Finite Group Databasebeta

← #11803601

Subgroups — #11803601

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic
2C2×#63894C211yesmaximal, characteristic, complemented
3C2×#63874C211yesmaximal, characteristic, complemented
4C3×#4984C211yesmaximal, characteristic, complemented
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6#10591380C212yesmaximal, complemented
7#10591378C212yesmaximal, complemented
8#10591325C211yesmaximal, characteristic, complemented
9#10591320C211yesmaximal, characteristic, complemented
10#10591320C212yesmaximal, complemented
11#10591202C212yesmaximal, complemented
12#76198—31nomaximal
13#73763—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4⋊(C3⋊D3)C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#624C2212yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×#3752C2212yes—
20#64104C418yescomplemented
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×#3724C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×#3722C2211yescharacteristic
30C2×#3722C2211yescharacteristic
31C2×#3722C2212yes—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yes—
35#63894—24no—
36#63874—24no—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×#895—31no—
41C2×#895—31no—
42C2×#895—61no—
43C2×#893—31no—
44C2×C4×D12—31no—
45C2×#872—31no—
46C2×#872—31no—
47C3×#389—31no—
48C3×C4×C4⋊C4—31no—
49#4989—32no—
50#4988—31no—
51#4988—32no—
52#4987—31no—
53#4987—31no—
54#4984D311yescharacteristic, complemented
55Dic3×C4⋊C4D311yescharacteristic, complemented
56#4940—32no—
57#4939—32no—
58#4939—31no—
59#4669—32no—
60#4668—32no—
61#4665—32no—
62#4665—32no—
63C23×C3⋊D3C2312yes—
64C23×C3⋊D3C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)—22no—
70C2×C4⋊(C3⋊D3)—42no—
71C2×C4⋊(C3⋊D3)—42no—
72C2×C4⋊(C3⋊D3)C2×C414yes—
73C2×C4⋊(C3⋊D3)C2×C418yescomplemented
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3C2×C414yescomplemented
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C2×#624—24no—
84C2×#624—42no—
85C2×#624—42no—
86C32×C4⋊C4C2×C414yescomplemented
87#3752C2×C418yescomplemented
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3—42no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3—42no—
93C3×C4×Dic3D414yescomplemented
94#3724—22no—
95#3724—22no—
96#3722—22no—
97#3722—22no—
98#3722—24no—
99#3722—42no—
100#3722—42no—
101#3722—42no—
102#2324—91noSylow
103C22×D12—31no—
104C22×D12—31no—
105C22×D12—32no—
106C22×D12—32no—
107C22×D12—61no—
108C22×D12—62no—
109C22×C4×D3—31no—
110C22×C4×D3—31no—
111C22×C4×D3—32no—
112C22×C4×D3—32no—
113C22×C4×D3—61no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—32no—
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×C3×C42—31no—
121C2×C3×C42—31no—
122C2×C3×C42—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—62no—
138C2×C4⋊Dic3C2×D311yescharacteristic
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×C4⋊Dic3C2×D312yes—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—31no—
145C2×C4×Dic3C2×D311yescharacteristic
146C2×C4×Dic3C2×D312yes—
147C2×C4×Dic3C2×D311yescharacteristic
148#895—38no—
149#895—38no—
150#895—68no—
151#893—64no—
152C4×D12—64no—
153#872—64no—
154#872—64no—
155C3×#95—32no—
156C3×#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95C2×D312yes—
160C3⋊#95C2×D312yes—
161C23×C32C2411yescharacteristic
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—21no—
173C22×C3⋊D3—22no—
174C22×C3⋊D3C22×C414yes—
175C22×C3⋊D3C22×C412yes—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4C22×C414yes—
