Finite Group Databasebeta

← C2×#11861057 #72227382

Subgroups — C2×#11861057 #72227382

Order 2304.

5760 conjugacy classes of subgroups.

The subgroup lattice has 1067 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10594684C211yesmaximal, characteristic
2C2×#10594669C212yesmaximal, complemented
3C2×#10590920C212yesmaximal, complemented
4C2×#10590390C212yesmaximal, complemented
5C2×#10590922C212yesmaximal, complemented
6#11861057C2116yesmaximal, direct product factor
7C2×C3×#4717C212yesmaximal, complemented
8C2×#10590913C211yesmaximal, characteristic, complemented
9C2×#10590393C212yesmaximal, complemented
10C2×C3⋊D3×#97C211yesmaximal, characteristic, complemented
11C2×D3×#444—32nomaximal
12C2×#64306C2212yes—
13C22×C8×C3⋊D3C2211yescharacteristic
14C22×C8×C3⋊D3C2211yescharacteristic
15C2×C42×C3⋊D3C2211yescharacteristic
16C2×C3×#904C2212yes—
17C2×C3×#901C2214yescomplemented
18C2×#63822C2212yes—
19C2×#63818C2212yes—
20C2×#63815C2214yescomplemented
21C2×#63810C412yescomplemented
22C2×#63809C412yescomplemented
23C2×#63805—22no—
24C2×#63803—22no—
25C2×#63802C411yescharacteristic, complemented
26#10594684C418yescomplemented
27#10594684C2218yes—
28C2×#63797C411yescharacteristic, complemented
29C2×#63796C412yescomplemented
30#10594669—28no—
31#10594669C22116yescomplemented
32C2×#63791—22no—
33C2×D32×C8—22no—
34C2×C32×#97C2211yescharacteristic, complemented
35C2×#63642C2211yescharacteristic, complemented
36C2×#63642C2211yescharacteristic, complemented
37C2×#63630C2211yescharacteristic, complemented
38C3⋊D3×#97C2218yescomplemented
39C2×C3×#819C2212yescomplemented
40C2×C3×#805C2214yescomplemented
41C3×#4717C22116yescomplemented
42C2×#63578C2212yescomplemented
43C2×#63568C2214yescomplemented
44#10590922C22116yescomplemented
45#10590920C22116yescomplemented
46#10590913C2218yescomplemented
47#10590393C22116yescomplemented
48#10590390C22116yescomplemented
49C2×D3×#135—32no—
50C2×D3×#131—34no—
51C2×C3×#444—32no—
52C2×#5197—32no—
53C2×#5145—34no—
54D3×#444—332no—
55C2×D3×#108—32no—
56C2×#4894—32no—
57C2×D3×#104—34no—
58C2×#4823—34no—
59C2×#4717D312yescomplemented
60C2×D3×#97—32no—
61C2×D3×#97—61no—
62C22×C4×C3⋊D3—21no—
63C22×C4×C3⋊D3C2311yescharacteristic
64C2×C3×#235C2314yes—
65C2×#3811—22no—
66C2×#3805—22no—
67#64306—24no—
68#64306—24no—
69#64306C2×C418yes—
70#64306C2318yes—
71C2×#3802C2×C412yes—
72C2×C4×D32—22no—
73C2×#3798—22no—
74C2×#3797C2×C412yes—
75C2×#3796C2×C414yes—
76C22×C32×C8C2311yescharacteristic
77C22×C32×C8C2311yescharacteristic
78C2×C32×C42C2311yescharacteristic
79C2×C4×C3⋊Dic3—21no—
80C2×C4×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊(C3⋊C8)C2311yescharacteristic
82C22×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C8×C3⋊D3C2×C411yescharacteristic
84C2×C8×C3⋊D3C2×C411yescharacteristic
85C2×C8×C3⋊D3C2×C414yes—
86C2×C8×C3⋊D3C2×C411yescharacteristic
87C2×C8×C3⋊D3C2×C411yescharacteristic
88C2×C8×C3⋊D3D412yes—
89C2×C8×C3⋊D3D414yes—
90C2×C8×C3⋊D3D412yes—
91C2×C8×C3⋊D3C2314yes—
92C2×C8×C3⋊D3C2314yes—
93C42×C3⋊D3—22no—
94C42×C3⋊D3C2314yes—
95C2×C3×#208C2314yes—
96C2×C3×Dic12C2×C412yescomplemented
