Finite Group Databasebeta

← #11909920

Subgroups — #11909920

Order 1152.

2133 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×#5567C211yesmaximal, characteristic, complemented
4#10595361C212yesmaximal, complemented
5#10595349C212yesmaximal, complemented
6#10594474C214yesmaximal, complemented
7#10594471C214yesmaximal, complemented
8#10594357C212yesmaximal, complemented
9#10594337C212yesmaximal, complemented
10#10593943C212yesmaximal
11#10593942C212yesmaximal, complemented
12#10593904C211yesmaximal, characteristic, complemented
13#10593882C212yesmaximal, complemented
14#10593875C211yesmaximal, characteristic
15#10593866C211yesmaximal, characteristic, complemented
16#10593864C211yesmaximal, characteristic, complemented
17#10593853C212yesmaximal, complemented
18#87025—31nomaximal
19#86993—31nomaximal
20C2×Q8×C3⋊D3C2211yescharacteristic
21C2×D3×Dic6C2212yes—
22C32×C4×Q8C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4⋊C4×C3⋊D3C2212yes—
26#64096C2211yescharacteristic
27#64096C2212yes—
28C42×C3⋊D3C2211yescharacteristic
29C42×C3⋊D3C2212yes—
30C4×#634C2212yes—
31C4×#634C2211yescharacteristic
32C3×#946C2212yes—
33C3×#944C2212yes—
34C3×#898C2214yes—
35C3×#892C2212yes—
36C3×#889C2214yes—
37C3×#887C2212yes—
38C3×#875C2212yes—
39C3×C4×D12C2211yescharacteristic
40C3×#870C2212yes—
41C3×#869C2211yescharacteristic
42C3×#869C2211yescharacteristic
43C3×C4×Dic6C2212yes—
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2212yes—
46#63919C2212yes—
47C4×#627C2214yes—
48#63916C2211yescharacteristic
49C4×#626C2212yes—
50#63899C2214yes—
51#63898C2212yes—
52#63896C2214yes—
53#63881C2214yes—
54#63878C2214yes—
55#63877C2214yes—
56#63874C2214yes—
57#63873C2212yes—
58#63872C2211yescharacteristic
59#63872C2212yes—
60#63871C2212yes—
61#63871C2212yes—
62#63871C2211yescharacteristic
63#63870C2214yes—
64#63869C2212yes—
65#63867C2214yes—
66#63865C2214yes—
67#63863C2211yescharacteristic
68#63862C2214yes—
69#63862C2212yes—
70#63861C2214yes—
71#63859C2214yes—
72#63856C2212yes—
73#63855C2212yes—
74#63853C2214yes—
75#63853C2212yes—
76#63849C2212yes—
77#63847C2214yes—
78#63845C2214yes—
79#63844C2212yes—
80#63843C2212yes—
81#63843C2212yes—
82#63843C2212yes—
83#63840C2214yes—
84#63837C2214yes—
85C3×#557—31no—
86C3×#556—31no—
87#5731—32no—
88#5728—31no—
89#5728—31no—
90#5727—32no—
91#5727—31no—
92#5721—31no—
93#5708—34no—
94#5701—34no—
95#5696—34no—
96#5693—34no—
97#5691—32no—
98#5685—32no—
99#5680—32no—
100#5671—32no—
101#5632—32no—
102#5625—32no—
103#5584D311yescharacteristic, complemented
104#5581—32no—
105#5580—31no—
106#5578—32no—
107#5578—32no—
108#5572—32no—
109C4×D3×Q8—31no—
110C4×D3×Q8—31no—
111C4×D3×Q8—61no—
112#5569—32no—
113#5568—32no—
114#5567—31no—
115#5567D311yescharacteristic, complemented
116#5557—31no—
117D4×Dic6—31no—
118#5529—32no—
119#5516—32no—
120C2×C32×Q8C2311yescharacteristic
121Q8×C3⋊D3—24no—
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2312yes—
125C2×C4×C3⋊D3C2312yes—
