Finite Group Databasebeta

← #11808810

Subgroups — #11808810

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C2×C4×#627C211yesmaximal, characteristic, complemented
3C4×#3757C211yesmaximal, characteristic, complemented
4C3×C4×#217C211yesmaximal, characteristic, complemented
5#10591717C211yesmaximal, characteristic, complemented
6#10591709C211yesmaximal, characteristic
7#10591708C211yesmaximal, characteristic
8#10591692C211yesmaximal, characteristic, complemented
9#10591297C211yesmaximal, characteristic, complemented
10#10591293C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
12C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
13#10591222C211yesmaximal, characteristic, complemented
14#10591199C211yesmaximal, characteristic, complemented
15#10591196C211yesmaximal, characteristic, complemented
16#82348—31nomaximal
17#73481—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C3×C4×#67—24no—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C4×#627—24no—
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×C3×C4×D4—31no—
56C2×C4×#67D311yescharacteristic
57C2×C4×Dic6—31no—
58C2×C4×Dic6—31no—
59C3×C4×C22⋊C4—31no—
60#5222—31no—
61#5222—31no—
62C4×#217—31no—
63C4×#217—31no—
64C4×#217—31no—
65C4×#217—31no—
66C4×#217—61no—
67C4×#217D311yescharacteristic, complemented
68#4985—31no—
69#4985—31no—
70#4961—31no—
71#4959—31no—
72#4953—31no—
73#4953—31no—
74#4952—31no—
75#4947—31no—
76#4947—31no—
77#4947—31no—
78C4×(C2×D3)⋊C4—31no—
79C4×(C2×D3)⋊C4—31no—
80#4932—31no—
81#4932—31no—
82#4675—31no—
83#4673—31no—
84#4660—31no—
85#4658—31no—
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4—22no—
89C22×C32×C4—22no—
90C22×C32×C4—22no—
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×#627—22no—
111C2×#627—22no—
112C2×#627—22no—
113#3757—22no—
114#3757—22no—
115C4×C3⋊Dic3—22no—
116C4×C3⋊Dic3—22no—
117C3×#217—22no—
118C3×#217—22no—
119C3×#217—22no—
120C3×(C2×D3)⋊C4—22no—
121C3×Dic3⋊C4—22no—
122C3×C4×Dic3—22no—
123C3×C4×Dic3—22no—
124C3×C4×Dic3D414yes—
125#3724—22no—
126Dic3⋊Dic3—22no—
127Dic3⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130(C2×D3)⋊Dic3—22no—
131(C2×D3)⋊Dic3—22no—
132#2398—91noSylow
133C22×C3×D4—31no—
134C23×C3×C4—21no—
135C23×C3×C4—31no—
136C23×C3×C4C2×D311yescharacteristic
137C23×C3×C4C2×D311yescharacteristic
138C22×#67C2×D311yescharacteristic
139C22×C4×D3C2×D311yescharacteristic
140C22×Dic6—31no—
141C22×Dic6—31no—
142C3×C4×D4—64no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C42—31no—
149C2×C3×C42—31no—
150C2×C3×C42—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—31no—
157C2×#217—31no—
158C2×#217—31no—
159C2×#217—61no—
160C2×#217—61no—
161C2×#217C2×D311yescharacteristic
162C2×#217C2×D311yescharacteristic
163C2×#217C2×D311yescharacteristic
164C4×#67—24no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4C2×D311yescharacteristic
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4C2×D311yescharacteristic
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—61no—
182C2×C4×Dic3—61no—
183C2×C4×Dic3C2×D311yescharacteristic
184C2×C4×Dic3C2×D311yescharacteristic
185C2×C4×Dic3C2×D311yescharacteristic
186C4×Dic6—64no—
187C4×Dic6—64no—
188C3×#95—31no—
189C3×#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—61no—
211C3⋊#95—61no—
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32#4112yes—
221C23×C32C2411yescharacteristic
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—44no—
233C2×C32×C4C2×D412yes—
234C2×C32×C4#4112yes—
235C2×C32×C4#4112yes—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3#4112yes—
248C3×#67—28no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
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—
268C2×C3×Dic3C2×D412yes—
269C2×C3×Dic3#4112yes—
270C3×C4×D3—44no—
271#627—28no—
272C2×C4×Q8—91no—
273C2×C4×D4—31no—
274#400—91no—
275#400—91no—
276#397—91no—
277#397—91no—
