Finite Group Databasebeta

← #11804923

Subgroups — #11804923

Order 1152.

1893 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2C2×C4×#634C211yesmaximal, characteristic, complemented
3C2×#63844C211yesmaximal, characteristic, complemented
4C3×#4939C211yesmaximal, characteristic, complemented
5C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#10591386C212yesmaximal, complemented
7#10591385C212yesmaximal, complemented
8#10591369C212yesmaximal, complemented
9#10591368C212yesmaximal, complemented
10#10591318C211yesmaximal, characteristic, complemented
11#10591313C211yesmaximal, characteristic, complemented
12#76301—31nomaximal
13#73454—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#625C2212yes—
18C22×D3×Dic3C2212yes—
19C2×#3795—24no—
20C2×#3795—24no—
21C2×#3795C418yescomplemented
22C2×C32×C42C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2212yes—
25C2×C4×C3⋊Dic3C2212yes—
26C4×#634—24no—
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×Dic32C2212yes—
38#63844—24no—
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41#63579C2212yes—
42C22×#237—31no—
43C22×#235—31no—
44C2×#887—31no—
45C2×C4×Dic6—31no—
46C2×C4×Dic6—31no—
47C2×C4×Dic6—31no—
48C2×C4×Dic6—61no—
49C3×#390—31no—
50C3×C4×C22⋊C4—31no—
51#5221—31no—
52#5212—31no—
53#4987—31no—
54#4957—32no—
55#4957—32no—
56#4957—32no—
57#4957—32no—
58#4942—32no—
59Dic3×C22⋊C4—32no—
60#4939—31no—
61#4939D311yescharacteristic, complemented
62C4×(C2×D3)⋊C4D311yescharacteristic, complemented
63#4667—32no—
64#4666—32no—
65C23×C3×D3C2312yes—
66C23×C3×D3C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2312yes—
72C2×#634C2×C414yes—
73C2×#634D414yes—
74C2×#634D414yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C2×C3×D12—22no—
80C2×C3×D12—22no—
81C2×C3×D12C2×C414yes—
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3C2×C414yes—
85C2×#625—24no—
86C2×#625—24no—
87C2×#625C2×C418yes—
88C2×D3×Dic3—24no—
89C2×D3×Dic3—24no—
90C2×D3×Dic3C2×C418yes—
91#3795—232no—
92C32×C42—22no—
93C4⋊(C3⋊Dic3)—22no—
94#3750—24no—
95C4×C3⋊Dic3—24no—
96C3×(C2×D3)⋊C4—22no—
97C3×(C2×D3)⋊C4—24no—
98C3×(C2×D3)⋊C4—22no—
99C3×(C2×D3)⋊C4—42no—
100C3×C4⋊Dic3—22no—
101C3×C4×Dic3—22no—
102#3724—24no—
103(C2×D3)⋊Dic3—24no—
104(C2×D3)⋊Dic3—42no—
105(C2×D3)⋊Dic3—42no—
106Dic32—24no—
107#2341—91noSylow
108C22×C3×D4—31no—
109C23×C3×C4—31no—
110C22×#67—32no—
111C22×#67—32no—
112C23×Dic3—32no—
113C2×#237—38no—
114C2×#237—64no—
115C2×#237—64no—
116C2×#235—38no—
117C2×#235—64no—
118C2×#235—64no—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—32no—
121C22×C4×D3C2×D311yescharacteristic
122C22×Dic6—31no—
123C22×Dic6—31no—
124C22×Dic6—61no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C22⋊C4—32no—
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4—31no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C42—21no—
131C2×C3×C42—31no—
132C2×C3×C42C2×D311yescharacteristic
133C2×C3×C42C2×D311yescharacteristic