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×#634C2312yes—
128C2×#634C2311yescharacteristic
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×#627C2314yes—
135C2×#626C2312yes—
136C2×D3×Dic3C2314yes—
137D3×Dic6—28no—
138C32×C4⋊C4C2311yescharacteristic
139C32×C4⋊C4C2312yes—
140C32×C42C2312yes—
141C32×C42C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2312yes—
143C4⋊(C3⋊Dic3)C2311yescharacteristic
144#3750C2312yes—
145#3750C2312yes—
146#3750C2312yes—
147C4×C3⋊Dic3C2311yescharacteristic
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2311yescharacteristic
150C4×C3⋊Dic3C2312yes—
151C4×C3⋊Dic3C2311yescharacteristic
152C4×C3⋊Dic3C2312yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2314yes—
167C3×C4×Dic3C2314yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2314yes—
170#3724C2314yes—
171#3724C2314yes—
172#3724C2314yes—
173Dic3⋊Dic3C2312yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179#3722C2314yes—
180#3722C2312yes—
181(C2×D3)⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185Dic32C2314yes—
186Dic32C2314yes—
187#3523—91noSylow
188C2×D3×Q8—31no—
189C2×D3×Q8—31no—
190C2×D3×Q8—32no—
191C2×D3×Q8—61no—
192C22×Dic6—32no—
193C3×C4⋊Q8—32no—
194C3×C4⋊Q8—31no—
195C3×C4⋊Q8—31no—
196C3×#126—34no—
197C3×#125—34no—
198C3×#125—32no—
199C3×#124—32no—
200C3×C22⋊Q8—32no—
201C3×C4×Q8—21no—
202C3×C4×Q8—32no—
203C3×C4×Q8—31no—
204C3×C4×Q8—32no—
205C3×C4×Q8—32no—
206C3×C4×Q8C2×D311yescharacteristic
207C3×C4×Q8C2×D311yescharacteristic
208C3×C4×D4—31no—
209C3×#117—32no—
210#947—31no—
211#946—32no—
212#946—32no—
213#946—32no—
214#946—31no—
215#946C2×D312yes—
216Q8×Dic3—31no—
217Q8×Dic3—31no—
218Q8×Dic3—32no—
219Q8×Dic3—32no—
220Q8×Dic3—32no—
221Q8×Dic3—61no—
222#944—32no—
223#944—32no—
224#944C2×D312yes—
225#938—31no—
226#936—31no—
227D4×Dic3—32no—
228C4×#67—32no—
229#926—32no—
230#924—32no—
231#898—34no—
232#898—34no—
233#898—32no—
234#898C2×D314yes—
235#897—32no—
236#897—32no—
237#897—31no—
238#896—34no—
239#896—34no—
240#896—34no—
241#896—34no—
242#895—31no—
243#894—34no—
244#894—32no—
245#893—32no—
246#893—34no—
247#892—34no—
248#892—32no—
249#892—32no—
250#892C2×D312yes—
251D3×C4⋊C4—32no—
252D3×C4⋊C4—32no—
253D3×C4⋊C4—31no—
254D3×C4⋊C4—31no—
255D3×C4⋊C4—61no—
256D3×C4⋊C4—62no—
257#890—31no—
258#890—32no—
259#890—32no—
260#890—31no—
261#890—34no—
262#890—32no—
263#889—34no—
264#889—34no—
265#889—34no—
266#889—34no—
267#889—34no—
268#889—34no—
269#889C2×D314yes—
270#888—32no—
271#888—32no—
272#888—34no—
273#888—34no—
274#887—32no—
275#887—32no—
276#887—32no—
277#887—32no—
278#887—32no—
279#887—31no—
280#887—31no—
281#887—32no—
282#887—34no—
283#887—61no—
284#887—62no—
285#887C2×D312yes—
286#883—34no—
287#883—32no—
288#67⋊C4—34no—
289#879—34no—
290#879—34no—
291#879—32no—
292#879—34no—
293#878—34no—
294#878—34no—
295#877—34no—
296#877—34no—
297#876—34no—
298#875C2×D312yes—
299C4×D12—32no—
300C4×D12C2×D311yescharacteristic
301#872—32no—
302#872—34no—
303#872—34no—