97C3×#904C2×C418yescomplemented
98C3×#904C2318yes—
99C2×C3×D24C2×C412yescomplemented
100C2×C3×#204C2×C414yescomplemented
101C3×#901—28no—
102C3×#901C23116yescomplemented
103C2×C3×ΓL(1,𝔽25)—24no—
104C2×C3×D3×C8—24no—
105C2×#3718C2×C412yescomplemented
106C2×#3715C2×C414yescomplemented
107#63822C2×C418yescomplemented
108#63822C2318yes—
109C2×#3713C2×C412yescomplemented
110C2×#3712—22no—
111C2×#3711—24no—
112#63818—24no—
113#63818C2318yes—
114C2×#3710—22no—
115#63815—28no—
116#63815C23116yescomplemented
117C2×D3×C3⋊C8—24no—
118#63810C2×C4116yescomplemented
119#63809C2×C4116yescomplemented
120#63805—216no—
121#63803—216no—
122#63802C2×C418yescomplemented
123#63797C2×C418yescomplemented
124#63796C2×C4116yescomplemented
125#63791—216no—
126D32×C8—216no—
127C32×#97C2314yescomplemented
128#63642C2314yescomplemented
129#63642C2314yescomplemented
130#63630C2314yescomplemented
131C3×#819C2318yescomplemented
132C3×#805C23116yescomplemented
133#63578C2318yescomplemented
134#63568C23116yescomplemented
135C22×#444—91noSylow
136C2×D3×#41—34no—
137C2×C3×#135—32no—
138C2×C3×#131—34no—
139C2×#950—34no—
140C2×#948—34no—
141D3×#135—316no—
142D3×#135—316no—
143C2×#919—32no—
144C2×D3×Q16—32no—
145C2×#916—34no—
146C2×D3×SD16—34no—
147C2×#912—32no—
148C2×D3×D8—32no—
149D3×#131—332no—
150D3×#131—616no—
151C2×#907—34no—
152C2×#907—64no—
153C2×D3×M16—34no—
154C2×D3×M16—64no—
155C2×#904C2×D312yes—
156C2×#901—64no—
157C2×#901C2×D314yescomplemented
158C22×D3×C8—32no—
159C22×D3×C8—32no—
160C22×D3×C8—61no—
161C22×D3×C8—61no—
162C22×D3×C8—64no—
163C2×C42×D3—32no—
164C2×C42×D3—61no—
165C3×#444—316no—
166C2×C3×#108—32no—
167C2×C3×#104—34no—
168C2×C3×#97—21no—
169C2×C3×#97C2×D312yescomplemented
170C2×#837—34no—
171#5197—316no—
172#5145—332no—
173C2×#825—34no—
174C2×#822—34no—
175C2×#819C2×D312yescomplemented
176C2×#815—32no—
177C2×#815—32no—
178C2×#815—61no—
179C2×#815—61no—
180C2×#805C2×D314yescomplemented
181C2×#803—32no—
182C2×#803—61no—
183#4894—316no—
184D3×#108—316no—
185#4823—332no—
186D3×#104—332no—
187#4717C2×D3116yescomplemented
188D3×#97—316no—
189D3×#97—68no—
190C23×C3⋊D3#4111yescharacteristic
191C22×D32—22no—
192C22×C32×C4—21no—
193C22×C32×C4C2411yescharacteristic
194C22×C3⋊Dic3—21no—
195C22×C3⋊Dic3#4111yescharacteristic
196C2×C4×C3⋊D3—24no—
197C2×C4×C3⋊D3—44no—
198C2×C4×C3⋊D3C22×C411yescharacteristic
199C2×C4×C3⋊D3C22×C411yescharacteristic
200C2×C4×C3⋊D3C22×C412yes—
201C2×C4×C3⋊D3C2×D411yescharacteristic
202C2×C4×C3⋊D3C2×D411yescharacteristic
203C2×C4×C3⋊D3C2×D412yes—
204C2×C4×C3⋊D3#4112yes—
205C2×C4×C3⋊D3C2412yes—
206C2×C3×#67—24no—
207C3×#235—24no—
208C3×#235—24no—
209C3×#235C22×C418yes—
210C3×#235C2418yes—
211C2×C3×D12C22×C414yes—
212C2×C3×C4×D3—24no—
213C2×C3×Dic6C22×C414yes—
214#3811—28no—
215#3811—28no—
216C2×#627—22no—
217C2×#626—24no—
218C2×#625—22no—
219C2×#624—22no—
220#3805—28no—
221#3805—28no—
222C2×D3×Dic3—24no—
223#3802—24no—
224#3802C22×C418yes—
225C4×D32—28no—
226C4×D32—28no—
227#3798—28no—
228#3798—28no—
229#3797—24no—
230#3797C22×C418yes—
231#3796—28no—
232#3796C22×C4116yes—
233C2×C32×C8C22×C411yescharacteristic
