Finite Group Databasebeta

← C2×#10595132 #11901151

Subgroups — C2×#10595132 #11901151

Order 1152.

3493 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3805C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64148C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C2×C3×#938C211yesmaximal, characteristic, complemented
6C2×#63982C211yesmaximal, characteristic, complemented
7C2×#63971C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9C2×#63970C211yesmaximal, characteristic, complemented
10C2×#63964C211yesmaximal, characteristic, complemented
11C2×#63958C211yesmaximal, characteristic, complemented
12#10595132C2116yesmaximal, direct product factor
13C2×#63906C211yesmaximal, characteristic, complemented
14C2×#63899C211yesmaximal, characteristic, complemented
15C2×#63895C211yesmaximal, characteristic, complemented
16C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
17C2×#5608—31nomaximal
18C2×#5597—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic
28C22×C3×C4×D3C2211yescharacteristic
29C22×#627C2211yescharacteristic
30C22×#627C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#625C2211yescharacteristic
34C22×#624C2211yescharacteristic
35C2×#3805—28no—
36C2×#3805C2218yescomplemented
37C2×#3804—28no—
38C2×#3804C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic
40C22×D3×Dic3C2211yescharacteristic
41C22×D3×Dic3C2211yescharacteristic
42C2×#3757C2211yescharacteristic
43#64148C2218yescomplemented
44C2×#3752C2211yescharacteristic
45C2×#3750C2211yescharacteristic
46C2×C3×#217C2211yescharacteristic
47C2×C3×#217C2211yescharacteristic
48C2×C3×#217C2211yescharacteristic
49C3×#939C2218yescomplemented
50C3×#938C2218yescomplemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic
52C2×C3×C4⋊Dic3C2211yescharacteristic
53C2×C3×Dic3⋊C4C2211yescharacteristic
54#63982C2218yescomplemented
55#63971C2218yescomplemented
56#63971C2218yescomplemented
57#63970C2218yescomplemented
58C2×#3724C2211yescharacteristic
59C2×#3724C2211yescharacteristic
60C2×Dic3⋊Dic3C2211yescharacteristic
61C2×Dic3⋊Dic3C2211yescharacteristic
62C2×Dic3⋊Dic3C2211yescharacteristic
63#63964C2218yescomplemented
64C2×#3722C2211yescharacteristic
65C2×(C2×D3)⋊Dic3C2211yescharacteristic
66#63958C2218yescomplemented
67#63906C2218yescomplemented
68#63899C2218yescomplemented
69#63895C2218yescomplemented
70D3×Dic3⋊C4C2218yescomplemented
71C22×#237—31no—
72C22×#237—31no—
73C22×#237—31no—
74C22×#235—31no—
75C2×C3×#121—31no—
76C2×C3×#121—31no—
77C2×#939—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#939—31no—
82C2×#939—61no—
83C2×#939D311yescharacteristic, complemented
84C2×#938—31no—
85C2×#938—31no—
86C2×#938D311yescharacteristic, complemented
87C2×#930—31no—
88C2×#924—31no—
89C22×Dic3⋊C4—31no—
90#5608—316no—
91#5597—316no—
92C2×#897—31no—
93C2×#896—31no—
94C2×#896—31no—
95C2×D3×C4⋊C4—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#884—31no—