304#872—34no—
305C42×D3—32no—
306C42×D3—32no—
307C42×D3—31no—
308C42×D3—31no—
309C42×D3—61no—
310C42×D3—62no—
311#870—32no—
312#870—34no—
313#870C2×D312yes—
314#869C2×D311yescharacteristic
315#869C2×D311yescharacteristic
316C4×Dic6—32no—
317C4×Dic6—32no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—34no—
322C4×Dic6—34no—
323C4×Dic6—34no—
324C4×Dic6—61no—
325C4×Dic6—62no—
326C4×Dic6C2×D312yes—
327C4×Dic6C2×D312yes—
328C4×Dic6C2×D311yescharacteristic
329C22×C3⋊D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C32×Q8—22no—
332C2×C32×C4C2412yes—
333C2×C32×C4C2412yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3C2411yescharacteristic
338C2×C3⋊Dic3C2411yescharacteristic
339C2×C3⋊Dic3C2411yescharacteristic
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2412yes—
342C4×C3⋊D3—22no—
343C4×C3⋊D3—22no—
344C4×C3⋊D3—24no—
345C4×C3⋊D3—22no—
346C4×C3⋊D3—24no—
347#634—24no—
348#634#4114yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2414yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C3×D12—22no—
355C3×C4×D3—24no—
356C3×Dic6—24no—
357C3×Dic6—22no—
358C3×Dic6—24no—
359#627—28no—
360#626—24no—
361D3×Dic3—28no—
362#557—31no—
363#557—92no—
364#557—91no—
365#556—31no—
366#556—92no—
367#552—92no—
368#552—94no—
369D4×Q8—91no—
370D4×Q8—92no—
371#541—92no—
372#541—94no—
373#533—92no—
374#533—91no—
375#529—91no—
376#529—92no—
377#519—92no—
378C2×C4×Q8—91no—
379C2×C3×Q8—21no—
380C2×C3×Q8—31no—
381C2×C3×Q8—32no—
382C2×C3×Q8—32no—
383C2×C3×Q8C22×D311yescharacteristic
384C2×C3×Q8C22×D311yescharacteristic
385C2×C3×D4—31no—
386C22×C3×C4—32no—
387C2×#67—32no—
388C22×Dic3—34no—
389D3×Q8—68no—
390D3×Q8—64no—
391D3×Q8—64no—
392D3×Q8—68no—
393C2×D12—32no—
394C2×D12C22×D311yescharacteristic
395C2×C4×D3—34no—
396C2×C4×D3—31no—
397C2×C4×D3—31no—
398C2×C4×D3—32no—
399C2×C4×D3—32no—
400C2×C4×D3—31no—
401C2×C4×D3—32no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—32no—
405C2×C4×D3—31no—
406C2×C4×D3—61no—
407C2×C4×D3—62no—
408C2×C4×D3—61no—
409C2×C4×D3—61no—
410C2×C4×D3—62no—
411C2×C4×D3C22×D312yes—
412C2×Dic6—31no—
413C2×Dic6—31no—
414C2×Dic6—32no—
415C2×Dic6—32no—
416C2×Dic6—34no—
417C2×Dic6—34no—
418C2×Dic6—61no—
419C2×Dic6—62no—
420C2×Dic6—68no—
421C2×Dic6C22×D311yescharacteristic
422C2×Dic6C22×D312yes—
423C2×Dic6C22×D312yes—
424C3×C4⋊C4—21no—
425C3×C4⋊C4—22no—
426C3×C4⋊C4—31no—
427C3×C4⋊C4—32no—
428C3×C4⋊C4—32no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—31no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—32no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—34no—
436C3×C4⋊C4—32no—
437C3×C4⋊C4C22×D311yescharacteristic
438C3×C4⋊C4C22×D312yes—
439C3×C4⋊C4C22×D311yescharacteristic
440C3×C4⋊C4C22×D312yes—
441C3×C22⋊C4—34no—
442C3×C22⋊C4—32no—
443C3×C22⋊C4—34no—
444C3×C42—21no—
445C3×C42—22no—
446C3×C42—34no—
447C3×C42—32no—
448C3×C42—34no—
449C3×C42C22×D311yescharacteristic
450C3×C42C22×D312yes—
451C3×C42C22×D312yes—
452C3×C42C22×D311yescharacteristic
453#217—32no—
