Finite Group Databasebeta

← #11812848

Subgroups — #11812848

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic, complemented
3C2×#63952C211yesmaximal, characteristic, complemented
4C2×#63883C211yesmaximal, characteristic, complemented
5C3×#5222C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic, complemented
7#10591722C211yesmaximal, characteristic, complemented
8#10591722C211yesmaximal, characteristic, complemented
9#10591718C211yesmaximal, characteristic, complemented
10#10591717C211yesmaximal, characteristic, complemented
11#10591715C211yesmaximal, characteristic, complemented
12#10591702C211yesmaximal, characteristic, complemented
13#10591290C211yesmaximal, characteristic, complemented
14#10591272C211yesmaximal, characteristic, complemented
15#10591215C211yesmaximal, characteristic, complemented
16#82897—31nomaximal
17#77117—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27#64147—24no—
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C3×#935—24no—
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×#3724C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63952—24no—
48#63883—24no—
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×#123—31no—
58C2×#938—31no—
59C2×#938—31no—
60C2×#938—61no—
61C2×#935D311yescharacteristic, complemented
62C2×C4×#67—31no—
63C2×D3×C4⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C2×#67⋊C4—31no—
66C3×#394—31no—
67#5222D311yescharacteristic, complemented
68#5210—31no—
69#4989—31no—
70#4982—31no—
71#4982—31no—
72#4980—31no—
73#4956—31no—
74#4956—31no—
75#4956—31no—
76#4956—31no—
77#4956—31no—
78#4956—31no—
79#4953—31no—
80#4952—31no—
81#4951—31no—
82#4950—31no—
83#4949—31no—
84#4949—31no—
85#4945—31no—
86#4668—31no—
87#4655—31no—
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C2×C32×D4—22no—
92C2×C32×D4—22no—
93C2×C32×D4—41no—
94C22×C32×C4C2311yescharacteristic
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—22no—
98C2×#638—22no—
99C2×#638—22no—
100C2×#638D414yes—
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—41no—
107C22×C3×Dic3—22no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3—41no—
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C2×#624—22no—
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—22no—
122C2×#624—22no—
123C2×#624—41no—
124#3757—22no—
125#3757—22no—
126C4⋊(C3⋊Dic3)—22no—
127C3×#217—22no—
128C3×#217—22no—
129C3×#217—22no—
130C3×#217—22no—
131C3×#217—22no—
132C3×#217—22no—
133C3×#217—41no—
134C3×Dic3⋊C4—22no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4D414yescomplemented
137#3724—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—41no—
141#3722—22no—
142#3722—22no—
143Dic32—22no—
144#2443—91noSylow
145C22×C3×D4—21no—
146C22×C3×D4C2×D311yescharacteristic
147C22×C3×D4C2×D311yescharacteristic
148C23×C3×C4—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—31no—
152C22×#67—31no—
153C22×#67—61no—
154C22×#67—61no—
155C23×Dic3C2×D311yescharacteristic
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3—61no—
163C3×#123—64no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—61no—
179C2×#217—61no—
180C2×#217C2×D311yescharacteristic
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183C2×#217C2×D311yescharacteristic
184C2×#217C2×D311yescharacteristic
185C2×#217C2×D311yescharacteristic
186C2×#217C2×D311yescharacteristic
187#938—64no—
188#938—64no—
189#938—68no—
190#935—24no—
191C4×#67—64no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—31no—
199C2×C4⋊Dic3—31no—
200C2×C4⋊Dic3—31no—
201C2×C4⋊Dic3—61no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4C2×D311yescharacteristic
208C2×Dic3⋊C4C2×D311yescharacteristic
209C2×Dic3⋊C4C2×D311yescharacteristic
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212D3×C4⋊C4—64no—
