Finite Group Databasebeta

← D43×#2318 #25255227

Subgroups — D43×#2318 #25255227

Order 11008.

3262 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2#19137231C211yesmaximal, characteristic, complemented
3#19137230C211yesmaximal, characteristic, complemented
4#19137229C211yesmaximal, characteristic, complemented
5#19137228C211yesmaximal, characteristic, complemented
6#19137227C212yesmaximal, complemented
7#19137226C211yesmaximal, characteristic, complemented
8#19137225C212yesmaximal, complemented
9#19137224C211yesmaximal, characteristic, complemented
10#19137223C212yesmaximal, complemented
11#19137222C211yesmaximal, characteristic, complemented
12#19137221C212yesmaximal, complemented
13#388×D43C212yesmaximal, complemented
14#387×D43C212yesmaximal, complemented
15#386×D43C212yesmaximal
16#385×D43C212yesmaximal, complemented
17#383×D43C211yesmaximal, characteristic, complemented
18#382×D43C211yesmaximal, characteristic, complemented
19#381×D43C211yesmaximal, characteristic, complemented
20#380×D43C211yesmaximal, characteristic, complemented
21C4×C22⋊C4×D43C211yesmaximal, characteristic, complemented
22C2×#95×D43C211yesmaximal, characteristic, complemented
23C43×#2318C211yesmaximal, characteristic, complemented
24C22×D4×D43C2211yescharacteristic
25C23×C4×D43C2212yes—
26C23×C4×D43C2211yescharacteristic
27C23×C4×D43C2211yescharacteristic
28C2×C4×D172C2211yescharacteristic
29C2×D4×Dic43C2211yescharacteristic
30C2×#13063287C2211yescharacteristic
31C2×C4×C22⋊D43C2211yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×(C22⋊D43)⋊C4C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C2211yescharacteristic
35C4×D4×D43C4116yescomplemented
36C2×C4⋊C4×D43C2212yes—
37C2×C4⋊C4×D43C2212yes—
38C2×C4⋊C4×D43C2211yescharacteristic
39C2×C22⋊C4×D43C2212yes—
40C2×C22⋊C4×D43C2212yes—
41C2×C22⋊C4×D43C2212yes—
42C2×C22⋊C4×D43C2211yescharacteristic
43C2×C22⋊C4×D43C2211yescharacteristic
44C2×C42×D43C2212yes—
45C2×C42×D43C2211yescharacteristic
46#14582793C2212yescomplemented
47#14582792C2212yescomplemented
48#14582791C2212yescomplemented
49#14582790C2212yescomplemented
50#14582789C2212yescomplemented
51#14582788C2212yescomplemented
52#14582787C2212yescomplemented
53#14582786C2212yescomplemented
54#14582785C2212yescomplemented
55#14582784C2212yescomplemented
56#14582783C2212yescomplemented
57#14582782C2212yescomplemented
58#14582781C2212yescomplemented
59#14582780C2212yescomplemented
60#14582779C2212yes—
61#14582778C2212yes—
62#14582777C2212yes—
63#14582777C2212yes—
64#14582776C2212yes—
65#14582775C2212yes—
66#14582775C2212yes—
67#14582774C2212yescomplemented
68#14582773C2212yescomplemented
69#14582773C2212yescomplemented
70#14582772C2212yescomplemented
71#14582771C2212yescomplemented
72#14582770C2212yescomplemented
73#14582770C2212yescomplemented
74#14582767C2211yescharacteristic, complemented
75#14582766C2212yescomplemented
76#14582766C2211yescharacteristic, complemented
77#14582766C2212yescomplemented
78#14582766C2211yescharacteristic, complemented
79#14582765C2211yescharacteristic, complemented
80#14582764C2212yescomplemented
81#14582763C2212yescomplemented
82#14582763C2211yescharacteristic, complemented
83#14582763C2211yescharacteristic, complemented
84#14582762C2211yescharacteristic, complemented
85#14582761C2211yescharacteristic, complemented
86#14582761C2212yescomplemented
87#14582761C2211yescharacteristic, complemented
88#14582760C2212yescomplemented
89#14582759C2211yescharacteristic, complemented
90#14582758C2211yescharacteristic, complemented
91#14582758C2211yescharacteristic, complemented
