Finite Group Databasebeta

← C2×#11732123 #13513377

Subgroups — C2×#11732123 #13513377

Order 1792.

4262 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6502C211yesmaximal, characteristic
2C22×D4×Dic7C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D7C211yesmaximal, characteristic, complemented
4C2×C7×#386C211yesmaximal, characteristic, complemented
5C22×C7⋊#95C211yesmaximal, characteristic, complemented
6C2×#89728C211yesmaximal, characteristic, complemented
7C2×#89716C211yesmaximal, characteristic, complemented
8C2×#89730C211yesmaximal, characteristic, complemented
9C2×#89730C211yesmaximal, characteristic, complemented
10C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
12#11732123C2116yesmaximal, direct product factor
13C2×#89442C211yesmaximal, characteristic, complemented
14C2×#89427C211yesmaximal, characteristic, complemented
15C2×#89424C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C24×Dic7C2211yescharacteristic
23C24×Dic7C2211yescharacteristic
24C23×C4×D7C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C2×#6502C4116yescomplemented
32C2×#6502C2218yes—
33C2×D4×Dic7—28no—
34C2×D4×Dic7C2218yescomplemented
35C2×C4×C22⋊D7—28no—
36C2×C4×C22⋊D7C2218yescomplemented
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×(C2×D7)⋊C4C2211yescharacteristic
41C22×C4⋊Dic7C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C7×#386C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2218yescomplemented
60#89730C2218yescomplemented
61#89730C2218yescomplemented
62#89728C2218yescomplemented
63#89716C2218yescomplemented
64C22⋊C4×Dic7C2218yescomplemented
65C22⋊C4×Dic7C2218yescomplemented
66#89442C2218yescomplemented
67#89438C2218yescomplemented
68#89427C2218yescomplemented
69#89424C2218yescomplemented
70C2×#2364—71nomaximal, Sylow
71C25×C7C2311yescharacteristic
72C25×C7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C22×C7×D4—24no—
75C22×C7×D4—24no—
76C22×C7×D4C2×C418yescomplemented
77C22×C7×D4C2314yes—
78C23×C4×C7—24no—
79C23×C4×C7—24no—
80C23×C4×C7—42no—
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2314yes—
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C22×C22⋊D7—24no—
88C22×C22⋊D7—24no—
89C22×C22⋊D7—42no—
90C22×C22⋊D7—42no—
91C22×C22⋊D7C2×C418yescomplemented
92C22×C22⋊D7C2×C418yescomplemented
93C22×C22⋊D7C2314yes—
94C22×C22⋊D7C2314yes—
95C23×Dic7—24no—
96C23×Dic7—24no—
97C23×Dic7—24no—
98C23×Dic7—24no—
99C23×Dic7—42no—
100C23×Dic7—42no—
101C23×Dic7—42no—
102C23×Dic7—42no—
103C23×Dic7C2×C418yescomplemented
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2314yes—
106C23×Dic7C2314yes—
107C23×Dic7C2311yescharacteristic
108C23×Dic7C2311yescharacteristic
109C23×Dic7C2311yescharacteristic
110C23×Dic7C2311yescharacteristic
111C23×Dic7C2311yescharacteristic
112C23×Dic7C2311yescharacteristic
113C23×Dic7C2314yes—
114C22×C4×D7—24no—
115C22×C4×D7—24no—
116C22×C4×D7—42no—
117C22×C4×D7C2314yes—
118C2×C7×C22⋊C4—24no—
119C2×C7×C22⋊C4—24no—
120C2×C7×C22⋊C4—42no—
121C2×C7×C22⋊C4C2314yes—
122C2×C7×C22⋊C4C2314yes—
123C2×C7×C22⋊C4C2314yes—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7C2×C418yescomplemented
126C2×C22⋊Dic7D418yescomplemented
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130#6502C2×C4164yescomplemented
131D4×Dic7—232no—
132C4×C22⋊D7—232no—
133C2×(C2×D7)⋊C4—24no—
134C2×(C2×D7)⋊C4—24no—
135C2×(C2×D7)⋊C4—42no—
136C2×(C2×D7)⋊C4C2×C418yescomplemented