234C2×C32×C8C22×C411yescharacteristic
235C2×C32×C8C22×C412yes—
236C2×C32×C8C2×D412yes—
237C2×C32×C8C2×D412yes—
238C2×C32×C8C2412yes—
239C2×C32×C8C2412yes—
240C32×C42—21no—
241C32×C42C2412yes—
242C4×C3⋊Dic3—21no—
243C4×C3⋊Dic3—24no—
244C4×C3⋊Dic3C2412yes—
245C2×C3⋊(C3⋊C8)C22×C411yescharacteristic
246C2×C3⋊(C3⋊C8)C22×C412yes—
247C2×C3⋊(C3⋊C8)C22×C411yescharacteristic
248C2×C3⋊(C3⋊C8)C2×D412yes—
249C2×C3⋊(C3⋊C8)C2×D412yes—
250C2×C3⋊(C3⋊C8)C2412yes—
251C2×C3⋊(C3⋊C8)C2412yes—
252C8×C3⋊D3C22×C414yes—
253C8×C3⋊D3C22×C414yes—
254C8×C3⋊D3C22×C414yes—
255C8×C3⋊D3C22×C414yes—
256C8×C3⋊D3C2×D418yes—
257C8×C3⋊D3C2×D418yes—
258C3×#208—24no—
259C3×#208C2418yes—
260C2×C3×C3⋊C8—24no—
261C3×Dic12C22×C418yescomplemented
262C3×D24C22×C418yescomplemented
263C3×#204C22×C4116yescomplemented
264C3×ΓL(1,𝔽25)—216no—
265C3×D3×C8—216no—
266#3718C22×C418yescomplemented
267#3715C22×C4116yescomplemented
268#3713C22×C418yescomplemented
269#3712—28no—
270#3711—216no—
271#3710—28no—
272D3×C3⋊C8—216no—
273C22×#135—91no—
274C22×#131—92no—
275C2×#444—32no—
276C2×#444—92no—
277C2×#444—92no—
278C2×#444—92no—
279C2×#444—916no—
280C22×#108—91no—
281C22×#104—92no—
282C22×#97—91no—
283C2×C3×#41—34no—
284D3×#41—316no—
285D3×#41—316no—
286D3×#41—68no—
287D3×#41—68no—
288C2×#239—34no—
289C2×D3×Q8—34no—
290C2×#237—34no—
291C2×#237—64no—
292C2×D3×D4—34no—
293C2×D3×D4—64no—
294C2×#235—64no—
295C2×#235C22×D314yes—
296C22×C4×D3—32no—
297C22×C4×D3—61no—
298C22×C4×D3—64no—
299C22×C4×D3—62no—
300C22×C4×D3—62no—
301C3×#135—38no—
302C3×#135—38no—
303C2×C3×Q16—32no—
304C2×C3×SD16—34no—
305C2×C3×D8—32no—
306C3×#131—316no—
307C3×#131—68no—
308C2×C3×M16—34no—
309C2×C3×M16—64no—
310C22×C3×C8—21no—
311C22×C3×C8—21no—
312C22×C3×C8—64no—
313C22×C3×C8C22×D312yes—
314C22×C3×C8C22×D312yes—
315C2×C3×C42—21no—
316C2×C3×C42C22×D312yes—
317#950—316no—
318#950—316no—
319#948—316no—
320#948—68no—
321C2×#216—34no—
322C2×#215—34no—
323C2×#214—34no—
324C2×#213—34no—
325C2×C4×Dic3—32no—
326C2×C4×Dic3—61no—
327C2×C4×Dic3—62no—
328C2×C4×Dic3—62no—
329C2×#208—64no—
330C2×#208C22×D314yes—
331C22×C3⋊C8—32no—
332C22×C3⋊C8—32no—
333C22×C3⋊C8—61no—
334C22×C3⋊C8—61no—
335C22×C3⋊C8—64no—
336#919—316no—
337D3×Q16—316no—
338#916—332no—
339D3×SD16—332no—
340#912—316no—
341D3×D8—316no—
342#907—316no—
343#907—632no—
344#907—68no—
345D3×M16—316no—
346D3×M16—632no—
347D3×M16—68no—
348C2×Dic12C4×D312yescomplemented
349#904C4×D318yescomplemented
350#904C22×D318yes—
351C2×D24C4×D312yescomplemented
352C2×#204C4×D314yescomplemented
353#901—28no—
354#901—632no—
355#901C22×D3116yescomplemented
356C2×ΓL(1,𝔽25)—24no—
357C2×ΓL(1,𝔽25)—64no—
358C2×ΓL(1,𝔽25)—64no—
359C2×D3×C8—24no—
360C2×D3×C8—32no—
361C2×D3×C8—32no—
362C2×D3×C8—32no—
363C2×D3×C8—32no—
364C2×D3×C8—38no—
365C2×D3×C8—34no—
366C2×D3×C8—34no—
367C2×D3×C8—38no—
368C2×D3×C8—38no—
369C2×D3×C8—38no—
370C2×D3×C8—64no—
371C2×D3×C8—64no—
372C2×D3×C8—61no—
373C2×D3×C8—61no—
374C2×D3×C8—64no—
375C2×D3×C8—61no—
376C2×D3×C8—61no—
377C2×D3×C8—62no—
378C2×D3×C8—64no—
379C2×D3×C8—62no—
380C2×D3×C8—632no—
381C2×D3×C8—64no—
382C2×D3×C8—64no—
