Finite Group Databasebeta

← #11824573

Subgroups — #11824573

Order 1152.

1591 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63958C211yesmaximal, characteristic, complemented
2C2×#63958C211yesmaximal, characteristic, complemented
3C2×#63916C211yesmaximal, characteristic, complemented
4C2×#63880C211yesmaximal, characteristic, complemented
5#10592655C211yesmaximal, characteristic, complemented
6C3×#4960C211yesmaximal, characteristic, complemented
7C3×#4951C211yesmaximal, characteristic, complemented
8#10591721C211yesmaximal, characteristic, complemented
9#10591709C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591370C211yesmaximal, characteristic, complemented
12#10591348C211yesmaximal, characteristic, complemented
13#10591305C211yesmaximal, characteristic, complemented
14#10591297C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#76759—31nomaximal
17#75882—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45#63958—24no—
46#63958—24no—
47#63916—24no—
48#63880—24no—
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#938—31no—
58C2×#938—31no—
59C2×#938—31no—
60C2×#895—31no—
61C2×#884—31no—
62C2×#884—31no—
63C2×#67⋊C4—31no—
64C2×C4×D12—31no—
65C3×#392—31no—
66C3×#388—31no—
67#5222—31no—
68#5220—31no—
69#5220—31no—
70#4982—31no—
71#4961—31no—
72#4960D311yescharacteristic, complemented
73#4956—31no—
74#4956—31no—
75#4956—31no—
76#4956—31no—
77#4956—61no—
78#4953—31no—
79#4951—31no—
80#4951D311yescharacteristic, complemented
81#4940—31no—
82#4675—31no—
83#4665—31no—
84#4665—31no—
85D3×#95—31no—
86D3×#95—31no—
87#4661—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—
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3—41no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—41no—
107C2×C3×#67—41no—
108C2×C3×#67—41no—
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×D12—22no—
116C2×C3×D12—22no—
117C2×C3×D12—41no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—22no—
121C2×#626—22no—
122C2×#626—22no—
123C2×#626D414yescomplemented
124C2×#624—22no—
125C2×#624—22no—
126C2×#624—41no—
127C2×#624—41no—
128C2×#624—41no—
129C2×#624D414yescomplemented
130C2×D3×Dic3—22no—
131C2×D3×Dic3—41no—
132C2×D3×Dic3—41no—
133C32×C22⋊C4—22no—
134#3757—41no—
135#3752—22no—
136C3×#217—22no—
137C3×#217—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×C4⋊Dic3—22no—
141C3×C4×Dic3—22no—
142Dic3⋊Dic3—22no—
143Dic3⋊Dic3—22no—
144Dic3⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149(C2×D3)⋊Dic3—41no—
150#2543—91noSylow
151C22×C3×D4—31no—
152C22×C3×D4—31no—
153C22×C3×D4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—61no—
159C22×#67C2×D311yescharacteristic
160C22×#67C2×D311yescharacteristic
161C23×Dic3—31no—
162C22×D12—31no—
163C22×D12—31no—
164C22×D12C2×D311yescharacteristic
165C22×C4×D3—31no—
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—61no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C22⋊C4—21no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4C2×D311yescharacteristic
180C2×C3×C22⋊C4C2×D311yescharacteristic
181C2×C3×C42—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—61no—
190C2×#217C2×D311yescharacteristic
191C2×#217C2×D311yescharacteristic
192#938—64no—
193#938—64no—
194#938—64no—
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—61no—
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3C2×D311yescharacteristic
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×C4×Dic3C2×D311yescharacteristic
213#895—64no—
214#884—64no—
215#884—64no—
216#67⋊C4—64no—
217C4×D12—64no—
218C3×#95—31no—
