Finite Group Databasebeta

← #11805437

Subgroups — #11805437

Order 1152.

1761 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C4×#626C211yesmaximal, characteristic
3C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63881C212yesmaximal
5C3×#4987C211yesmaximal, characteristic, complemented
6C3×#4975C211yesmaximal, characteristic, complemented
7#10591372C212yesmaximal, complemented
8#10591325C211yesmaximal, characteristic, complemented
9#10591290C212yesmaximal, complemented
10Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#10591234C212yesmaximal, complemented
12#74360—31nomaximal
13#74010—31nomaximal
14C22×C4×C3⋊D3C2212yes—
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#626C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×#3750C2212yes—
22C4⋊C4×C3⋊D3—24no—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×#3722C2212yes—
32C2×#3722C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×Dic32C2212yes—
35C4×#626C418yescomplemented
36D3×C4⋊Dic3—24no—
37#63881—28no—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40#63579C2212yes—
41C2×C4×#67—31no—
42C22×C4⋊Dic3—31no—
43C2×#893—32no—
44C2×D3×C4⋊C4—31no—
45C2×D3×C4⋊C4—31no—
46C2×D3×C4⋊C4—31no—
47C2×D3×C4⋊C4—61no—
48C2×#67⋊C4—32no—
49C2×C4×D12—31no—
50C3×#384—31no—
51C3×#380—31no—
52#4989—32no—
53#4989—32no—
54#4987—31no—
55#4987—31no—
56#4987D311yescharacteristic, complemented
57#4975D311yescharacteristic, complemented
58Dic3×C4⋊C4—31no—
59#4972—32no—
60#4946—32no—
61C4×C4⋊Dic3—31no—
62#4668—32no—
63#4647—32no—
64C23×C3⋊D3C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3—22no—
72C2×C4×C3⋊D3—24no—
73C2×C4×C3⋊D3—24no—
74C2×C4×C3⋊D3—42no—
75C2×C4×C3⋊D3C2×C414yescomplemented
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3C2×C414yescomplemented
84C2×#626C2×C414yes—
85C2×#626D414yes—
86C2×#626Q814yes—
87C2×D3×Dic3—24no—
88C2×D3×Dic3—24no—
89C2×D3×Dic3—42no—
90C32×C4⋊C4—22no—
91C4⋊(C3⋊Dic3)D414yescomplemented
92#3750—24no—
93C3×(C2×D3)⋊C4—24no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3—22no—
96C3×Dic3⋊C4—24no—
97C3×Dic3⋊C4—42no—
98C3×C4×Dic3C2×C414yescomplemented
99Dic3⋊Dic3—24no—
100Dic3⋊Dic3C2×C414yescomplemented
101#3722—24no—
102#3722C2×C414yescomplemented
103(C2×D3)⋊Dic3C2×C414yescomplemented
104Dic32—24no—
105D4×C4⋊C4—91noSylow
106C23×C3×C4—31no—
107C22×#67—31no—
108C23×Dic3—32no—
109C22×D12—31no—
110C22×C4×D3—31no—
111C22×C4×D3—31no—
112C22×C4×D3—32no—
113C22×C4×D3—32no—
114C22×C4×D3—32no—
115C22×C4×D3—61no—
116C22×C4×D3—62no—
117C22×C4×D3C2×D311yescharacteristic
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—32no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4C2×D311yescharacteristic
124C2×C3×C4⋊C4C2×D311yescharacteristic
125C2×C3×C22⋊C4—32no—
126C2×C3×C42—31no—
127C2×#217—31no—
128C4×#67—38no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—31no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—32no—
139C2×C4⋊Dic3—61no—
140C2×C4⋊Dic3—64no—
141C2×C4⋊Dic3C2×D311yescharacteristic
142C2×C4⋊Dic3C2×D311yescharacteristic