134C2×#217—32no—
135C2×#217—32no—
136C2×#217—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4C2×D312yes—
141C2×(C2×D3)⋊C4C2×D311yescharacteristic
142C2×(C2×D3)⋊C4C2×D311yescharacteristic
143C2×(C2×D3)⋊C4C2×D312yes—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—61no—
147C2×C4⋊Dic3C2×D311yescharacteristic
148C2×Dic3⋊C4—32no—
149C2×Dic3⋊C4—32no—
150C2×Dic3⋊C4—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—62no—
153C2×C4×Dic3—32no—
154C2×C4×Dic3—32no—
155C2×C4×Dic3—32no—
156C2×C4×Dic3—32no—
157C2×C4×Dic3—62no—
158C2×C4×Dic3C2×D311yescharacteristic
159#887—64no—
160C4×Dic6—64no—
161C4×Dic6—64no—
162C4×Dic6—64no—
163C4×Dic6—68no—
164C3×#95—31no—
165C3×#95—31no—
166C3⋊#95—32no—
167C3⋊#95—32no—
168C3⋊#95C2×D311yescharacteristic
169C3⋊#95C2×D311yescharacteristic
170C23×C32C2411yescharacteristic
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—21no—
174C22×C3×D3—21no—
175C22×C3×D3—22no—
176C22×C3×D3—21no—
177C22×C3×D3—21no—
178C22×C3×D3—22no—
179C22×C3×D3—21no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—21no—
183C22×C3×D3C22×C414yes—
184C22×C3×D3C22×C412yes—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4C22×C412yes—
191C2×C32×C4C2×D412yes—
192C2×C32×C4C2×D412yes—
193C2×C32×C4#4112yescomplemented
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3C22×C414yes—
198C2×C3⋊Dic3C2×D414yes—
199C2×C3⋊Dic3C2×D414yes—
200#634C22⋊C4116yescomplemented
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3C22×C412yes—
212C2×C3×Dic3#4112yescomplemented
213C3×D12—28no—
214C3×C4×D3—28no—
215#625—216no—
216D3×Dic3—216no—
217C22×#41—91no—
218C2×C4×Q8—91no—
219C2×C4×Q8—91no—
220#390—31no—
221#390—91no—
222#390—92no—
223#390—92no—
224#380—92no—
225#380—91no—
226C4×C22⋊C4—31no—
227C4×C22⋊C4—92no—
228C24×C3—32no—
229C24×C3—31no—
230C23×D3C22×D312yes—
231C23×D3C22×D311yescharacteristic
232C2×C3×D4—34no—
233C2×C3×D4—62no—
234C2×C3×D4—62no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—34no—
241C22×C3×C4—32no—
242C22×C3×C4—31no—
243C22×C3×C4—62no—
244C22×C3×C4—62no—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C2×#67—38no—
252C2×#67—38no—
253C2×#67—64no—
254C2×#67—64no—
255C2×#67—64no—
256C2×#67—64no—
257C22×Dic3—32no—
258C22×Dic3—32no—
259C22×Dic3—38no—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—62no—
263C22×Dic3—62no—
264C22×Dic3—64no—
265C22×Dic3—64no—
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D311yescharacteristic
268C22×Dic3C22×D311yescharacteristic
269C22×Dic3C22×D311yescharacteristic
270#237—632no—
271#235—632no—
272C2×D12—22no—
273C2×D12—22no—
274C2×D12C4×D314yes—
275C2×C4×D3—22no—
276C2×C4×D3—22no—
277C2×C4×D3—38no—
278C2×C4×D3—64no—
279C2×C4×D3—64no—
280C2×C4×D3C4×D314yes—
281C2×Dic6—34no—
282C2×Dic6—34no—
283C2×Dic6—34no—
284C2×Dic6—34no—
285C2×Dic6—34no—
286C2×Dic6—34no—
287C2×Dic6—64no—
288C2×Dic6—64no—
289C2×Dic6—64no—
290C3×C4⋊C4—62no—
291C3×C22⋊C4—62no—