383C42×D3—38no—
384C42×D3—64no—
385C42×D3—64no—
386C42×D3—64no—
387C3×#108—38no—
388C3×#104—316no—
389C3×#97—24no—
390C3×#97C22×D318yescomplemented
391#837—316no—
392#825—316no—
393#822—316no—
394#819C22×D318yescomplemented
395#815—38no—
396#815—38no—
397#815—64no—
398#815—64no—
399#805C22×D3116yescomplemented
400#803—38no—
401#803—64no—
402C23×C32C2×#4111yescharacteristic
403C22×C3⋊D3—24no—
404C22×C3⋊D3C4×D411yescharacteristic
405C22×C3⋊D3C4×D412yes—
406C22×C3⋊D3C4×D411yescharacteristic
407C22×C3⋊D3C2×#4112yes—
408C22×C3×D3—24no—
409C2×D32—28no—
410C2×D32—48no—
411C2×C32×C4—22no—
412C2×C32×C4—42no—
413C2×C32×C4C23×C411yescharacteristic
414C2×C32×C4C23×C411yescharacteristic
415C2×C32×C4C22×D411yescharacteristic
416C2×C32×C4C22×D411yescharacteristic
417C2×C32×C4C2×#4111yescharacteristic
418C2×C32×C4C2511yescharacteristic
419C2×C3⋊Dic3—22no—
420C2×C3⋊Dic3—42no—
421C2×C3⋊Dic3C4×D411yescharacteristic
422C2×C3⋊Dic3C4×D412yes—
423C2×C3⋊Dic3C4×D411yescharacteristic
424C2×C3⋊Dic3C2×#4112yes—
425C4×C3⋊D3—48no—
426C4×C3⋊D3C4×D412yes—
427C4×C3⋊D3C4×D412yes—
428C4×C3⋊D3C4×D412yes—
429C4×C3⋊D3C4×D412yes—
430C4×C3⋊D3C23×C412yes—
431C4×C3⋊D3C23×C412yes—
432C4×C3⋊D3C22×D412yes—
433C4×C3⋊D3C22×D412yes—
434C3×#67—28no—
435C3×#67—28no—
436C2×C3×Dic3—24no—
437C3×D12—24no—
438C3×D12C23×C418yes—
439C3×C4×D3—28no—
440C3×C4×D3—28no—
441C3×Dic6—24no—
442C3×Dic6C23×C418yes—
443#627—28no—
444#626—216no—
445#625—28no—
446#624—28no—
447D3×Dic3—216no—
448C32×C8C23×C412yes—
449C32×C8C23×C412yes—
450C32×C8C22×D414yes—
451C3⋊(C3⋊C8)C23×C412yes—
452C3⋊(C3⋊C8)C23×C412yes—
453C3⋊(C3⋊C8)C22×D414yes—
454C3×C3⋊C8—28no—
455C22×#41—92no—
456C2×#135—32no—
457C2×#135—92no—
458C2×#135—92no—
459C2×#135—98no—
460C2×#135—98no—
461C2×#135—92no—
462C22×Q16—91no—
463C22×SD16—92no—
464C22×D8—91no—
465C2×#131—34no—
466C2×#131—94no—
467C2×#131—916no—
468C2×#131—182no—
469C2×#131—182no—
470C2×#131—188no—
471C22×M16—92no—
472C22×M16—182no—
473C23×C8—91no—
474C23×C8—91no—
475C23×C8—182no—
476C22×C42—91no—
477#444—316no—
478#444—916no—
479#444—916no—
480#444—916no—
481C2×#108—32no—
482C2×#108—98no—
483C2×#108—92no—
484C2×#104—34no—
485C2×#104—916no—
486C2×#104—94no—
487C2×#97—91no—
488C2×#97—91no—
489C2×#97—91no—
490C2×#97—98no—
491C2×#97D3211yescharacteristic, complemented
492C23×D3—32no—
493C23×D3—61no—
494C23×D3—64no—
495C3×#41—38no—
496C3×#41—38no—
497C3×#41—64no—
498C3×#41—64no—
499C2×C3×Q8—34no—
500C2×C3×D4—34no—
501C2×C3×D4—64no—
502C22×C3×C4—22no—
503C22×C3×C4—22no—
504C22×C3×C4—21no—
505C22×C3×C4—64no—
506C22×C3×C4C23×D312yes—
507C2×#67—24no—
508C2×#67—64no—
509C2×#67—64no—
510C22×Dic3—32no—
511C22×Dic3—61no—
512C22×Dic3—64no—
513C22×Dic3—62no—
514C22×Dic3—62no—
515#239—316no—
516#239—68no—
517D3×Q8—316no—
518D3×Q8—68no—
519#237—316no—
520#237—68no—
521#237—616no—
522#237—616no—
523D3×D4—316no—
524D3×D4—68no—
525D3×D4—616no—
526D3×D4—616no—
527#235—24no—
528#235—24no—
529#235—616no—
530#235—616no—
531#235C2×C4×D318yes—
532#235C23×D318yes—
533C2×D12—64no—
534C2×D12C2×C4×D314yes—
535C2×C4×D3—24no—
536C2×C4×D3—32no—
537C2×C4×D3—32no—
538C2×C4×D3—34no—