454#217—32no—
455#217—32no—
456#217—34no—
457(C2×D3)⋊C4—32no—
458(C2×D3)⋊C4—32no—
459(C2×D3)⋊C4—32no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—32no—
462(C2×D3)⋊C4—32no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4C22×D314yes—
466(C2×D3)⋊C4C22×D312yes—
467(C2×D3)⋊C4C22×D314yes—
468C4⋊Dic3—31no—
469C4⋊Dic3—32no—
470C4⋊Dic3—32no—
471C4⋊Dic3—31no—
472C4⋊Dic3—32no—
473C4⋊Dic3—32no—
474C4⋊Dic3—34no—
475C4⋊Dic3—34no—
476C4⋊Dic3—34no—
477C4⋊Dic3—32no—
478C4⋊Dic3—61no—
479C4⋊Dic3—62no—
480C4⋊Dic3C22×D312yes—
481C4⋊Dic3C22×D311yescharacteristic
482C4⋊Dic3C22×D312yes—
483C4⋊Dic3C22×D311yescharacteristic
484C4⋊Dic3C22×D312yes—
485C4⋊Dic3C22×D312yes—
486Dic3⋊C4—32no—
487Dic3⋊C4—32no—
488Dic3⋊C4—32no—
489Dic3⋊C4—32no—
490Dic3⋊C4—32no—
491Dic3⋊C4—32no—
492Dic3⋊C4—32no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—32no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—32no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—62no—
505Dic3⋊C4—62no—
506Dic3⋊C4—62no—
507Dic3⋊C4C22×D314yes—
508Dic3⋊C4C22×D314yes—
509Dic3⋊C4C22×D312yes—
510Dic3⋊C4C22×D314yes—
511Dic3⋊C4C22×D314yes—
512C4×Dic3—32no—
513C4×Dic3—31no—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—31no—
518C4×Dic3—31no—
519C4×Dic3—31no—
520C4×Dic3—32no—
521C4×Dic3—31no—
522C4×Dic3—31no—
523C4×Dic3—32no—
524C4×Dic3—34no—
525C4×Dic3—34no—
526C4×Dic3—34no—
527C4×Dic3—34no—
528C4×Dic3—62no—
529C4×Dic3—61no—
530C4×Dic3—62no—
531C4×Dic3—61no—
532C4×Dic3—61no—
533C4×Dic3—62no—
534C4×Dic3C22×D314yes—
535C4×Dic3C22×D314yes—
536C4×Dic3C22×D312yes—
537C22×C32C2511yescharacteristic
538C2×C3⋊D3—21no—
539C2×C3⋊D3—21no—
540C2×C3⋊D32−1+412yes—
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C32×C4—22no—
545C32×C4—22no—
546C32×C4—21no—
547C32×C4C2×#4112yes—
548C32×C42−1+412yes—
549C3⋊Dic3—21no—
550C3⋊Dic3—21no—
551C3⋊Dic3—21no—
552C3⋊Dic3—22no—
553C3⋊Dic3C2×#4114yes—
554C3×Dic3—24no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3—22no—
558C3×Dic3—24no—
559C22×Q8—92no—
560C22×Q8—91no—
561C4⋊Q8—32no—
562C4⋊Q8—31no—
563C4⋊Q8—31no—
564C4⋊Q8—92no—
565C4⋊Q8—94no—
566C4⋊Q8—92no—
567#126—34no—
568#126—94no—
569#126—92no—
570#126—94no—
571#126—94no—
572#125—34no—
573#125—32no—
574#125—94no—
575#125—92no—
576#125—91no—
577#125—94no—
578#125—92no—
579#125—94no—
580#125—94no—
581#124—32no—
582#124—91no—
583#123—94no—
584#123—92no—
585C22⋊Q8—32no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—91no—
590C22⋊Q8—92no—
591C22⋊Q8—92no—
592C22⋊Q8—92no—
593#121—91no—
594C4×Q8—32no—
595C4×Q8—31no—
596C4×Q8—32no—
597C4×Q8—32no—
598C4×Q8—94no—
599C4×Q8—92no—
600C4×Q8—94no—
601C4×Q8—92no—
602C4×Q8—92no—
603C4×Q8—92no—
604C4×Q8—91no—
605C4×Q8—91no—
606C4×Q8—92no—
607C4×Q8—91no—
608C4×Q8—92no—
609C4×Q8D3211yescharacteristic
610C4×D4—31no—
611C4×D4—92no—
612C4×D4—94no—
613C4×D4—92no—
614#117—32no—
615#117—94no—
616#117—94no—
617#117—92no—
618#117—94no—
619#117—92no—
620C2×C4⋊C4—92no—
621C2×C4⋊C4—91no—
622C2×C42—92no—
623C2×C42—91no—