99C2×#884—31no—
100C2×#878—31no—
101C2×#878—31no—
102C2×#878—31no—
103C2×#878—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C2×C32×D4—42no—
110C2×C32×D4C2314yes—
111C22×C32×C4C2311yescharacteristic
112C2×#638—24no—
113C2×#638—42no—
114C2×#638C2314yes—
115C2×#638C2314yes—
116C22×C3⋊Dic3—24no—
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2314yes—
119C22×C3⋊Dic3C2311yescharacteristic
120C22×C3⋊Dic3C2311yescharacteristic
121C2×C3×#67—24no—
122C2×C3×#67—24no—
123C2×C3×#67—24no—
124C2×C3×#67—42no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C22×C3×Dic3—24no—
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2314yes—
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C2×C3×C4×D3—42no—
138C2×C3×C4×D3C2314yes—
139C2×#627—24no—
140C2×#627—24no—
141C2×#627C2314yes—
142C2×#627C2314yes—
143C2×#626—24no—
144C2×#626—42no—
145C2×#626C2314yes—
146C2×#626C2314yes—
147C2×#625—24no—
148C2×#625C2314yes—
149C2×#624—24no—
150C2×#624C2314yes—
151#3805—232no—
152#3804—232no—
153C2×D3×Dic3—24no—
154C2×D3×Dic3—42no—
155C2×D3×Dic3D418yescomplemented
156C2×D3×Dic3C2314yes—
157C2×D3×Dic3C2314yes—
158C2×D3×Dic3C2314yes—
159#3757C2314yes—
160#3752C2314yes—
161#3750C2314yes—
162C3×#217C2314yes—
163C3×#217C2314yes—
164C3×#217C2314yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×C4⋊Dic3C2314yes—
167C3×Dic3⋊C4C2314yes—
168#3724C2314yes—
169#3724C2314yes—
170Dic3⋊Dic3C2314yes—
171Dic3⋊Dic3C2314yes—
172Dic3⋊Dic3C2314yes—
173#3722C2314yes—
174(C2×D3)⋊Dic3C2314yes—
175C2×#537—91noSylow
176C22×C3×D4—21no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4C2×D311yescharacteristic
182C22×C3×D4C2×D311yescharacteristic
183C23×C3×C4—31no—
184C23×C3×C4—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—61no—
194C22×#67—61no—
195C22×#67C2×D311yescharacteristic
196C22×#67C2×D311yescharacteristic
197C22×#67C2×D311yescharacteristic
198C22×#67C2×D311yescharacteristic
199C23×Dic3—31no—
200C23×Dic3—31no—
201C23×Dic3—31no—
202C23×Dic3—31no—
203C23×Dic3—31no—
204C23×Dic3—61no—
205C23×Dic3C2×D311yescharacteristic
206C2×#237—38no—
207C2×#237—38no—
208C2×#237—38no—
209C2×#237—68no—
210C2×#237—68no—
211C2×#237—68no—
212C2×#235—38no—
213C2×#235—68no—
214C22×D12—31no—
215C22×D12—31no—
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3C2×D311yescharacteristic
222C22×Dic6—31no—
223C22×Dic6—31no—
224C22×Dic6—31no—
225C22×Dic6—31no—
226C3×#121—38no—
227C3×#121—38no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×#217—31no—
235C2×#217—31no—
236C2×#217—31no—
237C2×#217—61no—
238C2×#217C2×D311yescharacteristic
239C2×#217C2×D311yescharacteristic
240C2×#217C2×D311yescharacteristic
241#939—38no—
242#939—38no—
243#939—38no—
244#939—38no—
245#939—38no—
246#939—68no—
247#939C2×D318yescomplemented
248#938—38no—
249#938—38no—
250#938C2×D318yescomplemented
251#930—38no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—61no—