292C3×C22⋊C4—64no—
293C3×C22⋊C4—62no—
294C3×C22⋊C4—122no—
295C3×C42—24no—
296C3×C42—22no—
297C3×C42—22no—
298C3×C42—62no—
299#217—64no—
300#217—122no—
301#217—122no—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—24no—
304(C2×D3)⋊C4—22no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—64no—
307(C2×D3)⋊C4—122no—
308(C2×D3)⋊C4—122no—
309C4⋊Dic3—22no—
310C4⋊Dic3—64no—
311C4⋊Dic3—62no—
312C4⋊Dic3—62no—
313Dic3⋊C4—64no—
314Dic3⋊C4—64no—
315Dic3⋊C4—64no—
316Dic3⋊C4—64no—
317Dic3⋊C4—68no—
318C4×Dic3—22no—
319C4×Dic3—64no—
320C4×Dic3—64no—
321C4×Dic3—64no—
322C4×Dic3—64no—
323C4×Dic3—68no—
324C22×C32C23×C411yescharacteristic
325C22×C32C22×D411yescharacteristic
326C22×C32C22×D411yescharacteristic
327C22×C32C2×#4111yescharacteristic
328C22×C32C2×#4111yescharacteristic
329C22×C32H(5,𝔽2)11yescharacteristic
330C22×C322−1+411yescharacteristic
331C2×C3×D3—24no—
332C2×C3×D3—22no—
333C2×C3×D3—22no—
334C2×C3×D3—24no—
335C2×C3×D3—22no—
336C2×C3×D3—24no—
337C2×C3×D3—42no—
338C2×C3×D3—41no—
339C2×C3×D3—41no—
340C2×C3×D3—42no—
341C2×C3×D3—42no—
342C2×C3×D3—41no—
343C2×C3×D3—41no—
344C2×C3×D3—42no—
345C32×C4—22no—
346C32×C4—41no—
347C32×C4C2×C22⋊C414yes—
348C3⋊Dic3—42no—
349C3⋊Dic3C2×C22⋊C418yes—
350C3×Dic3—22no—
351C3×Dic3—22no—
352C3×Dic3—42no—
353C3×Dic3—41no—
354C2×#41—98no—
355C2×#41—184no—
356C2×#41—184no—
357C22×Q8—91no—
358C22×D4—31no—
359C22×D4—92no—
360C23×C4—31no—
361C23×C4—92no—
362C4×Q8—184no—
363C4×Q8—184no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4—92no—
367C2×C4⋊C4—91no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—31no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—92no—
375C2×C42—31no—
376C2×C42—92no—
377C2×C42—92no—
378C2×C42D3211yescharacteristic
379#95—31no—
380#95—31no—
381#95—92no—
382C23×C3—21no—
383C23×C3—34no—
384C23×C3—32no—
385C23×C3—62no—
386C23×C3—62no—
387C23×C3—62no—
388C23×C3—62no—
389C23×C3—61no—
390C23×C3—61no—
391C23×C3—61no—
392C23×C3—61no—
393C23×C3—61no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3—61no—
397C23×C3C23×D311yescharacteristic
398C23×C3C23×D311yescharacteristic
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—22no—
404C22×D3—22no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—22no—
411C22×D3C2×C4×D314yes—
412C22×D3C2×C4×D312yes—
413C3×D4—68no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—68no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—61no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4—62no—
446C2×C3×C4C2×C4×D312yes—
447C2×C3×C4C2×C4×D312yes—
448C2×C3×C4#23512yescomplemented
449C2×C3×C4D3×D412yes—
450C2×C3×C4D3×D412yes—
451C2×C3×C4D3×D412yes—
452C2×C3×C4D3×D412yes—
453C2×C3×C4#23712yescomplemented
454#67—616no—
455#67—616no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—21no—
466C2×Dic3—34no—
467C2×Dic3—34no—
468C2×Dic3—34no—
469C2×Dic3—34no—
470C2×Dic3—34no—
471C2×Dic3—34no—
472C2×Dic3—64no—
473C2×Dic3—64no—
474C2×Dic3—64no—
