Finite Group Databasebeta

← C2×#11739800 #13521514

Subgroups — C2×#11739800 #13521514

Order 1792.

3938 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×C4×C7×D4C211yesmaximal, characteristic, complemented
2C22×#6498C211yesmaximal, characteristic, complemented
3C22×#6502C211yesmaximal, characteristic
4C22×#6449C211yesmaximal, characteristic, complemented
5C2×#89985C211yesmaximal, characteristic, complemented
6C2×#89985C211yesmaximal, characteristic, complemented
7C2×#89984C211yesmaximal, characteristic, complemented
8C22×C7⋊#95C211yesmaximal, characteristic, complemented
9#11739800C2116yesmaximal, direct product factor
10C2×#89766C211yesmaximal, characteristic, complemented
11C2×#89755C211yesmaximal, characteristic, complemented
12C2×#89725C211yesmaximal, characteristic, complemented
13C2×#89733C211yesmaximal, characteristic, complemented
14C2×#89722C211yesmaximal, characteristic, complemented
15C2×#89700C211yesmaximal, characteristic, complemented
16C2×#89712C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C24×C4×C7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C22⋊D7C2211yescharacteristic
22C24×Dic7C2211yescharacteristic
23C24×Dic7C2211yescharacteristic
24C2×C4×C7×D4—28no—
25C2×C4×C7×D4C2218yescomplemented
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C42×C7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C2×#6502—28no—
35C2×#6502C2218yes—
36C2×#6498—28no—
37C2×#6498C2218yescomplemented
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×(C2×D7)⋊C4C2211yescharacteristic
41C22×(C2×D7)⋊C4C2211yescharacteristic
42C22×(C2×D7)⋊C4C2211yescharacteristic
43C22×C4⋊Dic7C2211yescharacteristic
44C22×C4⋊Dic7C2211yescharacteristic
45C22×C4⋊Dic7C2211yescharacteristic
46C22×C4⋊Dic7C2211yescharacteristic
47C22×Dic7⋊C4C2211yescharacteristic
48C22×Dic7⋊C4C2211yescharacteristic
49C22×Dic7⋊C4C2211yescharacteristic
50C2×#6449—28no—
51C2×#6449C2218yescomplemented
52#89985C2218yescomplemented
53#89985C2218yescomplemented
54#89984C2218yescomplemented
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62C2×C7⋊#95C2211yescharacteristic
63C2×C7⋊#95C2218yescomplemented
64#89766C2218yescomplemented
65#89755C2218yescomplemented
66#89733C2218yescomplemented
67#89725C2218yescomplemented
68#89722C2218yescomplemented
69#89712C2218yescomplemented
70#89700C2218yescomplemented
71C2×#2425—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4D418yes—
78C22×C7×D4C2314yes—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—24no—
82C23×C4×C7—24no—
83C23×C4×C7—42no—
84C23×C4×C7—42no—
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2314yes—
87C23×C4×C7C2314yes—
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C22×C22⋊D7—24no—
93C22×C22⋊D7—24no—
94C22×C22⋊D7—24no—
95C22×C22⋊D7—24no—
96C22×C22⋊D7—24no—
97C22×C22⋊D7—42no—
98C22×C22⋊D7C2314yes—
99C22×C22⋊D7C2314yes—
100C23×Dic7—24no—
101C23×Dic7—24no—
102C23×Dic7—24no—
103C23×Dic7—24no—
104C23×Dic7—24no—
105C23×Dic7—42no—
106C23×Dic7C2314yes—
107C23×Dic7C2311yescharacteristic
108C23×Dic7C2311yescharacteristic
109C23×Dic7C2311yescharacteristic
110C23×Dic7C2311yescharacteristic
111C23×Dic7C2311yescharacteristic
112C23×Dic7C2311yescharacteristic
113C23×Dic7C2314yes—
114C23×Dic7C2311yescharacteristic
115C4×C7×D4—232no—
116C2×C7×C4⋊C4—24no—
117C2×C7×C4⋊C4C2314yes—
118C2×C7×C22⋊C4—24no—
119C2×C7×C22⋊C4D418yescomplemented