179C2×C32×C4C22×C412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4#4112yes—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3C22×C412yes—
185C4⋊(C3⋊D3)—28no—
186C4⋊(C3⋊D3)—48no—
187C4×C3⋊D3—28no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3C2×D412yes—
205C2×C3×Dic3C2×D412yes—
206#624—48no—
207C2×#121—91no—
208C2×C4×D4—91no—
209C2×#117—91no—
210#390—91no—
211#390—92no—
212#389—31no—
213#388—92no—
214#386—92no—
215#385—92no—
216#380—91no—
217C4×C4⋊C4—31no—
218C23×D3—32no—
219C23×D3—32no—
220C23×D3—31no—
221C23×D3—31no—
222C23×D3—61no—
223C23×D3—62no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—61no—
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D311yescharacteristic
242C22×Dic3C22×D311yescharacteristic
243C22×Dic3C22×D311yescharacteristic
244C22×Dic3C22×D311yescharacteristic
245C2×D12—34no—
246C2×D12—34no—
247C2×D12—38no—
248C2×D12—38no—
249C2×D12—64no—
250C2×D12—68no—
251C2×D12—62no—
252C2×D12—62no—
253C2×D12—62no—
254C2×D12—62no—
255C2×D12—122no—
256C2×D12—122no—
257C2×D12—122no—
258C2×D12—122no—
259C2×D12—122no—
260C2×D12—122no—
261C2×D12—124no—
262C2×D12—124no—
263C2×C4×D3—34no—
264C2×C4×D3—34no—
265C2×C4×D3—64no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—62no—
270C2×C4×D3—64no—
271C2×C4×D3—64no—
272C2×C4×D3—122no—
273C2×C4×D3—122no—
274C2×C4×D3—122no—
275C2×C4×D3—122no—
276C2×C4×D3—122no—
277C2×C4×D3—122no—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—62no—
280C3×C4⋊C4—62no—
281C3×C4⋊C4—122no—
282C3×C4⋊C4C4×D314yescomplemented
283C3×C4⋊C4C4×D314yescomplemented
284C3×C42—34no—
285C3×C42—62no—
286C3×C42—122no—
287(C2×D3)⋊C4—38no—
288(C2×D3)⋊C4—38no—
289(C2×D3)⋊C4—68no—
290(C2×D3)⋊C4—62no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—122no—
297(C2×D3)⋊C4—122no—
298(C2×D3)⋊C4—122no—
299(C2×D3)⋊C4—122no—
300(C2×D3)⋊C4—122no—
301(C2×D3)⋊C4—122no—
302C4⋊Dic3—22no—
303C4⋊Dic3—22no—
304C4⋊Dic3—42no—
305Dic3⋊C4—62no—
306Dic3⋊C4—62no—
307Dic3⋊C4—62no—
308Dic3⋊C4—62no—
309C4×Dic3—22no—
310C4×Dic3—42no—
311C4×Dic3D1214yescomplemented
312C22×C32C23×C411yescharacteristic
313C22×C32C22×D411yescharacteristic
314C22×C32C2×#4111yescharacteristic
315C22×C32H(5,𝔽2)11yescharacteristic
316C22×C32H(5,𝔽2)11yescharacteristic
317C22×C32H(5,𝔽2)11yescharacteristic
318C22×C322−1+411yescharacteristic
319C2×C3⋊D3—22no—
320C2×C3⋊D3—22no—
321C2×C3⋊D3—24no—
322C2×C3⋊D3—24no—
323C2×C3⋊D3—22no—
324C2×C3⋊D3—24no—
325C2×C3⋊D3—41no—
326C2×C3⋊D3—41no—
327C2×C3⋊D3—41no—
328C2×C3⋊D3—41no—
329C2×C3⋊D3—42no—
330C2×C3⋊D3—42no—
331C2×C3⋊D3—42no—
332C2×C3⋊D3—42no—
333C32×C4—24no—
334C32×C4C4×D414yes—
335C3⋊Dic3—22no—
336C3×Dic3—22no—
337C3×Dic3—22no—
338C3×Dic3—42no—
339C3×Dic3—41no—
340C3×Dic3—41no—
341C3×Dic3—42no—
342C22×D4—91no—
343C22×D4—92no—
344C23×C4—92no—
345C23×C4—91no—
346#121—98no—
347C4×D4—184no—
348#117—184no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—32no—
352C2×C4⋊C4—91no—
353C2×C4⋊C4—91no—
354C2×C4⋊C4D3211yescharacteristic
355C2×C22⋊C4—92no—
356C2×C22⋊C4—91no—
357C2×C22⋊C4—91no—
358C2×C22⋊C4—92no—
359C2×C22⋊C4—92no—
360C2×C22⋊C4—92no—
361C2×C22⋊C4—92no—
362C2×C42—31no—
363C2×C42—31no—
364C2×C42—32no—
365#95—32no—
366#95—32no—
367#95—92no—
368C23×C3—21no—
369C23×C3C23×D311yescharacteristic
370C23×C3C23×D311yescharacteristic
371C22×D3—34no—
372C22×D3—34no—
373C22×D3—32no—
374C22×D3—32no—
375C22×D3—62no—
376C22×D3—64no—
377C22×D3—62no—
378C22×D3—62no—
379C22×D3—61no—
380C22×D3—62no—
381C22×D3—61no—
382C22×D3—62no—
383C22×D3—61no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—62no—
387C22×D3—61no—
388C22×D3—61no—