92#14582757C2212yescomplemented
93#14582756C2212yescomplemented
94C22⋊C4×Dic43C2212yescomplemented
95C4×(C2×D43)⋊C4C2212yescomplemented
96C4×C22⋊Dic43C2211yescharacteristic, complemented
97#14582746C2211yescharacteristic, complemented
98#14582746C2211yescharacteristic, complemented
99C2×C43⋊#95C2212yescomplemented
100C2×C43⋊#95C2211yescharacteristic, complemented
101#95×D43C2211yescharacteristic
102#95×D43C2211yescharacteristic
103#95×D43C2212yes—
104#95×D43C2211yescharacteristic
105#95×D43C2211yescharacteristic
106#95×D43C2212yes—
107#95×D43C2212yes—
108#95×D43C2212yes—
109#95×D43C2212yes—
110#95×D43C2211yescharacteristic, complemented
111#95×D43C2212yescomplemented
112#95×D43C2211yescharacteristic, complemented
113C2×C4×D4×C43C2211yescharacteristic
114C43×#388C2212yescomplemented
115C43×#387C2212yescomplemented
116C43×#386C2212yes—
117C43×#385C2212yescomplemented
118C43×#383C2211yescharacteristic, complemented
119C43×#382C2211yescharacteristic, complemented
120C43×#381C2211yescharacteristic, complemented
121C43×#380C2211yescharacteristic, complemented
122C4×C22⋊C4×C43C2211yescharacteristic, complemented
123C2×#95×C43C2211yescharacteristic, complemented
124C24×D43C2311yescharacteristic
125C24×D43C2311yescharacteristic
126C22×D172C2311yescharacteristic
127C22×C22⋊D43C2311yescharacteristic
128C22×C22⋊D43C2311yescharacteristic
129C2×D4×D43—28no—
130C2×D4×D43C2×C418yes—
131C23×Dic43C2312yes—
132C23×Dic43C2311yescharacteristic
133C23×Dic43C2311yescharacteristic
134C22×C4×D43—28no—
135C22×C4×D43—44no—
136C22×C4×D43—44no—
137C22×C4×D43—44no—
138C22×C4×D43—44no—
139C22×C4×D43C2×C418yes—
140C22×C4×D43C2×C418yescomplemented
141C22×C4×D43C2312yes—
142C22×C4×D43C2312yes—
143C22×C4×D43C2312yes—
144C22×C4×D43C2312yes—
145C22×C4×D43C2311yescharacteristic
146C22×C4×D43C2311yescharacteristic
147C22×C4×D43C2311yescharacteristic
148C22×C4×D43C2311yescharacteristic
149C22×C4×D43C2311yescharacteristic
150C22×C4×D43C2312yes—
151C22×C4×D43C2312yes—
152C22×C4×D43C2311yescharacteristic
153C22×C4×D43C2311yescharacteristic
154C22×C4×D43C2311yescharacteristic
155C22×C4×D43C2311yescharacteristic
156C4×D172C2×C418yescomplemented
157D4×Dic43C2×C418yescomplemented
158#13063287C2×C418yescomplemented
159C4×C22⋊D43C2×C418yescomplemented
160C4×C22⋊D43C2×C418yescomplemented
161(C22⋊D43)⋊C4C2×C418yescomplemented
162(C22⋊D43)⋊C4C2×C418yescomplemented
163C2×C4⋊Dic43C2312yes—
164C2×C4⋊Dic43C2312yes—
165C2×C4⋊Dic43C2311yescharacteristic
166C2×Dic43⋊C4C2312yes—
167C2×Dic43⋊C4C2312yes—
168C2×Dic43⋊C4C2312yes—
169C2×Dic43⋊C4C2312yes—
170C2×Dic43⋊C4C2311yescharacteristic
171C2×Dic43⋊C4C2311yescharacteristic
172C4⋊C4×D43—44no—
173C4⋊C4×D43—44no—
174C4⋊C4×D43C2×C418yescomplemented
175C2×C22⋊Dic43C2312yes—
176C2×C22⋊Dic43C2312yes—
177C2×C22⋊Dic43C2312yes—
178C2×C22⋊Dic43C2311yescharacteristic
179C2×C22⋊Dic43C2311yescharacteristic
180C2×(C2×D43)⋊C4C2312yes—
181C2×(C2×D43)⋊C4C2312yes—
182C2×(C2×D43)⋊C4C2312yes—
183C2×(C2×D43)⋊C4C2312yes—
184C2×(C2×D43)⋊C4C2312yes—
185C2×(C2×D43)⋊C4C2312yes—
186C2×(C2×D43)⋊C4C2311yescharacteristic
187C2×(C2×D43)⋊C4C2311yescharacteristic
188C2×(C2×D43)⋊C4C2311yescharacteristic
189C2×(C2×D43)⋊C4C2311yescharacteristic
190C22⋊C4×D43—28no—
191C22⋊C4×D43—44no—
192C22⋊C4×D43—44no—
193C22⋊C4×D43C2×C418yes—
194C22⋊C4×D43C2×C418yescomplemented
195C2×C4×Dic43C2312yes—
196C2×C4×Dic43C2312yes—
197C2×C4×Dic43C2312yes—
198C2×C4×Dic43C2311yescharacteristic
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C42×D43—44no—
202C42×D43C2×C418yescomplemented
203C43⋊#95C2312yes—
204C43⋊#95C2312yes—