475C2×Dic3—616no—
476C2×Dic3—64no—
477C2×Dic3—62no—
478C2×Dic3—62no—
479C2×Dic3—62no—
480C2×Dic3—62no—
481C2×Dic3—62no—
482C2×Dic3—62no—
483C2×Dic3—122no—
484C2×Dic3—122no—
485C2×Dic3C2×C4×D312yes—
486C2×Dic3#23512yescomplemented
487D12—28no—
488C4×D3—28no—
489C4×D3—616no—
490Dic6—316no—
491Dic6—316no—
492Dic6—616no—
493C2×C32C22×C22⋊C411yescharacteristic
494C2×C32C4×#4111yescharacteristic
495C2×C32#52011yescharacteristic
496C2×C32#54811yescharacteristic
497C2×C32#54811yescharacteristic
498C2×C32#55011yescharacteristic
499C2×C32#55011yescharacteristic
500C3×D3—44no—
501C3×D3—42no—
502C24—31no—
503C24—32no—
504#41—1832no—
505C2×Q8—94no—
506C2×Q8—94no—
507C2×Q8—94no—
508C2×D4—34no—
509C2×D4—62no—
510C2×D4—62no—
511C2×D4—98no—
512C2×D4—184no—
513C2×D4—184no—
514C22×C4—31no—
515C22×C4—31no—
516C22×C4—34no—
517C22×C4—31no—
518C22×C4—32no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—98no—
522C22×C4—92no—
523C22×C4—92no—
524C22×C4—184no—
525C22×C4—184no—
526C22×C4C2×D3211yescharacteristic
527C22×C4C2×D3211yescharacteristic
528C22×C4C2×D3211yescharacteristic
529C4⋊C4—62no—
530C4⋊C4—184no—
531C4⋊C4—184no—
532C4⋊C4—182no—
533C22⋊C4—62no—
534C22⋊C4—62no—
535C22⋊C4—64no—
536C22⋊C4—122no—
537C22⋊C4—184no—
538C22⋊C4—362no—
539C22⋊C4—362no—
540C42—22no—
541C42—62no—
542C42—184no—
543C42—184no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—64no—
552C22×C3—64no—
553C22×C3—62no—
554C22×C3—64no—
555C22×C3—62no—
556C22×C3—62no—
557C22×C3—121no—
558C22×C3—121no—
559C22×C3—122no—
560C22×C3—122no—
561C22×C3—122no—
562C22×C3—122no—
563C22×C3—121no—
564C22×C3—121no—
565C22×C3C22×C4×D311yescharacteristic
566C22×C3C22×C4×D311yescharacteristic
567C22×C3C2×#23511yescharacteristic
568C22×C3C2×#23511yescharacteristic
569C22×C3C2×D3×D411yescharacteristic
570C22×C3C2×D3×D411yescharacteristic
571C22×C3C2×D3×D411yescharacteristic
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C2×#23711yescharacteristic
574C22×C3#100411yescharacteristic
575C22×C3D3×#4111yescharacteristic
576C22×C3#100911yescharacteristic
577C22×C3#101011yescharacteristic
578C22×C3#101011yescharacteristic
579C2×D3—22no—
580C2×D3—22no—
581C2×D3—24no—
582C2×D3—22no—
583C2×D3—24no—
584C2×D3—24no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C2×D3—42no—
592C2×D3—42no—
593C3×C4—24no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—24no—
597C3×C4—42no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—62no—
601C3×C4—62no—
602C3×C4—121no—
603C3×C4—122no—
604C3×C4D3×C22⋊C414yes—
605C3×C4D3×C22⋊C414yes—
606Dic3—22no—
607Dic3—22no—
608Dic3—38no—
609Dic3—38no—
610Dic3—42no—
611Dic3—41no—
612Dic3—68no—
613Dic3—124no—
614Dic3—122no—
615Dic3—122no—
616C32#234111yescharacteristic, complemented, Sylow
617C23—32no—
618C23—34no—
619C23—61no—
620C23—62no—
621C23—61no—
622C23—62no—
623C23—61no—
624C23—62no—
625C23—61no—
626C23—62no—
627C23—62no—
628C23—61no—
629C23—61no—
630C23—62no—
