Finite Group Databasebeta

← #11824576

Subgroups — #11824576

Order 1152.

1661 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2C2×#63910C211yesmaximal, characteristic, complemented
3C2×#63910C211yesmaximal, characteristic, complemented
4C2×#63894C211yesmaximal, characteristic, complemented
5C3×#4990C211yesmaximal, characteristic, complemented
6C3×#4982C211yesmaximal, characteristic, complemented
7#10591395C211yesmaximal, characteristic, complemented
8#10591392C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591380C211yesmaximal, characteristic, complemented
11#10591380C211yesmaximal, characteristic, complemented
12#10591370C211yesmaximal, characteristic, complemented
13#10591289C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591204C211yesmaximal, characteristic, complemented
16#77957—31nomaximal
17#75882—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31#64104—24no—
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46#63910—24no—
47#63910—24no—
48#63894—24no—
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#895—31no—
58C2×#895—31no—
59C2×#895—31no—
60C2×#895—31no—
61C2×#895—61no—
62C2×#893—31no—
63C2×#884—31no—
64C2×#884—31no—
65C2×C4×D12—31no—
66C3×#398—31no—
67C3×#388—31no—
68#4992—31no—
69#4991—31no—
70#4990—31no—
71#4990D311yescharacteristic, complemented
72#4982D311yescharacteristic, complemented
73#4961—31no—
74#4960—31no—
75#4956—31no—
76#4956—31no—
77#4940—31no—
78#4675—31no—
79#4671—31no—
80#4665—31no—
81#4665—31no—
82#4665—31no—
83#4665—31no—
84#4665—31no—
85#4665—31no—
86D3×#95—31no—
87D3×#95—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)—22no—
100C2×C4⋊(C3⋊D3)—22no—
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—41no—
104C2×C4⋊(C3⋊D3)D414yescomplemented
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—22no—
107C2×C4×C3⋊D3—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—22no—
121C2×#626—41no—
122C2×#626—41no—
123C2×#626—41no—
124C2×#624—22no—
125C2×#624—22no—
126C2×#624—22no—
127C2×#624—41no—
128C2×#624—41no—
129C2×#624—41no—
130C2×#624—41no—
131C2×#624—41no—
132C2×#624D414yescomplemented
133C32×C4⋊C4—22no—
134#3752—22no—
135#3752—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×C4⋊Dic3—22no—
140C3×Dic3⋊C4—22no—
141C3×Dic3⋊C4—22no—
142C3×C4×Dic3—22no—
143#3722—22no—
144#3722—22no—
145#3722—22no—
146#3722—22no—
147#3722—22no—
148#3722—41no—
149(C2×D3)⋊Dic3—41no—
150#2543—91noSylow
151C22×#67—31no—
152C22×#67—31no—
153C22×#67—31no—
154C22×D12—31no—
155C22×D12—31no—
156C22×D12—31no—
157C22×D12—31no—
158C22×D12—31no—
159C22×D12—31no—
160C22×D12—31no—
161C22×D12—31no—
162C22×D12—31no—
163C22×D12—61no—
164C22×D12—61no—
165C22×D12—61no—
166C22×C4×D3—31no—
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—61no—
175C2×C3×C4⋊C4—21no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4C2×D311yescharacteristic
180C2×C3×C4⋊C4C2×D311yescharacteristic
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C42—31no—
185C2×#217—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
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×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×C4⋊Dic3C2×D311yescharacteristic
209C2×Dic3⋊C4C2×D311yescharacteristic
210C2×Dic3⋊C4C2×D311yescharacteristic
211C2×C4×Dic3C2×D311yescharacteristic
212#895—64no—
213#895—64no—
214#895—64no—
215#895—64no—
216#895—68no—
217#893—64no—
218#884—64no—
219#884—64no—
220C4×D12—64no—
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—31no—
232C3⋊#95C2×D311yescharacteristic
233C3⋊#95C2×D311yescharacteristic
234C3⋊#95C2×D311yescharacteristic
235C3⋊#95C2×D311yescharacteristic
236C3⋊#95C2×D311yescharacteristic
237C23×C32C2411yescharacteristic
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
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⋊D3C2×D412yes—
256C22×C3⋊D3C2×D412yes—
257C22×C3⋊D3C2×D412yes—
258C22×C3⋊D3#4112yes—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C2×D412yes—
274C2×C32×C4#4112yes—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C4⋊(C3⋊D3)—28no—