205C43⋊#95C2312yes—
206C43⋊#95C2312yes—
207C43⋊#95C2312yes—
208C43⋊#95C2312yes—
209C43⋊#95C2312yes—
210C43⋊#95C2312yes—
211C43⋊#95C2312yes—
212C43⋊#95C2312yes—
213C43⋊#95C2312yes—
214C43⋊#95C2312yes—
215C43⋊#95C2312yes—
216C43⋊#95C2311yescharacteristic
217C43⋊#95C2312yes—
218C43⋊#95C2311yescharacteristic
219C43⋊#95C2311yescharacteristic
220C43⋊#95C2311yescharacteristic
221C43⋊#95C2312yes—
222C43⋊#95C2312yes—
223C43⋊#95C2312yes—
224C43⋊#95C2312yes—
225C43⋊#95C2312yes—
226C22×D4×C43C2311yescharacteristic
227C23×C4×C43C2312yes—
228C23×C4×C43C2311yescharacteristic
229C23×C4×C43C2311yescharacteristic
230C4×D4×C43C2×C418yescomplemented
231C2×C4⋊C4×C43C2312yes—
232C2×C4⋊C4×C43C2312yes—
233C2×C4⋊C4×C43C2311yescharacteristic
234C2×C22⋊C4×C43C2312yes—
235C2×C22⋊C4×C43C2312yes—
236C2×C22⋊C4×C43C2312yes—
237C2×C22⋊C4×C43C2311yescharacteristic
238C2×C22⋊C4×C43C2311yescharacteristic
239C2×C42×C43C2312yes—
240C2×C42×C43C2311yescharacteristic
241#95×C43C2312yes—
242#95×C43C2312yes—
243#95×C43C2312yes—
244#95×C43C2312yes—
245#95×C43C2311yescharacteristic
246#95×C43C2311yescharacteristic
247#95×C43C2311yescharacteristic
248#95×C43C2311yescharacteristic
249#95×C43C2312yes—
250C24×C43C2411yescharacteristic
251C24×C43C2411yescharacteristic
252C23×D43—24no—
253C23×D43—22no—
254C23×D43—22no—
255C23×D43—24no—
256C23×D43—22no—
257C23×D43—24no—
258C23×D43—22no—
259C23×D43C22×C414yes—
260C23×D43C22×C414yes—
261C23×D43#4118yes—
262C23×D43C2411yescharacteristic
263C23×D43C2411yescharacteristic
264C23×D43C2411yescharacteristic
265C2×D4×C43—24no—
266C2×D4×C43C22×C414yes—
267C22×C4×C43—24no—
268C22×C4×C43—42no—
269C22×C4×C43—42no—
270C22×C4×C43—42no—
271C22×C4×C43—42no—
272C22×C4×C43C22×C414yes—
273C22×C4×C43C22×C414yescomplemented
274C22×C4×C43C2412yes—
275C22×C4×C43C2412yes—
276C22×C4×C43C2412yes—
277C22×C4×C43C2412yes—
278C22×C4×C43C2411yescharacteristic
279C22×C4×C43C2411yescharacteristic
280C22×C4×C43C2411yescharacteristic
281C22×C4×C43C2411yescharacteristic
282C22×C4×C43C2411yescharacteristic
283C2×C22⋊D43—24no—
284C2×C22⋊D43—24no—
285C2×C22⋊D43C22×C414yes—
286C2×C22⋊D43C22×C414yes—
287C22×Dic43—24no—
288C22×Dic43—42no—
289C22×Dic43—42no—
290C22×Dic43—42no—
291C22×Dic43—42no—
292C22×Dic43C22×C414yes—
293C22×Dic43C22×C414yescomplemented
294C22×Dic43C2412yes—
295C22×Dic43C2412yes—
296C22×Dic43C2412yes—
297C22×Dic43C2412yes—
298C22×Dic43C2411yescharacteristic
299C22×Dic43C2411yescharacteristic
300C22×Dic43C2411yescharacteristic
301C22×Dic43C2411yescharacteristic
302C22×Dic43C2411yescharacteristic
303D4×D43—232no—
304C2×D172—24no—
305C2×D172C22×C414yes—
306C2×C4×D43—24no—
307C2×C4×D43—24no—
308C2×C4×D43—24no—
309C2×C4×D43—24no—
310C2×C4×D43—24no—
311C2×C4×D43—24no—
312C2×C4×D43—24no—
313C2×C4×D43—24no—
314C2×C4×D43—22no—
315C2×C4×D43—24no—
316C2×C4×D43—24no—
317C2×C4×D43—24no—
318C2×C4×D43—24no—
319C2×C4×D43—24no—
320C2×C4×D43—24no—
321C2×C4×D43—24no—
322C2×C4×D43—24no—
323C2×C4×D43—24no—
324C2×C4×D43—22no—
325C2×C4×D43—24no—
326C2×C4×D43—416no—
327C2×C4×D43—416no—
328C2×C4×D43—42no—
329C2×C4×D43—42no—
330C2×C4×D43—42no—
331C2×C4×D43—42no—
332C2×C4×D43—42no—
333C2×C4×D43—42no—
334C2×C4×D43—42no—
335C2×C4×D43—42no—
336C2×C4×D43—432no—
337C2×C4×D43C22×C414yes—
338C2×C4×D43C22×C414yes—
339C2×C4×D43C22×C414yes—
340C2×C4×D43C22×C414yes—
341C2×C4×D43C22×C414yes—
342C2×C4×D43C22×C414yes—
343C2×C4×D43C22×C414yes—
344C2×C4×D43C22×C414yescomplemented
345C2×C4×D43C22×C414yescomplemented
346C4⋊C4×C43—42no—
347C4⋊C4×C43—42no—
348C4⋊C4×C43C22×C414yescomplemented
349C22⋊C4×C43—24no—
350C22⋊C4×C43—42no—