624C23×C3—32no—
625C22×D3—31no—
626C22×D3—31no—
627C22×D3—61no—
628C22×D3C23×D312yes—
629C3×Q8—24no—
630C3×Q8—22no—
631C3×Q8—22no—
632C3×Q8—64no—
633C3×Q8—64no—
634C3×Q8—62no—
635C3×D4—62no—
636C2×C3×C4—21no—
637C2×C3×C4—22no—
638C2×C3×C4—21no—
639C2×C3×C4—22no—
640C2×C3×C4—21no—
641C2×C3×C4—34no—
642C2×C3×C4—32no—
643C2×C3×C4—34no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—64no—
647C2×C3×C4C23×D312yes—
648C2×C3×C4C23×D312yes—
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D312yes—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657#67—64no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—31no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—31no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—61no—
669C2×Dic3—62no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—62no—
673C2×Dic3—68no—
674C2×Dic3C23×D314yes—
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D314yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D312yes—
679D12—22no—
680D12—64no—
681C4×D3—24no—
682C4×D3—64no—
683C4×D3—64no—
684C4×D3—68no—
685C4×D3—64no—
686C4×D3—62no—
687C4×D3—64no—
688C4×D3—62no—
689C4×D3—64no—
690C4×D3—68no—
691C4×D3—64no—
692C4×D3—62no—
693C4×D3—62no—
694C4×D3—62no—
695C4×D3—62no—
696C4×D3—122no—
697C4×D3—124no—
698Dic6—22no—
699Dic6—24no—
700Dic6—24no—
701Dic6—34no—
702Dic6—34no—
703Dic6—64no—
704Dic6—68no—
705Dic6—68no—
706Dic6—64no—
707Dic6—64no—
708Dic6—68no—
709C2×C32C22×#4111yescharacteristic
710C2×C32C2×2−1+411yescharacteristic
711C2×C32C2×2−1+411yescharacteristic
712C3⋊D3—22no—
713C3×D3—42no—
714C2×Q8—31no—
715C2×Q8—32no—
716C2×Q8—32no—
717C2×Q8—94no—
718C2×Q8—91no—
719C2×Q8—92no—
720C2×Q8—188no—
721C2×Q8—184no—
722C2×Q8C2×D3211yescharacteristic
723C2×D4—31no—
724C2×D4—92no—
725C22×C4—32no—
726C22×C4—94no—
727C22×C4—91no—
728C22×C4—91no—
729C22×C4—92no—
730C22×C4—92no—
731C22×C4—91no—
732C4⋊C4—32no—
733C4⋊C4—34no—
734C4⋊C4—32no—
735C4⋊C4—32no—
736C4⋊C4—31no—
737C4⋊C4—32no—
738C4⋊C4—34no—
739C4⋊C4—31no—
740C4⋊C4—34no—
741C4⋊C4—34no—
742C4⋊C4—32no—
743C4⋊C4—94no—
744C4⋊C4—92no—
745C4⋊C4—94no—
746C4⋊C4—92no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—92no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—92no—
753C4⋊C4—92no—
754C4⋊C4—91no—
755C4⋊C4—92no—
756C4⋊C4—92no—
757C4⋊C4C2×D3211yescharacteristic
758C4⋊C4C2×D3212yes—
759C22⋊C4—34no—
760C22⋊C4—32no—
761C22⋊C4—34no—
762C22⋊C4—92no—
763C22⋊C4—94no—
764C22⋊C4—92no—
765C22⋊C4—92no—
766C22⋊C4—94no—
767C22⋊C4—92no—
768C42—34no—
769C42—34no—
770C42—32no—
771C42—94no—
772C42—94no—
773C42—92no—
774C42—91no—
775C42—92no—
776C42—91no—
777C42—92no—
778C42—91no—
779C42C2×D3211yescharacteristic
780C42C2×D3212yes—
781C22×C3—21no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3C24×D311yescharacteristic
786C22×C3C24×D311yescharacteristic
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—32no—
791C2×D3—32no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—61no—
796C2×D3—61no—
797C2×D3—61no—
