Finite Group Databasebeta

← C2×#19147627 #25977566

Subgroups — C2×#19147627 #25977566

Order 11008.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583627C211yesmaximal, characteristic, complemented
2C2×#14583621C211yesmaximal, characteristic
3#19147627C2116yesmaximal, direct product factor
4C2×#14583293C211yesmaximal, characteristic
5C2×#14583292C211yesmaximal, characteristic
6C2×#14583277C211yesmaximal, characteristic, complemented
7C2×#14583124C211yesmaximal, characteristic
8C2×#14583121C211yesmaximal, characteristic
9C2×#14583109C211yesmaximal, characteristic, complemented
10C2×#14583108C211yesmaximal, characteristic, complemented
11C2×#14583108C211yesmaximal, characteristic, complemented
12C2×#14583103C211yesmaximal, characteristic
13C2×#14583027C211yesmaximal, characteristic, complemented
14C2×#14583005C211yesmaximal, characteristic, complemented
15C2×#14582986C211yesmaximal, characteristic
16C2×C43×#441C211yesmaximal, characteristic, complemented
17C22×Dic172C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621885C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621873C2211yescharacteristic
24C22×#10621884C2211yescharacteristic
25#14583627—24no—
26#14583627C2218yescomplemented
27#14583621—24no—
28#14583621C2218yes—
29C2×#13063325C2211yescharacteristic
30C2×#13063323C2211yescharacteristic
31C2×#13063323C2211yescharacteristic
32C2×#13063323C2211yescharacteristic
33C2×#13063320—21no—
34C2×#13063319—21no—
35C2×#13063317—21no—
36C2×#13063315—21no—
37C2×#13063315—21no—
38C2×#13063314C2211yescharacteristic
39C2×#13063313C2211yescharacteristic
40C2×#13063303—21no—
41C2×C4×Dic86—21no—
42C2×C4×Dic86C2211yescharacteristic
43C2×#13063290C2211yescharacteristic
44C2×#13063290C2211yescharacteristic
45C2×#13063290C2211yescharacteristic
46C2×#13063287C2211yescharacteristic
47C2×#13063282—21no—
48#14583293C2218yes—
49#14583292C2218yes—
50#14583277C2218yescomplemented
51#14583124C2218yes—
52#14583121C2218yes—
53#14583109C2218yescomplemented
54#14583108C2218yescomplemented
55#14583108C2218yescomplemented
56#14583103C2218yes—
57#14583027C2218yescomplemented
58#14583005C2218yescomplemented
59#14582986C2218yes—
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×Q8×C43C2211yescharacteristic
72C43×#441C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86D411yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C4×D43—21no—
83C2×Dic172—24no—
84C2×Dic172—42no—
85C2×Dic172C2314yes—
86C2×Dic172C2314yes—
87C2×#10621885—42no—
88C2×#10621885—42no—
89C2×#10621885—42no—
90C2×#10621885C2314yes—
91C2×#10621885C2314yes—
92C2×#10621885C2314yes—
93C2×#10621873—24no—
94C2×#10621873—42no—
95C2×#10621873C2314yes—
96C2×#10621873C2314yes—
97C2×#10621884—42no—
98C2×#10621884C2314yes—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101#13063325—22no—
102#13063325C2314yes—
103#13063323—22no—
104#13063323—22no—
105#13063323—22no—
106#13063323C2314yes—
107#13063323C2314yes—
108#13063323C2314yes—
109#13063320—28no—
110#13063319—28no—
111#13063317—28no—
112#13063315—28no—
113#13063315—28no—
114#13063314—22no—
115#13063314C2314yes—
116#13063313—22no—
117#13063313C2314yes—
118#13063303—28no—
119C4×Dic86—28no—
120C4×Dic86D414yes—
121C4×Dic86C2314yes—
122#13063290—22no—
123#13063290—22no—
124#13063290—22no—
125#13063290C2314yes—
126#13063290C2314yes—
127#13063290C2314yes—
128#13063287—22no—
129#13063287C2314yes—
130#13063282—28no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43D411yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C2×Dic43⋊C4D411yescharacteristic
