Finite Group Databasebeta

← D97⋊#421 #27158363

Subgroups — D97⋊#421 #27158363

Order 12416.

772 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D97⋊M16C211yesmaximal, characteristic, complemented
2C2×#15690889C211yesmaximal, characteristic, complemented
3#20261734C212yesmaximal, complemented
4#20261733C212yesmaximal, complemented
5#20261732C214yesmaximal, complemented
6D97⋊#104C214yesmaximal, complemented
7C2×#41×D97C211yesmaximal, characteristic
8C2×#13095521C2212yescomplemented
9D97⋊M16—21no—
10D97⋊M16—21no—
11D97⋊M16C2212yescomplemented
12D97⋊M16C2212yescomplemented
13C2×#13095520—21no—
14C2×#13095519—21no—
15#15690889—21no—
16#15690889—21no—
17#15690889C2212yescomplemented
18#15690889C2212yescomplemented
19C2×C4⋊#87604—21no—
20C2×C22⋊#87604—21no—
21C2×C4×#87604C2212yescomplemented
22#15690875C2218yescomplemented
23#15690874C2218yescomplemented
24C2×#13095512C2211yescharacteristic
25C2×#13095511—21no—
26C2×#13095511C411yescharacteristic, complemented
27C2×#13095510—21no—
28C2×#13095510C2211yescharacteristic
29#41×D97—21no—
30#41×D97—21no—
31#41×D97—21no—
32#41×D97—21no—
33#41×D97C412yescomplemented
34#41×D97C412yescomplemented
35#41×D97C2212yes—
36#41×D97C2212yes—
37C2×Q8×D97C411yescharacteristic, complemented
38C2×D4×D97—21no—
39C2×D4×D97C411yescharacteristic, complemented
40C22×C4×D97—21no—
41C22×C4×D97C2211yescharacteristic
42C2×#41×C97C411yescharacteristic, complemented
43C22×#87604—22no—
44#13095521—22no—
45#13095521C2314yescomplemented
46#13095520—22no—
47#13095520—22no—
48#13095519—22no—
49#13095519—22no—
50C2×#11715897—22no—
51C4⋊#87604—22no—
52C4⋊#87604—22no—
53C22⋊#87604—22no—
54C22⋊#87604—22no—
55C4×#87604—22no—
56C4×#87604C2314yescomplemented
57C23×D97—21no—
58C23×D97D411yescharacteristic
59#13095512—21no—
60#13095512—21no—
61#13095512C2×C412yescomplemented
62#13095512C2312yes—
63#13095511—21no—
64#13095511—21no—
65#13095511—22no—
66#13095511—22no—
67#13095511—22no—
68#13095511—22no—
69#13095511C2×C412yes—
70#13095511C2×C412yescomplemented
71#13095510—22no—
72#13095510—22no—
73#13095510—22no—
74#13095510—22no—
75#13095510—21no—
76#13095510—21no—
77#13095510C2×C412yescomplemented
78#13095510C2312yes—
79C2×Dic194—21no—
80C2×Dic194C2×C411yescharacteristic, complemented
81Q8×D97—21no—
82Q8×D97—21no—
83Q8×D97C2×C412yes—
84Q8×D97C2×C412yescomplemented
85C2×D388—21no—
86C2×D388C2×C411yescharacteristic, complemented
87C2×C22⋊D97—21no—
88C2×C22⋊D97—21no—
89C2×C22⋊D97—21no—
90D4×D97—22no—
91D4×D97—22no—
92D4×D97—22no—
93D4×D97—22no—
94D4×D97—21no—
95D4×D97—21no—
96D4×D97C2×C412yes—
97D4×D97C2×C412yescomplemented
98C22×Dic97—21no—
99C22×Dic97D411yescharacteristic
100C2×C4×D97—21no—
101C2×C4×D97—21no—
102C2×C4×D97—21no—
103C2×C4×D97—22no—
104C2×C4×D97—22no—
105C2×C4×D97—22no—
106C2×C4×D97—22no—
107C2×C4×D97C2×C411yescharacteristic
108C2×C4×D97C2×C411yescharacteristic
109C2×C4×D97C2×C411yescharacteristic
110C2×C4×D97D411yescharacteristic
111C2×C4×D97D411yescharacteristic
112C2×C4×D97D411yescharacteristic
113C2×C4×D97D411yescharacteristic
114C2×C4×D97D411yescharacteristic
115C2×C4×D97D411yescharacteristic