120C2×C7×C22⋊C4C2314yes—
121C2×C7×C22⋊C4C2314yes—
122C2×C42×C7—24no—
123C2×C42×C7C2314yes—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7—24no—
126C2×C22⋊Dic7—24no—
127C2×C22⋊Dic7—24no—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132#6502—232no—
133#6498—232no—
134C2×(C2×D7)⋊C4—24no—
135C2×(C2×D7)⋊C4—24no—
136C2×(C2×D7)⋊C4—24no—
137C2×(C2×D7)⋊C4—24no—
138C2×(C2×D7)⋊C4—42no—
139C2×(C2×D7)⋊C4C2314yes—
140C2×(C2×D7)⋊C4C2314yes—
141C2×(C2×D7)⋊C4C2314yes—
142C2×(C2×D7)⋊C4C2314yes—
143C2×(C2×D7)⋊C4C2314yes—
144C2×C4⋊Dic7—24no—
145C2×C4⋊Dic7—24no—
146C2×C4⋊Dic7—24no—
147C2×C4⋊Dic7—42no—
148C2×C4⋊Dic7C2314yes—
149C2×C4⋊Dic7C2314yes—
150C2×C4⋊Dic7C2314yes—
151C2×C4⋊Dic7C2314yes—
152C2×Dic7⋊C4—24no—
153C2×Dic7⋊C4—24no—
154C2×Dic7⋊C4—24no—
155C2×Dic7⋊C4C2314yes—
156C2×Dic7⋊C4C2314yes—
157C2×Dic7⋊C4C2314yes—
158#6449—232no—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×#123—71no—
168C22×#123—71no—
169C22×#121—71no—
170C22×C4×D4D711yescharacteristic, complemented
171#2425—716no—
172C2×#398—71no—
173C2×#397—71no—
174C2×#396—71no—
175C2×#394—71no—
176C2×#389—71no—
177C2×#388—71no—
178C2×#386—71no—
179C2×#386—71no—
180C2×#385—71no—
181C2×#380—71no—
182C22×#95—71no—
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×C7—22no—
192C24×C7—22no—
193C24×C7C2×D414yes—
194C24×C7C2×D414yes—
195C24×C7C2×D414yes—
196C24×C7#4114yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7—22no—
205C23×D7—22no—
206C23×D7—22no—
207C23×D7C2412yes—
208C2×C7×D4—232no—
209C2×C7×D4—28no—
210C2×C7×D4—28no—
211C2×C7×D4C2×D4116yes—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—28no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—28no—
225C22×C4×C7—28no—
226C22×C4×C7—28no—
227C22×C4×C7—44no—
228C22×C4×C7—44no—
229C22×C4×C7—416no—
230C22×C4×C7—416no—
231C22×C4×C7C2×D414yes—
232C22×C4×C7C2×D414yes—
233C22×C4×C7C2×D414yes—
234C22×C4×C7#4114yes—
235C22×C4×C7C2412yes—
236C22×C4×C7C2412yes—
237C22×C4×C7C2412yes—
238C22×C4×C7C2412yes—
239C22×C4×C7C2412yes—
240C2×C22⋊D7—28no—
241C2×C22⋊D7—28no—
242C2×C22⋊D7—28no—
243C2×C22⋊D7—28no—
244C2×C22⋊D7—28no—
245C2×C22⋊D7—44no—
246C2×C22⋊D7—416no—
247C2×C22⋊D7—416no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—28no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—28no—
261C22×Dic7—28no—
262C22×Dic7—22no—
263C22×Dic7—22no—
264C22×Dic7—28no—
265C22×Dic7—22no—
266C22×Dic7—22no—
267C22×Dic7—22no—
268C22×Dic7—22no—
269C22×Dic7—22no—
270C22×Dic7—22no—
271C22×Dic7—22no—
272C22×Dic7—28no—
273C22×Dic7—44no—
274C22×Dic7—416no—
275C22×Dic7—416no—
276C22×Dic7#4114yes—
277C22×Dic7C2412yes—
278C22×Dic7C2412yes—
279C22×Dic7C2412yes—
280C22×Dic7C2412yes—
281C22×Dic7C2412yes—
282C22×Dic7C2412yes—
283C22×Dic7C2412yes—
284C7×C4⋊C4—28no—
285C7×C22⋊C4—28no—
286C7×C22⋊C4C2×D4116yescomplemented
287C42×C7—28no—
288C22⋊Dic7—28no—
289C22⋊Dic7—28no—
290C22⋊Dic7—28no—
291C22⋊Dic7—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—28no—
294(C2×D7)⋊C4—28no—
295(C2×D7)⋊C4—28no—
296(C2×D7)⋊C4—44no—
297C4⋊Dic7—28no—
298C4⋊Dic7—28no—
299C4⋊Dic7—28no—
300C4⋊Dic7—44no—
301Dic7⋊C4—28no—
302Dic7⋊C4—28no—
303Dic7⋊C4—28no—
304C23×D4—71no—
305C23×D4—71no—
306C23×D4C2×D711yescharacteristic
307C24×C4—71no—
308C24×C4—71no—
309C24×C4C2×D711yescharacteristic
310C24×C4C2×D711yescharacteristic
311C2×#123—78no—
312C2×#123—78no—
313C2×#123—148no—
314C2×#123—148no—
315C2×#121—78no—