144C2×Dic43⋊C4D411yescharacteristic
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×C4×Dic43—21no—
151C2×C4×Dic43—21no—
152C2×C4×Dic43—21no—
153C2×C4×Dic43C2311yescharacteristic
154C2×C4×Dic43C2311yescharacteristic
155C4⋊(C43⋊C8)C2314yes—
156Dic43⋊C8C2314yes—
157Dic43⋊C8C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
160#13063248C2314yes—
161#13063245C2314yes—
162#13063235C2314yes—
163C8×Dic43C2314yes—
164C22×Q8×C43C2311yescharacteristic
165C22×Q8×C43C2311yescharacteristic
166C2×Q16×C43—24no—
167C2×Q16×C43C2314yes—
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C4×Q8×C43—22no—
171C4×Q8×C43—22no—
172C4×Q8×C43C2314yes—
173C4×Q8×C43C2314yes—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C42×C43—21no—
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#106×C43C2314yes—
182#103×C43C2314yes—
183#103×C43C2314yes—
184#97×C43C2314yes—
185C23×D43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43—22no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43C2412yes—
193C2×Q8×C43C2412yes—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C2×D172—21no—
209C2×D172—22no—
210C2×D172—22no—
211C2×D172C2412yes—
212C2×C4×D43—24no—
213C2×C4×D43—44no—
214C2×Dic86—24no—
215C2×Dic86—22no—
216C2×Dic86—22no—
217C2×Dic86—22no—
218C2×Dic86—22no—
219C2×Dic86—22no—
220C2×Dic86—22no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86C2×D414yes—
225C2×Dic86C2412yes—
226C2×Dic86C2412yes—
227C2×Dic86C2412yes—
228Q16×C43—28no—
229C2×C8×C43—22no—
230C2×C8×C43#4114yes—
231C2×C8×C43C2412yes—
232C2×C8×C43C2412yes—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C42×C43—24no—
240C42×C43—24no—
241C42×C43C2×D412yes—
242C42×C43C2412yes—
243#10621885—44no—
244#10621885—44no—
245#10621885—44no—
246#10621884—44no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43—24no—
254C4⋊Dic43C2×D414yes—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4C2×D414yes—
265Dic43⋊C4C2×D414yes—
266C4×Dic43—24no—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43C2×D412yes—
270C4×Dic43C2×D412yes—
271C4×Dic43C2412yes—
272C4×Dic43C2412yes—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8C2412yes—
276C2×C43⋊C8C2412yes—
277Dic172—28no—
278Dic172—44no—
279#10621873—28no—
280#10621873—44no—
281C23×C43C22×D411yescharacteristic
282C22×D43—22no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—22no—
289Q8×C43—22no—
290Q8×C43—42no—
291Q8×C43—42no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D412yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4112yes—
306C2×C4×C43H(5,𝔽2)12yes—
307C2×C4×C43C2511yescharacteristic
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43#13714yes—
318C2×Dic43C22×D412yes—
319C2×Dic43C22×D412yes—
320C2×Dic43C22×D412yes—
321C2×Dic43C22×D412yes—
322D172—22no—
323D172—22no—
324D172—42no—
325C4×D43—48no—
326Dic86—28no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86—22no—
331Dic86—22no—
332Dic86—22no—
333Dic86—42no—
334Dic86—42no—
335Dic86—42no—
336C8×C43—22no—
337C8×C43C2×#4114yes—
338C43⋊C8—22no—
339C43⋊C8—22no—
340C2×#3398—431nomaximal, Sylow
341C22×C43#55012yes—
342C22×C43C2×#13712yes—
343C22×C43#57812yes—
344C22×C43C23×D411yescharacteristic
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—84no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43#55012yes—
356C4×C43C22×#4111yescharacteristic
357C4×C43C2×H(5,𝔽2)11yescharacteristic
358Dic43—22no—
359Dic43—22no—
360Dic43—22no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43C2×#13714yes—