116C2×C4×D97C2311yescharacteristic
117C2×C4×D97C2311yescharacteristic
118C2×C4×D97C2311yescharacteristic
119#41×C97—21no—
120#41×C97—21no—
121#41×C97C2×C412yes—
122#41×C97C2×C412yescomplemented
123C2×Q8×C97C2×C411yescharacteristic, complemented
124C2×D4×C97—21no—
125C2×D4×C97C2×C411yescharacteristic, complemented
126C22×C4×C97—21no—
127C22×C4×C97C2×C411yescharacteristic
128C23×C97—21no—
129C23×C97C22⋊C411yescharacteristic
130C22×D97—21no—
131C22×D97—22no—
132C22×D97—22no—
133C22×D97—42no—
134C22×D97—44no—
135C22×D97C22⋊C411yescharacteristic
136C22×D97C22⋊C411yescharacteristic
137C22×D97C22⋊C411yescharacteristic
138C22×D97C2×D411yescharacteristic
139C22×D97C2×D411yescharacteristic
140C22×D97C2×D411yescharacteristic
141C2×#87604—24no—
142C2×#87604—44no—
143Q8×C97—21no—
144Q8×C97C22×C412yes—
145D4×C97—22no—
146D4×C97—22no—
147D4×C97—21no—
148D4×C97C22×C412yes—
149C2×C4×C97—21no—
150C2×C4×C97—22no—
151C2×C4×C97—22no—
152C2×C4×C97C22⋊C411yescharacteristic
153C2×C4×C97C22⋊C411yescharacteristic
154C2×C4×C97C22⋊C411yescharacteristic
155C2×C4×C97C22×C411yescharacteristic
156C2×C4×C97C22×C411yescharacteristic
157C2×C4×C97C22×C411yescharacteristic
158C22⋊D97—22no—
159C22⋊D97—22no—
160C22⋊D97—22no—
161C22⋊D97—22no—
162C22⋊D97—22no—
163C22⋊D97—22no—
164C2×Dic97—21no—
165C2×Dic97—22no—
166C2×Dic97—22no—
167C2×Dic97C22⋊C411yescharacteristic
168C2×Dic97C22⋊C411yescharacteristic
169C2×Dic97C22⋊C411yescharacteristic
170C2×Dic97C2×D411yescharacteristic
171C2×Dic97C2×D411yescharacteristic
172C2×Dic97C2×D411yescharacteristic
173D388—22no—
174D388—22no—
175D388—21no—
176D388C22×C412yes—
177C4×D97—22no—
178C4×D97—22no—
179C4×D97—22no—
180C4×D97—22no—
181C4×D97—22no—
182C4×D97—22no—
183C4×D97C22⋊C411yescharacteristic
184C4×D97C22⋊C411yescharacteristic
185C4×D97C22⋊C411yescharacteristic
186C4×D97C22⋊C411yescharacteristic
187C4×D97C22⋊C411yescharacteristic
188C4×D97C22⋊C411yescharacteristic
189C4×D97C22×C411yescharacteristic
190C4×D97C22×C411yescharacteristic
191C4×D97C22×C411yescharacteristic
192C4×D97C2×D411yescharacteristic
193C4×D97C2×D411yescharacteristic
194C4×D97C2×D411yescharacteristic
195C4×D97C2×D411yescharacteristic
196C4×D97C2×D411yescharacteristic
197C4×D97C2×D411yescharacteristic
198C4×D97C2411yescharacteristic
199Dic194—21no—
200Dic194—22no—
201Dic194—22no—
202Dic194C22×C412yes—
203#11715897—24no—
204C22×C97—22no—
205C22×C97—41no—
206C22×C97—42no—
207C22×C97C2×C22⋊C411yescharacteristic
208C22×C97C2×C22⋊C411yescharacteristic
209C22×C97C2×C22⋊C411yescharacteristic
210C2×D97—22no—
211C2×D97—22no—
212C2×D97—22no—
213C2×D97—22no—
214C2×D97—41no—
215C2×D97—41no—
216C2×D97—41no—
217C2×D97—44no—
218C2×D97—42no—
219C2×D97—44no—
220C2×D97C2×C22⋊C411yescharacteristic
221C2×D97C2×C22⋊C411yescharacteristic
222C2×D97C2×C22⋊C411yescharacteristic
223C2×D97C22×D411yescharacteristic
224#87604—44no—
225C4×C97—22no—
226C4×C97C2×C22⋊C411yescharacteristic
227C4×C97C2×C22⋊C411yescharacteristic
228C4×C97C2×C22⋊C411yescharacteristic
229C4×C97C23×C411yescharacteristic
230Dic97—22no—
231Dic97C2×C22⋊C411yescharacteristic
232Dic97C2×C22⋊C411yescharacteristic