316C2×#121—148no—
317C2×C4×D4—28no—
318C2×C4×D4C2×D718yescomplemented
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—71no—
326C22×C4⋊C4C2×D711yescharacteristic
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C22⋊C4—71no—
335C22×C22⋊C4—71no—
336C22×C22⋊C4C2×D711yescharacteristic
337C22×C22⋊C4C2×D711yescharacteristic
338C22×C42C2×D711yescharacteristic
339#398—78no—
340#397—78no—
341#396—78no—
342#394—78no—
343#389—78no—
344#388—78no—
345#386—78no—
346#386—78no—
347#385—78no—
348#380—78no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—78no—
355C2×#95—71no—
356C2×#95—71no—
357C2×#95—71no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—28no—
361C23×C7—28no—
362C23×C7—28no—
363C23×C7—28no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—28no—
369C23×C7—28no—
370C23×C7—28no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7#121116yes—
382C23×C7C22×D414yes—
383C23×C7C22×D414yes—
384C23×C7C22×D412yes—
385C23×C7C22×D414yes—
386C23×C7C22×D412yes—
387C23×C7C2×#4114yes—
388C23×C7C2×#4112yes—
389C23×C7C2×#4112yes—
390C23×C7C2×#4112yes—
391C23×C7H(5,𝔽2)12yes—
392C23×C72−1+412yes—
393C23×C7C2511yescharacteristic
394C22×D7—22no—
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×D7—44no—
406C22×D7—44no—
407C22×D7—44no—
408C7×D4—232no—
409C2×C4×C7—28no—
410C2×C4×C7—28no—
411C2×C4×C7—28no—
412C2×C4×C7—28no—
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—22no—
423C2×C4×C7—22no—
424C2×C4×C7—416no—
425C2×C4×C7—416no—
426C2×C4×C7—44no—
427C2×C4×C7C22×D414yes—
428C2×C4×C7C22×D414yes—
429C2×C4×C7C22×D414yes—
430C2×C4×C7C2×#4114yes—
431C22⋊D7—416no—
432C22⋊D7—416no—
433C2×Dic7—28no—
434C2×Dic7—22no—
435C2×Dic7—22no—
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—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—416no—
455C2×Dic7—416no—
456C2×Dic7—44no—
457C2×Dic7—44no—
458C2×Dic7—44no—
459C2×Dic7—44no—
460C2×Dic7—44no—
461C2×Dic7—44no—
462C2×Dic7C2×#4114yes—
463C25—71no—
464C25C22×D711yescharacteristic
465C25C22×D711yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—74no—
469C22×D4—74no—
470C22×D4—144no—
471C22×D4—144no—
472C22×D4—144no—
473C22×D4—144no—
474C22×D4—144no—
475C22×D4—282no—
476C22×D4D2818yes—
477C22×D4C22×D714yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—42no—
483C23×C4—42no—
484C23×C4—71no—
485C23×C4—74no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—74no—
493C23×C4—144no—
494C23×C4—144no—
495C23×C4—144no—
496C23×C4—144no—
497C23×C4—144no—
498C23×C4—282no—
499C23×C4C22×D711yescharacteristic
500C23×C4C22×D714yes—
501C23×C4C22×D714yes—
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D711yescharacteristic
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506#123—1432no—
507#123—1432no—
508#121—1432no—
509C4×D4—232no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—74no—
512C2×C4⋊C4—74no—
513C2×C4⋊C4—74no—
514C2×C4⋊C4—74no—
515C2×C4⋊C4—74no—
516C2×C4⋊C4—74no—
517C2×C4⋊C4—74no—
518C2×C4⋊C4—144no—
519C2×C4⋊C4—144no—
520C2×C4⋊C4—144no—
521C2×C4⋊C4—144no—
522C2×C4⋊C4—144no—
523C2×C4⋊C4—144no—
524C2×C4⋊C4—282no—
525C2×C4⋊C4C22×D714yes—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—74no—
532C2×C22⋊C4—74no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4—74no—
535C2×C22⋊C4—74no—
536C2×C22⋊C4—144no—
537C2×C22⋊C4—144no—
538C2×C22⋊C4—144no—
539C2×C22⋊C4—144no—
540C2×C22⋊C4—144no—
541C2×C22⋊C4—144no—