365C2×#557—431no—
366C2×#556—431no—
367#3398—4316no—
368C2×#497—431no—
369C2×#497—431no—
370C2×#494—431no—
371C2×#464—431no—
372C2×#464—431no—
373C2×#462—431no—
374C2×#462—431no—
375C2×#462—431no—
376C2×#461—431no—
377C2×#446—431no—
378C2×#441—431no—
379C2×#441D4311yescharacteristic, complemented
380C2×C4×SD16—431no—
381C2×C43#339814yescomplemented
382C2×C43C2×#55011yescharacteristic
383C2×C43C22×#13711yescharacteristic
384C2×C43C2×#57811yescharacteristic
385D43—82no—
386C22×Q16—431no—
387C22×Q16—431no—
388C22×Q16—431no—
389C22×Q16—431no—
390C22×Q16—431no—
391C22×Q16C2×D4311yescharacteristic
392C22×SD16—431no—
393C22×SD16—431no—
394C22×SD16—431no—
395#557—438no—
396#557—864no—
397#556—438no—
398#556—864no—
399C2×C4⋊Q8—431no—
400C2×C4⋊Q8—431no—
401C2×C4⋊Q8—431no—
402C2×C4⋊Q8—431no—
403C2×#126—861no—
404C2×#126—861no—
405C2×#125—861no—
406C2×#125—861no—
407C2×#125—861no—
408C2×#124—431no—
409C2×#124—431no—
410C2×C22⋊Q8—861no—
411C2×C4×Q8—431no—
412C2×C4×Q8—431no—
413C2×C4×Q8—431no—
414C2×C4×Q8—431no—
415C2×C4×Q8—861no—
416C2×C4×Q8C2×D4311yescharacteristic
417C2×C4×Q8C2×D4311yescharacteristic
418C2×C4×D4—431no—
419C2×#117—861no—
420#497—438no—
421#497—438no—
422#494—438no—
423#464—438no—
424#464—438no—
425#462—438no—
426#462—438no—
427#462—438no—
428#461—438no—
429#446—438no—
430#441—438no—
431#441C2×D4318yescomplemented
432C4×SD16—438no—
433C2×#106C2×D4311yescharacteristic
434C2×C4⋊C8—431no—
435C2×C4⋊C8—431no—
436C2×C4⋊C8—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#103C2×D4311yescharacteristic
441C2×#103C2×D4311yescharacteristic
442C2×#102—431no—
443C2×#97—431no—
444C2×#97C2×D4311yescharacteristic
445C2×C4×C8—431no—
446C43C2×#339811yescharacteristic, complemented, Sylow
447C22×Q8—431no—
448C22×Q8—431no—
449C22×Q8—431no—
450C22×Q8—431no—
451C22×Q8C22×D4311yescharacteristic
452C22×Q8C22×D4311yescharacteristic
453C22×D4—431no—
454C23×C4—861no—
455C2×Q16—24no—
456C2×Q16—434no—
457C2×Q16—434no—
458C2×Q16—434no—
459C2×Q16—434no—
460C2×Q16—434no—
461C2×Q16—864no—
462C2×Q16—1722no—
463C2×Q16—1722no—
464C2×Q16—1722no—
465C2×Q16—1722no—
466C2×Q16C22×D4314yes—
467C2×SD16—434no—
468C2×SD16—434no—
469C2×SD16—434no—
470C2×SD16—864no—
471C2×SD16—1722no—
472C2×SD16—1722no—
473C22×C8—431no—
474C22×C8—431no—
475C22×C8C22×D4311yescharacteristic
476C22×C8C22×D4311yescharacteristic
477C4⋊Q8—434no—
478C4⋊Q8—434no—
479C4⋊Q8—434no—
480C4⋊Q8—434no—
481C4⋊Q8—862no—
482C4⋊Q8—862no—
483C4⋊Q8—862no—
484C4⋊Q8—862no—
485#126—868no—
486#126—868no—
487#125—868no—
488#125—868no—
489#125—868no—
490#124—434no—
491#124—434no—
492#124—862no—
493#124—862no—
494C22⋊Q8—868no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×Q8—434no—
498C4×Q8—434no—
499C4×Q8—434no—
500C4×Q8—434no—
501C4×Q8—434no—
502C4×Q8—868no—
503C4×Q8—862no—
504C4×Q8—862no—
505C4×Q8—862no—
506C4×Q8C22×D4314yes—
507C4×Q8C22×D4314yes—
508C4×D4—434no—
509C4×D4—862no—
510#117—868no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C42—21no—
535C2×C42—21no—
536C2×C42—431no—
537C2×C42—431no—
538C2×C42—861no—
539C2×C42—861no—
540C2×C42—861no—
541C2×C42C22×D4311yescharacteristic
542#106C22×D4314yes—
543C4⋊C8—434no—
544C4⋊C8—434no—
545C4⋊C8—434no—
546#103—434no—
547#103—434no—
548#103—434no—
549#103C22×D4314yes—
550#103C22×D4314yes—
551#102—434no—
552#97—434no—
553#97C22×D4314yes—
554C4×C8—434no—
555C24—861no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—434no—
563C2×Q8—432no—
564C2×Q8—432no—
565C2×Q8—432no—
566C2×Q8—864no—