389C22×D3—61no—
390C22×D3—62no—
391C22×D3—61no—
392C22×D3—62no—
393C22×D3—61no—
394C22×D3—62no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3—62no—
401C22×D3—61no—
402C22×D3—61no—
403C22×D3—121no—
404C22×D3—121no—
405C22×D3—121no—
406C22×D3—121no—
407C22×D3—122no—
408C22×D3—122no—
409C22×D3—122no—
410C22×D3—122no—
411C22×D3—122no—
412C22×D3—122no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—32no—
422C2×C3×C4—32no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—61no—
431C2×C3×C4—62no—
432C2×C3×C4—61no—
433C2×C3×C4—62no—
434C2×C3×C4—61no—
435C2×C3×C4—62no—
436C2×C3×C4—61no—
437C2×C3×C4—62no—
438C2×C3×C4—62no—
439C2×C3×C4—61no—
440C2×C3×C4—62no—
441C2×C3×C4C2×C4×D314yes—
442C2×C3×C4C2×C4×D314yes—
443C2×C3×C4C2×C4×D312yes—
444C2×C3×C4C2×C4×D312yes—
445C2×C3×C4C2×D1212yes—
446C2×C3×C4#23512yes—
447C2×C3×C4D3×D412yes—
448C2×C3×C4#23912yes—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—22no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—21no—
459C2×Dic3—22no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—22no—
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—32no—
466C2×Dic3—32no—
467C2×Dic3—62no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—121no—
473C2×Dic3—121no—
474C2×Dic3C2×D1212yes—
475C2×Dic3C2×D1212yes—
476D12—68no—
477D12—68no—
478D12—128no—
479D12—128no—
480D12—128no—
481D12—1216no—
482C4×D3—68no—
483C4×D3—68no—
484C4×D3—128no—
485C4×D3—128no—
486C4×D3—128no—
487C2×C32C2×C4×D411yescharacteristic
488C2×C32#51811yescharacteristic
489C2×C32#52011yescharacteristic
490C2×C32#53511yescharacteristic
491C2×C32#53711yescharacteristic
492C2×C32#54011yescharacteristic
493C2×C32#54211yescharacteristic
494C3⋊D3—42no—
495C3⋊D3—44no—
496C24—92no—
497C24—91no—
498C2×D4—94no—
499C2×D4—98no—
500C2×D4—182no—
501C2×D4—182no—
502C2×D4—362no—
503C2×D4—362no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—31no—
510C22×C4—91no—
511C22×C4—94no—
512C22×C4—184no—
513C22×C4—182no—
514C22×C4—182no—
515C22×C4—362no—
516C22×C4—362no—
517C22×C4C2×D3212yes—
518C22×C4C2×D3211yescharacteristic
519C4⋊C4—62no—
520C4⋊C4—62no—
521C4⋊C4—122no—
522C4⋊C4—182no—
523C4⋊C4—182no—
524C4⋊C4#62414yescomplemented
525C22⋊C4—98no—
526C22⋊C4—182no—
527C22⋊C4—182no—
528C22⋊C4—184no—
529C22⋊C4—362no—
530C22⋊C4—362no—
531C22⋊C4—362no—
532C42—34no—
533C42—62no—
534C42—122no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3C22×C4×D311yescharacteristic
543C22×C3C22×C4×D311yescharacteristic
544C22×C3C22×D1211yescharacteristic
545C22×C3C2×#23511yescharacteristic
546C22×C3C2×D3×D411yescharacteristic
547C22×C3#100411yescharacteristic
548C22×C3#100411yescharacteristic
549C22×C3C2×#23911yescharacteristic
550C22×C3#100711yescharacteristic
551C22×C3#100711yescharacteristic
552C22×C3#100911yescharacteristic
553C22×C3#100911yescharacteristic
554C22×C3#100911yescharacteristic
555C22×C3#100911yescharacteristic
556C2×D3—64no—
557C2×D3—62no—
558C2×D3—64no—
559C2×D3—62no—
560C2×D3—64no—
561C2×D3—62no—
562C2×D3—62no—
563C2×D3—64no—
564C2×D3—64no—
565C2×D3—64no—
566C2×D3—62no—
567C2×D3—64no—
568C2×D3—62no—
569C2×D3—122no—
570C2×D3—122no—
571C2×D3—124no—
572C2×D3—124no—
573C2×D3—124no—
574C2×D3—122no—
575C2×D3—122no—
576C2×D3—122no—
577C2×D3—122no—
578C2×D3—121no—
579C2×D3—122no—
580C2×D3—121no—
581C2×D3—122no—
582C2×D3—121no—
583C2×D3—122no—
584C2×D3—122no—
585C2×D3—121no—
586C2×D3—121no—
587C2×D3—122no—
588C2×D3—121no—
589C2×D3—122no—
590C2×D3—122no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—122no—
594C2×D3—242no—