278#394—91no—
279#394—91no—
280#393—91no—
281#393—91no—
282C4×C22⋊C4—31no—
283C4×C22⋊C4—91no—
284C4×C22⋊C4—91no—
285C4×C22⋊C4—91no—
286#376—91no—
287C24×C3—21no—
288C24×C3—31no—
289C24×C3C22×D311yescharacteristic
290C24×C3C22×D311yescharacteristic
291C23×D3C22×D311yescharacteristic
292C2×C3×D4—62no—
293C2×C3×D4—62no—
294C2×C3×D4—62no—
295C22×C3×C4—24no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—42no—
312C22×C3×C4—42no—
313C22×C3×C4—62no—
314C22×C3×C4—62no—
315C22×C3×C4—62no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—22no—
321C2×#67—22no—
322C2×#67—22no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C2×C4×D3—22no—
343C2×C4×D3—22no—
344C2×C4×D3—22no—
345C2×Dic6—62no—
346C2×Dic6—62no—
347C2×Dic6—62no—
348C2×Dic6—62no—
349C2×Dic6—62no—
350C2×Dic6—62no—
351C3×C4⋊C4—62no—
352C3×C22⋊C4—62no—
353C3×C22⋊C4—62no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—62no—
356C3×C42—34no—
357C3×C42—62no—
358C3×C42—62no—
359#217—22no—
360#217—22no—
361#217—22no—
362#217—62no—
363#217—62no—
364#217—62no—
365#217—62no—
366#217—62no—
367#217—64no—
368#217—64no—
369#217—62no—
370#217—62no—
371#217—62no—
372(C2×D3)⋊C4—22no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—62no—
375(C2×D3)⋊C4—62no—
376(C2×D3)⋊C4—62no—
377C4⋊Dic3—62no—
378C4⋊Dic3—62no—
379Dic3⋊C4—22no—
380Dic3⋊C4—62no—
381Dic3⋊C4—62no—
382Dic3⋊C4—62no—
383Dic3⋊C4—62no—
384C4×Dic3—22no—
385C4×Dic3—22no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—62no—
389C4×Dic3—62no—
390C4×Dic3—122no—
391C4×Dic3—122no—
392C4×Dic3#6714yes—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32C2×#4111yescharacteristic
404C22×C32C2×#4111yescharacteristic
405C22×C32C2×#4111yescharacteristic
406C22×C32C2×#4111yescharacteristic
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C32×C4—41no—
415C32×C4#12414yes—
416C3⋊Dic3—22no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×Q8—91no—
428C22×D4—31no—
429C23×C4—31no—
430C23×C4D3211yescharacteristic
431C4×Q8—184no—
432C4×D4—64no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C42—31no—
448C2×C42—31no—
449C2×C42—31no—
450C2×C42—91no—
451C2×C42—91no—
452#95—31no—
453#95—31no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463#95—91no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—22no—
480C23×C3—32no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3#23512yes—
492C23×C3#23512yes—
493C23×C3C23×D311yescharacteristic
494C23×C3C23×D311yescharacteristic
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3#23512yes—
502C3×D4—68no—
503C2×C3×C4—22no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—48no—
519C2×C3×C4—44no—
520C2×C3×C4—44no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—124no—
540C2×C3×C4#23512yes—
541C2×C3×C4D3×D412yes—
542C2×C3×C4#23712yes—
543C2×C3×C4#23712yes—
544C2×C3×C4#23712yes—
545C2×C3×C4C2×#6712yes—
546#67—28no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—62no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—62no—
573C2×Dic3—62no—
574C2×Dic3—62no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3#23512yes—
602C2×Dic3C2×#6712yes—
603C2×Dic3C2×#6712yes—
604C4×D3—44no—
605Dic6—68no—
606Dic6—68no—
607C2×C32—42no—
608C2×C32#52511yescharacteristic
609C2×C32#52511yescharacteristic
610C2×C32C2×#12411yescharacteristic
611C2×C32#52911yescharacteristic
612C2×C32#52911yescharacteristic
613C2×C32#52911yescharacteristic
614C2×C32#52911yescharacteristic
615C3×D3—42no—
616C24—31no—
617C24C2×D3211yescharacteristic
618C2×Q8—182no—
619C2×Q8—182no—
620C2×Q8—182no—
621C2×D4—62no—
622C2×D4—62no—
623C2×D4—62no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—91no—
638C22×C4—91no—
639C22×C4—91no—
640C22×C4—91no—
641C22×C4C2×D3211yescharacteristic
642C22×C4C2×D3211yescharacteristic
643C4⋊C4—62no—
644C4⋊C4—182no—
645C4⋊C4—182no—
646C4⋊C4—182no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—62no—