542C2×C22⋊C4—144no—
543C2×C22⋊C4—144no—
544C2×C22⋊C4—282no—
545C2×C22⋊C4C22⋊D718yescomplemented
546C2×C22⋊C4C22×D714yes—
547C2×C22⋊C4C22×D714yes—
548C2×C42—24no—
549C2×C42C22×D714yes—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95—74no—
555#95—74no—
556#95—74no—
557#95—74no—
558C22×C7—24no—
559C22×C7—232no—
560C22×C7—24no—
561C22×C7—24no—
562C22×C7—24no—
563C22×C7—24no—
564C22×C7—24no—
565C22×C7—24no—
566C22×C7—24no—
567C22×C7—24no—
568C22×C7—42no—
569C22×C7—416no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7C2×#12118yes—
574C22×C7C2×#12114yes—
575C22×C7#52914yes—
576C22×C7#53914yes—
577C22×C7#54614yes—
578C22×C7#54614yes—
579C22×C7#54714yes—
580C22×C7#54714yes—
581C22×C7C23×D411yescharacteristic
582C22×C7C23×D411yescharacteristic
583C22×C7C22×#4111yescharacteristic
584C22×C7C22×#4111yescharacteristic
585C22×C7C22×#4111yescharacteristic
586C22×C7C2×H(5,𝔽2)11yescharacteristic
587C22×C7C2×2−1+411yescharacteristic
588C2×D7—42no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—42no—
594C2×D7—42no—
595C2×D7—88no—
596C4×C7—24no—
597C4×C7—24no—
598C4×C7—24no—
599C4×C7—24no—
600C4×C7—42no—
601Dic7—24no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606Dic7—42no—
607Dic7—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—72no—
619C24—142no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24—142no—
626C24C2×D2814yes—
627C24C2×D2814yes—
628C24#115714yes—
629C24C2×C22⋊D714yes—
630C24C23×D712yes—
631C24C23×D712yes—
632C24C23×D711yescharacteristic
633C2×D4—232no—
634C2×D4—28no—
635C2×D4—28no—
636C2×D4—148no—
637C2×D4—148no—
638C2×D4—148no—
639C2×D4—148no—
640C2×D4—148no—
641C2×D4—284no—
642C2×D4—2816no—
643C2×D4—2816no—
644C2×D4C2×D28116yes—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—28no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—28no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—416no—
663C22×C4—416no—
664C22×C4—74no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—148no—
673C22×C4—142no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—148no—
682C22×C4—148no—
683C22×C4—148no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4—142no—
693C22×C4—142no—
694C22×C4—142no—
695C22×C4—142no—
696C22×C4—148no—
697C22×C4—284no—
698C22×C4—2816no—
699C22×C4—2816no—
700C22×C4C2×D2814yes—
701C22×C4#115914yes—
702C22×C4C2×C22⋊D714yes—
703C22×C4C2×C22⋊D714yes—
704C22×C4C23×D712yes—
705C22×C4C23×D712yes—
706C22×C4C23×D712yes—
707C22×C4C23×D712yes—
708C22×C4C23×D712yes—
709C4⋊C4—28no—
710C4⋊C4—148no—
711C4⋊C4—148no—
712C4⋊C4—148no—
713C4⋊C4—148no—
714C4⋊C4—148no—
715C4⋊C4—148no—
716C4⋊C4—284no—
717C22⋊C4—28no—
718C22⋊C4—148no—
719C22⋊C4—148no—
720C22⋊C4—148no—
721C22⋊C4—148no—
722C22⋊C4—148no—
723C22⋊C4—148no—
724C22⋊C4—148no—
725C22⋊C4—148no—
726C22⋊C4—284no—
727C22⋊C4C2×C22⋊D7116yescomplemented
728C42—28no—
729C2×C7—28no—
730C2×C7—44no—
731C2×C7#242518yescomplemented
732C2×C7C22×#12111yescharacteristic
733C2×C7C2×#52911yescharacteristic
734C2×C7C2×#53911yescharacteristic
735C2×C7C2×#54611yescharacteristic
736C2×C7C2×#54611yescharacteristic
737C2×C7C2×#54711yescharacteristic
738C2×C7C2×#54711yescharacteristic
739D7—82no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—142no—
764C23—142no—
765C23—142no—
766C23—142no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—284no—
771C23—284no—
772C23—284no—
773C23—284no—