798C2×D3—61no—
799C3×C4—24no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—21no—
804C3×C4—22no—
805C3×C4—21no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—42no—
809C3×C4—41no—
810C3×C4—64no—
811C3×C4—62no—
812C3×C4—64no—
813C3×C4—62no—
814C3×C4—62no—
815C3×C4#100712yes—
816C3×C4D3×#4112yes—
817C3×C4D3×#4112yes—
818C3×C4#101012yes—
819Dic3—22no—
820Dic3—24no—
821Dic3—22no—
822Dic3—24no—
823Dic3—22no—
824Dic3—34no—
825Dic3—34no—
826Dic3—64no—
827Dic3—62no—
828Dic3—62no—
829Dic3—61no—
830Dic3—61no—
831Dic3—61no—
832Dic3—61no—
833Dic3—61no—
834Dic3—62no—
835Dic3—61no—
836Dic3—62no—
837Dic3—121no—
838Dic3—122no—
839C32#352311yescharacteristic, complemented, Sylow
840C23—32no—
841C23—91no—
842Q8—22no—
843Q8—64no—
844Q8—62no—
845Q8—64no—
846Q8—94no—
847Q8—184no—
848Q8—188no—
849D4—62no—
850D4—184no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—34no—
854C2×C4—32no—
855C2×C4—34no—
856C2×C4—64no—
857C2×C4—92no—
858C2×C4—91no—
859C2×C4—91no—
860C2×C4—92no—
861C2×C4—91no—
862C2×C4—184no—
863C2×C4—184no—
864C2×C4—182no—
865C2×C4—188no—
866C2×C4—182no—
867C2×C4—182no—
868C2×C4C22×D3212yes—
869C2×C4C22×D3211yescharacteristic
870C2×C4C22×D3212yes—
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3211yescharacteristic
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—122no—
877C2×C3C2×#100711yescharacteristic
878C2×C3C2×D3×#4111yescharacteristic
879C2×C3C2×D3×#4111yescharacteristic
880C2×C3C2×#101011yescharacteristic
881C2×C3D3×2−1+411yescharacteristic
882C2×C3D3×2−1+411yescharacteristic
883D3—42no—
884D3—64no—
885D3—62no—
886D3—62no—
887C22—62no—
888C22—62no—
889C22—62no—
890C22—92no—
891C22—181no—
892C22—181no—
893C22C23×D3211yescharacteristic
894C4—22no—
895C4—22no—
896C4—21no—
897C4—62no—
898C4—64no—
899C4—62no—
900C4—64no—
901C4—62no—
902C4—94no—
903C4—181no—
904C4—181no—
905C4—181no—
906C4—182no—
907C4#6430612yes—
908C4#6431512yes—
909C3—21no—
910C3#8699311yescharacteristic, complemented
911C3#8702511yescharacteristic, complemented
912C2—122no—
913C2—182no—
914C2C2×#6430611yescharacteristic
915C2C2×#6431511yescharacteristic
916C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radical#63916C22
hypercenterC4×Q8D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
2. C3×#5584C2semidirect
3. C3×#5567C2semidirect
4. #10595361C2semidirect
5. #10595349C2semidirect
6. #10594474C2semidirect
7. #10594471C2semidirect
8. #10594357C2semidirect
9. #10594337C2semidirect
11. #10593942C2semidirect
12. #10593904C2semidirect
13. #10593882C2semidirect
15. #10593866C2semidirect
16. #10593864C2semidirect
17. #10593853C2semidirect
103. #5584D3semidirect
115. #5567D3semidirect
839. C32#3523semidirect
910. C3#86993semidirect
911. C3#87025semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×#55842
C3×#55672
#105953612
#105953492
#105944742
#105944712
#105943572
#105943372
#105939432
#105939422
#105939042
#105938822
#105938752
#105938662
#105938642
#105938532
#870253
#869933