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⋊#95—61no—
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⋊D3C2×D412yes—
249C22×C3⋊D3C2×D412yes—
250C22×C3⋊D3#4112yes—
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×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3C2×D412yes—
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—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C4×C3⋊D3—44no—
282C3×#67—44no—
283C3×#67—44no—
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×Dic3C2×D412yes—
299C2×C3×Dic3C2×D412yes—
300C2×C3×Dic3C2×D412yes—
301C2×C3×Dic3#4112yes—
302C3×D12—44no—
303#626—28no—
304#626—44no—
305#624—44no—
306#624—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—31no—
316#388—31no—
317#388—91no—
318#386—91no—
319#386—91no—
320#386—91no—
321#386—91no—
322C2×#95—91no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3—31no—
326C24×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C23×D3—31no—
329C23×D3—31no—
330C23×D3—61no—
331C23×D3C22×D311yescharacteristic
332C23×D3C22×D311yescharacteristic
333C2×C3×D4—62no—
334C2×C3×D4—62no—
335C2×C3×D4—62no—
336C2×C3×D4—62no—
337C2×C3×D4—62no—
338C2×C3×D4—121no—
339C2×C3×D4—121no—
340C2×C3×D4—121no—
341C2×C3×D4—121no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—22no—
355C2×#67—22no—
356C2×#67—22no—
357C2×#67—34no—
358C2×#67—41no—
359C2×#67—41no—
360C2×#67—41no—
361C2×#67—62no—
362C2×#67—62no—
363C2×#67—62no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—64no—
373C2×#67—122no—
374C2×#67—122no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—62no—
385C22×Dic3—121no—
386C22×Dic3—121no—
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C2×D12—22no—
394C2×D12—22no—
395C2×D12—34no—
396C2×D12—41no—
397C2×D12—62no—
398C2×D12—62no—
399C2×D12—62no—
400C2×D12—62no—
401C2×D12—62no—
402C2×C4×D3—34no—
403C2×C4×D3—34no—
404C2×C4×D3—62no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—122no—
414C2×C4×D3—122no—
415C2×C4×D3—121no—
416C2×C4×D3—121no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—121no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
422C2×C4×D3—121no—
423C2×C4×D3—122no—
424C2×C4×D3—121no—
425C2×C4×D3—121no—
426C3×C4⋊C4—62no—
427C3×C22⋊C4—22no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—42no—
430C3×C22⋊C4—62no—
431C3×C22⋊C4—62no—
432C3×C22⋊C4—62no—
433C3×C22⋊C4—62no—
434C3×C42—62no—
435#217—22no—
436#217—22no—
437#217—62no—
438#217—62no—
439#217—62no—
440#217—62no—
441#217—121no—
442#217—121no—
443#217—121no—
444#217—122no—
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—122no—
454(C2×D3)⋊C4—121no—
455C4⋊Dic3—22no—
456C4⋊Dic3—62no—
457C4⋊Dic3—62no—
458C4⋊Dic3—62no—
459Dic3⋊C4—62no—
460Dic3⋊C4—62no—
461Dic3⋊C4—62no—
462C4×Dic3—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
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#12114yes—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
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—41no—
498C32×C4—22no—
499C32×C4—41no—
500C3⋊Dic3—41no—
501C3⋊Dic3—41no—
502C3⋊Dic3—41no—
503C3×Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C22×D4—31no—
510C22×D4—31no—
511C22×D4—31no—
512C22×D4—91no—
513C22×D4—91no—
514C22×D4—91no—
515C23×C4—91no—
516C23×C4—91no—
517C23×C4—91no—
518C23×C4—91no—
519#121—184no—
520#121—184no—
521#121—184no—
522C4×D4—184no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4D3211yescharacteristic
539C2×C42—31no—
540#95—31no—
541#95—31no—
542#95—31no—
543#95—91no—
544#95—91no—
545#95—91no—
546#95—91no—
547#95—91no—
548C23×C3—22no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