351C22⋊C4×C43—42no—
352C22⋊C4×C43C22×C414yes—
353C22⋊C4×C43C22×C414yescomplemented
354C42×C43—42no—
355C42×C43C22×C414yescomplemented
356C22⋊Dic43—24no—
357C22⋊Dic43—42no—
358C22⋊Dic43—42no—
359C22⋊Dic43C22×C414yes—
360C22⋊Dic43C22×C414yescomplemented
361(C2×D43)⋊C4—24no—
362(C2×D43)⋊C4—24no—
363(C2×D43)⋊C4—42no—
364(C2×D43)⋊C4—42no—
365(C2×D43)⋊C4—42no—
366(C2×D43)⋊C4—42no—
367(C2×D43)⋊C4C22×C414yes—
368(C2×D43)⋊C4C22×C414yes—
369(C2×D43)⋊C4C22×C414yescomplemented
370(C2×D43)⋊C4C22×C414yescomplemented
371C4⋊Dic43—42no—
372C4⋊Dic43—42no—
373C4⋊Dic43C22×C414yescomplemented
374Dic43⋊C4—42no—
375Dic43⋊C4—42no—
376Dic43⋊C4—42no—
377Dic43⋊C4—42no—
378Dic43⋊C4C22×C414yescomplemented
379Dic43⋊C4C22×C414yescomplemented
380C4×Dic43—42no—
381C4×Dic43—42no—
382C4×Dic43—42no—
383C4×Dic43C22×C414yescomplemented
384C4×Dic43C22×C414yescomplemented
385C4×Dic43C22×C414yescomplemented
386C23×C43—22no—
387C23×C43—21no—
388C23×C43—21no—
389C23×C43—22no—
390C23×C43—21no—
391C23×C43—22no—
392C23×C43—21no—
393C23×C43C23×C412yes—
394C23×C43C23×C412yes—
395C23×C43C2×#4114yes—
396C23×C43C2511yescharacteristic
397C22×D43—22no—
398C22×D43—21no—
399C22×D43—21no—
400C22×D43—28no—
401C22×D43—28no—
402C22×D43—216no—
403C22×D43—216no—
404C22×D43—22no—
405C22×D43—21no—
406C22×D43—22no—
407C22×D43—21no—
408C22×D43—28no—
409C22×D43—28no—
410C22×D43—28no—
411C22×D43—48no—
412C22×D43—48no—
413C22×D43#117116yes—
414C22×D43C23×C412yes—
415C22×D43C23×C412yes—
416C22×D43C23×C412yes—
417C22×D43C2×#4114yes—
418C22×D43C2×#4114yes—
419C22×D43H(5,𝔽2)14yes—
420C22×D43H(5,𝔽2)12yes—
421C22×D432−1+412yes—
422D4×C43—28no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—21no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—21no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—22no—
440C2×C4×C43—22no—
441C2×C4×C43—44no—
442C2×C4×C43—44no—
443C2×C4×C43—48no—
444C2×C4×C43C23×C412yes—
445C2×C4×C43C23×C412yes—
446C2×C4×C43C23×C412yes—
447C2×C4×C43C23×C412yes—
448C2×C4×C43C23×C412yes—
449C22⋊D43—28no—
450C22⋊D43—28no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—21no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—21no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—44no—
470C2×Dic43—44no—
471C2×Dic43—48no—
472C2×Dic43C23×C412yes—
473C2×Dic43C23×C412yes—
474C2×Dic43C23×C412yes—
475C2×Dic43C23×C412yes—
476C2×Dic43C23×C412yes—
477D172—28no—
478C4×D43—28no—
479C4×D43—28no—
480C4×D43—28no—
481C4×D43—28no—
482C4×D43—28no—
483C4×D43—44no—
484C4×D43—44no—
485C4×D43—44no—
486C4×D43—44no—
487C4×D43—48no—
488C4×D43—48no—
489C4×D43—48no—
490C4×D43—48no—
491C4×D43—48no—
492C4×D43—48no—
493C2×#2318—431nomaximal, Sylow
494C22×C43—22no—
495C22×C43—22no—
496C22×C43—24no—
497C22×C43—24no—
498C22×C43—22no—
499C22×C43—22no—
500C22×C43—22no—
501C22×C43—42no—
502C22×C43—42no—
503C22×C43C2×#11714yes—
504C22×C43C24×C411yescharacteristic
505C22×C43C22×#4112yes—
506C22×C43C2×H(5,𝔽2)12yes—
507C22×C43C2×H(5,𝔽2)11yescharacteristic
508C22×C43C2×2−1+411yescharacteristic
509C2×D43—22no—
510C2×D43—22no—
511C2×D43—24no—
512C2×D43—24no—
513C2×D43—232no—
514C2×D43—22no—
515C2×D43—22no—
516C2×D43—22no—
517C2×D43—42no—
518C2×D43—42no—
519C2×D43—416no—
520C2×D43C2×#11714yes—
521C2×D43C2×#11714yes—
522C2×D43#51814yes—
523C2×D43#52014yes—
524C2×D43#53818yes—
525C2×D43#53918yes—
526C4×C43—22no—
527C4×C43—22no—
528C4×C43—22no—
529C4×C43—22no—
530C4×C43—22no—
531C4×C43—42no—
532C4×C43—42no—
533C4×C43—42no—
534C4×C43—42no—
535Dic43—22no—
536Dic43—22no—
537Dic43—22no—
538Dic43—22no—
539Dic43—22no—
540Dic43—42no—
541Dic43—42no—
542Dic43—42no—