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4—32no—
147C2×Dic3⋊C4—62no—
148C2×Dic3⋊C4C2×D312yes—
149C2×Dic3⋊C4C2×D312yes—
150C2×C4×Dic3—32no—
151C2×C4×Dic3—32no—
152C2×C4×Dic3C2×D311yescharacteristic
153#893—68no—
154D3×C4⋊C4—64no—
155D3×C4⋊C4—64no—
156D3×C4⋊C4—64no—
157D3×C4⋊C4—68no—
158#67⋊C4—68no—
159C4×D12—38no—
160C3×#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—32no—
164C3⋊#95—32no—
165C3⋊#95C2×D312yes—
166C23×C32C2411yescharacteristic
167C22×C3⋊D3—21no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3C22×C412yes—
172C22×C3⋊D3C2×D412yes—
173C22×C3⋊D3C2×Q812yes—
174C22×C3×D3—21no—
175C22×C3×D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3—21no—
178C22×C3×D3C22×C412yes—
179C22×C3×D3C2×D412yes—
180C22×C3×D3C2×Q812yes—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C2×D412yes—
186C2×C32×C4#4112yes—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3C22×C412yes—
192C2×C3⋊Dic3C2×D414yes—
193C4×C3⋊D3—28no—
194C4×C3⋊D3—48no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3C22×C412yes—
206C2×C3×Dic3C22×C412yes—
207C2×C3×Dic3C22×C412yes—
208C2×C3×Dic3C2×D412yes—
209C2×C3×Dic3C2×Q812yes—
210C3×C4×D3—28no—
211#626C4⋊C4116yescomplemented
212D3×Dic3—48no—
213C2×C4×D4—91no—
214C2×C4×D4—92no—
215C22×C4⋊C4—91no—
216C22×C4⋊C4—91no—
217#389—92no—
218#385—92no—
219#385—92no—
220#384—31no—
221#380—31no—
222#380—91no—
223C4×C4⋊C4—91no—
224C24×C3—31no—
225C23×D3—31no—
226C23×D3—31no—
227C23×D3—61no—
228C23×D3C22×D311yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4—22no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—34no—
235C22×C3×C4—32no—
236C22×C3×C4—32no—
237C22×C3×C4—62no—
238C22×C3×C4—62no—
239C22×C3×C4C22×D312yes—
240C22×C3×C4C22×D312yes—
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C2×#67—34no—
244C2×#67—34no—
245C2×#67—34no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—32no—
249C22×Dic3—32no—
250C22×Dic3—61no—
251C22×Dic3—62no—
252C22×Dic3—64no—
253C22×Dic3—64no—
254C22×Dic3—122no—
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D311yescharacteristic
259C22×Dic3C22×D311yescharacteristic
260C2×D12—34no—
261C2×D12—34no—
262C2×D12—34no—
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—34no—
266C2×C4×D3—34no—
267C2×C4×D3—64no—
268C2×C4×D3—64no—
269C2×C4×D3—64no—
270C2×C4×D3—62no—
271C2×C4×D3—62no—
272C2×C4×D3—62no—
273C2×C4×D3—62no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×C4×D3—64no—
277C2×C4×D3—64no—
278C2×C4×D3—64no—
279C2×C4×D3—68no—
280C2×C4×D3—64no—
281C2×C4×D3—124no—
282C2×C4×D3—122no—
283C2×C4×D3—122no—
284C2×C4×D3—122no—
285C2×C4×D3—124no—
286C2×C4×D3C4×D314yescomplemented
287C3×C4⋊C4—24no—
288C3×C4⋊C4—22no—
289C3×C4⋊C4—22no—
290C3×C4⋊C4—64no—
291C3×C4⋊C4—62no—
292C3×C4⋊C4—62no—
293C3×C4⋊C4—122no—
294C3×C22⋊C4—64no—
295C3×C42—34no—
296#217—34no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—34no—
300(C2×D3)⋊C4—34no—
301(C2×D3)⋊C4—64no—
302(C2×D3)⋊C4—64no—
303C4⋊Dic3—22no—
304C4⋊Dic3—22no—
305C4⋊Dic3—34no—
306C4⋊Dic3—34no—