258C2×(C2×D3)⋊C4C2×D311yescharacteristic
259C2×C4⋊Dic3—31no—
260C2×C4⋊Dic3—31no—
261C2×C4⋊Dic3—31no—
262C2×C4⋊Dic3C2×D311yescharacteristic
263#924—38no—
264C2×Dic3⋊C4—31no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—31no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4—31no—
273C2×Dic3⋊C4—38no—
274C2×Dic3⋊C4—61no—
275C2×Dic3⋊C4C2×D311yescharacteristic
276#897—38no—
277#896—38no—
278#896—38no—
279D3×C4⋊C4—38no—
280#884—38no—
281#884—38no—
282#884—38no—
283#884—38no—
284#878—38no—
285#878—38no—
286#878—38no—
287#878—38no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32—22no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32C2412yes—
295C23×C32C2412yes—
296C23×C32C2411yescharacteristic
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3C2412yes—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3C2×D414yes—
307C22×C3×D3C2412yes—
308C22×C3×D3C2412yes—
309C32×D4—44no—
310C2×C32×C4—22no—
311C2×C32×C4C2412yes—
312#638—28no—
313#638—44no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3—28no—
317C2×C3⋊Dic3C2×D414yes—
318C2×C3⋊Dic3C2412yes—
319C2×C3⋊Dic3C2412yes—
320C2×C3⋊Dic3C2412yes—
321C3×#67—28no—
322C3×#67—28no—
323C3×#67—28no—
324C3×#67—44no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3—28no—
331C2×C3×Dic3C2×D414yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C3×C4×D3—44no—
339#627—28no—
340#627—28no—
341#626—28no—
342#626—44no—
343#625—28no—
344#624—28no—
345D3×Dic3—28no—
346D3×Dic3—44no—
347D3×Dic3C2×D4116yescomplemented
348C22×#41—91no—
349C22×#41—91no—
350#537—916no—
351C2×C22⋊Q8—91no—
352C2×C22⋊Q8—91no—
353C2×C22⋊Q8—91no—
354C2×C22⋊Q8—91no—
355C2×#121—31no—
356C2×#121—31no—
357C2×#121—91no—
358C2×#121—91no—
359C2×#121—91no—
360C2×#121—91no—
361C2×#121—91no—
362C2×#121—91no—
363C22×C4⋊C4—91no—
364C24×C3—21no—
365C24×C3—21no—
366C24×C3—31no—
367C24×C3—31no—
368C24×C3C22×D311yescharacteristic
369C24×C3C22×D311yescharacteristic
370C24×C3C22×D311yescharacteristic
371C24×C3C22×D311yescharacteristic
372C23×D3—31no—
373C23×D3—31no—
374C23×D3—61no—
375C23×D3C22×D311yescharacteristic
376C23×D3C22×D311yescharacteristic
377C2×C3×D4—24no—
378C2×C3×D4—34no—
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—42no—
383C2×C3×D4—42no—
384C2×C3×D4—44no—
385C2×C3×D4—64no—
386C2×C3×D4—64no—
387C2×C3×D4—64no—
388C2×C3×D4—122no—
389C2×C3×D4C22×D314yes—
390C2×C3×D4C22×D314yes—
391C22×C3×C4—21no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—34no—
399C22×C3×C4—34no—
400C22×C3×C4—64no—
401C22×C3×C4—122no—
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C2×#67—24no—
405C2×#67—24no—
406C2×#67—24no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—42no—
416C2×#67—64no—
417C2×#67—64no—
418C2×#67—64no—
419C2×#67—64no—
420C2×#67—64no—
421C2×#67—64no—
422C2×#67—64no—
423C2×#67—124no—
424C2×#67—122no—
425C2×#67—122no—
426C2×#67—122no—
427C2×#67—124no—
428C2×#67C22×D314yes—
429C2×#67C22×D314yes—