631C23C22×D3211yescharacteristic
632Q8—916no—
633D4—68no—
634D4—1816no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—68no—
647C2×C4—61no—
648C2×C4—62no—
649C2×C4—61no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—61no—
653C2×C4—94no—
654C2×C4—94no—
655C2×C4—94no—
656C2×C4—1816no—
657C2×C4—182no—
658C2×C4—182no—
659C2×C4—182no—
660C2×C4#379512yescomplemented
661C2×C4C4×D3212yes—
662C2×C4#380212yes—
663C2×C4#381112yes—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—122no—
672C2×C3—124no—
673C2×C3C4×#23511yescharacteristic
674C2×C3C2×D3×C22⋊C411yescharacteristic
675C2×C3C2×D3×C22⋊C411yescharacteristic
676C2×C3#552311yescharacteristic
677C2×C3C4×#23711yescharacteristic
678C2×C3#554611yescharacteristic
679C2×C3#555211yescharacteristic
680C2×C3#555211yescharacteristic
681C2×C3#555311yescharacteristic
682C2×C3#555311yescharacteristic
683C2×C3#559811yescharacteristic
684C2×C3#559911yescharacteristic
685C2×C3#567711yescharacteristic
686C2×C3#571811yescharacteristic
687D3—44no—
688D3—42no—
689C22—62no—
690C22—64no—
691C22—62no—
692C22—64no—
693C22—62no—
694C22—64no—
695C22—121no—
696C22—122no—
697C22—121no—
698C22—122no—
699C22—121no—
700C22—122no—
701C22—121no—
702C22—122no—
703C22C2×#379511yescharacteristic
704C22#6429811yescharacteristic
705C22C2×C4×D3211yescharacteristic
706C22C2×#380211yescharacteristic
707C22D3×#23511yescharacteristic
708C22#6430711yescharacteristic
709C22C2×#381111yescharacteristic
710C4—22no—
711C4—41no—
712C4—62no—
713C4—62no—
714C4—98no—
715C4—121no—
716C4—122no—
717C4—362no—
718C4#6392114yes—
719C3—21no—
720C3#7345411yescharacteristic, complemented
721C3#7630111yescharacteristic, complemented
722C2—122no—
723C2—124no—
724C2C4×#379511yescharacteristic
725C2#1059388711yescharacteristic
726C2#1059390511yescharacteristic
727C2#1059390611yescharacteristic
728C2#1059491811yescharacteristic
729C2#1059491911yescharacteristic
730C2C2×#6392111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#3795C2
hypercenterC2×C42D32
hypocenterC32#2341
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×#634C2semidirect
3. C2×#63844C2semidirect
4. C3×#4939C2semidirect
5. C3×C4×(C2×D3)⋊C4C2semidirect
6. #10591386C2semidirect
7. #10591385C2semidirect
8. #10591369C2semidirect
9. #10591368C2semidirect
10. #10591318C2semidirect
11. #10591313C2semidirect
21. C2×#3795C4semidirect
61. #4939D3semidirect
62. C4×(C2×D3)⋊C4D3semidirect
193. C2×C32×C4#41semidirect
200. #634C22⋊C4semidirect
212. C2×C3×Dic3#41semidirect
448. C2×C3×C4#235semidirect
453. C2×C3×C4#237semidirect
486. C2×Dic3#235semidirect
616. C32#2341semidirect
660. C2×C4#3795semidirect
720. C3#73454semidirect
721. C3#76301semidirect

Maximal subgroups

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

subgroupindex
C22×#37952
C2×C4×#6342
C2×#638442
C3×#49392
C3×C4×(C2×D3)⋊C42
#105913862
#105913852
#105913692
#105913682
#105913182
#105913132
#763013
#734543