Finite Group Databasebeta

← C2×#11740030 #13521228

Subgroups — C2×#11740030 #13521228

Order 1792.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#120C211yesmaximal, characteristic
2C23×C22⋊Dic7C211yesmaximal, characteristic, complemented
3C22×#6498C211yesmaximal, characteristic, complemented
4C22×D4×Dic7C211yesmaximal, characteristic, complemented
5C2×#90019C211yesmaximal, characteristic, complemented
6C2×#89994C211yesmaximal, characteristic, complemented
7C2×#89994C211yesmaximal, characteristic, complemented
8C2×#89992C211yesmaximal, characteristic, complemented
9C2×#89992C211yesmaximal, characteristic, complemented
10#11740030C2116yesmaximal, direct product factor
11C2×#89721C211yesmaximal, characteristic, complemented
12C2×#89725C211yesmaximal, characteristic, complemented
13C2×#89716C211yesmaximal, characteristic, complemented
14C2×#89716C211yesmaximal, characteristic, complemented
15C2×#89718C211yesmaximal, characteristic, complemented
16C2×#89714C211yesmaximal, characteristic, complemented
17C26×C7C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C23×C7×D4C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C24×Dic7C2211yescharacteristic
23C24×Dic7C2211yescharacteristic, complemented
24C2×C7×#120—28no—
25C2×C7×#120C2218yes—
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic7—28no—
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×C22⋊Dic7C2211yescharacteristic
36C22×C22⋊Dic7C2211yescharacteristic
37C22×C22⋊Dic7C2211yescharacteristic
38C22×C22⋊Dic7C2211yescharacteristic
39C22×C22⋊Dic7C2211yescharacteristic
40C22×C22⋊Dic7C2218yescomplemented
41C22×C22⋊Dic7C2211yescharacteristic, complemented
42C22×C22⋊Dic7C2211yescharacteristic, complemented
43C22×C22⋊Dic7C2211yescharacteristic, complemented
44C2×#6498—28no—
45C2×#6498C2218yescomplemented
46C2×D4×Dic7—28no—
47C2×D4×Dic7C2218yescomplemented
48C22×C4⋊Dic7C2211yescharacteristic, complemented
49C22×Dic7⋊C4C2211yescharacteristic, complemented
50C22×Dic7⋊C4C2211yescharacteristic, complemented
51C22×Dic7⋊C4C2211yescharacteristic, complemented
52C22×Dic7⋊C4C2211yescharacteristic, complemented
53C22×C4×Dic7C2211yescharacteristic, complemented
54#90019C2218yescomplemented
55#89994C2218yescomplemented
56#89994C2218yescomplemented
57#89992C2218yescomplemented
58#89992C2218yescomplemented
59C2×C7⋊#95C2211yescharacteristic, complemented
60C2×C7⋊#95C2211yescharacteristic, complemented
61C2×C7⋊#95C2211yescharacteristic, complemented