430C2×#67C22×D314yes—
431C2×#67C22×D314yes—
432C22×Dic3—24no—
433C22×Dic3—31no—
434C22×Dic3—31no—
435C22×Dic3—38no—
436C22×Dic3—34no—
437C22×Dic3—34no—
438C22×Dic3—34no—
439C22×Dic3—31no—
440C22×Dic3—31no—
441C22×Dic3—31no—
442C22×Dic3—31no—
443C22×Dic3—34no—
444C22×Dic3—34no—
445C22×Dic3—61no—
446C22×Dic3—61no—
447C22×Dic3—61no—
448C22×Dic3—64no—
449C22×Dic3—64no—
450C22×Dic3—64no—
451C22×Dic3—64no—
452C22×Dic3—124no—
453C22×Dic3—122no—
454C22×Dic3C22×D314yes—
455C22×Dic3C22×D311yescharacteristic
456C22×Dic3C22×D311yescharacteristic
457C22×Dic3C22×D311yescharacteristic
458C22×Dic3C22×D311yescharacteristic
459C22×Dic3C22×D311yescharacteristic
460C22×Dic3C22×D311yescharacteristic
461#237—632no—
462#237—632no—
463#237—632no—
464#235—632no—
465C2×D12—34no—
466C2×D12—34no—
467C2×D12—64no—
468C2×D12—122no—
469C2×C4×D3—38no—
470C2×C4×D3—34no—
471C2×C4×D3—34no—
472C2×C4×D3—34no—
473C2×C4×D3—34no—
474C2×C4×D3—34no—
475C2×C4×D3—42no—
476C2×C4×D3—64no—
477C2×C4×D3—64no—
478C2×C4×D3—64no—
479C2×C4×D3—122no—
480C2×C4×D3C22×D314yes—
481C2×Dic6—34no—
482C2×Dic6—34no—
483C2×Dic6—34no—
484C2×Dic6—34no—
485C2×Dic6—64no—
486C2×Dic6—64no—
487C2×Dic6—64no—
488C2×Dic6—64no—
489C3×C4⋊C4—34no—
490C3×C4⋊C4—34no—
491C3×C22⋊C4—34no—
492C3×C22⋊C4—34no—
493C3×C22⋊C4—34no—
494C3×C22⋊C4—34no—
495#217—34no—
496#217—34no—
497#217—34no—
498#217—64no—
499#217C22×D314yes—
500#217C22×D314yes—
501#217C22×D314yes—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—64no—
508(C2×D3)⋊C4C22×D314yes—
509C4⋊Dic3—34no—
510C4⋊Dic3—34no—
511C4⋊Dic3—34no—
512C4⋊Dic3C22×D314yes—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—64no—
523Dic3⋊C4C22×D314yes—
524C22×C32—22no—
525C22×C32—22no—
526C22×C32—22no—
527C22×C32—22no—
528C22×C32—22no—
529C22×C32—22no—
530C22×C32—44no—
531C22×C32—44no—
532C22×C32C22×D412yes—
533C22×C32H(5,𝔽2)12yes—
534C22×C322−1+412yes—
535C22×C32C2511yescharacteristic
536C2×C3⋊D3—22no—
537C2×C3⋊D3—22no—
538C2×C3⋊D3—22no—
539C2×C3⋊D3—44no—
540C2×C3×D3—28no—
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—44no—
547C2×C3×D3C22×D414yes—
548C32×C4—22no—
549C3⋊Dic3—22no—
550C3⋊Dic3—22no—
551C3⋊Dic3C22×D414yes—
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3C22×D414yes—
558C2×#41—98no—
559C2×#41—98no—
560C2×#41—188no—
561C2×#41—188no—
562C22×Q8—91no—
563C22×Q8—91no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—31no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C22×D4—91no—
573C22×D4D3211yescharacteristic
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—91no—
577C23×C4—91no—
578C23×C4—91no—
579C23×C4—91no—
580C23×C4—91no—
581C22⋊Q8—98no—
582C22⋊Q8—98no—
583C22⋊Q8—98no—
584C22⋊Q8—98no—
585#121—38no—
586#121—38no—
587#121—98no—
588#121—98no—
589#121—98no—
590#121—98no—
591#121—98no—
592#121—98no—
593C2×C4⋊C4—31no—
594C2×C4⋊C4—31no—
595C2×C4⋊C4—98no—
596C2×C4⋊C4—91no—
597C2×C4⋊C4—91no—
598C2×C4⋊C4—91no—
599C2×C4⋊C4—91no—