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—32no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3C23×D311yescharacteristic
585C23×C3C23×D311yescharacteristic
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—32no—
600C22×D3—32no—
601C22×D3—32no—
602C22×D3—32no—
603C22×D3—32no—
604C22×D3—32no—
605C22×D3—62no—
606C22×D3—62no—
607C22×D3—62no—
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×D3D3×D412yes—
621C3×D4—124no—
622C3×D4—124no—
623C3×D4—124no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—22no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
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#23512yes—
659C2×C3×C4#23712yes—
660#67—44no—
661#67—44no—
662#67—68no—
663#67—124no—
664#67—124no—
665#67—124no—
666#67—128no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—121no—
702C2×Dic3—121no—
703C2×Dic3—121no—
704C2×Dic3—121no—
705C2×Dic3—121no—
706C2×Dic3—121no—
707C2×Dic3—121no—
708C2×Dic3—124no—
709C2×Dic3D3×D412yes—
710C2×Dic3D3×D412yes—
711C2×Dic3D3×D412yes—
712C2×Dic3#23712yes—
713D12—44no—
714D12—68no—
715D12—124no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—124no—
719C4×D3—124no—
720C4×D3—124no—
721C4×D3—124no—
722C4×D3—128no—
723C4×D3—124no—
724C2×C32—81no—
725C2×C32C2×#12111yescharacteristic
726C2×C32#53211yescharacteristic
727C2×C32#53411yescharacteristic
728C2×C32#54611yescharacteristic
729C2×C32#54611yescharacteristic
730C2×C32#55311yescharacteristic
731C2×C32#55311yescharacteristic
732C3⋊D3—24no—
733C3×D3—42no—
734C3×D3—81no—
735C24—31no—
736C24—31no—
737C24—91no—
738C24C2×D3211yescharacteristic
739C2×D4—62no—
740C2×D4—62no—
741C2×D4—62no—
742C2×D4—62no—
743C2×D4—62no—
744C2×D4—94no—
745C2×D4—121no—
746C2×D4—121no—
747C2×D4—121no—
748C2×D4—121no—
749C2×D4—182no—
750C2×D4—182no—
751C2×D4—182no—
752C2×D4—182no—
753C2×D4—182no—
754C2×D4—182no—
755C2×D4—182no—
756C2×D4—182no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—94no—
764C22×C4—91no—
765C22×C4—91no—
766C22×C4—91no—
767C22×C4—182no—
768C22×C4—182no—
769C22×C4—182no—
770C22×C4—182no—
771C22×C4—182no—
772C22×C4—361no—
773C22×C4—361no—
774C22×C4—361no—
775C22×C4—361no—
776C22×C4—361no—
777C22×C4—361no—
778C22×C4C2×D3211yescharacteristic
779C22×C4C2×D3211yescharacteristic
780C4⋊C4—62no—
781C4⋊C4—182no—
782C4⋊C4—182no—
783C4⋊C4—182no—
784C22⋊C4—22no—
785C22⋊C4—62no—
786C22⋊C4—62no—
787C22⋊C4—62no—
788C22⋊C4—62no—
789C22⋊C4—182no—
790C22⋊C4—182no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—361no—
795C22⋊C4—361no—
796C42—62no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—81no—
825C22×C3—81no—
826C22×C3—81no—
827C22×C3—81no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3—121no—
837C22×C3—121no—
838C22×C3—121no—
839C22×C3C2×#23511yescharacteristic
840C22×C3C2×D3×D411yescharacteristic
841C22×C3C2×D3×D411yescharacteristic
842C22×C3C2×D3×D411yescharacteristic
843C22×C3C2×D3×D411yescharacteristic
844C22×C3C2×#23711yescharacteristic
845C22×C3C2×#23711yescharacteristic
846C22×C3#100411yescharacteristic
847C22×C3#100411yescharacteristic
848C22×C3D3×#4111yescharacteristic
849C22×C3D3×#4111yescharacteristic
850C22×C3D3×#4111yescharacteristic
851C22×C3#100911yescharacteristic
852C22×C3#100911yescharacteristic
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—34no—
857C2×D3—34no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—41no—
868C2×D3—41no—
869C2×D3—64no—
870C2×D3—62no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—122no—
883C2×D3—122no—
884C2×D3—122no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3—122no—