543Dic43—42no—
544C22×C4×D4—431no—
545#2318—432no—
546#2318—432no—
547#2318—432no—
548#2318—432no—
549#2318—431no—
550#2318—431no—
551#2318—431no—
552#2318—431no—
553#2318—431no—
554#2318—431no—
555#2318—431no—
556#2318D4311yescharacteristic, direct product factor
557C2×#388—432no—
558C2×#387—432no—
559C2×#386—432no—
560C2×#385—432no—
561C2×#383—431no—
562C2×#382—431no—
563C2×#381—431no—
564C2×#380—431no—
565C2×C4×C22⋊C4—431no—
566C22×#95—431no—
567C2×C43—24no—
568C2×C43—42no—
569C2×C43C22×#11711yescharacteristic
570C2×C43C2×#51811yescharacteristic
571C2×C43C2×#52011yescharacteristic
572C2×C43C2×#53812yes—
573C2×C43C2×#53912yes—
574D43—24no—
575D43—42no—
576D43#231818yesdirect product factor
577C23×D4—431no—
578C24×C4—431no—
579C24×C4—431no—
580C24×C4—432no—
581C2×C4×D4—431no—
582C2×C4×D4—431no—
583C2×C4×D4—431no—
584C2×C4×D4—4316no—
585C2×C4×D4—431no—
586C2×C4×D4—431no—
587C2×C4×D4—431no—
588C2×C4×D4—431no—
589C2×C4×D4C2×D4311yescharacteristic
590C22×C4⋊C4—431no—
591C22×C4⋊C4—432no—
592C22×C4⋊C4—432no—
593C22×C22⋊C4—431no—
594C22×C22⋊C4—431no—
595C22×C22⋊C4—432no—
596C22×C22⋊C4—432no—
597C22×C22⋊C4—432no—
598C22×C42—431no—
599C22×C42—432no—
600#388—432no—
601#388—432no—
602#388—432no—
603#388—432no—
604#388—432no—
605#388—432no—
606#388—432no—
607#388C2×D4312yescomplemented
608#387—432no—
609#387—432no—
610#387—432no—
611#387—432no—
612#387—432no—
613#387—432no—
614#387—432no—
615#387C2×D4312yescomplemented
616#386—432no—
617#386—432no—
618#386—432no—
619#386—432no—
620#386—432no—
621#386—432no—
622#386—432no—
623#386C2×D4312yes—
624#385—432no—
625#385—432no—
626#385—432no—
627#385—432no—
628#385—432no—
629#385—432no—
630#385—432no—
631#385C2×D4312yescomplemented
632#383—431no—
633#383—432no—
634#383—432no—
635#383—431no—
636#383—431no—
637#383C2×D4311yescharacteristic, complemented
638#382—432no—
639#382—431no—
640#382—432no—
641#382—431no—
642#382—431no—
643#382C2×D4311yescharacteristic, complemented
644#381—431no—
645#381—432no—
646#381—432no—
647#381—431no—
648#381—431no—
649#381C2×D4311yescharacteristic, complemented
650#380—431no—
651#380—432no—
652#380—432no—
653#380—431no—
654#380—431no—
655#380C2×D4311yescharacteristic, complemented
656C4×C22⋊C4—431no—
657C4×C22⋊C4—432no—
658C4×C22⋊C4—432no—
659C4×C22⋊C4—431no—
660C4×C22⋊C4—431no—
661C4×C22⋊C4C2×D4311yescharacteristic, complemented
662C2×#95—432no—
663C2×#95—431no—
664C2×#95—432no—
665C2×#95—431no—
666C2×#95—431no—
667C2×#95—431no—
668C2×#95—431no—
669C2×#95—432no—
670C2×#95—431no—
671C2×#95—431no—
672C2×#95—432no—
673C2×#95—432no—
674C2×#95—432no—
675C2×#95—432no—
676C2×#95C2×D4311yescharacteristic, complemented
677C43C2×#231811yescharacteristic, complemented, Sylow
678C25—431no—
679C25—431no—
680C22×D4—431no—
681C22×D4—431no—
682C22×D4—438no—
683C22×D4—431no—
684C22×D4—868no—
685C22×D4C22×D4311yescharacteristic
686C23×C4—431no—
687C23×C4—431no—
688C23×C4—431no—
689C23×C4—431no—
690C23×C4—431no—
691C23×C4—431no—
692C23×C4—431no—
693C23×C4—438no—
694C23×C4—438no—
695C23×C4—431no—
696C23×C4—431no—
697C23×C4—431no—
698C23×C4—431no—
699C23×C4—432no—
700C23×C4—432no—
701C23×C4—432no—
702C23×C4—432no—
703C23×C4—432no—
704C23×C4—432no—
705C23×C4—432no—
706C23×C4—868no—
707C23×C4—1724no—
708C23×C4—1724no—
709C23×C4—1724no—
710C23×C4—1724no—
711C23×C4C22×D4312yes—
712C23×C4C22×D4311yescharacteristic
713C23×C4C22×D4311yescharacteristic
714C4×D4—438no—
715C4×D4—438no—
716C4×D4—438no—
717C4×D4—438no—
718C4×D4—438no—
719C4×D4—438no—
720C4×D4—438no—
721C4×D4C4×D4318yescomplemented
722C2×C4⋊C4—431no—
723C2×C4⋊C4—431no—