600C2×C4⋊C4—91no—
601C2×C4⋊C4—91no—
602C2×C22⋊C4—31no—
603C2×C22⋊C4—31no—
604C2×C22⋊C4—31no—
605C2×C22⋊C4—31no—
606C2×C22⋊C4—91no—
607C2×C22⋊C4—91no—
608C2×C22⋊C4—91no—
609C2×C22⋊C4—91no—
610C23×C3—24no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—22no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—22no—
625C23×C3—21no—
626C23×C3—34no—
627C23×C3—32no—
628C23×C3—32no—
629C23×C3—42no—
630C23×C3—42no—
631C23×C3—42no—
632C23×C3—42no—
633C23×C3—42no—
634C23×C3—62no—
635C23×C3—62no—
636C23×C3—62no—
637C23×C3—62no—
638C23×C3—62no—
639C23×C3C23×D312yes—
640C23×C3C23×D312yes—
641C23×C3C23×D312yes—
642C23×C3C23×D312yes—
643C23×C3C23×D311yescharacteristic
644C23×C3C23×D311yescharacteristic
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—32no—
651C22×D3—32no—
652C22×D3—62no—
653C22×D3—62no—
654C22×D3—62no—
655C22×D3—62no—
656C22×D3—62no—
657C22×D3—62no—
658C22×D3—62no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3D3×D414yes—
663C22×D3C23×D312yes—
664C22×D3C23×D312yes—
665C3×D4—44no—
666C3×D4—44no—
667C3×D4—48no—
668C3×D4—68no—
669C3×D4—68no—
670C3×D4—68no—
671C3×D4—124no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—34no—
676C2×C3×C4—32no—
677C2×C3×C4—32no—
678C2×C3×C4—32no—
679C2×C3×C4—32no—
680C2×C3×C4—32no—
681C2×C3×C4—32no—
682C2×C3×C4—42no—
683C2×C3×C4—68no—
684C2×C3×C4—62no—
685C2×C3×C4—62no—
686C2×C3×C4—62no—
687C2×C3×C4—62no—
688C2×C3×C4—62no—
689C2×C3×C4—124no—
690C2×C3×C4C23×D312yes—
691C2×C3×C4C23×D312yes—
692#67—28no—
693#67—28no—
694#67—28no—
695#67—44no—
696#67—68no—
697#67—68no—
698#67—68no—
699#67—68no—
700#67—68no—
701#67—128no—
702#67—124no—
703#67—124no—
704#67—124no—
705#67—128no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—28no—
712C2×Dic3—34no—
713C2×Dic3—34no—
714C2×Dic3—32no—
715C2×Dic3—32no—
716C2×Dic3—316no—
717C2×Dic3—32no—
718C2×Dic3—32no—
719C2×Dic3—32no—
720C2×Dic3—32no—
721C2×Dic3—64no—
722C2×Dic3—62no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—68no—
726C2×Dic3—68no—
727C2×Dic3—68no—
728C2×Dic3—62no—
729C2×Dic3—62no—
730C2×Dic3—62no—
731C2×Dic3—62no—
732C2×Dic3—128no—
733C2×Dic3—122no—
734C2×Dic3—122no—
735C2×Dic3—124no—
736C2×Dic3D3×D414yes—
737C2×Dic3C23×D312yes—
738C2×Dic3C23×D312yes—
739C2×Dic3C23×D312yes—
740C2×Dic3C23×D312yes—
741C2×Dic3C23×D312yes—
742C2×Dic3C23×D312yes—
743D12—68no—
744D12—124no—
745C4×D3—316no—
746C4×D3—44no—
747C4×D3—68no—
748C4×D3—68no—
749C4×D3—68no—
750C4×D3—124no—
751Dic6—68no—
752Dic6—68no—
753Dic6—68no—
754Dic6—68no—
755C2×C32—42no—
756C2×C32—42no—
757C2×C32#53714yescomplemented
758C2×C32C23×D411yescharacteristic
759C2×C32C2×H(5,𝔽2)11yescharacteristic
760C2×C32C2×2−1+411yescharacteristic
761C3⋊D3—42no—
762C3×D3—24no—
763C3×D3—42no—
764C24—31no—
765C24—31no—
766C24—91no—
767C24C2×D3211yescharacteristic
768C24C2×D3211yescharacteristic
769#41—1832no—
770#41—1832no—
771C2×Q8—94no—
772C2×Q8—94no—
773C2×Q8—184no—