233Dic97C2×C22⋊C411yescharacteristic
234Dic97C22×D411yescharacteristic
235C2×C97—21no—
236C2×C97—21no—
237C2×C97—21no—
238C2×C97—42no—
239C2×C97C22×C22⋊C411yescharacteristic
240D97—21no—
241D97—21no—
242D97—21no—
243D97—42no—
244D97#42112yescomplemented
245C2×#421—971nomaximal, Sylow
246C97C2×#42111yescharacteristic, complemented, Sylow
247C22×#41—971no—
248C22×M16—971no—
249C2×#117—971no—
250#421—974no—
251#421—972no—
252#421—972no—
253C2×#104—974no—
254C2×#41—972no—
255C2×#41—972no—
256C2×#41—972no—
257C2×#41—972no—
258C2×#41—971no—
259C2×#41—971no—
260C2×#41—971no—
261C2×#41—1941no—
262C2×#41—1941no—
263C2×#41—1941no—
264C2×#41—1941no—
265C2×#41—1941no—
266C2×#41—1941no—
267C2×#41#8760411yescharacteristic, complemented
268C22×Q8—971no—
269C22×D4—971no—
270C22×D4—1941no—
271C23×C4—971no—
272C23×C4—1941no—
273C2×M16—972no—
274C2×M16—972no—
275C2×M16—972no—
276C2×M16—1941no—
277C2×M16—1941no—
278C2×M16—1941no—
279C22×C8—1941no—
280#117—972no—
281#117—972no—
282#117—1941no—
283#117—1941no—
284C2×C4⋊C4—1941no—
285C2×C22⋊C4—1941no—
286C2×C42—972no—
287#104—978no—
288#104—978no—
289C24—971no—
290C24—1941no—
291#41—21no—
292#41—21no—
293#41—972no—
294#41—972no—
295#41—972no—
296#41—972no—
297#41—972no—
298#41—972no—
299#41—1942no—
300#41—1942no—
301#41—1942no—
302#41—1942no—
303#41—1942no—
304#41—1942no—
305#41—1942no—
306#41—1942no—
307#41—1941no—
308#41—1941no—
309#41—1941no—
310#41—1941no—
311#41—1941no—
312#41—1941no—
313#41C2×#8760412yes—
314#41C2×#8760412yescomplemented
315C2×Q8—972no—
316C2×Q8—972no—
317C2×Q8—971no—
318C2×Q8—1941no—
319C2×Q8—1941no—
320C2×Q8—1941no—
321C2×Q8C2×#8760411yescharacteristic, complemented
322C2×D4—21no—
323C2×D4—972no—
324C2×D4—972no—
325C2×D4—971no—
326C2×D4—1941no—
327C2×D4—1941no—
328C2×D4—1941no—
329C2×D4—1941no—
330C2×D4—1942no—
331C2×D4—1942no—
332C2×D4—1942no—
333C2×D4—1942no—
334C2×D4—1941no—
335C2×D4—1941no—
336C2×D4C2×#8760411yescharacteristic, complemented
337C22×C4—21no—
338C22×C4—971no—
339C22×C4—971no—
340C22×C4—971no—
341C22×C4—971no—
342C22×C4—971no—
343C22×C4—971no—
344C22×C4—971no—
345C22×C4—971no—
346C22×C4—971no—
347C22×C4—971no—
348C22×C4—971no—
349C22×C4—971no—
350C22×C4—971no—
351C22×C4—1941no—
352C22×C4—1942no—
353C22×C4—1942no—
354C22×C4—1942no—
355C22×C4—1942no—
356C22×C4—1941no—
357C22×C4—1941no—
358C22×C4—1942no—
359C22×C4—1941no—
360C22×C4C2×#8760411yescharacteristic
361M16—974no—
362M16—1942no—
363M16—1942no—
364M16—1942no—
365C2×C8—1942no—
366C2×C8—1942no—
367C2×C8—1942no—
368C4⋊C4—1942no—
369C4⋊C4—1942no—
370C22⋊C4—1942no—
371C22⋊C4—1942no—
372C42—974no—
373C42—1942no—
374C23—21no—
375C23—971no—
376C23—971no—
377C23—971no—
378C23—971no—
379C23—971no—
380C23—971no—
381C23—3884no—
382C23—3882no—
383C23—1942no—
384C23—1942no—
385C23—1941no—
386C23C22⋊#8760411yescharacteristic
387Q8—21no—
388Q8—972no—
389Q8—1942no—
390Q8—1942no—
391Q8—1941no—
392Q8C22×#8760412yes—
393D4—22no—
394D4—22no—
395D4—21no—
396D4—972no—
397D4—1942no—
398D4—1942no—
399D4—1942no—
400D4—1942no—
401D4—1942no—
402D4—1942no—
403D4—1942no—
404D4—1942no—
405D4—1941no—