62C2×C7⋊#95C2211yescharacteristic, complemented
63C2×C7⋊#95C2211yescharacteristic, complemented
64C2×C7⋊#95C2211yescharacteristic, complemented
65#89725C2218yescomplemented
66#89721C2218yescomplemented
67#89718C2218yescomplemented
68#89716C2218yescomplemented
69#89716C2218yescomplemented
70#89714C2218yescomplemented
71C2×#2418—71nomaximal, Sylow
72C25×C7—24no—
73C25×C7—24no—
74C25×C7—24no—
75C25×C7—24no—
76C25×C7—24no—
77C25×C7—42no—
78C25×C7—42no—
79C25×C7C2311yescharacteristic
80C25×C7C2311yescharacteristic
81C25×C7C2311yescharacteristic
82C25×C7C2314yes—
83C25×C7C2311yescharacteristic
84C22×C7×D4—24no—
85C22×C7×D4—24no—
86C22×C7×D4—24no—
87C22×C7×D4—24no—
88C22×C7×D4—24no—
89C22×C7×D4—24no—
90C22×C7×D4—42no—
91C22×C7×D4—42no—
92C22×C7×D4D418yes—
93C22×C7×D4C2314yes—
94C22×C7×D4C2314yes—
95C22×C7×D4C2314yes—
96C23×C4×C7C2311yescharacteristic
97C23×C4×C7C2311yescharacteristic
98C23×C4×C7C2311yescharacteristic
99C23×Dic7—24no—
100C23×Dic7—24no—
101C23×Dic7—24no—
102C23×Dic7—24no—
103C23×Dic7—24no—
104C23×Dic7—24no—
105C23×Dic7—42no—
106C23×Dic7—42no—
107C23×Dic7—42no—
108C23×Dic7C2311yescharacteristic
109C23×Dic7C2311yescharacteristic
110C23×Dic7C2311yescharacteristic
111C23×Dic7C2311yescharacteristic
112C23×Dic7C2311yescharacteristic
113C23×Dic7C2311yescharacteristic
114C23×Dic7C2314yes—
115C23×Dic7C2314yes—
116C23×Dic7C2311yescharacteristic
117C23×Dic7C2311yescharacteristic
118C23×Dic7C2314yescomplemented
119C7×#120—232no—
120C2×C7×C22⋊C4—24no—
121C2×C7×C22⋊C4—24no—
122C2×C7×C22⋊C4—24no—
123C2×C7×C22⋊C4C2314yes—
124C2×C7×C22⋊C4C2314yes—
125C2×C7×C22⋊C4C2314yes—
126C2×C22⋊Dic7—24no—
127C2×C22⋊Dic7—24no—
128C2×C22⋊Dic7—24no—
129C2×C22⋊Dic7—24no—
130C2×C22⋊Dic7—24no—
131C2×C22⋊Dic7—24no—
132C2×C22⋊Dic7—24no—
133C2×C22⋊Dic7—24no—
134C2×C22⋊Dic7—24no—
135C2×C22⋊Dic7—232no—
136C2×C22⋊Dic7—42no—
137C2×C22⋊Dic7—42no—
138C2×C22⋊Dic7—42no—
139C2×C22⋊Dic7D418yescomplemented
140C2×C22⋊Dic7C2314yes—
141C2×C22⋊Dic7C2314yes—
142C2×C22⋊Dic7C2314yes—
143C2×C22⋊Dic7C2314yes—
144C2×C22⋊Dic7C2314yes—
145C2×C22⋊Dic7C2314yes—
146C2×C22⋊Dic7C2314yes—
147C2×C22⋊Dic7C2314yes—
148C2×C22⋊Dic7C2314yes—
149C2×C22⋊Dic7C2314yes—
150C2×C22⋊Dic7C2314yescomplemented
151C2×C22⋊Dic7C2314yescomplemented
152C2×C22⋊Dic7C2314yescomplemented
153#6498—232no—
154D4×Dic7—232no—
155C2×C4⋊Dic7—24no—
156C2×C4⋊Dic7C2314yescomplemented
157C2×Dic7⋊C4—24no—
158C2×Dic7⋊C4—24no—
159C2×Dic7⋊C4—42no—
160C2×Dic7⋊C4—42no—
161C2×Dic7⋊C4C2314yescomplemented