724C2×C4⋊C4—431no—
725C2×C4⋊C4—438no—
726C2×C4⋊C4—432no—
727C2×C4⋊C4—432no—
728C2×C4⋊C4—432no—
729C2×C4⋊C4—432no—
730C2×C4⋊C4—432no—
731C2×C4⋊C4—432no—
732C2×C4⋊C4—1724no—
733C2×C4⋊C4—1724no—
734C2×C4⋊C4C22×D4312yes—
735C2×C4⋊C4C22×D4312yes—
736C2×C4⋊C4C22×D4311yescharacteristic
737C2×C22⋊C4—431no—
738C2×C22⋊C4—431no—
739C2×C22⋊C4—431no—
740C2×C22⋊C4—431no—
741C2×C22⋊C4—431no—
742C2×C22⋊C4—431no—
743C2×C22⋊C4—438no—
744C2×C22⋊C4—438no—
745C2×C22⋊C4—432no—
746C2×C22⋊C4—432no—
747C2×C22⋊C4—432no—
748C2×C22⋊C4—432no—
749C2×C22⋊C4—432no—
750C2×C22⋊C4—432no—
751C2×C22⋊C4—432no—
752C2×C22⋊C4—432no—
753C2×C22⋊C4—432no—
754C2×C22⋊C4—868no—
755C2×C22⋊C4—1724no—
756C2×C22⋊C4—1724no—
757C2×C22⋊C4C22×D4312yes—
758C2×C22⋊C4C22×D4312yes—
759C2×C22⋊C4C22×D4312yes—
760C2×C22⋊C4C22×D4311yescharacteristic
761C2×C22⋊C4C22×D4311yescharacteristic
762C2×C42—431no—
763C2×C42—431no—
764C2×C42—431no—
765C2×C42—438no—
766C2×C42—432no—
767C2×C42—432no—
768C2×C42—432no—
769C2×C42—1724no—
770C2×C42C22×D4312yes—
771C2×C42C22×D4311yescharacteristic
772#95—432no—
773#95—431no—
774#95—432no—
775#95—431no—
776#95—432no—
777#95—432no—
778#95—432no—
779#95—432no—
780#95—431no—
781#95—432no—
782#95—431no—
783#95—432no—
784#95—432no—
785#95—432no—
786#95—432no—
787#95—432no—
788#95—432no—
789#95—432no—
790#95—432no—
791#95—432no—
792#95—432no—
793#95—432no—
794#95—432no—
795#95C22×D4311yescharacteristic
796#95C22×D4311yescharacteristic
797#95C22×D4312yes—
798#95C22×D4311yescharacteristic
799#95C22×D4311yescharacteristic
800#95C22×D4312yes—
801#95C22×D4312yes—
802#95C22×D4312yes—
803#95C22×D4312yes—
804C24—431no—
805C24—434no—
806C24—438no—
807C24—431no—
808C24—434no—
809C24—431no—
810C24—864no—
811C24—862no—
812C24—862no—
813C24—862no—
814C24—864no—
815C24—864no—
816C24—862no—
817C24C23×D4311yescharacteristic
818C24C23×D4311yescharacteristic
819C2×D4—24no—
820C2×D4—434no—
821C2×D4—434no—
822C2×D4—434no—
823C2×D4—864no—
824C2×D4—8632no—
825C2×D4—864no—
826C2×D4—864no—
827C2×D4C2×C4×D4314yes—
828C22×C4—24no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—431no—
834C22×C4—431no—
835C22×C4—431no—
836C22×C4—431no—
837C22×C4—431no—
838C22×C4—434no—
839C22×C4—434no—
840C22×C4—434no—
841C22×C4—434no—
842C22×C4—434no—
843C22×C4—434no—
844C22×C4—434no—
845C22×C4—434no—
846C22×C4—434no—
847C22×C4—434no—
848C22×C4—434no—
849C22×C4—432no—
850C22×C4—432no—
851C22×C4—432no—
852C22×C4—432no—
853C22×C4—864no—
854C22×C4—862no—
855C22×C4—864no—
856C22×C4—864no—
857C22×C4—864no—
858C22×C4—862no—
859C22×C4—864no—
860C22×C4—864no—
861C22×C4—864no—
862C22×C4—864no—
863C22×C4—864no—
864C22×C4—864no—
865C22×C4—864no—
866C22×C4—864no—
867C22×C4—864no—
868C22×C4—864no—
869C22×C4—864no—
870C22×C4—864no—
871C22×C4—864no—
872C22×C4—864no—
873C22×C4—864no—
874C22×C4—1722no—
875C22×C4—1722no—
876C22×C4—1722no—
877C22×C4—1722no—
878C22×C4—1722no—
879C22×C4—1722no—
880C22×C4—1722no—
881C22×C4—1722no—
882C22×C4—17216no—
883C22×C4—17216no—
884C22×C4—17232no—
885C22×C4—1722no—
886C22×C4—1722no—
887C22×C4—1722no—
888C22×C4—1722no—
889C22×C4C2×C4×D4314yes—
890C22×C4C2×C4×D4314yescomplemented
891C22×C4C23×D4312yes—
892C22×C4C23×D4312yes—
893C22×C4C23×D4312yes—
894C22×C4C23×D4312yes—
895C22×C4C23×D4311yescharacteristic
896C22×C4C23×D4311yescharacteristic
897C22×C4C23×D4311yescharacteristic
898C22×C4C23×D4311yescharacteristic
899C22×C4C23×D4311yescharacteristic
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—434no—
903C4⋊C4—434no—
904C4⋊C4—434no—
905C4⋊C4—1722no—
906C4⋊C4—1722no—
907C4⋊C4—1722no—
908C4⋊C4—1722no—
909C4⋊C4—1722no—
