124no—
731C4×D3—124no—
732C2×C32—81no—
733C2×C32C2×#12111yescharacteristic
734C2×C32#53211yescharacteristic
735C2×C32#53411yescharacteristic
736C2×C32#54611yescharacteristic
737C2×C32#54611yescharacteristic
738C2×C32#55311yescharacteristic
739C2×C32#55311yescharacteristic
740C3⋊D3—42no—
741C3⋊D3—81no—
742C3×D3—24no—
743C24—31no—
744C24—91no—
745C24—91no—
746C24C2×D3211yescharacteristic
747C2×D4—62no—
748C2×D4—62no—
749C2×D4—62no—
750C2×D4—94no—
751C2×D4—182no—
752C2×D4—182no—
753C2×D4—182no—
754C2×D4—182no—
755C2×D4—182no—
756C2×D4—182no—
757C2×D4—182no—
758C2×D4—182no—
759C2×D4—182no—
760C2×D4—182no—
761C2×D4—361no—
762C2×D4—361no—
763C2×D4—361no—
764C2×D4—361no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—31no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—62no—
773C22×C4—62no—
774C22×C4—94no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—121no—
778C22×C4—182no—
779C22×C4—182no—
780C22×C4—182no—
781C22×C4—361no—
782C22×C4—361no—
783C22×C4—361no—
784C22×C4—361no—
785C22×C4—361no—
786C22×C4C2×D3211yescharacteristic
787C22×C4C2×D3211yescharacteristic
788C4⋊C4—62no—
789C4⋊C4—182no—
790C4⋊C4—182no—
791C4⋊C4—182no—
792C22⋊C4—22no—
793C22⋊C4—62no—
794C22⋊C4—62no—
795C22⋊C4—62no—
796C22⋊C4—121no—
797C22⋊C4—182no—
798C22⋊C4—182no—
799C22⋊C4—182no—
800C22⋊C4—182no—
801C22⋊C4—182no—
802C22⋊C4—182no—
803C22⋊C4—361no—
804C42—62no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—34no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3C2×#23511yescharacteristic
841C22×C3C2×#23511yescharacteristic
842C22×C3C2×D3×D411yescharacteristic
843C22×C3C2×D3×D411yescharacteristic
844C22×C3C2×D3×D411yescharacteristic
845C22×C3C2×D3×D411yescharacteristic
846C22×C3C2×#23711yescharacteristic
847C22×C3#100411yescharacteristic
848C22×C3D3×#4111yescharacteristic
849C22×C3D3×#4111yescharacteristic
850C22×C3D3×#4111yescharacteristic
851C22×C3#100911yescharacteristic
852C22×C3#100911yescharacteristic
853C22×C3#100911yescharacteristic
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—22no—
858C2×D3—22no—
859C2×D3—22no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—122no—
867C2×D3—122no—
868C2×D3—122no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—122no—
878C2×D3—122no—
879C2×D3—122no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—121no—
894C2×D3—241no—
895C2×D3—241no—
896C2×D3—241no—
897C2×D3—241no—
898C2×D3—241no—
899C2×D3—241no—
900C2×D3—241no—
901C2×D3—241no—
902C2×D3#88414yes—
903C3×C4—22no—
904C3×C4—22no—
905C3×C4—42no—
906C3×C4—41no—
907C3×C4—41no—
908C3×C4—62no—
909C3×C4—62no—
910C3×C4—81no—
911C3×C4—121no—
912C3×C4—121no—
913C3×C4—121no—
914C3×C4—121no—
915C3×C4—121no—
916Dic3—22no—
917Dic3—22no—
918Dic3—41no—
919Dic3—41no—
920Dic3—41no—
921Dic3—41no—
922Dic3—41no—
923Dic3—62no—
924Dic3—62no—
925Dic3—62no—
926Dic3—62no—
927Dic3—122no—
928Dic3—122no—
929C32#254311yescharacteristic, complemented, Sylow
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—32no—
938C23—32no—
939C23—32no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—92no—
945C23—181no—
946C23—181no—
947C23—181no—
948C23—181no—
949C23—181no—
950C23—181no—
951C23—181no—
952C23—181no—