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×(C2×D7)⋊C4C2314yes—
141C2×C4⋊Dic7—24no—
142C2×C4⋊Dic7C2314yes—
143C2×Dic7⋊C4—24no—
144C2×Dic7⋊C4C2×C418yescomplemented
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×C4×Dic7—24no—
148C2×C4×Dic7—24no—
149C2×C4×Dic7—42no—
150C2×C4×Dic7—42no—
151C2×C4×Dic7C2314yes—
152C2×C4×Dic7C2314yes—
153C2×C4×Dic7C2314yes—
154C2×C4×Dic7C2314yes—
155C7×#95C2314yes—
156C7×#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C22×#121—71no—
166C22×C4×D4—71no—
167C22×C4×D4—71no—
168#2364—716no—
169C2×#388—71no—
170C2×#388—71no—
171C2×#387—71no—
172C2×#387—71no—
173C2×#386—71no—
174C2×#386—71no—
175C2×#386—71no—
176C2×#386D711yescharacteristic, complemented
177C2×C4×C22⋊C4—71no—
178C2×C4×C22⋊C4—71no—
179C2×C4×C22⋊C4—71no—
180C22×#95—71no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7C22×C414yes—
192C24×C7C22×C414yes—
193C24×C7C2×D414yes—
194C24×C7#4114yes—
195C24×C7C2412yes—
196C24×C7C2412yes—
197C24×C7C2411yescharacteristic
198C23×D7—22no—
199C23×D7—22no—
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7C22×C414yes—
205C23×D7C2412yes—
206C2×C7×D4—232no—
207C2×C7×D4—28no—
208C2×C7×D4—28no—
209C2×C7×D4C22×C4116yescomplemented
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—28no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—28no—
225C22×C4×C7—44no—
226C22×C4×C7—416no—
227C22×C4×C7C22×C414yes—
228C22×C4×C7#4114yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C2×C22⋊D7—232no—
235C2×C22⋊D7—28no—
236C2×C22⋊D7—28no—
237C2×C22⋊D7—416no—
238C2×C22⋊D7—44no—
239C2×C22⋊D7—44no—
240C2×C22⋊D7C22×C4116yescomplemented
241C2×C22⋊D7C22×C4116yescomplemented
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—28no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—28no—
259C22×Dic7—28no—
260C22×Dic7—28no—
261C22×Dic7—416no—
262C22×Dic7—44no—
263C22×Dic7—44no—
264C22×Dic7—44no—
265C22×Dic7—44no—
266C22×Dic7—416no—
267C22×Dic7—416no—
268C22×Dic7C22×C414yes—
269C22×Dic7C22×C414yes—
270C22×Dic7C22×C414yes—
271C22×Dic7C22×C4116yescomplemented
272C22×Dic7C2×D414yes—
273C22×Dic7C2×D414yes—
274C22×Dic7#4114yes—
275C22×Dic7C2412yes—
276C22×Dic7C2412yes—
277C22×Dic7C2412yes—
278C22×Dic7C2412yes—
279C22×Dic7C2412yes—
280C22×Dic7C2412yes—
281C22×Dic7C2412yes—
282C2×C4×D7—28no—
283C2×C4×D7—28no—
284C2×C4×D7—44no—
285C2×C4×D7—416no—
286C7×C22⋊C4—28no—
287C7×C22⋊C4—28no—
288C7×C22⋊C4—44no—
289C22⋊Dic7—28no—
290C22⋊Dic7C22×C4116yescomplemented
291C22⋊Dic7C2×D4116yescomplemented
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—28no—
294(C2×D7)⋊C4—44no—
295(C2×D7)⋊C4C22×C4116yescomplemented
296C4⋊Dic7—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4C22×C4116yescomplemented
299C4×Dic7—28no—
300C4×Dic7—28no—
301C4×Dic7—44no—
302C4×Dic7—44no—
303C23×D4—71no—
304C23×D4—71no—
305C23×D4C2×D711yescharacteristic
306C24×C4—71no—
307C24×C4—71no—
308C24×C4—71no—
309C24×C4—71no—
310C24×C4C2×D711yescharacteristic
311C2×#121—716no—
312C2×#121—78no—
313C2×C4×D4—78no—
314C2×C4×D4—78no—
315C2×C4×D4—148no—
316C2×C4×D4—148no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C22⋊C4—71no—
321C22×C22⋊C4—71no—
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4C2×D711yescharacteristic
328C22×C22⋊C4C2×D711yescharacteristic
329C22×C22⋊C4C2×D711yescharacteristic
330C22×C42—71no—
331C22×C42—71no—
332C22×C42—71no—
333C22×C42—71no—
334#388—78no—
335#388—78no—
336#387—78no—
337#387—78no—
338#386—78no—
339#386—78no—
340#386—78no—