307C4⋊Dic3—34no—
308C4⋊Dic3—64no—
309C4⋊Dic3—64no—
310Dic3⋊C4—24no—
311Dic3⋊C4—34no—
312Dic3⋊C4—42no—
313Dic3⋊C4—64no—
314Dic3⋊C4—64no—
315Dic3⋊C4—64no—
316Dic3⋊C4—68no—
317C4×Dic3—64no—
318C4×Dic3—64no—
319C4×Dic3C4×D314yescomplemented
320C22×C32C23×C411yescharacteristic
321C22×C32C22×D411yescharacteristic
322C22×C32C22×D411yescharacteristic
323C22×C32C22×Q811yescharacteristic
324C22×C32C2×#4111yescharacteristic
325C22×C32H(5,𝔽2)11yescharacteristic
326C22×C322−1+411yescharacteristic
327C2×C3⋊D3—22no—
328C2×C3⋊D3—22no—
329C2×C3⋊D3—22no—
330C2×C3⋊D3—22no—
331C2×C3⋊D3—22no—
332C2×C3⋊D3—22no—
333C2×C3⋊D3C2×C4⋊C414yescomplemented
334C2×C3×D3—22no—
335C2×C3×D3—22no—
336C2×C3×D3—22no—
337C2×C3×D3—22no—
338C2×C3×D3—22no—
339C2×C3×D3—22no—
340C2×C3×D3C2×C4⋊C414yescomplemented
341C32×C4—42no—
342C32×C4C4×D414yescomplemented
343C3⋊Dic3—22no—
344C3⋊Dic3—24no—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C3×Dic3—42no—
348C3×Dic3—42no—
349C3×Dic3C2×C4⋊C414yescomplemented
350C22×D4—91no—
351C23×C4—31no—
352C23×C4—92no—
353C23×C4—91no—
354C23×C4—92no—
355C4×D4—98no—
356C4×D4—188no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—91no—
362C2×C4⋊C4—91no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—184no—
366C2×C4⋊C4—184no—
367C2×C4⋊C4D3211yescharacteristic
368C2×C22⋊C4—32no—
369C2×C22⋊C4—91no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—92no—
372C2×C42—31no—
373C2×C42—92no—
374#95—32no—
375#95—92no—
376#95—92no—
377C23×C3—21no—
378C23×C3—32no—
379C23×C3—32no—
380C23×C3—32no—
381C23×C3—61no—
382C23×C3—61no—
383C23×C3—61no—
384C23×C3—61no—
385C23×C3C23×D311yescharacteristic
386C23×C3C23×D311yescharacteristic
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—32no—
392C22×D3—32no—
393C22×D3—32no—
394C22×D3—32no—
395C22×D3—32no—
396C22×D3—32no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3—62no—
401C22×D3—62no—
402C22×D3—62no—
403C22×D3—62no—
404C22×D3—61no—
405C22×D3—61no—
406C22×D3—61no—
407C22×D3—61no—
408C22×D3—61no—
409C22×D3—61no—
410C22×D3—61no—
411C22×D3—61no—
412C22×D3C2×C4×D312yes—
413C22×D3D3×D412yes—
414C22×D3D3×Q812yes—
415C2×C3×C4—24no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—32no—
426C2×C3×C4—32no—
427C2×C3×C4—32no—
428C2×C3×C4—32no—
429C2×C3×C4—32no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—61no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—68no—
437C2×C3×C4—62no—
438C2×C3×C4—62no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4C2×C4×D312yes—
444C2×C3×C4C2×C4×D312yes—
445C2×C3×C4D3×D412yes—
446C2×C3×C4D3×D412yes—
447C2×C3×C4#23712yes—
448C2×C3×C4#23912yes—
449#67—316no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—32no—
461C2×Dic3—32no—
462C2×Dic3—34no—
463C2×Dic3—34no—
464C2×Dic3—62no—
465C2×Dic3—64no—
466C2×Dic3—62no—
467C2×Dic3—62no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—62no—
474C2×Dic3—61no—
475C2×Dic3—62no—
476C2×Dic3—122no—
477C2×Dic3—122no—
478C2×Dic3—128no—
479C2×Dic3C2×C4×D312yes—
480C2×Dic3C2×C4×D312yes—
481C2×Dic3C2×C4×D312yes—