774C2×Q8—184no—
775C2×D4—34no—
776C2×D4—34no—
777C2×D4—34no—
778C2×D4—34no—
779C2×D4—42no—
780C2×D4—64no—
781C2×D4—64no—
782C2×D4—64no—
783C2×D4—94no—
784C2×D4—94no—
785C2×D4—94no—
786C2×D4—94no—
787C2×D4—94no—
788C2×D4—122no—
789C2×D4—184no—
790C2×D4—184no—
791C2×D4—184no—
792C2×D4—362no—
793C2×D4—362no—
794C2×D4C2×D3214yes—
795C22×C4—31no—
796C22×C4—34no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—34no—
803C22×C4—64no—
804C22×C4—94no—
805C22×C4—94no—
806C22×C4—98no—
807C22×C4—94no—
808C22×C4—94no—
809C22×C4—91no—
810C22×C4—94no—
811C22×C4—91no—
812C22×C4—91no—
813C22×C4—122no—
814C22×C4—184no—
815C22×C4—184no—
816C22×C4—184no—
817C22×C4—362no—
818C22×C4C2×D3211yescharacteristic
819C4⋊C4—34no—
820C4⋊C4—34no—
821C4⋊C4—94no—
822C4⋊C4—94no—
823C4⋊C4—94no—
824C4⋊C4—94no—
825C4⋊C4—94no—
826C4⋊C4—94no—
827C22⋊C4—34no—
828C22⋊C4—34no—
829C22⋊C4—34no—
830C22⋊C4—34no—
831C22⋊C4—94no—
832C22⋊C4—94no—
833C22⋊C4—94no—
834C22⋊C4—94no—
835C22×C3—24no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—22no—
849C22×C3—22no—
850C22×C3—22no—
851C22×C3—21no—
852C22×C3—34no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—48no—
859C22×C3—44no—
860C22×C3—44no—
861C22×C3—44no—
862C22×C3—44no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—68no—
866C22×C3—62no—
867C22×C3—62no—
868C22×C3—62no—
869C22×C3—84no—
870C22×C3—124no—
871C22×C3C2×D3×D412yes—
872C22×C3C2×D3×D412yes—
873C22×C3#100412yes—
874C22×C3#100412yes—
875C22×C3#101012yes—
876C22×C3#101012yes—
877C22×C3C24×D311yescharacteristic
878C22×C3C24×D311yescharacteristic
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—28no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—44no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—122no—
893C2×D3—122no—
894C2×D3—122no—
895C2×D3—124no—
896C2×D3—124no—
897C2×D3—244no—
898C2×D3C2×D3×D414yes—
899C3×C4—22no—
900C3×C4—22no—
901C3×C4—34no—
902C3×C4—42no—
903C3×C4—62no—
904C3×C4—62no—
905C3×C4—62no—
906C3×C4—62no—
907C3×C4—62no—
908Dic3—22no—
909Dic3—22no—
910Dic3—22no—
911Dic3—22no—
912Dic3—22no—
913Dic3—34no—
914Dic3—34no—
915Dic3—64no—
916Dic3—62no—
917Dic3—62no—
918Dic3—62no—
919Dic3—62no—
920Dic3—122no—
921Dic3—122no—
922Dic3C2×D3×D414yes—
923C32C2×#53711yescharacteristic, complemented, Sylow
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—34no—
931C23—32no—
932C23—32no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—92no—
939C23—182no—
940C23—182no—
941C23—182no—
942C23C22×D3212yes—
943C23C22×D3212yes—
944C23C22×D3211yescharacteristic
945Q8—188no—
946Q8—188no—
947D4—44no—
948D4—68no—
949D4—68no—
950D4—68no—
951D4—124no—
952D4—188no—
953D4—188no—
954D4—188no—
955D4—364no—
956D4—364no—
957C2×C4—22no—
958C2×C4—34no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—32no—
962C2×C4—32no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—68no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—916no—