406D4C22×#8760412yes—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—971no—
411C2×C4—971no—
412C2×C4—971no—
413C2×C4—971no—
414C2×C4—971no—
415C2×C4—971no—
416C2×C4—971no—
417C2×C4—971no—
418C2×C4—971no—
419C2×C4—971no—
420C2×C4—971no—
421C2×C4—971no—
422C2×C4—971no—
423C2×C4—971no—
424C2×C4—971no—
425C2×C4—971no—
426C2×C4—971no—
427C2×C4—971no—
428C2×C4—971no—
429C2×C4—971no—
430C2×C4—971no—
431C2×C4—971no—
432C2×C4—3884no—
433C2×C4—1942no—
434C2×C4—1942no—
435C2×C4—1942no—
436C2×C4—1942no—
437C2×C4—1942no—
438C2×C4—1942no—
439C2×C4—1944no—
440C2×C4—1941no—
441C2×C4—1942no—
442C2×C4—1942no—
443C2×C4C22⋊#8760411yescharacteristic
444C2×C4C22⋊#8760411yescharacteristic
445C2×C4C22⋊#8760411yescharacteristic
446C2×C4C22×#8760411yescharacteristic
447C2×C4C22×#8760411yescharacteristic
448C2×C4C22×#8760411yescharacteristic
449C8—1944no—
450C22—22no—
451C22—41no—
452C22—42no—
453C22—971no—
454C22—971no—
455C22—971no—
456C22—971no—
457C22—3882no—
458C22—3881no—
459C22—3881no—
460C22—3881no—
461C22—3884no—
462C22—3884no—
463C22—1942no—
464C22—1942no—
465C22—1942no—
466C22—1942no—
467C22C2×C22⋊#8760411yescharacteristic
468C22C2×C22⋊#8760411yescharacteristic
469C22C2×C22⋊#8760411yescharacteristic
470C4—22no—
471C4—971no—
472C4—971no—
473C4—971no—
474C4—971no—
475C4—3884no—
476C4—1942no—
477C4C2×C22⋊#8760411yescharacteristic
478C4C2×C22⋊#8760411yescharacteristic
479C4C2×C22⋊#8760411yescharacteristic
480C4C23×#8760411yescharacteristic
481C2—21no—
482C2—21no—
483C2—21no—
484C2—42no—
485C2—972no—
486C2—3882no—
487C2—1941no—
488C2—1941no—
489C2—1941no—
490C2C22×C22⋊#8760411yescharacteristic
subgroupG/H
centerC4C2×C22⋊#87604
commutatorC4×C97C23×C4
FrattiniC4C23×#87604
FittingC2×#41×C97C4
socleC2×C97C22×C22⋊C4
prime radicalC2×#41×D97C2
cosocleC4×D97C24
hypercenterC2×#41#87604
hypocenterC97C2×#421
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D97⋊M16C2semidirect
2. C2×#15690889C2semidirect
3. #20261734C2semidirect
4. #20261733C2semidirect
5. #20261732C2semidirect
6. D97⋊#104C2semidirect
8. C2×#13095521C22semidirect
11. D97⋊M16C22semidirect
12. D97⋊M16C22semidirect
17. #15690889C22semidirect
18. #15690889C22semidirect
21. C2×C4×#87604C22semidirect
22. #15690875C22semidirect
23. #15690874C22semidirect
26. C2×#13095511C4semidirect
33. #41×D97C4semidirect
34. #41×D97C4semidirect
37. C2×Q8×D97C4semidirect
39. C2×D4×D97C4semidirect
42. C2×#41×C97C4semidirect
45. #13095521C23semidirect
56. C4×#87604C23semidirect
61. #13095512C2×C4semidirect
70. #13095511C2×C4semidirect
77. #13095510C2×C4semidirect
80. C2×Dic194C2×C4semidirect
84. Q8×D97C2×C4semidirect
86. C2×D388C2×C4semidirect
97. D4×D97C2×C4semidirect
122. #41×C97C2×C4semidirect
123. C2×Q8×C97C2×C4semidirect
125. C2×D4×C97C2×C4semidirect
244. D97#421semidirect
246. C97C2×#421semidirect
267. C2×#41#87604semidirect
314. #41C2×#87604semidirect
321. C2×Q8C2×#87604semidirect
336. C2×D4C2×#87604semidirect

Maximal subgroups

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

subgroupindex
C2×D97⋊M162
C2×#156908892
#202617342
#202617332
#202617322
D97⋊#1042
C2×#41×D972
C2×#42197