341#386C2×D718yescomplemented
342C4×C22⋊C4—78no—
343C4×C22⋊C4—78no—
344C4×C22⋊C4—78no—
345C2×#95—78no—
346C2×#95—71no—
347C2×#95—71no—
348C2×#95—71no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95C2×D711yescharacteristic
355C2×#95C2×D711yescharacteristic
356C23×C7—28no—
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—28no—
361C23×C7—28no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—28no—
367C23×C7—28no—
368C23×C7—28no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7C4×D4116yes—
380C23×C7C23×C414yes—
381C23×C7C23×C414yes—
382C23×C7C23×C412yes—
383C23×C7C22×D414yes—
384C23×C7C22×D412yes—
385C23×C7C2×#4114yes—
386C23×C7C2×#4112yes—
387C23×C7C2×#4112yes—
388C23×C7C2×#4112yes—
389C23×C7H(5,𝔽2)12yes—
390C23×C7H(5,𝔽2)12yes—
391C23×C7C2511yescharacteristic
392C22×D7—28no—
393C22×D7—28no—
394C22×D7—28no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—44no—
402C22×D7—44no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7C23×C414yes—
406C7×D4—232no—
407C2×C4×C7—28no—
408C2×C4×C7—28no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—416no—
423C2×C4×C7—44no—
424C2×C4×C7—44no—
425C2×C4×C7—44no—
426C2×C4×C7C23×C414yes—
427C2×C4×C7C2×#4114yes—
428C22⋊D7—232no—
429C22⋊D7—416no—
430C2×Dic7—28no—
431C2×Dic7—28no—
432C2×Dic7—28no—
433C2×Dic7—28no—
434C2×Dic7—28no—
435C2×Dic7—28no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—416no—
452C2×Dic7—416no—
453C2×Dic7—416no—
454C2×Dic7—44no—
455C2×Dic7C23×C414yes—
456C2×Dic7C23×C414yes—
457C2×Dic7C23×C414yes—
458C2×Dic7C22×D414yes—
459C2×Dic7C22×D414yes—
460C2×Dic7C2×#4114yes—
461C4×D7—416no—
462C25—71no—
463C25C22×D711yescharacteristic
464C25C22×D711yescharacteristic
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—78no—
468C22×D4—74no—
469C22×D4—78no—
470C22×D4—74no—
471C22×D4—144no—
472C22×D4—144no—
473C22×D4—282no—
474C22×D4—282no—
475C22×D4C4×D718yescomplemented
476C22×D4C22×D714yes—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—78no—
487C23×C4—74no—
488C23×C4—71no—
489C23×C4—74no—
490C23×C4—74no—
491C23×C4—74no—
492C23×C4—144no—
493C23×C4—144no—
494C23×C4—144no—
495C23×C4—144no—
496C23×C4—144no—
497C23×C4—144no—
498C23×C4—282no—
499C23×C4—282no—
500C23×C4—282no—
501C23×C4—282no—
502C23×C4—282no—
503C23×C4C22×D711yescharacteristic
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506C23×C4C22×D714yes—
507C23×C4C22×D711yescharacteristic
508C23×C4C22×D711yescharacteristic
509#121—764no—
510C4×D4—1432no—
511C4×D4—1432no—
512C2×C4⋊C4—78no—
513C2×C4⋊C4—74no—
514C2×C4⋊C4—74no—
515C2×C4⋊C4—74no—
516C2×C4⋊C4—144no—
517C2×C4⋊C4—144no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—78no—
522C2×C22⋊C4—78no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—78no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—144no—
532C2×C22⋊C4—144no—
533C2×C22⋊C4—144no—
534C2×C22⋊C4—282no—
535C2×C22⋊C4C22×D714yes—
536C2×C22⋊C4C22×D714yes—
537C2×C22⋊C4C22×D714yes—
538C2×C42—74no—
539C2×C42—74no—
540C2×C42—74no—
541C2×C42—74no—
542C2×C42—144no—
543C2×C42—144no—
544C2×C42—282no—
545C2×C42—282no—
546#95—74no—
547#95—74no—
548#95—74no—
549#95—74no—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95C22×D714yes—
555#95C22×D714yes—
556C22×C7—232no—
557C22×C7—24no—
558C22×C7—24no—
559C22×C7—24no—
560C22×C7—24no—
561C22×C7—24no—
562C22×C7—24no—
563C22×C7—24no—
564C22×C7—24no—
565C22×C7—24no—
566C22×C7—416no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7C2×C4×D418yes—