888C3×C4—22no—
889C3×C4—22no—
890C3×C4—42no—
891C3×C4—41no—
892C3×C4—41no—
893C3×C4—62no—
894C3×C4—62no—
895C3×C4—62no—
896C3×C4—62no—
897C3×C4—81no—
898C3×C4—121no—
899C3×C4—121no—
900Dic3—22no—
901Dic3—22no—
902Dic3—22no—
903Dic3—22no—
904Dic3—41no—
905Dic3—41no—
906Dic3—122no—
907Dic3—122no—
908Dic3—121no—
909Dic3—121no—
910Dic3—121no—
911Dic3—121no—
912Dic3—121no—
913Dic3—121no—
914Dic3—241no—
915C32#254311yescharacteristic, complemented, Sylow
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—32no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—92no—
938C23—92no—
939C23—92no—
940C23—181no—
941C23—181no—
942C23—181no—
943C23—181no—
944C23C22×D3211yescharacteristic
945D4—124no—
946D4—124no—
947D4—124no—
948D4—188no—
949D4—364no—
950D4—364no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—181no—
982C2×C4—181no—
983C2×C4—364no—
984C2×C4—364no—
985C2×C4—364no—
986C2×C4—364no—
987C2×C4#380412yes—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—82no—
996C2×C3—81no—
997C2×C3—81no—
998C2×C3—122no—
999C2×C3—241no—
1000C2×C3#553011yescharacteristic
1001C2×C3#554811yescharacteristic
1002C2×C3#555011yescharacteristic
1003C2×C3#558911yescharacteristic
1004C2×C3#559111yescharacteristic
1005C2×C3#559111yescharacteristic
1006C2×C3D3×#12111yescharacteristic
1007C2×C3D3×#12111yescharacteristic
1008C2×C3#561411yescharacteristic
1009C2×C3#561411yescharacteristic
1010C2×C3#565311yescharacteristic
1011C2×C3#567611yescharacteristic
1012C2×C3#570911yescharacteristic
1013C2×C3#571611yescharacteristic
1014D3—42no—
1015D3—64no—
1016D3—64no—
1017D3—81no—
1018D3—124no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—94no—
1030C22—121no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—121no—
1036C22—121no—
1037C22—121no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—182no—
1042C22—182no—
1043C22—182no—
1044C22—182no—
1045C22—182no—
1046C22—182no—
1047C22#6430611yescharacteristic
1048C22#6430711yescharacteristic
1049C22D32×D411yescharacteristic
1050C22D32×D411yescharacteristic
1051C22D3×#23711yescharacteristic
1052C22#6431411yescharacteristic
1053C22C2×#380411yescharacteristic
1054C4—22no—
1055C4—41no—
1056C4—62no—
1057C4—62no—
1058C4—62no—
1059C4—62no—
1060C4—121no—
1061C4—121no—
1062C4—361no—
1063C4—361no—
1064C4—361no—
1065C3—21no—
1066C3#7588211yescharacteristic, complemented
1067C3#7675911yescharacteristic, complemented
1068C2—81no—
1069C2—122no—
1070C2—184no—
1071C2—241no—
1072C2#1059421711yescharacteristic
1073C2#1059426211yescharacteristic
1074C2#1059426511yescharacteristic
1075C2#1059428111yescharacteristic
1076C2#1059496711yescharacteristic
1077C2#1059513511yescharacteristic
1078C2#1059513911yescharacteristic
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×#63958C2semidirect
2. C2×#63958C2semidirect
3. C2×#63916C2semidirect
4. C2×#63880C2semidirect
5. #10592655C2semidirect
6. C3×#4960C2semidirect
7. C3×#4951C2semidirect
8. #10591721C2semidirect
9. #10591709C2semidirect
10. #10591376C2semidirect
11. #10591370C2semidirect
12. #10591348C2semidirect
13. #10591305C2semidirect
14. #10591297C2semidirect
15. #10591275C2semidirect
72. #4960D3semidirect
80. #4951D3semidirect
123. C2×#626D4semidirect
129. C2×#624D4semidirect
915. C32#2543semidirect
1066. C3#75882semidirect
1067. C3#76759semidirect

Maximal subgroups

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

subgroupindex
C2×#639582
C2×#639162
C2×#638802
#105926552
C3×#49602
C3×#49512
#105917212
#105917092
#105913762
#105913702
#105913482
#105913052
#105912972
#105912752
#767593
#758823