953C23—181no—
954C23—181no—
955C23—181no—
956C23—181no—
957C23—181no—
958C23C22×D3211yescharacteristic
959D4—124no—
960D4—188no—
961D4—364no—
962D4—364no—
963D4—364no—
964D4—364no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—32no—
971C2×C4—32no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—92no—
992C2×C4—92no—
993C2×C4—124no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—181no—
997C2×C4—181no—
998C2×C4—364no—
999C2×C4—364no—
1000C2×C4—364no—
1001C2×C4#380412yes—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—64no—
1010C2×C3—82no—
1011C2×C3—81no—
1012C2×C3—81no—
1013C2×C3C2×#88411yescharacteristic
1014C2×C3#553011yescharacteristic
1015C2×C3#554011yescharacteristic
1016C2×C3#554811yescharacteristic
1017C2×C3#555011yescharacteristic
1018C2×C3#556511yescharacteristic
1019C2×C3#559111yescharacteristic
1020C2×C3#559611yescharacteristic
1021C2×C3D3×#12111yescharacteristic
1022C2×C3#560511yescharacteristic
1023C2×C3#565311yescharacteristic
1024C2×C3#565411yescharacteristic
1025C2×C3#567611yescharacteristic
1026C2×C3#570911yescharacteristic
1027D3—24no—
1028D3—122no—
1029D3—122no—
1030D3—242no—
1031D3—242no—
1032D3—241no—
1033D3—241no—
1034C22—34no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—182no—
1049C22—182no—
1050C22—182no—
1051C22—361no—
1052C22—361no—
1053C22—361no—
1054C22—361no—
1055C22—361no—
1056C22—361no—
1057C22—361no—
1058C22—361no—
1059C22—361no—
1060C22—361no—
1061C22—361no—
1062C22D3×#23511yescharacteristic
1063C22#6430811yescharacteristic
1064C22D32×D411yescharacteristic
1065C22D32×D411yescharacteristic
1066C22#6431211yescharacteristic
1067C22#6431411yescharacteristic
1068C22C2×#380411yescharacteristic
1069C4—22no—
1070C4—41no—
1071C4—62no—
1072C4—62no—
1073C4—121no—
1074C4—121no—
1075C4—121no—
1076C4—121no—
1077C4—121no—
1078C4—182no—
1079C4—182no—
1080C3—21no—
1081C3#7475211yescharacteristic, complemented
1082C3#7588211yescharacteristic, complemented
1083C2—64no—
1084C2—81no—
1085C2—362no—
1086C2—721no—
1087C2#1059409711yescharacteristic
1088C2D3×#88411yescharacteristic
1089C2#1059426411yescharacteristic
1090C2#1059428211yescharacteristic
1091C2#1059494611yescharacteristic
1092C2#1059513111yescharacteristic
1093C2#1059513511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2543
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#63971C2semidirect
2. C2×#63971C2semidirect
3. C2×#63909C2semidirect
4. C2×#63880C2semidirect
5. #10592659C2semidirect
6. C3×#4956C2semidirect
7. C3×#4951C2semidirect
8. #10591722C2semidirect
9. #10591712C2semidirect
10. #10591380C2semidirect
11. #10591364C2semidirect
12. D3×C3⋊#95C2semidirect
13. #10591345C2semidirect
14. #10591216C2semidirect
15. #10591202C2semidirect
77. #4956D3semidirect
78. #4951D3semidirect
123. C2×#626D4semidirect
132. C2×D3×Dic3D4semidirect
929. C32#2543semidirect
1081. C3#74752semidirect
1082. C3#75882semidirect

Maximal subgroups

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

subgroupindex
C2×#639712
C2×#639092
C2×#638802
#105926592
C3×#49562
C3×#49512
#105917222
#105917122
#105913802
#105913642
D3×C3⋊#952
#105913452
#105912162
#105912022
#758823
#747523