595C2×D3—242no—
596C2×D3—242no—
597C2×D3—242no—
598C3×C4—24no—
599C3×C4—24no—
600C3×C4—24no—
601C3×C4—44no—
602C3×C4—62no—
603C3×C4—62no—
604C3×C4—122no—
605C3×C4—121no—
606C3×C4—122no—
607C3×C4—121no—
608C3×C4C4×D1214yes—
609C3×C4#89314yes—
610Dic3—22no—
611Dic3—22no—
612Dic3—42no—
613Dic3—42no—
614Dic3—41no—
615Dic3—41no—
616Dic3—62no—
617Dic3—62no—
618Dic3—122no—
619C32#232411yescharacteristic, complemented, Sylow
620C23—94no—
621C23—92no—
622C23—181no—
623C23—182no—
624C23—181no—
625C23—182no—
626C23—182no—
627C23—182no—
628C23—181no—
629C23—181no—
630C23—181no—
631C23—182no—
632C23—181no—
633C23—182no—
634C23C22×D3211yescharacteristic
635D4—188no—
636D4—368no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—32no—
640C2×C4—32no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—62no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—62no—
653C2×C4—61no—
654C2×C4—62no—
655C2×C4—61no—
656C2×C4—62no—
657C2×C4—92no—
658C2×C4—181no—
659C2×C4—181no—
660C2×C4—188no—
661C2×C4—368no—
662C2×C4#379912yes—
663C2×C4D3×D1212yes—
664C2×C4C2×#62414yes—
665C2×C4C2×#62412yes—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3C2×C4×D1211yescharacteristic
674C2×C3C2×#89311yescharacteristic
675C2×C3#551011yescharacteristic
676C2×C3#552511yescharacteristic
677C2×C3#554511yescharacteristic
678C2×C3#554511yescharacteristic
679C2×C3#556211yescharacteristic
680C2×C3#557411yescharacteristic
681C2×C3#557411yescharacteristic
682C2×C3#558211yescharacteristic
683C2×C3#560711yescharacteristic
684C2×C3#562911yescharacteristic
685C2×C3#569711yescharacteristic
686C2×C3#573311yescharacteristic
687D3—124no—
688D3—122no—
689D3—124no—
690D3—122no—
691D3—124no—
692D3—244no—
693C22—182no—
694C22—184no—
695C22—182no—
696C22—184no—
697C22—182no—
698C22—184no—
699C22—361no—
700C22—362no—
701C22—361no—
702C22—362no—
703C22—362no—
704C22—361no—
705C22—361no—
706C22—362no—
707C22C2×#379911yescharacteristic
708C22C2×D3×D1211yescharacteristic
709C22#6431411yescharacteristic
710C22#6431411yescharacteristic
711C22#6431611yescharacteristic
712C22#6432011yescharacteristic
713C22C22×#62411yescharacteristic
714C4—24no—
715C4—62no—
716C4—62no—
717C4—122no—
718C4—122no—
719C4—121no—
720C4—121no—
721C4—182no—
722C4#6389414yes—
723C3—21no—
724C3#7376311yescharacteristic, complemented
725C3#7619811yescharacteristic, complemented
726C2—362no—
727C2—364no—
728C2#1059435211yescharacteristic
729C2#1059452311yescharacteristic
730C2#1059459411yescharacteristic
731C2#1059462811yescharacteristic
732C2C2×#6389411yescharacteristic
733C2#1059522311yescharacteristic
734C2#1059535311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#64104C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63894C2semidirect
3. C2×#63874C2semidirect
4. C3×#4984C2semidirect
5. C3×Dic3×C4⋊C4C2semidirect
6. #10591380C2semidirect
7. #10591378C2semidirect
8. #10591325C2semidirect
9. #10591320C2semidirect
10. #10591320C2semidirect
11. #10591202C2semidirect
20. #64104C4semidirect
54. #4984D3semidirect
55. Dic3×C4⋊C4D3semidirect
73. C2×C4⋊(C3⋊D3)C2×C4semidirect
76. C2×C4×C3⋊D3C2×C4semidirect
86. C32×C4⋊C4C2×C4semidirect
87. #3752C2×C4semidirect
93. C3×C4×Dic3D4semidirect
282. C3×C4⋊C4C4×D3semidirect
283. C3×C4⋊C4C4×D3semidirect
311. C4×Dic3D12semidirect
524. C4⋊C4#624semidirect
619. C32#2324semidirect
724. C3#73763semidirect
725. C3#76198semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×#638942
C2×#638742
C3×#49842
C3×Dic3×C4⋊C42
#105913802
#105913782
#105913252
#105913202
#105912022
#761983
#737633