910C4⋊C4—1722no—
911C4⋊C4C2×C4×D4314yescomplemented
912C22⋊C4—24no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—434no—
916C22⋊C4—434no—
917C22⋊C4—434no—
918C22⋊C4—434no—
919C22⋊C4—434no—
920C22⋊C4—434no—
921C22⋊C4—864no—
922C22⋊C4—864no—
923C22⋊C4—864no—
924C22⋊C4—1722no—
925C22⋊C4—1722no—
926C22⋊C4—1722no—
927C22⋊C4—1722no—
928C22⋊C4—1722no—
929C22⋊C4—1722no—
930C22⋊C4C2×C4×D4314yes—
931C22⋊C4C2×C4×D4314yescomplemented
932C42—42no—
933C42—434no—
934C42—434no—
935C42—434no—
936C42—1722no—
937C42—1722no—
938C42—1722no—
939C42C2×C4×D4314yescomplemented
940C23—22no—
941C23—21no—
942C23—21no—
943C23—22no—
944C23—21no—
945C23—22no—
946C23—21no—
947C23—432no—
948C23—434no—
949C23—434no—
950C23—432no—
951C23—432no—
952C23—4316no—
953C23—432no—
954C23—434no—
955C23—432no—
956C23—868no—
957C23—8616no—
958C23—868no—
959C23—8616no—
960C23—868no—
961C23—868no—
962C23—868no—
963C23—862no—
964C23—861no—
965C23—861no—
966C23—862no—
967C23—861no—
968C23—862no—
969C23—861no—
970C23—1728no—
971C23—1728no—
972C23C22×C4×D4312yes—
973C23C22×C4×D4312yes—
974C23#41×D4314yes—
975C23C24×D4311yescharacteristic
976D4—28no—
977D4—868no—
978D4—868no—
979D4—868no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—44no—
999C2×C4—44no—
1000C2×C4—48no—
1001C2×C4—432no—
1002C2×C4—432no—
1003C2×C4—432no—
1004C2×C4—432no—
1005C2×C4—432no—
1006C2×C4—868no—
1007C2×C4—868no—
1008C2×C4—868no—
1009C2×C4—868no—
1010C2×C4—868no—
1011C2×C4—862no—
1012C2×C4—862no—
1013C2×C4—861no—
1014C2×C4—862no—
1015C2×C4—862no—
1016C2×C4—861no—
1017C2×C4—862no—
1018C2×C4—862no—
1019C2×C4—862no—
1020C2×C4—862no—
1021C2×C4—862no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—862no—
1027C2×C4—862no—
1028C2×C4—862no—
1029C2×C4—1724no—
1030C2×C4—1724no—
1031C2×C4—1724no—
1032C2×C4—1724no—
1033C2×C4—1728no—
1034C2×C4—1728no—
1035C2×C4—1728no—
1036C2×C4—1728no—
1037C2×C4—1728no—
1038C2×C4—1728no—
1039C2×C4—1724no—
1040C2×C4—1724no—
1041C2×C4—1728no—
1042C2×C4C22×C4×D4312yes—
1043C2×C4C22×C4×D4312yes—
1044C2×C4C22×C4×D4312yes—
1045C2×C4C22×C4×D4312yes—
1046C2×C4C22×C4×D4312yes—
1047C22—22no—
1048C22—22no—
1049C22—24no—
1050C22—24no—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—42no—
1055C22—42no—
1056C22—434no—
1057C22—434no—
1058C22—438no—
1059C22—438no—
1060C22—434no—
1061C22—434no—
1062C22—8632no—
1063C22—862no—
1064C22—862no—
1065C22—864no—
1066C22—864no—
1067C22—862no—
1068C22—862no—
1069C22—862no—
1070C22—17216no—
1071C22—1722no—
1072C22—1722no—
1073C22#117×D4314yes—
1074C22C23×C4×D4311yescharacteristic
1075C22C2×#41×D4312yes—
1076C22H(5,𝔽2)×D4312yes—
1077C22H(5,𝔽2)×D4311yescharacteristic
1078C222−1+4×D4311yescharacteristic
1079C4—22no—
1080C4—22no—
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—862no—
1089C4—862no—
1090C4—862no—
1091C4—862no—
1092C4—862no—
1093C4—1722no—
1094C4—1722no—
1095C4—1722no—
1096C4—1722no—
1097C2—24no—
1098C2—42no—
1099C2—438no—
1100C2—864no—
1101C2—1722no—
1102C2C2×#117×D4311yescharacteristic
1103C2#518×D4311yescharacteristic
1104C2#520×D4311yescharacteristic
1105C2#538×D4312yes—
1106C2#539×D4312yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2318C2
socle, cosocleC23×C43C25
prime radicalC22×D4×D43C22
hypercenter#2318D43
hypocenterC43C2×#2318
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #19137231C2semidirect
3. #19137230C2semidirect
4. #19137229C2semidirect
5. #19137228C2semidirect
6. #19137227C2semidirect
7. #19137226C2semidirect
8. #19137225C2semidirect
9. #19137224C2semidirect
10. #19137223C2semidirect
11. #19137222C2semidirect
12. #19137221C2semidirect