539C2×C4×D3—32no—
540C2×C4×D3—32no—
541C2×C4×D3—34no—
542C2×C4×D3—34no—
543C2×C4×D3—34no—
544C2×C4×D3—62no—
545C2×C4×D3—62no—
546C2×C4×D3—61no—
547C2×C4×D3—61no—
548C2×C4×D3—62no—
549C2×C4×D3—62no—
550C2×C4×D3—61no—
551C2×C4×D3—61no—
552C2×C4×D3—616no—
553C2×C4×D3—616no—
554C2×C4×D3—64no—
555C2×C4×D3—64no—
556C2×C4×D3—68no—
557C2×C4×D3—68no—
558C2×C4×D3—128no—
559C2×C4×D3—128no—
560C2×Dic6—64no—
561C2×Dic6C2×C4×D314yes—
562C3×Q16—38no—
563C3×SD16—316no—
564C3×D8—38no—
565C3×M16—38no—
566C3×M16—64no—
567C3×M16—616no—
568C2×C3×C8—22no—
569C2×C3×C8—22no—
570C2×C3×C8—21no—
571C2×C3×C8—21no—
572C2×C3×C8—22no—
573C2×C3×C8—22no—
574C2×C3×C8—22no—
575C2×C3×C8—64no—
576C2×C3×C8—616no—
577C2×C3×C8C2×C4×D312yes—
578C2×C3×C8C2×C4×D312yes—
579C2×C3×C8C2×C4×D314yes—
580C2×C3×C8D3×D414yes—
581C2×C3×C8D3×D414yes—
582C2×C3×C8C23×D314yes—
583C2×C3×C8C23×D314yes—
584C3×C42—22no—
585C3×C42—22no—
586C3×C42—22no—
587C3×C42C23×D314yes—
588#216—316no—
589#215—316no—
590#214—316no—
591#213—316no—
592C4×Dic3—34no—
593C4×Dic3—62no—
594C4×Dic3—68no—
595C4×Dic3—68no—
596C4×Dic3—62no—
597C4×Dic3—62no—
598#208—24no—
599#208—616no—
600#208C23×D318yes—
601C2×C3⋊C8—24no—
602C2×C3⋊C8—32no—
603C2×C3⋊C8—32no—
604C2×C3⋊C8—34no—
605C2×C3⋊C8—34no—
606C2×C3⋊C8—34no—
607C2×C3⋊C8—34no—
608C2×C3⋊C8—34no—
609C2×C3⋊C8—62no—
610C2×C3⋊C8—62no—
611C2×C3⋊C8—61no—
612C2×C3⋊C8—61no—
613C2×C3⋊C8—62no—
614C2×C3⋊C8—62no—
615C2×C3⋊C8—62no—
616C2×C3⋊C8—616no—
617Dic12C2×C4×D318yescomplemented
618D24C2×C4×D318yescomplemented
619#204C2×C4×D3116yescomplemented
620ΓL(1,𝔽25)—216no—
621ΓL(1,𝔽25)—616no—
622ΓL(1,𝔽25)—616no—
623D3×C8—216no—
624D3×C8—38no—
625D3×C8—38no—
626D3×C8—38no—
627D3×C8—38no—
628D3×C8—316no—
629D3×C8—316no—
630D3×C8—64no—
631D3×C8—64no—
632D3×C8—64no—
633D3×C8—64no—
634D3×C8—68no—
635D3×C8—68no—
636D3×C8—616no—
637D3×C8—616no—
638C22×C32—22no—
639C22×C32C2×C4×D411yescharacteristic
640C22×C32C2×C4×D411yescharacteristic
641C22×C32C22×#4111yescharacteristic
642C2×C3⋊D3—22no—
643C2×C3⋊D3—24no—
644C2×C3⋊D3—24no—
645C2×C3⋊D3#44414yescomplemented
646C2×C3⋊D3C2×C4×D412yes—
647C2×C3⋊D3C2×C4×D412yes—
648C2×C3×D3—28no—
649C2×C3×D3—48no—
650D32—416no—
651C32×C4—42no—
652C32×C4C2×C4×D411yescharacteristic
653C32×C4C2×C4×D411yescharacteristic
654C32×C4C24×C411yescharacteristic
655C32×C4C23×D411yescharacteristic
656C3⋊Dic3—42no—
657C3⋊Dic3C2×C4×D412yes—
658C3⋊Dic3C2×C4×D412yes—
659C3×Dic3—28no—
660C2×#41—34no—
661C2×#41—94no—
662C2×#41—98no—
663C2×#41—98no—
664C2×#41—182no—
665C2×#41—182no—
666C2×#41—184no—
667C2×#41—184no—
668C22×Q8—92no—
669C22×D4—92no—
670C22×D4—182no—
671C23×C4—91no—
672C23×C4—181no—
673C23×C4—182no—
674#135—38no—
675#135—38no—
676#135—916no—
677#135—916no—
678#135—98no—
679#135—98no—
680C2×Q16—32no—
681C2×Q16—98no—
682C2×Q16—92no—
683C2×SD16—34no—
684C2×SD16—916no—
685C2×SD16—94no—
686C2×D8—32no—
687C2×D8—98no—
688C2×D8—92no—
689#131—316no—
690#131—68no—
691#131—916no—
692#131—1816no—
693#131—1816no—
694#131—188no—
695C2×M16—34no—
696C2×M16—64no—
697C2×M16—98no—
698C2×M16—182no—
699C2×M16—184no—
700C2×M16—1816no—
701C2×M16—184no—