213D3×C4⋊C4—64no—
214#67⋊C4—64no—
215C3×#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
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⋊#95C2×D311yescharacteristic
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32C2×D412yes—
245C23×C32C2411yescharacteristic
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3C2×D412yes—
251C22×C3⋊D3#4112yes—
252C22×C3⋊D3#4112yes—
253C32×D4—44no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D412yes—
257#638—28no—
258#638—44no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3C2×D412yes—
268C4×C3⋊D3—44no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
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—
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—44no—
291C2×C3×Dic3C2×D412yes—
292C2×C3×Dic3C2×D412yes—
293C2×C3×Dic3#4112yes—
294#624—28no—
295#624—44no—
296C2×#123—31no—
297C2×#121—91no—
298C2×C4×D4—91no—
299C22×C4⋊C4—91no—
300#399—91no—
301#398—91no—
302#397—91no—
303#394—31no—
304#388—91no—
305#387—91no—
306#386—91no—
307#386—91no—
308#386—91no—
309#385—91no—
310#385—91no—
311C24×C3—21no—
312C24×C3—21no—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C24×C3C22×D311yescharacteristic
316C24×C3C22×D311yescharacteristic
317C23×D3—31no—
318C23×D3—31no—
319C23×D3—61no—
320C2×C3×D4—24no—
321C2×C3×D4—22no—
322C2×C3×D4—22no—
323C2×C3×D4—22no—
324C2×C3×D4—22no—
325C2×C3×D4—42no—
326C2×C3×D4—41no—
327C2×C3×D4—41no—
328C2×C3×D4—42no—
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—62no—
339C22×C3×C4—62no—
340C22×C3×C4—121no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C2×#67—34no—
344C2×#67—34no—
345C2×#67—64no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—62no—
354C2×#67—62no—
355C2×#67—62no—
356C2×#67—64no—
357C2×#67—122no—
358C2×#67—122no—
359C2×#67—122no—
360C2×#67—122no—
361C22×Dic3—22no—
362C22×Dic3—22no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—41no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—62no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—64no—
393C2×C4×D3—62no—
394C2×C4×D3—62no—
395C2×C4×D3—62no—
396C2×C4×D3—122no—
397C2×C4×D3—121no—
398C2×C4×D3—121no—
399C2×C4×D3—121no—
400C2×C4×D3—121no—
401C2×C4×D3—122no—
402C3×C4⋊C4—34no—
403C3×C4⋊C4—62no—
404C3×C4⋊C4—62no—
405C3×C22⋊C4—62no—
406C3×C22⋊C4—62no—
407C3×C22⋊C4—62no—
408C3×C22⋊C4—62no—
409C3×C22⋊C4—62no—
410C3×C22⋊C4—62no—
411C3×C22⋊C4—121no—
412#217—22no—
413#217—22no—
414#217—22no—
415#217—22no—
416#217—22no—
417#217—22no—
418#217—41no—
419#217—62no—
420#217—62no—
421#217—64no—
422#217—64no—
423#217—62no—
424#217—62no—
425(C2×D3)⋊C4—62no—
426(C2×D3)⋊C4—62no—
427(C2×D3)⋊C4—62no—
428(C2×D3)⋊C4—62no—
429C4⋊Dic3—62no—
430C4⋊Dic3—62no—
431C4⋊Dic3—62no—
432C4⋊Dic3—64no—
433C4⋊Dic3—62no—
434C4⋊Dic3—121no—
435Dic3⋊C4—22no—
436Dic3⋊C4—22no—
437Dic3⋊C4—62no—
438Dic3⋊C4—62no—
439Dic3⋊C4—62no—
440Dic3⋊C4—62no—
441Dic3⋊C4—121no—
442Dic3⋊C4#6714yescomplemented
443C4×Dic3—62no—
444C4×Dic3—62no—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32C22×D411yescharacteristic
460C22×C32C22×D411yescharacteristic
461C22×C32C2×#4111yescharacteristic
462C22×C32C2×#4111yescharacteristic
463C22×C32C2×#4111yescharacteristic
464C22×C32H(5,𝔽2)11yescharacteristic
465C22×C322−1+411yescharacteristic
466C2×C3⋊D3—22no—
467C2×C3⋊D3—22no—
468C2×C3⋊D3—22no—
469C2×C3⋊D3—22no—
470C2×C3⋊D3—22no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3#12314yescomplemented
473C32×C4—22no—
474C3⋊Dic3—22no—
475C3⋊Dic3—41no—
476C3⋊Dic3—41no—
477C3×Dic3—22no—
478C3×Dic3—22no—
479C3×Dic3—22no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C22×D4—91no—
486C22×D4—91no—
487C22×D4D3211yescharacteristic
488C23×C4—31no—
489C23×C4—91no—
490C23×C4—91no—