482C2×Dic3D3×D412yes—
483C2×Dic3D3×Q812yes—
484D12—316no—
485C4×D3—28no—
486C4×D3—616no—
487C4×D3—68no—
488C4×D3—68no—
489C4×D3—128no—
490C4×D3—128no—
491C4×D3—128no—
492C4×D3—1216no—
493C2×C32C22×C4⋊C411yescharacteristic
494C2×C32C2×C4×D411yescharacteristic
495C2×C32#52011yescharacteristic
496C2×C32D4211yescharacteristic
497C2×C32#54711yescharacteristic
498C2×C32D4×Q811yescharacteristic
499C2×C32#55411yescharacteristic
500C3⋊D3—24no—
501C3×D3—24no—
502C24—31no—
503C24—91no—
504C2×D4—94no—
505C2×D4—94no—
506C2×D4—94no—
507C22×C4—31no—
508C22×C4—31no—
509C22×C4—31no—
510C22×C4—34no—
511C22×C4—32no—
512C22×C4—32no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—91no—
516C22×C4—92no—
517C22×C4—94no—
518C22×C4—184no—
519C22×C4—184no—
520C22×C4—184no—
521C22×C4—184no—
522C22×C4—182no—
523C22×C4—182no—
524C22×C4—362no—
525C22×C4—362no—
526C22×C4C2×D3212yes—
527C22×C4C2×D3211yescharacteristic
528C4⋊C4—22no—
529C4⋊C4—64no—
530C4⋊C4—62no—
531C4⋊C4—62no—
532C4⋊C4—94no—
533C4⋊C4—94no—
534C4⋊C4—122no—
535C4⋊C4—184no—
536C4⋊C4—184no—
537C22⋊C4—64no—
538C22⋊C4—94no—
539C22⋊C4—94no—
540C22⋊C4—184no—
541C42—34no—
542C42—184no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—34no—
551C22×C3—62no—
552C22×C3—62no—
553C22×C3—62no—
554C22×C3—62no—
555C22×C3—62no—
556C22×C3—62no—
557C22×C3C22×C4×D311yescharacteristic
558C22×C3C22×C4×D311yescharacteristic
559C22×C3C2×D3×D411yescharacteristic
560C22×C3C2×D3×D411yescharacteristic
561C22×C3C2×D3×D411yescharacteristic
562C22×C3C2×D3×D411yescharacteristic
563C22×C3C2×#23711yescharacteristic
564C22×C3#100411yescharacteristic
565C22×C3C2×D3×Q811yescharacteristic
566C22×C3C2×D3×Q811yescharacteristic
567C22×C3C2×#23911yescharacteristic
568C22×C3#100711yescharacteristic
569C22×C3#100911yescharacteristic
570C22×C3#101011yescharacteristic
571C2×D3—22no—
572C2×D3—22no—
573C2×D3—22no—
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—22no—
577C2×D3—34no—
578C2×D3—34no—
579C2×D3—64no—
580C2×D3—64no—
581C2×D3—64no—
582C2×D3—64no—
583C2×D3—64no—
584C2×D3—64no—
585C2×D3—64no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—62no—
589C2×D3—62no—
590C2×D3—62no—
591C2×D3—62no—
592C2×D3—62no—
593C2×D3—62no—
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3D3×C4⋊C414yescomplemented
599C3×C4—24no—
600C3×C4—34no—
601C3×C4—44no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—62no—
605C3×C4—62no—
606C3×C4—122no—
607C3×C4—122no—
608C3×C4#67⋊C414yescomplemented
609C3×C4#89314yescomplemented
610Dic3—22no—
611Dic3—22no—
612Dic3—42no—
613Dic3—42no—
614Dic3—64no—
615Dic3—64no—
616Dic3—62no—
617Dic3—62no—
618Dic3—64no—
619Dic3—124no—
620Dic3D3×C4⋊C414yescomplemented
621C32D4×C4⋊C411yescharacteristic, complemented, Sylow
622C23—32no—
623C23—32no—
624C23—32no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—92no—
630C23—92no—
631C23—92no—
632C23—181no—
633C23—181no—
634C23—181no—
635C23—181no—
636C23C22×D3211yescharacteristic
637D4—916no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—32no—