162C2×Dic7⋊C4C2314yescomplemented
163C2×Dic7⋊C4C2314yescomplemented
164C2×Dic7⋊C4C2314yescomplemented
165C2×C4×Dic7—24no—
166C2×C4×Dic7C2314yescomplemented
167C7⋊#95C2314yescomplemented
168C7⋊#95C2314yescomplemented
169C7⋊#95C2314yescomplemented
170C7⋊#95C2314yescomplemented
171C7⋊#95C2314yescomplemented
172C7⋊#95C2314yescomplemented
173C22×#123—71no—
174C22×#120D711yescharacteristic
175C22×C4×D4—71no—
176C23×C22⋊C4—71no—
177#2418—716no—
178C2×#399—71no—
179C2×#397—71no—
180C2×#394—71no—
181C2×#394—71no—
182C2×#388—71no—
183C2×#388—71no—
184C2×#386—71no—
185C2×#386—71no—
186C2×#385—71no—
187C2×#380—71no—
188C2×#379—71no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—232no—
194C24×C7—28no—
195C24×C7—22no—
196C24×C7—22no—
197C24×C7—22no—
198C24×C7—22no—
199C24×C7—22no—
200C24×C7—22no—
201C24×C7—22no—
202C24×C7—28no—
203C24×C7—28no—
204C24×C7—22no—
205C24×C7—22no—
206C24×C7—22no—
207C24×C7—22no—
208C24×C7—22no—
209C24×C7—22no—
210C24×C7—22no—
211C24×C7—22no—
212C24×C7—22no—
213C24×C7—22no—
214C24×C7—22no—
215C24×C7—28no—
216C24×C7—28no—
217C24×C7—44no—
218C24×C7—44no—
219C24×C7—416no—
220C24×C7—416no—
221C24×C7—416no—
222C24×C7—416no—
223C24×C7—416no—
224C24×C7—416no—
225C24×C7C2×D414yes—
226C24×C7C2×D414yes—
227C24×C7C2×D414yes—
228C24×C7#4114yes—
229C24×C7#4114yes—
230C24×C7#4114yes—
231C24×C7C2412yes—
232C24×C7C2412yes—
233C24×C7C2412yes—
234C24×C7C2412yes—
235C24×C7C2411yescharacteristic
236C2×C7×D4—232no—
237C2×C7×D4—28no—
238C2×C7×D4—28no—
239C2×C7×D4—28no—
240C2×C7×D4—28no—
241C2×C7×D4—28no—
242C2×C7×D4—28no—
243C2×C7×D4—44no—
244C2×C7×D4—44no—
245C2×C7×D4—416no—
246C2×C7×D4—416no—
247C2×C7×D4C2×D4116yes—
248C22×C4×C7—22no—
249C22×C4×C7—22no—
250C22×C4×C7—22no—
251C22×C4×C7—22no—
252C22×C4×C7—22no—
253C22×C4×C7—22no—
254C22×C4×C7—22no—
255C22×C4×C7—22no—
256C22×C4×C7C2×D414yes—
257C22×C4×C7C2412yes—
258C22×C4×C7C2412yes—
259C22×C4×C7C2412yes—
260C22×Dic7—22no—
261C22×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7—22no—
264C22×Dic7—22no—
265C22×Dic7—22no—
266C22×Dic7—22no—
267C22×Dic7—22no—
268C22×Dic7—22no—
269C22×Dic7—28no—
270C22×Dic7—28no—
271C22×Dic7—22no—
272C22×Dic7—22no—
273C22×Dic7—22no—
274C22×Dic7—22no—
275C22×Dic7—22no—
276C22×Dic7—22no—
277C22×Dic7—28no—
278C22×Dic7—22no—
279C22×Dic7—22no—
280C22×Dic7—22no—
281C22×Dic7—22no—
282C22×Dic7—22no—
283C22×Dic7—22no—
284C22×Dic7—22no—
285C22×Dic7—28no—
286C22×Dic7—28no—
287C22×Dic7—28no—
288C22×Dic7—44no—
289C22×Dic7—44no—