491C23×C4—91no—
492#123—64no—
493#121—184no—
494C4×D4—184no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—91no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—184no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C42—91no—
516#95—31no—
517#95—91no—
518#95—91no—
519#95—91no—
520#95—91no—
521#95—91no—
522#95—91no—
523#95—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—22no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—22no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3D3×D412yes—
566C23×C3D3×D412yes—
567C23×C3C23×D311yescharacteristic
568C23×C3C23×D311yescharacteristic
569C22×D3—32no—
570C22×D3—32no—
571C22×D3—32no—
572C22×D3—32no—
573C22×D3—32no—
574C22×D3—32no—
575C22×D3—62no—
576C22×D3—62no—
577C22×D3—62no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—61no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—121no—
587C22×D3—121no—
588C22×D3—121no—
589C22×D3—121no—
590C3×D4—44no—
591C3×D4—44no—
592C3×D4—48no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—22no—
600C2×C3×C4—32no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—124no—
625C2×C3×C4D3×D412yes—
626C2×C3×C4C2×#6712yes—
627#67—68no—
628#67—68no—
629#67—128no—
630#67—124no—
631#67—124no—
632#67—128no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—44no—
657C2×Dic3—62no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—121no—
677C2×Dic3—121no—
678C2×Dic3—121no—
679C2×Dic3—121no—
680C2×Dic3—121no—
681C2×Dic3—121no—
682C2×Dic3#23712yes—
683C2×Dic3C2×#6712yes—
684C2×Dic3C2×#6712yes—
685C4×D3—68no—
686C4×D3—68no—
687C4×D3—124no—
688C4×D3—124no—
689C4×D3—124no—
690C4×D3—124no—
691C4×D3—128no—
692C2×C32—42no—
693C2×C32—81no—
694C2×C32C2×#12311yescharacteristic
695C2×C32#52511yescharacteristic
696C2×C32#53911yescharacteristic
697C2×C32D4211yescharacteristic
698C2×C32#54711yescharacteristic
699C2×C32#54811yescharacteristic
700C2×C32#55311yescharacteristic
701C3⋊D3—24no—
702C24—91no—
703C24C2×D3211yescharacteristic
704C24C2×D3211yescharacteristic
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—41no—
708C2×D4—94no—
709C2×D4—182no—
710C2×D4—182no—
711C2×D4—182no—
712C2×D4—182no—
713C2×D4—182no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—62no—
723C22×C4—62no—
724C22×C4—91no—
725C22×C4—91no—
726C22×C4—91no—
727C22×C4—121no—
728C22×C4—182no—
729C22×C4—182no—
730C22×C4—182no—
731C22×C4—182no—
732C22×C4—182no—
733C22×C4—182no—
734C22×C4—182no—
735C22×C4—361no—
736C22×C4—361no—
737C22×C4C2×D3211yescharacteristic
738C4⋊C4—34no—
739C4⋊C4—62no—
740C4⋊C4—62no—
741C4⋊C4—182no—
742C4⋊C4—182no—
743C4⋊C4—182no—
744C4⋊C4—182no—
745C4⋊C4—361no—
746C22⋊C4—62no—
747C22⋊C4—62no—
748C22⋊C4—62no—
749C22⋊C4—62no—
750C22⋊C4—62no—
751C22⋊C4—62no—
752C22⋊C4—121no—
753C22⋊C4—182no—
754C22⋊C4—182no—
755C22⋊C4—182no—
756C22⋊C4—182no—
757C42—182no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—42no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—42no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—81no—
800C22×C3—81no—
801C22×C3—81no—
802C22×C3—81no—
803C22×C3—81no—
804C22×C3—81no—
805C22×C3—81no—
806C22×C3—81no—
807C22×C3C2×D3×D411yescharacteristic
808C22×C3C2×D3×D411yescharacteristic
809C22×C3C2×D3×D411yescharacteristic
810C22×C3C2×#23711yescharacteristic
811C22×C3#100411yescharacteristic
812C22×C3#100411yescharacteristic
813C22×C3D3×#4111yescharacteristic
814C22×C3D3×#4111yescharacteristic
815C22×C3D3×#4111yescharacteristic
816C22×C3D3×#4111yescharacteristic
817C22×C3D3×#4111yescharacteristic
818C22×C3#101011yescharacteristic
819C22×C3#101011yescharacteristic
820C22×C3C22×#6711yescharacteristic
821C2×D3—34no—
822C2×D3—34no—
823C2×D3—64no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—122no—