702C22×C8—64no—
703C22×C8—91no—
704C22×C8—91no—
705C22×C8—94no—
706C22×C8—94no—
707C22×C8—91no—
708C22×C8—91no—
709C22×C8—91no—
710C22×C8—91no—
711C22×C8—94no—
712C22×C8—92no—
713C22×C8—94no—
714C22×C8—92no—
715C22×C8—1816no—
716C22×C8—182no—
717C22×C8—184no—
718C22×C8C2×D3211yescharacteristic
719C22×C8C2×D3211yescharacteristic
720C2×C42—91no—
721C2×C42—94no—
722C2×C42—182no—
723C2×C42—181no—
724C2×C42C2×D3211yescharacteristic
725#108—38no—
726#108—98no—
727#104—316no—
728#104—916no—
729#97—94no—
730#97—94no—
731#97—94no—
732#97C2×D3214yescomplemented
733C23×C3—21no—
734C23×C3—64no—
735C23×C3D3×#4112yes—
736C22×D3—24no—
737C22×D3—32no—
738C22×D3—34no—
739C22×D3—32no—
740C22×D3—34no—
741C22×D3—61no—
742C22×D3—61no—
743C22×D3—62no—
744C22×D3—62no—
745C22×D3—616no—
746C22×D3—68no—
747C22×D3—68no—
748C22×D3—1216no—
749C3×Q8—38no—
750C3×Q8—64no—
751C3×D4—38no—
752C3×D4—68no—
753C3×D4—68no—
754C3×D4—64no—
755C2×C3×C4—24no—
756C2×C3×C4—24no—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—44no—
764C2×C3×C4—44no—
765C2×C3×C4—64no—
766C2×C3×C4—68no—
767C2×C3×C4—68no—
768C2×C3×C4C22×C4×D312yes—
769C2×C3×C4C22×C4×D312yes—
770C2×C3×C4C2×D3×D412yes—
771C2×C3×C4C2×D3×D412yes—
772C2×C3×C4D3×#4112yes—
773C2×C3×C4C24×D312yes—
774#67—28no—
775#67—28no—
776#67—616no—
777#67—616no—
778C2×Dic3—24no—
779C2×Dic3—34no—
780C2×Dic3—32no—
781C2×Dic3—32no—
782C2×Dic3—34no—
783C2×Dic3—61no—
784C2×Dic3—61no—
785C2×Dic3—62no—
786C2×Dic3—62no—
787C2×Dic3—616no—
788C2×Dic3—64no—
789C2×Dic3—64no—
790C2×Dic3—124no—
791C2×Dic3—124no—
792D12—24no—
793D12—616no—
794D12C22×C4×D318yes—
795C4×D3—28no—
796C4×D3—28no—
797C4×D3—34no—
798C4×D3—34no—
799C4×D3—34no—
800C4×D3—34no—
801C4×D3—34no—
802C4×D3—34no—
803C4×D3—34no—
804C4×D3—34no—
805C4×D3—62no—
806C4×D3—62no—
807C4×D3—62no—
808C4×D3—62no—
809C4×D3—62no—
810C4×D3—62no—
811C4×D3—62no—
812C4×D3—62no—
813C4×D3—616no—
814C4×D3—616no—
815C4×D3—1216no—
816C4×D3—1216no—
817Dic6—24no—
818Dic6—616no—
819Dic6C22×C4×D318yes—
820C3×C8—22no—
821C3×C8—22no—
822C3×C8—24no—
823C3×C8—68no—
824C3×C8C22×C4×D314yes—
825C3×C8C22×C4×D314yes—
826C3×C8C2×D3×D418yes—
827C3⋊C8—28no—
828C3⋊C8—34no—
829C3⋊C8—34no—
830C3⋊C8—38no—
831C3⋊C8—62no—
832C3⋊C8—62no—
833C3⋊C8—64no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32C2×#44412yescomplemented
837C2×C32C22×C4×D411yescharacteristic
838C3⋊D3—22no—
839C3⋊D3C2×#44414yescomplemented
840C3×D3—48no—
841C24—91no—
842C24—182no—
843#41—38no—
844#41—38no—
845#41—64no—
846#41—64no—
847#41—916no—
848#41—188no—
849#41—188no—
850#41—188no—
851#41—188no—
852#41—188no—
853C2×Q8—34no—
854C2×Q8—98no—
855C2×Q8—182no—
856C2×Q8—184no—
857C2×D4—34no—
858C2×D4—64no—
859C2×D4—98no—
860C2×D4—184no—
861C2×D4—184no—
862C2×D4—182no—
863C2×D4—188no—
864C2×D4—188no—
865C22×C4—21no—
866C22×C4—64no—
867C22×C4—91no—
868C22×C4—91no—
869C22×C4—91no—
870C22×C4—92no—
871C22×C4—92no—
872C22×C4—91no—
873C22×C4—91no—
874C22×C4—92no—
875C22×C4—92no—
876C22×C4—184no—
877C22×C4—188no—
878C22×C4—188no—
879C22×C4—182no—
880C22×C4—184no—
881C22×C4—181no—
882C22×C4—364no—
883C22×C4C22×D3211yescharacteristic