650C22⋊C4—62no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—182no—
654C22⋊C4—182no—
655C22⋊C4—182no—
656C22⋊C4—182no—
657C42—34no—
658C42—62no—
659C42—62no—
660C42—182no—
661C42—182no—
662C22×C3—24no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3C2×#23511yescharacteristic
698C22×C3C2×#23511yescharacteristic
699C22×C3C2×#23511yescharacteristic
700C22×C3C2×#23511yescharacteristic
701C22×C3C2×#23511yescharacteristic
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×#23711yescharacteristic
704C22×C3C2×#23711yescharacteristic
705C22×C3C2×#23711yescharacteristic
706C22×C3D3×#4111yescharacteristic
707C22×C3D3×#4111yescharacteristic
708C22×C3D3×#4111yescharacteristic
709C22×C3D3×#4111yescharacteristic
710C22×C3C22×#6711yescharacteristic
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C3×C4—24no—
719C3×C4—42no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—62no—
723C3×C4—62no—
724C3×C4—62no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4#88514yes—
730C3×C4#93614yes—
731Dic3—22no—
732Dic3—22no—
733Dic3—22no—
734Dic3—41no—
735Dic3—41no—
736Dic3—41no—
737Dic3—41no—
738Dic3—62no—
739Dic3—62no—
740Dic3—122no—
741Dic3—122no—
742Dic3—122no—
743Dic3—122no—
744Dic3—121no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749Dic3—121no—
750C32#239811yescharacteristic, complemented, Sylow
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—32no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—61no—
763C23—61no—
764C23#379812yes—
765C23C22×D3211yescharacteristic
766Q8—188no—
767D4—68no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—44no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—92no—
794C2×C4—124no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4#380412yes—
807C2×C4#380512yes—
808C2×C4D3×#6712yes—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—44no—
817C2×C3—42no—
818C2×C3—42no—
819C2×C3—122no—
820C2×C3#547911yescharacteristic
821C2×C3C2×#88511yescharacteristic
822C2×C3#552811yescharacteristic
823C2×C3#553811yescharacteristic
824C2×C3#553811yescharacteristic
825C2×C3#553811yescharacteristic
826C2×C3#553811yescharacteristic
827C2×C3#553811yescharacteristic
828C2×C3#554711yescharacteristic
829C2×C3#554711yescharacteristic
830C2×C3#555711yescharacteristic
831C2×C3#579111yescharacteristic
832C2×C3C2×#93611yescharacteristic
833C2×C3#582811yescharacteristic
834D3—42no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22C2×#379811yescharacteristic
850C22D3×#23511yescharacteristic
851C22D3×#23511yescharacteristic
852C22#6430611yescharacteristic
853C22C2×#380411yescharacteristic
854C22C2×#380511yescharacteristic
855C22C2×D3×#6711yescharacteristic
856C4—41no—
857C4—62no—
858C4—62no—
859C4—62no—
860C4—121no—
861C4—121no—
862C4—121no—
863C4—121no—
864C4—182no—
865C4—361no—
866C4—361no—
867C4—361no—
868C4#6395914yes—
869C3—21no—
870C3#7348111yescharacteristic, complemented
871C3#8234811yescharacteristic, complemented
872C2—42no—
873C2—122no—
874C2#1059483911yescharacteristic
875C2#1059493311yescharacteristic
876C2#1059493411yescharacteristic
877C2#1059500211yescharacteristic
878C2#1059503311yescharacteristic
879C2#1059506011yescharacteristic
880C2C2×#6395911yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#627C2semidirect
3. C4×#3757C2semidirect
4. C3×C4×#217C2semidirect
5. #10591717C2semidirect
8. #10591692C2semidirect
9. #10591297C2semidirect
10. #10591293C2semidirect
11. C4×(C2×D3)⋊Dic3C2semidirect
12. C4×(C2×D3)⋊Dic3C2semidirect
13. #10591222C2semidirect
14. #10591199C2semidirect
15. #10591196C2semidirect
67. C4×#217D3semidirect
750. C32#2398semidirect
870. C3#73481semidirect
871. C3#82348semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×C4×#6272
C4×#37572
C3×C4×#2172
#105917172
#105917092
#105917082
#105916922
#105912972
#105912932
C4×(C2×D3)⋊Dic32
#105912222
#105911992
#105911962
#823483
#734813