837C2×D3—122no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—122no—
841C2×D3—122no—
842C3×C4—24no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—62no—
846C3×C4—62no—
847C3×C4—62no—
848C3×C4—121no—
849C3×C4—121no—
850C3×C4—121no—
851C3×C4—121no—
852C3×C4—121no—
853Dic3—22no—
854Dic3—22no—
855Dic3—22no—
856Dic3—41no—
857Dic3—41no—
858Dic3—41no—
859Dic3—41no—
860Dic3—41no—
861Dic3—62no—
862Dic3—62no—
863Dic3—122no—
864Dic3—122no—
865Dic3—122no—
866Dic3—121no—
867Dic3—121no—
868Dic3—121no—
869Dic3—121no—
870C32#244311yescharacteristic, complemented, Sylow
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—92no—
885C23—92no—
886C23—92no—
887C23—181no—
888C23—181no—
889C23—181no—
890C23—181no—
891C23#381112yes—
892C23C22×D3211yescharacteristic
893D4—44no—
894D4—188no—
895D4—364no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—32no—
899C2×C4—32no—
900C2×C4—32no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—92no—
923C2×C4—124no—
924C2×C4—188no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4—181no—
928C2×C4—181no—
929C2×C4—181no—
930C2×C4—181no—
931C2×C4—181no—
932C2×C4—181no—
933C2×C4—364no—
934C2×C4—364no—
935C2×C4D3×#6712yes—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—42no—
944C2×C3—42no—
945C2×C3—82no—
946C2×C3—82no—
947C2×C3—81no—
948C2×C3—81no—
949C2×C3#559011yescharacteristic
950C2×C3#560611yescharacteristic
951C2×C3#561111yescharacteristic
952C2×C3#561411yescharacteristic
953C2×C3D3×#12311yescharacteristic
954C2×C3D3×#12311yescharacteristic
955C2×C3#565511yescharacteristic
956C2×C3#566011yescharacteristic
957C2×C3#566011yescharacteristic
958C2×C3#566111yescharacteristic
959C2×C3#567711yescharacteristic
960C2×C3D4×#6711yescharacteristic
961C2×C3#582811yescharacteristic
962C2×C3#583111yescharacteristic
963D3—64no—
964D3—64no—
965D3—124no—
966C22—22no—
967C22—22no—
968C22—22no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—41no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—41no—
980C22—94no—
981C22—182no—
982C22—182no—
983C22—182no—
984C22—182no—
985C22—182no—
986C22—182no—
987C22#6430911yescharacteristic
988C22D3×#23711yescharacteristic
989C22#6431211yescharacteristic
990C22#6431211yescharacteristic
991C22C2×D3×#6711yescharacteristic
992C22C2×#381111yescharacteristic
993C22#6433011yescharacteristic
994C4—22no—
995C4—62no—
996C4—62no—
997C4—62no—
998C4—121no—
999C4—121no—
1000C4—121no—
1001C4—121no—
1002C4—121no—
1003C4—182no—
1004C4—361no—
1005C4—361no—
1006C3—21no—
1007C3#7711711yescharacteristic, complemented
1008C3#8289711yescharacteristic, complemented
1009C2—42no—
1010C2—81no—
1011C2—184no—
1012C2#1059516211yescharacteristic
1013C2#1059516911yescharacteristic
1014C2#1059519511yescharacteristic
1015C2#1059520911yescharacteristic
1016C2#1059523711yescharacteristic
1017C2#1059530111yescharacteristic
1018C2#1059552611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×#64147C2
hypercenterC22×D4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#935C2semidirect
3. C2×#63952C2semidirect
4. C2×#63883C2semidirect
5. C3×#5222C2semidirect
6. #10591722C2semidirect
7. #10591722C2semidirect
8. #10591722C2semidirect
9. #10591718C2semidirect
10. #10591717C2semidirect
11. #10591715C2semidirect
12. #10591702C2semidirect
13. #10591290C2semidirect
14. #10591272C2semidirect
15. #10591215C2semidirect
61. C2×#935D3semidirect
67. #5222D3semidirect
136. C3×Dic3⋊C4D4semidirect
442. Dic3⋊C4#67semidirect
472. C2×C3⋊D3#123semidirect
870. C32#2443semidirect
1007. C3#77117semidirect
1008. C3#82897semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C2×C3×#9352
C2×#639522
C2×#638832
C3×#52222
#105917222
#105917182
#105917172
#105917152
#105917022
#105912902
#105912722
#105912152
#828973
#771173