279C4⋊(C3⋊D3)—44no—
280C4⋊(C3⋊D3)—44no—
281C4×C3⋊D3—44no—
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—
302C2×C3×Dic3#4112yes—
303#626—44no—
304#626—44no—
305#626—44no—
306#624—44no—
307#624—44no—
308#624—44no—
309C2×#121—91no—
310C2×#121—91no—
311C2×#121—91no—
312C2×C4×D4—91no—
313#398—31no—
314#397—91no—
315#394—91no—
316#392—91no—
317#388—31no—
318#388—91no—
319#386—91no—
320#386—91no—
321#386—91no—
322#386—91no—
323C2×#95—91no—
324C24×C3—31no—
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—31no—
328C23×D3—31no—
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—61no—
332C23×D3—61no—
333C23×D3—61no—
334C23×D3C22×D311yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
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×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—62no—
354C2×#67—62no—
355C2×#67—62no—
356C2×#67—62no—
357C2×#67—121no—
358C2×#67—121no—
359C2×#67—121no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—61no—
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C2×D12—34no—
371C2×D12—34no—
372C2×D12—64no—
373C2×D12—62no—
374C2×D12—62no—
375C2×D12—62no—
376C2×D12—62no—
377C2×D12—62no—
378C2×D12—62no—
379C2×D12—62no—
380C2×D12—62no—
381C2×D12—62no—
382C2×D12—62no—
383C2×D12—62no—
384C2×D12—62no—
385C2×D12—64no—
386C2×D12—64no—
387C2×D12—62no—
388C2×D12—62no—
389C2×D12—62no—
390C2×D12—62no—
391C2×D12—62no—
392C2×D12—62no—
393C2×D12—62no—
394C2×D12—62no—
395C2×D12—122no—
396C2×D12—122no—
397C2×D12—122no—
398C2×D12—122no—
399C2×D12—122no—
400C2×D12—121no—
401C2×D12—121no—
402C2×D12—122no—
403C2×D12—121no—
404C2×D12—121no—
405C2×D12—121no—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—64no—
415C2×C4×D3—62no—
416C2×C4×D3—62no—
417C2×C4×D3—62no—
418C2×C4×D3—62no—
419C2×C4×D3—122no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
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—
429C2×C4×D3—121no—
430C2×C4×D3—121no—
431C2×C4×D3—121no—
432C2×C4×D3—122no—
433C3×C4⋊C4—24no—
434C3×C4⋊C4—22no—
435C3×C4⋊C4—22no—
436C3×C4⋊C4—62no—
437C3×C4⋊C4—62no—
438C3×C4⋊C4—62no—
439C3×C22⋊C4—62no—
440C3×C22⋊C4—62no—
441C3×C22⋊C4—62no—
442C3×C42—62no—
443#217—121no—
444(C2×D3)⋊C4—22no—
445(C2×D3)⋊C4—22no—
446(C2×D3)⋊C4—22no—
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—62no—
455(C2×D3)⋊C4—62no—
456(C2×D3)⋊C4—64no—
457(C2×D3)⋊C4—64no—
458(C2×D3)⋊C4—62no—
459(C2×D3)⋊C4—62no—
460(C2×D3)⋊C4—62no—
461(C2×D3)⋊C4—62no—
462(C2×D3)⋊C4—62no—
463(C2×D3)⋊C4—121no—
464(C2×D3)⋊C4—121no—
465(C2×D3)⋊C4—121no—
466C4⋊Dic3—22no—
467Dic3⋊C4—22no—
468Dic3⋊C4—22no—
469C4×Dic3—22no—
470C22×C32C22×D411yescharacteristic
471C22×C32C22×D411yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32C2×#4111yescharacteristic
474C22×C32C2×#4111yescharacteristic
475C22×C32H(5,𝔽2)11yescharacteristic
476C22×C32H(5,𝔽2)11yescharacteristic
477C2×C3⋊D3—22no—
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3—22no—
481C2×C3⋊D3—22no—
482C2×C3⋊D3—22no—
483C2×C3⋊D3—22no—
484C2×C3⋊D3—22no—
485C2×C3⋊D3—22no—
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—41no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3#12114yes—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C32×C4—22no—
506C32×C4—22no—
507C32×C4—41no—
508C3⋊Dic3—41no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—41no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C22×D4—91no—
517C22×D4—91no—
518C22×D4—91no—
519C22×D4—91no—
520C22×D4—91no—
521C22×D4—91no—
522C23×C4—91no—
523C23×C4—91no—
524C23×C4—91no—
525C23×C4—91no—
526#121—184no—
527#121—184no—
528#121—184no—
529C4×D4—184no—
530C2×C4⋊C4—31no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—31no—
533C2×C4⋊C4D3211yescharacteristic
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C42—31no—
547#95—31no—
548#95—31no—
549#95—31no—
550#95—31no—
551#95—31no—
552#95—91no—
553#95—91no—
554#95—91no—
555C23×C3—21no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3C23×D311yescharacteristic
564C23×C3C23×D311yescharacteristic
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—32no—