13. #388×D43C2semidirect
14. #387×D43C2semidirect
16. #385×D43C2semidirect
17. #383×D43C2semidirect
18. #382×D43C2semidirect
19. #381×D43C2semidirect
20. #380×D43C2semidirect
21. C4×C22⋊C4×D43C2semidirect
22. C2×#95×D43C2semidirect
23. C43×#2318C2semidirect
35. C4×D4×D43C4semidirect
46. #14582793C22semidirect
47. #14582792C22semidirect
48. #14582791C22semidirect
49. #14582790C22semidirect
50. #14582789C22semidirect
51. #14582788C22semidirect
52. #14582787C22semidirect
53. #14582786C22semidirect
54. #14582785C22semidirect
55. #14582784C22semidirect
56. #14582783C22semidirect
57. #14582782C22semidirect
58. #14582781C22semidirect
59. #14582780C22semidirect
67. #14582774C22semidirect
68. #14582773C22semidirect
69. #14582773C22semidirect
70. #14582772C22semidirect
71. #14582771C22semidirect
72. #14582770C22semidirect
73. #14582770C22semidirect
74. #14582767C22semidirect
75. #14582766C22semidirect
76. #14582766C22semidirect
77. #14582766C22semidirect
78. #14582766C22semidirect
79. #14582765C22semidirect
80. #14582764C22semidirect
81. #14582763C22semidirect
82. #14582763C22semidirect
83. #14582763C22semidirect
84. #14582762C22semidirect
85. #14582761C22semidirect
86. #14582761C22semidirect
87. #14582761C22semidirect
88. #14582760C22semidirect
89. #14582759C22semidirect
90. #14582758C22semidirect
91. #14582758C22semidirect
92. #14582757C22semidirect
93. #14582756C22semidirect
94. C22⋊C4×Dic43C22semidirect
95. C4×(C2×D43)⋊C4C22semidirect
96. C4×C22⋊Dic43C22semidirect
97. #14582746C22semidirect
98. #14582746C22semidirect
99. C2×C43⋊#95C22semidirect
100. C2×C43⋊#95C22semidirect
110. #95×D43C22semidirect
111. #95×D43C22semidirect
112. #95×D43C22semidirect
114. C43×#388C22semidirect
115. C43×#387C22semidirect
117. C43×#385C22semidirect
118. C43×#383C22semidirect
119. C43×#382C22semidirect
120. C43×#381C22semidirect
121. C43×#380C22semidirect
122. C4×C22⋊C4×C43C22semidirect
123. C2×#95×C43C22semidirect
140. C22×C4×D43C2×C4semidirect
156. C4×D172C2×C4semidirect
157. D4×Dic43C2×C4semidirect
158. #13063287C2×C4semidirect
159. C4×C22⋊D43C2×C4semidirect
160. C4×C22⋊D43C2×C4semidirect
161. (C22⋊D43)⋊C4C2×C4semidirect
162. (C22⋊D43)⋊C4C2×C4semidirect
174. C4⋊C4×D43C2×C4semidirect
194. C22⋊C4×D43C2×C4semidirect
202. C42×D43C2×C4semidirect
230. C4×D4×C43C2×C4semidirect
273. C22×C4×C43C22×C4semidirect
293. C22×Dic43C22×C4semidirect
344. C2×C4×D43C22×C4semidirect
345. C2×C4×D43C22×C4semidirect
348. C4⋊C4×C43C22×C4semidirect
353. C22⋊C4×C43C22×C4semidirect
355. C42×C43C22×C4semidirect
360. C22⋊Dic43C22×C4semidirect
369. (C2×D43)⋊C4C22×C4semidirect
370. (C2×D43)⋊C4C22×C4semidirect
373. C4⋊Dic43C22×C4semidirect
378. Dic43⋊C4C22×C4semidirect
379. Dic43⋊C4C22×C4semidirect
383. C4×Dic43C22×C4semidirect
384. C4×Dic43C22×C4semidirect
385. C4×Dic43C22×C4semidirect
556. #2318D43direct (N × H)
576. D43#2318direct (N × H)
607. #388C2×D43semidirect
615. #387C2×D43semidirect
631. #385C2×D43semidirect
637. #383C2×D43semidirect
643. #382C2×D43semidirect
649. #381C2×D43semidirect
655. #380C2×D43semidirect
661. C4×C22⋊C4C2×D43semidirect
676. C2×#95C2×D43semidirect
677. C43C2×#2318semidirect
721. C4×D4C4×D43semidirect
890. C22×C4C2×C4×D43semidirect
911. C4⋊C4C2×C4×D43semidirect
931. C22⋊C4C2×C4×D43semidirect
939. C42C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
#191372312
#191372302
#191372292
#191372282
#191372272
#191372262
#191372252
#191372242
#191372232
#191372222
#191372212
#388×D432
#387×D432
#386×D432
#385×D432
#383×D432
#382×D432
#381×D432
#380×D432
C4×C22⋊C4×D432
C2×#95×D432
C43×#23182
C2×#231843