884Q16—38no—
885Q16—98no—
886SD16—316no—
887SD16—916no—
888D8—38no—
889D8—98no—
890M16—38no—
891M16—64no—
892M16—616no—
893M16—188no—
894M16—1816no—
895C2×C8—64no—
896C2×C8—616no—
897C2×C8—91no—
898C2×C8—91no—
899C2×C8—92no—
900C2×C8—92no—
901C2×C8—92no—
902C2×C8—92no—
903C2×C8—92no—
904C2×C8—94no—
905C2×C8—94no—
906C2×C8—94no—
907C2×C8—94no—
908C2×C8—98no—
909C2×C8—98no—
910C2×C8—188no—
911C2×C8—1816no—
912C2×C8C4×D3211yescharacteristic
913C2×C8C4×D3211yescharacteristic
914C2×C8C4×D3212yes—
915C2×C8#380212yes—
916C2×C8#380212yes—
917C2×C8C22×D3212yes—
918C2×C8C22×D3212yes—
919C42—21no—
920C42—92no—
921C42—184no—
922C42—181no—
923C42C22×D3212yes—
924C22×C3—24no—
925C22×C3—24no—
926C22×C3—21no—
927C22×C3—21no—
928C22×C3—21no—
929C22×C3—68no—
930C22×C3—128no—
931C22×C3C4×D3×D412yes—
932C22×C3C4×D3×D412yes—
933C22×C3C2×D3×#4112yes—
934C2×D3—28no—
935C2×D3—34no—
936C2×D3—38no—
937C2×D3—34no—
938C2×D3—48no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—64no—
942C2×D3—68no—
943C2×D3—68no—
944C2×D3—68no—
945C2×D3—68no—
946C2×D3—64no—
947C2×D3—64no—
948C2×D3—1232no—
949C3×C4—21no—
950C3×C4—21no—
951C3×C4—21no—
952C3×C4—21no—
953C3×C4—44no—
954C3×C4—44no—
955C3×C4—68no—
956C3×C4C4×D3×D412yes—
957C3×C4C4×D3×D412yes—
958C3×C4C23×C4×D312yes—
959C3×C4C22×D3×D412yes—
960Dic3—28no—
961Dic3—34no—
962Dic3—34no—
963Dic3—62no—
964Dic3—62no—
965Dic3—124no—
966Dic3—124no—
967C32C22×#44411yescharacteristic, complemented, Sylow
968C23—64no—
969C23—91no—
970C23—92no—
971C23—92no—
972C23—91no—
973C23—184no—
974C23—188no—
975C23—368no—
976C23#6430611yescharacteristic
977Q8—38no—
978Q8—64no—
979Q8—188no—
980D4—38no—
981D4—68no—
982D4—68no—
983D4—64no—
984D4—1816no—
985D4—188no—
986C2×C4—22no—
987C2×C4—42no—
988C2×C4—64no—
989C2×C4—68no—
990C2×C4—68no—
991C2×C4—92no—
992C2×C4—91no—
993C2×C4—91no—
994C2×C4—92no—
995C2×C4—92no—
996C2×C4—92no—
997C2×C4—92no—
998C2×C4—92no—
999C2×C4—92no—
1000C2×C4—92no—
1001C2×C4—92no—
1002C2×C4—92no—
1003C2×C4—188no—
1004C2×C4—1816no—
1005C2×C4—182no—
1006C2×C4—368no—
1007C2×C4—362no—
1008C2×C4C2×C4×D3211yescharacteristic
1009C2×C4C2×C4×D3211yescharacteristic
1010C2×C4C2×#380211yescharacteristic
1011C2×C4C2×#380211yescharacteristic
1012C2×C4#6430611yescharacteristic
1013C2×C4C23×D3211yescharacteristic
1014C8—68no—
1015C8—92no—
1016C8—92no—
1017C8—94no—
1018C8C2×C4×D3212yes—
1019C8C2×C4×D3212yes—
1020C8C2×#380214yes—
1021C2×C3—22no—
1022C2×C3—22no—
1023C2×C3—22no—
1024C2×C3—22no—
1025C2×C3—22no—
1026C2×C3—21no—
1027C2×C3—128no—
1028C2×C3D3×#44414yescomplemented
1029C2×C3C2×C4×D3×D412yes—
1030D3—38no—
1031D3—48no—
1032D3—64no—
1033D3—64no—
1034D3—64no—
1035C22—22no—
1036C22—68no—
1037C22—94no—
1038C22—92no—
1039C22—92no—
1040C22—128no—
1041C22—184no—
1042C22—184no—
1043C22—182no—
1044C22—3616no—
1045C22C4×#380211yescharacteristic
1046C22C4×#380211yescharacteristic
1047C22C2×#6430611yescharacteristic
1048C4—42no—
1049C4—68no—
1050C4—92no—
1051C4—92no—
1052C4—362no—
1053C4C4×#380211yescharacteristic
1054C4C4×#380211yescharacteristic
1055C4C22×C4×D3211yescharacteristic