573C22×D3—32no—
574C22×D3—32no—
575C22×D3—32no—
576C22×D3—32no—
577C22×D3—32no—
578C22×D3—32no—
579C22×D3—32no—
580C22×D3—62no—
581C22×D3—62no—
582C22×D3—62no—
583C22×D3—62no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
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—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—62no—
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—61no—
617C22×D3—61no—
618C22×D3—61no—
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—121no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3—121no—
632C22×D3—121no—
633C22×D3—121no—
634C22×D3—121no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—22no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
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—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4#23512yes—
680C2×C3×C4D3×D412yes—
681C2×C3×C4D3×D412yes—
682C2×C3×C4#23912yes—
683#67—124no—
684#67—124no—
685#67—124no—
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—21no—
701C2×Dic3—21no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—62no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3D3×D412yes—
714C2×Dic3D3×D412yes—
715C2×Dic3#23912yes—
716D12—68no—
717D12—68no—
718D12—128no—
719D12—124no—
720D12—124no—
721D12—128no—
722D12—124no—
723D12—124no—
724D12—128no—
725D12—124no—
726D12—124no—
727D12—124no—
728C4×D3—124no—
729C4×D3—124no—
730C4×D3—124no—
731C4×D3—124no—
732C4×D3—124no—
733C4×D3—124no—
734C4×D3—124no—
735C4×D3—124no—
736C4×D3—128no—
737C2×C32C2×#12111yescharacteristic
738C2×C32#53211yescharacteristic
739C2×C32#53411yescharacteristic
740C2×C32#54611yescharacteristic
741C2×C32#54611yescharacteristic
742C2×C32#55311yescharacteristic
743C2×C32#55311yescharacteristic
744C3⋊D3—24no—
745C3⋊D3—42no—
746C3⋊D3—81no—
747C3×D3—81no—
748C24—31no—
749C24—91no—
750C24—91no—
751C24—91no—
752C2×D4—94no—
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—182no—
762C2×D4—182no—
763C2×D4—182no—
764C2×D4—182no—
765C2×D4—182no—
766C2×D4—361no—
767C2×D4—361no—
768C2×D4—361no—
769C2×D4—361no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—31no—
776C22×C4—31no—
777C22×C4—94no—
778C22×C4—91no—
779C22×C4—182no—
780C22×C4—182no—
781C22×C4—182no—
782C22×C4—182no—
783C22×C4—182no—
784C22×C4—361no—
785C22×C4—361no—
786C22×C4—361no—
787C22×C4—361no—
788C22×C4—361no—
789C22×C4—361no—
790C22×C4C2×D3211yescharacteristic
791C22×C4C2×D3211yescharacteristic
792C22×C4C2×D3211yescharacteristic
793C4⋊C4—22no—
794C4⋊C4—62no—
795C4⋊C4—62no—
796C4⋊C4—62no—
797C22⋊C4—62no—
798C22⋊C4—62no—
799C22⋊C4—62no—
800C22⋊C4—182no—
801C22⋊C4—182no—
802C22⋊C4—182no—
803C22⋊C4—182no—
804C22⋊C4—182no—
805C22⋊C4—182no—
806C22⋊C4—182no—
807C22⋊C4—361no—
808C22⋊C4—361no—
809C42—62no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3C2×#23511yescharacteristic
825C22×C3C2×D3×D411yescharacteristic
826C22×C3C2×D3×D411yescharacteristic
827C22×C3C2×D3×D411yescharacteristic
828C22×C3C2×D3×D411yescharacteristic
829C22×C3C2×#23911yescharacteristic
830C22×C3C2×#23911yescharacteristic
831C22×C3D3×#4111yescharacteristic
832C22×C3D3×#4111yescharacteristic
833C22×C3D3×#4111yescharacteristic
834C22×C3#100911yescharacteristic
835C22×C3#100911yescharacteristic
836C22×C3#100911yescharacteristic
837C22×C3#100911yescharacteristic
838C2×D3—34no—
839C2×D3—34no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—41no—
847C2×D3—64no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—62no—
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—122no—
870C2×D3—122no—
871C2×D3—122no—
872C2×D3—122no—
873C2×D3—122no—
874C2×D3—122no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—122no—
884C2×D3—122no—
885C2×D3—122no—
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—121no—
895C2×D3—121no—
896C2×D3—121no—
897C2×D3—121no—
898C2×D3—121no—
899C2×D3—121no—
900C2×D3—241no—
901C2×D3—241no—
902C2×D3—241no—
903C2×D3—241no—
904C2×D3—241no—
905C2×D3—241no—
906C2×D3—241no—
907C2×D3—241no—
908C3×C4—24no—
909C3×C4—22no—