572C22×C7C2×C4×D414yes—
573C22×C7C4×#4114yes—
574C22×C7#51814yes—
575C22×C7#54614yes—
576C22×C7#54614yes—
577C22×C7#55314yes—
578C22×C7#55314yes—
579C22×C7C24×C411yescharacteristic
580C22×C7C23×D411yescharacteristic
581C22×C7C22×#4111yescharacteristic
582C22×C7C22×#4111yescharacteristic
583C22×C7C22×#4111yescharacteristic
584C22×C7C2×H(5,𝔽2)11yescharacteristic
585C22×C7C2×H(5,𝔽2)11yescharacteristic
586C2×D7—24no—
587C2×D7—24no—
588C2×D7—24no—
589C2×D7—416no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—42no—
594C4×C7—24no—
595C4×C7—24no—
596C4×C7—42no—
597C4×C7—42no—
598C4×C7—42no—
599Dic7—24no—
600Dic7—24no—
601Dic7—24no—
602Dic7—24no—
603Dic7—24no—
604Dic7—24no—
605Dic7—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—74no—
617C24—72no—
618C24—142no—
619C24—142no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24C2×C4×D714yes—
625C24C2×C4×D714yes—
626C24D4×D714yes—
627C24#115914yes—
628C24C23×D712yes—
629C24C23×D712yes—
630C24C23×D711yescharacteristic
631C2×D4—232no—
632C2×D4—28no—
633C2×D4—28no—
634C2×D4—716no—
635C2×D4—716no—
636C2×D4—1432no—
637C2×D4—148no—
638C2×D4—148no—
639C2×D4—2816no—
640C2×D4—284no—
641C2×D4—284no—
642C2×D4C2×C4×D7116yescomplemented
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—28no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—28no—
658C22×C4—44no—
659C22×C4—416no—
660C22×C4—74no—
661C22×C4—74no—
662C22×C4—74no—
663C22×C4—74no—
664C22×C4—74no—
665C22×C4—74no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—716no—
673C22×C4—72no—
674C22×C4—148no—
675C22×C4—148no—
676C22×C4—148no—
677C22×C4—148no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—148no—
692C22×C4—142no—
693C22×C4—142no—
694C22×C4—148no—
695C22×C4—284no—
696C22×C4—2816no—
697C22×C4—2816no—
698C22×C4—284no—
699C22×C4—284no—
700C22×C4—284no—
701C22×C4—284no—
702C22×C4—2816no—
703C22×C4—2816no—
704C22×C4C2×C4×D714yes—
705C22×C4#115914yes—
706C22×C4C23×D712yes—
707C22×C4C23×D712yes—
708C22×C4C23×D712yes—
709C22×C4C23×D712yes—
710C22×C4C23×D712yes—
711C4⋊C4—716no—
712C4⋊C4—148no—
713C4⋊C4—148no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—44no—
717C22⋊C4—716no—
718C22⋊C4—716no—
719C22⋊C4—716no—
720C22⋊C4—148no—
721C22⋊C4—148no—
722C22⋊C4—148no—
723C22⋊C4—284no—
724C42—148no—
725C42—148no—
726C42—284no—
727C42—284no—
728C2×C7—28no—
729C2×C7—44no—
730C2×C7#236418yescomplemented
731C2×C7C22×C4×D411yescharacteristic
732C2×C7C2×C4×#4111yescharacteristic
733C2×C7C2×#51811yescharacteristic
734C2×C7C2×#54611yescharacteristic
735C2×C7C2×#54611yescharacteristic
736C2×C7C2×#55311yescharacteristic
737C2×C7C2×#55311yescharacteristic
738D7—44no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—28no—
750C23—28no—
751C23—28no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—74no—
763C23—148no—
764C23—148no—
765C23—148no—
766C23—142no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—142no—
772C23—284no—
773C23—284no—
774C23—284no—
775C23—284no—
776C23(C22⋊D7)⋊C4116yes—
777C23C22×C4×D714yes—
778C23C22×C4×D714yes—
779C23C22×C4×D712yes—
780C23C2×D4×D714yes—
781C23C2×D4×D712yes—
782C23C2×#115914yes—
783C23C2×#115912yes—
784C23C2×#115912yes—
785C23#654812yes—
786C23D7×#4112yes—
787C23#655312yes—
788C23C24×D711yescharacteristic
789D4—232no—
790D4—1432no—
791D4—2816no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—416no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—74no—
812C2×C4—74no—