642C2×C4—32no—
643C2×C4—32no—
644C2×C4—32no—
645C2×C4—32no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—68no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—92no—
658C2×C4—94no—
659C2×C4—181no—
660C2×C4—182no—
661C2×C4—182no—
662C2×C4—181no—
663C2×C4—188no—
664C2×C4—368no—
665C2×C4—368no—
666C2×C4#379612yes—
667C2×C4C4×D3212yes—
668C2×C4#381112yes—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—64no—
677C2×C3C2×#67⋊C411yescharacteristic
678C2×C3C2×D3×C4⋊C411yescharacteristic
679C2×C3C2×D3×C4⋊C411yescharacteristic
680C2×C3C2×#89311yescharacteristic
681C2×C3#550411yescharacteristic
682C2×C3#552311yescharacteristic
683C2×C3#560911yescharacteristic
684C2×C3#561111yescharacteristic
685C2×C3#563211yescharacteristic
686C2×C3#563511yescharacteristic
687C2×C3#571711yescharacteristic
688C2×C3#572611yescharacteristic
689C2×C3#572711yescharacteristic
690C2×C3#573011yescharacteristic
691D3—24no—
692D3—68no—
693D3—64no—
694D3—64no—
695C22—34no—
696C22—62no—
697C22—62no—
698C22—62no—
699C22—62no—
700C22—62no—
701C22—62no—
702C22—94no—
703C22—182no—
704C22—182no—
705C22—182no—
706C22—182no—
707C22—182no—
708C22—182no—
709C22C2×#379611yescharacteristic
710C22C2×C4×D3211yescharacteristic
711C22D32×D411yescharacteristic
712C22#6431411yescharacteristic
713C22#6431511yescharacteristic
714C22D32×Q811yescharacteristic
715C22C2×#381111yescharacteristic
716C4—34no—
717C4—42no—
718C4—62no—
719C4—62no—
720C4—122no—
721C4—122no—
722C4—182no—
723C4—184no—
724C4#6388114yescomplemented
725C3—21no—
726C3#7401011yescharacteristic, complemented
727C3#7436011yescharacteristic, complemented
728C2—64no—
729C2—184no—
730C2#1059437311yescharacteristic
731C2#1059439311yescharacteristic
732C2#1059451011yescharacteristic
733C2D32×C4⋊C411yescharacteristic
734C2C2×#6388111yescharacteristic
735C2#1059529711yescharacteristic
736C2#1059536111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
3. C2×D3×C4⋊Dic3C2semidirect
5. C3×#4987C2semidirect
6. C3×#4975C2semidirect
7. #10591372C2semidirect
8. #10591325C2semidirect
9. #10591290C2semidirect
10. Dic3×C4⋊Dic3C2semidirect
11. #10591234C2semidirect
35. C4×#626C4semidirect
56. #4987D3semidirect
57. #4975D3semidirect
75. C2×C4×C3⋊D3C2×C4semidirect
83. C2×C3×C4×D3C2×C4semidirect
91. C4⋊(C3⋊Dic3)D4semidirect
98. C3×C4×Dic3C2×C4semidirect
100. Dic3⋊Dic3C2×C4semidirect
102. #3722C2×C4semidirect
103. (C2×D3)⋊Dic3C2×C4semidirect
211. #626C4⋊C4semidirect
286. C2×C4×D3C4×D3semidirect
319. C4×Dic3C4×D3semidirect
333. C2×C3⋊D3C2×C4⋊C4semidirect
340. C2×C3×D3C2×C4⋊C4semidirect
342. C32×C4C4×D4semidirect
349. C3×Dic3C2×C4⋊C4semidirect
598. C2×D3D3×C4⋊C4semidirect
608. C3×C4#67⋊C4semidirect
609. C3×C4#893semidirect
620. Dic3D3×C4⋊C4semidirect
621. C32D4×C4⋊C4semidirect
724. C4#63881semidirect
726. C3#74010semidirect
727. C3#74360semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×C4×#6262
C2×D3×C4⋊Dic32
C2×#638812
C3×#49872
C3×#49752
#105913722
#105913252
#105912902
Dic3×C4⋊Dic32
#105912342
#743603
#740103