910C3×C4—22no—
911C3×C4—22no—
912C3×C4—22no—
913C3×C4—42no—
914C3×C4—42no—
915C3×C4—41no—
916C3×C4—41no—
917C3×C4—62no—
918C3×C4—62no—
919C3×C4—62no—
920C3×C4—121no—
921C3×C4—121no—
922C3×C4—121no—
923C3×C4—121no—
924Dic3—22no—
925Dic3—22no—
926Dic3—22no—
927Dic3—41no—
928Dic3—41no—
929Dic3—41no—
930Dic3—41no—
931Dic3—122no—
932Dic3—121no—
933Dic3—121no—
934C32#254311yescharacteristic, complemented, Sylow
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—92no—
943C23—92no—
944C23—92no—
945C23—92no—
946C23—181no—
947C23—181no—
948C23—181no—
949C23—181no—
950C23—181no—
951C23—181no—
952C23—181no—
953C23—181no—
954C23—181no—
955C23—181no—
956C23—181no—
957C23—181no—
958C23—181no—
959C23—181no—
960C23—181no—
961C23—181no—
962C23—181no—
963C23C22×D3211yescharacteristic
964D4—188no—
965D4—364no—
966D4—364no—
967D4—364no—
968D4—364no—
969D4—364no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—32no—
978C2×C4—32no—
979C2×C4—32no—
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—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—61no—
995C2×C4—61no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—181no—
999C2×C4—181no—
1000C2×C4—181no—
1001C2×C4—364no—
1002C2×C4—364no—
1003C2×C4—364no—
1004C2×C4—364no—
1005C2×C4#379912yes—
1006C2×C4#381112yes—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—241no—
1015C2×C3#553011yescharacteristic
1016C2×C3#554811yescharacteristic
1017C2×C3#555011yescharacteristic
1018C2×C3D3×#12111yescharacteristic
1019C2×C3D3×#12111yescharacteristic
1020C2×C3#563011yescharacteristic
1021C2×C3#563011yescharacteristic
1022C2×C3#565311yescharacteristic
1023C2×C3#565311yescharacteristic
1024C2×C3#567611yescharacteristic
1025C2×C3#569511yescharacteristic
1026C2×C3#569511yescharacteristic
1027C2×C3#570911yescharacteristic
1028C2×C3#572511yescharacteristic
1029D3—64no—
1030D3—64no—
1031D3—81no—
1032D3—124no—
1033D3—122no—
1034D3—122no—
1035D3—242no—
1036D3—242no—
1037D3—241no—
1038D3—241no—
1039C22—94no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22—121no—
1045C22—121no—
1046C22—121no—
1047C22—182no—
1048C22—182no—
1049C22—182no—
1050C22—182no—
1051C22—182no—
1052C22—182no—
1053C22—182no—
1054C22—182no—
1055C22—182no—
1056C22—361no—
1057C22—361no—
1058C22—361no—
1059C22—361no—
1060C22—361no—
1061C22—361no—
1062C22—361no—
1063C22—361no—
1064C22—361no—
1065C22—361no—
1066C22—361no—
1067C22C2×#379911yescharacteristic
1068C22#6430811yescharacteristic
1069C22D32×D411yescharacteristic
1070C22#6431211yescharacteristic
1071C22D3×#23911yescharacteristic
1072C22#6432011yescharacteristic
1073C22C2×#381111yescharacteristic
1074C4—22no—
1075C4—22no—
1076C4—41no—
1077C4—62no—
1078C4—62no—
1079C4—62no—
1080C4—121no—
1081C4—121no—
1082C4—121no—
1083C4—121no—
1084C4—361no—
1085C3—21no—
1086C3#7588211yescharacteristic, complemented
1087C3#7795711yescharacteristic, complemented
1088C2—184no—
1089C2—241no—
1090C2—362no—
1091C2—721no—
1092C2#1059446811yescharacteristic
1093C2#1059451811yescharacteristic
1094C2#1059457811yescharacteristic
1095C2#1059461011yescharacteristic
1096C2#1059501811yescharacteristic
1097C2#1059529811yescharacteristic
1098C2#1059543111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2543
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64104C2semidirect
2. C2×#63910C2semidirect
3. C2×#63910C2semidirect
4. C2×#63894C2semidirect
5. C3×#4990C2semidirect
6. C3×#4982C2semidirect
7. #10591395C2semidirect
8. #10591392C2semidirect
9. #10591387C2semidirect
10. #10591380C2semidirect
11. #10591380C2semidirect
12. #10591370C2semidirect
13. #10591289C2semidirect
14. #10591275C2semidirect
15. #10591204C2semidirect
71. #4990D3semidirect
72. #4982D3semidirect
104. C2×C4⋊(C3⋊D3)D4semidirect
132. C2×#624D4semidirect
934. C32#2543semidirect
1086. C3#75882semidirect
1087. C3#77957semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×#639102
C2×#638942
C3×#49902
C3×#49822
#105913952
#105913922
#105913872
#105913802
#105913702
#105912892
#105912752
#105912042
#779573
#758823