972C2×C4—94no—
973C2×C4—92no—
974C2×C4—92no—
975C2×C4—92no—
976C2×C4—124no—
977C2×C4—188no—
978C2×C4—188no—
979C2×C4—188no—
980C2×C4—182no—
981C2×C4—182no—
982C2×C4—364no—
983C2×C4C22×D3212yes—
984C2×C3—24no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—44no—
989C2×C3—42no—
990C2×C3—42no—
991C2×C3—42no—
992C2×C3—42no—
993C2×C3—64no—
994C2×C3—82no—
995C2×C3—122no—
996C2×C3#559714yescomplemented
997C2×C3#560814yescomplemented
998C2×C3C22×D3×D411yescharacteristic
999C2×C3C22×D3×D411yescharacteristic
1000C2×C3C2×#100411yescharacteristic
1001C2×C3C2×#100411yescharacteristic
1002C2×C3C2×#101011yescharacteristic
1003C2×C3C2×#101011yescharacteristic
1004D3—24no—
1005D3—42no—
1006D3—122no—
1007D3—122no—
1008D3—242no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—34no—
1016C22—44no—
1017C22—44no—
1018C22—68no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—124no—
1025C22—182no—
1026C22—182no—
1027C22—182no—
1028C22—364no—
1029C22#6430912yes—
1030C22D32×D412yes—
1031C22#6433012yes—
1032C22C23×D3211yescharacteristic
1033C4—22no—
1034C4—34no—
1035C4—62no—
1036C4—62no—
1037C4—62no—
1038C4—62no—
1039C4—62no—
1040C4—94no—
1041C4—182no—
1042C4—182no—
1043C3—21no—
1044C3C2×#559711yescharacteristic, complemented
1045C3C2×#560811yescharacteristic, complemented
1046C2—42no—
1047C2—42no—
1048C2—64no—
1049C2—122no—
1050C2—362no—
1051C2#1059513214yesdirect product factor
1052C2C2×#6430911yescharacteristic
1053C2C2×D32×D411yescharacteristic
1054C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3805C2semidirect
2. C22×#3804C2semidirect
3. C2×#64148C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×#938C2semidirect
6. C2×#63982C2semidirect
7. C2×#63971C2semidirect
8. C2×#63971C2semidirect
9. C2×#63970C2semidirect
10. C2×#63964C2semidirect
11. C2×#63958C2semidirect
12. #10595132C2direct (N × H)
13. C2×#63906C2semidirect
14. C2×#63899C2semidirect
15. C2×#63895C2semidirect
16. C2×D3×Dic3⋊C4C2semidirect
36. C2×#3805C22semidirect
38. C2×#3804C22semidirect
43. #64148C22semidirect
49. C3×#939C22semidirect
50. C3×#938C22semidirect
54. #63982C22semidirect
55. #63971C22semidirect
56. #63971C22semidirect
57. #63970C22semidirect
63. #63964C22semidirect
66. #63958C22semidirect
67. #63906C22semidirect
68. #63899C22semidirect
69. #63895C22semidirect
70. D3×Dic3⋊C4C22semidirect
83. C2×#939D3semidirect
86. C2×#938D3semidirect
155. C2×D3×Dic3D4semidirect
247. #939C2×D3semidirect
250. #938C2×D3semidirect
347. D3×Dic3C2×D4semidirect
757. C2×C32#537semidirect
923. C32C2×#537semidirect
996. C2×C3#5597semidirect
997. C2×C3#5608semidirect
1044. C3C2×#5597semidirect
1045. C3C2×#5608semidirect
1051. C2#10595132direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C22×#38042
C2×#641482
C2×C3×#9392
C2×C3×#9382
C2×#639822
C2×#639712
C2×#639702
C2×#639642
C2×#639582
#105951322
C2×#639062
C2×#638992
C2×#638952
C2×D3×Dic3⋊C42
C2×#56083
C2×#55973