1056C4C22×#380211yescharacteristic
1057C3—21no—
1058C3C2×D3×#44412yescomplemented
1059C2—21no—
1060C2—21no—
1061C2—94no—
1062C2—128no—
1063C2—182no—
1064C2#1186105712yesdirect product factor
1065C2C2×C4×#380211yescharacteristic
subgroupG/H
centerC2×C4C2×#3802
commutatorC32×C4C24×C4
FrattiniC2×C4C23×D32
FittingC2×C32×#97C22
socleC22×C32C2×C4×D4
prime radicalC2×#10594684C2
cosocleC2×C32×C4C25
hypercenterC2×#97D32
hypocenterC32C22×#444
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C2×#10594669C2semidirect
3. C2×#10590920C2semidirect
4. C2×#10590390C2semidirect
5. C2×#10590922C2semidirect
6. #11861057C2direct (N × H)
7. C2×C3×#4717C2semidirect
8. C2×#10590913C2semidirect
9. C2×#10590393C2semidirect
10. C2×C3⋊D3×#97C2semidirect
17. C2×C3×#901C22semidirect
20. C2×#63815C22semidirect
21. C2×#63810C4semidirect
22. C2×#63809C4semidirect
25. C2×#63802C4semidirect
26. #10594684C4semidirect
28. C2×#63797C4semidirect
29. C2×#63796C4semidirect
31. #10594669C22semidirect
34. C2×C32×#97C22semidirect
35. C2×#63642C22semidirect
36. C2×#63642C22semidirect
37. C2×#63630C22semidirect
38. C3⋊D3×#97C22semidirect
39. C2×C3×#819C22semidirect
40. C2×C3×#805C22semidirect
41. C3×#4717C22semidirect
42. C2×#63578C22semidirect
43. C2×#63568C22semidirect
44. #10590922C22semidirect
45. #10590920C22semidirect
46. #10590913C22semidirect
47. #10590393C22semidirect
48. #10590390C22semidirect
59. C2×#4717D3semidirect
96. C2×C3×Dic12C2×C4semidirect
97. C3×#904C2×C4semidirect
99. C2×C3×D24C2×C4semidirect
100. C2×C3×#204C2×C4semidirect
102. C3×#901C23semidirect
105. C2×#3718C2×C4semidirect
106. C2×#3715C2×C4semidirect
107. #63822C2×C4semidirect
109. C2×#3713C2×C4semidirect
116. #63815C23semidirect
118. #63810C2×C4semidirect
119. #63809C2×C4semidirect
122. #63802C2×C4semidirect
123. #63797C2×C4semidirect
124. #63796C2×C4semidirect
127. C32×#97C23semidirect
128. #63642C23semidirect
129. #63642C23semidirect
130. #63630C23semidirect
131. C3×#819C23semidirect
132. C3×#805C23semidirect
133. #63578C23semidirect
134. #63568C23semidirect
157. C2×#901C2×D3semidirect
169. C2×C3×#97C2×D3semidirect
175. C2×#819C2×D3semidirect
180. C2×#805C2×D3semidirect
187. #4717C2×D3semidirect
261. C3×Dic12C22×C4semidirect
262. C3×D24C22×C4semidirect
263. C3×#204C22×C4semidirect
266. #3718C22×C4semidirect
267. #3715C22×C4semidirect
268. #3713C22×C4semidirect
348. C2×Dic12C4×D3semidirect
349. #904C4×D3semidirect
351. C2×D24C4×D3semidirect
352. C2×#204C4×D3semidirect
355. #901C22×D3semidirect
390. C3×#97C22×D3semidirect
394. #819C22×D3semidirect
399. #805C22×D3semidirect
491. C2×#97D32semidirect
617. Dic12C2×C4×D3semidirect
618. D24C2×C4×D3semidirect
619. #204C2×C4×D3semidirect
645. C2×C3⋊D3#444semidirect
732. #97C2×D32semidirect
836. C2×C32C2×#444semidirect
839. C3⋊D3C2×#444semidirect
967. C32C22×#444semidirect
1028. C2×C3D3×#444semidirect
1058. C3C2×D3×#444semidirect
1064. C2#11861057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#105946842
C2×#105946692
C2×#105909202
C2×#105903902
C2×#105909222
#118610572
C2×C3×#47172
C2×#105909132
C2×#105903932
C2×C3⋊D3×#972
C2×D3×#4443