567C2×Q8—861no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—862no—
571C2×Q8—862no—
572C2×Q8—862no—
573C2×Q8—862no—
574C2×Q8—862no—
575C2×Q8—862no—
576C2×Q8C23×D4312yes—
577C2×Q8C23×D4312yes—
578C2×D4—432no—
579C2×D4—861no—
580C2×D4—862no—
581C2×D4—862no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—431no—
589C22×C4—431no—
590C22×C4—864no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—1724no—
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598Q16—28no—
599Q16—868no—
600Q16—1724no—
601Q16—1724no—
602Q16—1724no—
603Q16—1724no—
604SD16—868no—
605SD16—1724no—
606SD16—1724no—
607C2×C8—22no—
608C2×C8—432no—
609C2×C8—432no—
610C2×C8—862no—
611C2×C8—862no—
612C2×C8#1062189814yes—
613C2×C8C23×D4312yes—
614C2×C8C23×D4312yes—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—434no—
620C4⋊C4—434no—
621C4⋊C4—434no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4C23×D4312yes—
634C4⋊C4C23×D4312yes—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C22⋊C4—864no—
640C42—24no—
641C42—24no—
642C42—432no—
643C42—432no—
644C42—432no—
645C42—432no—
646C42—864no—
647C42—864no—
648C42—864no—
649C42D4×D4312yes—
650C42C23×D4312yes—
651C23—862no—
652C23—1722no—
653C23—1722no—
654C23—1722no—
655C23C2×D4×D4311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—868no—
663Q8—862no—
664Q8—862no—
665Q8—862no—
666Q8—862no—
667Q8—862no—
668Q8—862no—
669Q8—1722no—
670Q8—1722no—
671Q8—1722no—
672D4—862no—
673D4—862no—
674D4—1722no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—434no—
686C2×C4—432no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—432no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—1728no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4C2×D4×D4312yes—
701C2×C4C2×D4×D4312yes—
702C2×C4C2×D4×D4311yescharacteristic
703C2×C4C2×#1062189812yes—
704C2×C4#1306337112yes—
705C2×C4C24×D4311yescharacteristic
706C8—22no—
707C8—862no—
708C8—862no—
709C8C2×#1062189814yes—
710C22—3444no—
711C22—1722no—
712C22—1722no—
713C22—1722no—
714C22#1458357012yes—
715C22#137×D4312yes—
716C22#1458371512yes—
717C22C22×D4×D4311yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—434no—
725C4—862no—
726C4—862no—
727C4—862no—
728C4—1722no—
729C4—1722no—
730C4—1722no—
731C4#1458357012yes—
732C4C22×#1062189811yescharacteristic
733C4C2×#1306337111yescharacteristic
734C2—3442no—
735C2#1914762714yesdirect product factor
736C2C2×#1458357011yescharacteristic
737C2C2×#137×D4311yescharacteristic
738C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#441C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC2×#441D43
hypocenterC43C2×#3398
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×#14583627C2semidirect
3. #19147627C2direct (N × H)
6. C2×#14583277C2semidirect
9. C2×#14583109C2semidirect
10. C2×#14583108C2semidirect
11. C2×#14583108C2semidirect
13. C2×#14583027C2semidirect
14. C2×#14583005C2semidirect
16. C2×C43×#441C2semidirect
26. #14583627C22semidirect
50. #14583277C22semidirect
53. #14583109C22semidirect
54. #14583108C22semidirect
55. #14583108C22semidirect
57. #14583027C22semidirect
58. #14583005C22semidirect
72. C43×#441C22semidirect
379. C2×#441D43semidirect
381. C2×C43#3398semidirect
431. #441C2×D43semidirect
446. C43C2×#3398semidirect
735. C2#19147627direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836272
C2×#145836212
#191476272
C2×#145832932
C2×#145832922
C2×#145832772
C2×#145831242
C2×#145831212
C2×#145831092
C2×#145831082
C2×#145831032
C2×#145830272
C2×#145830052
C2×#145829862
C2×C43×#4412
C2×#339843