813C2×C4—74no—
814C2×C4—74no—
815C2×C4—74no—
816C2×C4—74no—
817C2×C4—148no—
818C2×C4—148no—
819C2×C4—148no—
820C2×C4—148no—
821C2×C4—148no—
822C2×C4—148no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—142no—
833C2×C4—142no—
834C2×C4—142no—
835C2×C4—142no—
836C2×C4—142no—
837C2×C4—142no—
838C2×C4—2816no—
839C2×C4—2816no—
840C2×C4—2816no—
841C2×C4—2816no—
842C2×C4—284no—
843C2×C4C22×C4×D714yes—
844C2×C4C2×#115914yes—
845C7C2×#236411yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—232no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—416no—
861C22—144no—
862C22—144no—
863C22—144no—
864C22—282no—
865C22—282no—
866C22—282no—
867C22—282no—
868C22—2816no—
869C22C2×(C22⋊D7)⋊C418yes—
870C22C2×(C22⋊D7)⋊C414yes—
871C22C4×#115914yes—
872C22#9023614yes—
873C22#9028214yes—
874C22#9029214yes—
875C22#9030914yes—
876C22#9034514yes—
877C22C23×C4×D711yescharacteristic
878C22C22×D4×D711yescharacteristic
879C22C22×#115911yescharacteristic
880C22C22×#115911yescharacteristic
881C22C2×#654811yescharacteristic
882C22C2×D7×#4111yescharacteristic
883C22C2×#655311yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—144no—
890C4—144no—
891C4—144no—
892C4—144no—
893C4—144no—
894C4—144no—
895C4—282no—
896C2—28no—
897C2—44no—
898C2—284no—
899C2#1173212318yesdirect product factor
900C2C22×(C22⋊D7)⋊C411yescharacteristic
901C2C2×C4×#115911yescharacteristic
902C2C2×#9023611yescharacteristic
903C2C2×#9028211yescharacteristic
904C2C2×#9030911yescharacteristic
905C2C2×#9029211yescharacteristic
906C2C2×#9034511yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC22×#6502C2
cosocleC23×C7C25
hypercenterC2×#386D7
hypocenterC7C2×#2364
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic7C2semidirect
3. C22×C4×C22⋊D7C2semidirect
4. C2×C7×#386C2semidirect
5. C22×C7⋊#95C2semidirect
6. C2×#89728C2semidirect
7. C2×#89716C2semidirect
8. C2×#89730C2semidirect
9. C2×#89730C2semidirect
10. C2×C22⋊C4×Dic7C2semidirect
11. C2×C22⋊C4×Dic7C2semidirect
12. #11732123C2direct (N × H)
13. C2×#89442C2semidirect
14. C2×#89427C2semidirect
15. C2×#89424C2semidirect
16. C2×#89438C2semidirect
31. C2×#6502C4semidirect
34. C2×D4×Dic7C22semidirect
36. C2×C4×C22⋊D7C22semidirect
48. C7×#386C22semidirect
59. C2×C7⋊#95C22semidirect
60. #89730C22semidirect
61. #89730C22semidirect
62. #89728C22semidirect
63. #89716C22semidirect
64. C22⋊C4×Dic7C22semidirect
65. C22⋊C4×Dic7C22semidirect
66. #89442C22semidirect
67. #89438C22semidirect
68. #89427C22semidirect
69. #89424C22semidirect
76. C22×C7×D4C2×C4semidirect
91. C22×C22⋊D7C2×C4semidirect
92. C22×C22⋊D7C2×C4semidirect
103. C23×Dic7C2×C4semidirect
125. C2×C22⋊Dic7C2×C4semidirect
126. C2×C22⋊Dic7D4semidirect
130. #6502C2×C4semidirect
136. C2×(C2×D7)⋊C4C2×C4semidirect
144. C2×Dic7⋊C4C2×C4semidirect
176. C2×#386D7semidirect
209. C2×C7×D4C22×C4semidirect
240. C2×C22⋊D7C22×C4semidirect
241. C2×C22⋊D7C22×C4semidirect
271. C22×Dic7C22×C4semidirect
290. C22⋊Dic7C22×C4semidirect
291. C22⋊Dic7C2×D4semidirect
295. (C2×D7)⋊C4C22×C4semidirect
298. Dic7⋊C4C22×C4semidirect
341. #386C2×D7semidirect
475. C22×D4C4×D7semidirect
642. C2×D4C2×C4×D7semidirect
730. C2×C7#2364semidirect
845. C7C2×#2364semidirect
899. C2#11732123direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65022
C22×D4×Dic72
C22×C4×C22⋊D72
C2×C7×#3862
C22×C7⋊#952
C2×#897282
C2×#897162
C2×#897302
C2×C22⋊C4×Dic72
#117321232
C2×#894422
C2×#894272
C2×#894242
C2×#894382
C2×#23647