290C22×Dic7—44no—
291C22×Dic7—416no—
292C22×Dic7—416no—
293C22×Dic7—416no—
294C22×Dic7C2×D414yes—
295C22×Dic7C2×D414yes—
296C22×Dic7C2412yes—
297C22×Dic7C2412yes—
298C22×Dic7C2412yes—
299C22×Dic7C2412yes—
300C22×Dic7C2412yes—
301C22×Dic7C2412yes—
302C22×Dic7C2412yes—
303C22×Dic7C2412yes—
304C7×C22⋊C4—28no—
305C7×C22⋊C4—28no—
306C7×C22⋊C4—28no—
307C22⋊Dic7—28no—
308C22⋊Dic7—28no—
309C22⋊Dic7—28no—
310C22⋊Dic7—28no—
311C22⋊Dic7—28no—
312C22⋊Dic7—28no—
313C22⋊Dic7—28no—
314C22⋊Dic7—28no—
315C22⋊Dic7—28no—
316C22⋊Dic7—44no—
317C22⋊Dic7—44no—
318C22⋊Dic7—44no—
319C22⋊Dic7C2×D4116yescomplemented
320C4⋊Dic7—28no—
321Dic7⋊C4—28no—
322Dic7⋊C4—28no—
323Dic7⋊C4—44no—
324Dic7⋊C4—44no—
325C4×Dic7—28no—
326C26C2×D711yescharacteristic
327C23×D4C2×D711yescharacteristic
328C23×D4C2×D711yescharacteristic
329C23×D4C2×D711yescharacteristic
330C24×C4—71no—
331C24×C4—71no—
332C24×C4—71no—
333C2×#123—78no—
334C2×#123—148no—
335C2×#120—28no—
336C2×#120C2×D718yes—
337C2×C4×D4—78no—
338C2×C4×D4—148no—
339C22×C4⋊C4—71no—
340C22×C4⋊C4—71no—
341C22×C4⋊C4—71no—
342C22×C4⋊C4—71no—
343C22×C4⋊C4—71no—
344C22×C22⋊C4—71no—
345C22×C22⋊C4—71no—
346C22×C22⋊C4—71no—
347C22×C22⋊C4—71no—
348C22×C22⋊C4—71no—
349C22×C22⋊C4—71no—
350C22×C22⋊C4—71no—
351C22×C22⋊C4—78no—
352C22×C22⋊C4—71no—
353C22×C22⋊C4—71no—
354C22×C22⋊C4—71no—
355C22×C22⋊C4—71no—
356C22×C22⋊C4—71no—
357C22×C22⋊C4—71no—
358C22×C22⋊C4—148no—
359C22×C22⋊C4C2×D711yescharacteristic
360C22×C22⋊C4C2×D711yescharacteristic
361C22×C22⋊C4C2×D711yescharacteristic
362C22×C42—71no—
363#399—78no—
364#397—78no—
365#394—78no—
366#394—78no—
367#388—78no—
368#388—78no—
369#386—78no—
370#386—78no—
371#385—78no—
372#380—78no—
373#379—78no—
374C2×#95—71no—
375C2×#95—71no—
376C2×#95—71no—
377C2×#95—71no—
378C2×#95—71no—
379C2×#95—71no—
380C23×C7—28no—
381C23×C7—28no—
382C23×C7—28no—
383C23×C7—28no—
384C23×C7—28no—
385C23×C7—28no—
386C23×C7—22no—
387C23×C7—22no—
388C23×C7—22no—
389C23×C7—22no—
390C23×C7—232no—
391C23×C7—28no—
392C23×C7—28no—
393C23×C7—28no—
394C23×C7—28no—
395C23×C7—28no—
396C23×C7—28no—
397C23×C7—28no—
398C23×C7—28no—
399C23×C7—28no—
400C23×C7—22no—
401C23×C7—22no—
402C23×C7—22no—
403C23×C7—22no—
404C23×C7—22no—
405C23×C7—22no—
406C23×C7—22no—
407C23×C7—22no—
408C23×C7—22no—
409C23×C7—22no—
410C23×C7—22no—
411C23×C7—22no—
412C23×C7—22no—
413C23×C7—22no—
414C23×C7—22no—
415C23×C7—22no—
416C23×C7—22no—
417C23×C7—22no—
418C23×C7—416no—
419C23×C7—416no—
420C23×C7—416no—