774C23—284no—
775C23—284no—
776C23—284no—
777C23#6493116yes—
778C23C22×D2814yes—
779C23C22×D2814yes—
780C23C22×D2812yes—
781C23C2×#115714yes—
782C23C2×#115712yes—
783C23C2×#115912yes—
784C23#654812yes—
785C23D7×#4112yes—
786C23#655412yes—
787C23C22×C22⋊D714yes—
788C23C22×C22⋊D712yes—
789C23C24×D711yescharacteristic
790D4—232no—
791D4—2816no—
792D4—2816no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
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—22no—
808C2×C4—416no—
809C2×C4—416no—
810C2×C4—44no—
811C2×C4—74no—
812C2×C4—148no—
813C2×C4—142no—
814C2×C4—142no—
815C2×C4—142no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
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—2816no—
834C2×C4—2816no—
835C2×C4—284no—
836C2×C4—284no—
837C2×C4—284no—
838C2×C4—284no—
839C2×C4—284no—
840C2×C4—284no—
841C2×C4C22×D2814yes—
842C2×C4C2×#115914yes—
843C2×C4C22×C22⋊D714yes—
844C2×C4C22×C22⋊D714yes—
845C7C2×#242511yescharacteristic, 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—282no—
862C22—282no—
863C22—282no—
864C22—282no—
865C22—282no—
866C22—282no—
867C22—282no—
868C22—568no—
869C22#9022914yes—
870C22#9024514yes—
871C22#9024614yes—
872C22#9025514yes—
873C22C2×#649318yes—
874C22C2×#649314yes—
875C22#9049714yes—
876C22#9051514yes—
877C22C23×D2811yescharacteristic
878C22C22×#115711yescharacteristic
879C22C22×#115911yescharacteristic
880C22C2×#654811yescharacteristic
881C22C2×D7×#4111yescharacteristic
882C22C2×#655411yescharacteristic
883C22C23×C22⋊D711yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—144no—
890C4—282no—
891C4—282no—
892C4—282no—
893C4—282no—
894C4—282no—
895C4—282no—
896C2—28no—
897C2—44no—
898C2—562no—
899C2#1173980018yesdirect product factor
900C2C2×#9022911yescharacteristic
901C2C2×#9025511yescharacteristic
902C2C2×#9024611yescharacteristic
903C2C2×#9024511yescharacteristic
904C2C22×#649311yescharacteristic
905C2C2×#9049711yescharacteristic
906C2C2×#9051511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C4×C7×D4C2
socleC24×C7C24
prime radicalC22×#6502C2
hypercenterC22×C4×D4D7
hypocenterC7C2×#2425
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C7×D4C2semidirect
2. C22×#6498C2semidirect
4. C22×#6449C2semidirect
5. C2×#89985C2semidirect
6. C2×#89985C2semidirect
7. C2×#89984C2semidirect
8. C22×C7⋊#95C2semidirect
9. #11739800C2direct (N × H)
10. C2×#89766C2semidirect
11. C2×#89755C2semidirect
12. C2×#89725C2semidirect
13. C2×#89733C2semidirect
14. C2×#89722C2semidirect
15. C2×#89700C2semidirect
16. C2×#89712C2semidirect
25. C2×C4×C7×D4C22semidirect
37. C2×#6498C22semidirect
51. C2×#6449C22semidirect
52. #89985C22semidirect
53. #89985C22semidirect
54. #89984C22semidirect
63. C2×C7⋊#95C22semidirect
64. #89766C22semidirect
65. #89755C22semidirect
66. #89733C22semidirect
67. #89725C22semidirect
68. #89722C22semidirect
69. #89712C22semidirect
70. #89700C22semidirect
119. C2×C7×C22⋊C4D4semidirect
170. C22×C4×D4D7semidirect
286. C7×C22⋊C4C2×D4semidirect
318. C2×C4×D4C2×D7semidirect
545. C2×C22⋊C4C22⋊D7semidirect
727. C22⋊C4C2×C22⋊D7semidirect
731. C2×C7#2425semidirect
845. C7C2×#2425semidirect
899. C2#11739800direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C22×#64982
C22×#65022
C22×#64492
C2×#899852
C2×#899842
C22×C7⋊#952
#117398002
C2×#897662
C2×#897552
C2×#897252
C2×#897332
C2×#897222
C2×#897002
C2×#897122
C2×#24257