421C23×C7—416no—
422C23×C7—4128no—
423C23×C7—416no—
424C23×C7—44no—
425C23×C7—44no—
426C23×C7—416no—
427C23×C7—44no—
428C23×C7—44no—
429C23×C7—44no—
430C23×C7—44no—
431C23×C7—44no—
432C23×C7—44no—
433C23×C7—44no—
434C23×C7—44no—
435C23×C7—44no—
436C23×C7—44no—
437C23×C7#123116yescomplemented
438C23×C7C22×D414yes—
439C23×C7C22×D412yes—
440C23×C7C22×D414yes—
441C23×C7C22×D414yes—
442C23×C7C22×D412yes—
443C23×C7C2×#4114yes—
444C23×C7C2×#4114yes—
445C23×C7C2×#4114yes—
446C23×C7C2×#4112yes—
447C23×C7C2×#4112yes—
448C23×C7C2×#4112yes—
449C23×C7H(5,𝔽2)12yes—
450C23×C7H(5,𝔽2)12yes—
451C23×C7C2511yescharacteristic
452C7×D4—232no—
453C7×D4—416no—
454C7×D4—416no—
455C2×C4×C7—28no—
456C2×C4×C7—22no—
457C2×C4×C7—22no—
458C2×C4×C7—22no—
459C2×C4×C7—22no—
460C2×C4×C7—22no—
461C2×C4×C7—22no—
462C2×C4×C7—22no—
463C2×C4×C7—22no—
464C2×C4×C7—44no—
465C2×C4×C7—44no—
466C2×C4×C7C22×D414yes—
467C2×Dic7—28no—
468C2×Dic7—28no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—22no—
480C2×Dic7—22no—
481C2×Dic7—22no—
482C2×Dic7—22no—
483C2×Dic7—22no—
484C2×Dic7—22no—
485C2×Dic7—22no—
486C2×Dic7—22no—
487C2×Dic7—22no—
488C2×Dic7—22no—
489C2×Dic7—22no—
490C2×Dic7—22no—
491C2×Dic7—416no—
492C2×Dic7—416no—
493C2×Dic7—416no—
494C2×Dic7—44no—
495C2×Dic7—44no—
496C2×Dic7—44no—
497C2×Dic7—44no—
498C2×Dic7—44no—
499C2×Dic7—44no—
500C2×Dic7C22×D414yes—
501C2×Dic7C22×D414yes—
502C25—24no—
503C25—24no—
504C25—24no—
505C25—24no—
506C25—24no—
507C25—42no—
508C25—42no—
509C25C22×D711yescharacteristic
510C25C22×D711yescharacteristic
511C25C22×D711yescharacteristic
512C25C22×D714yes—
513C25C22×D711yescharacteristic
514C22×D4—24no—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—42no—
521C22×D4—42no—
522C22×D4C22⋊D718yes—
523C22×D4C22×D714yes—
524C22×D4C22×D714yes—
525C22×D4C22×D714yes—
526C23×C4—71no—
527C23×C4—71no—
528C23×C4—71no—
529C23×C4—71no—
530C23×C4—71no—
531C23×C4—71no—
532C23×C4—71no—
533C23×C4—71no—
534C23×C4—74no—
535C23×C4—74no—
536C23×C4—74no—
537C23×C4—144no—
538C23×C4—144no—
539C23×C4—144no—
540C23×C4—144no—
541C23×C4—144no—
542C23×C4—144no—
543C23×C4—282no—
544C23×C4—282no—
545C23×C4—282no—
546C23×C4C22×D711yescharacteristic
547C23×C4C22×D711yescharacteristic
548C23×C4C22×D711yescharacteristic
549#123—1432no—
550#120—232no—
551C4×D4—1432no—
552C2×C4⋊C4—74no—
553C2×C4⋊C4—74no—
554C2×C4⋊C4—74no—
555C2×C4⋊C4—74no—
556C2×C4⋊C4—74no—
557C2×C4⋊C4—144no—
558C2×C4⋊C4—144no—
559C2×C4⋊C4—144no—
560C2×C4⋊C4—282no—
561C2×C4⋊C4—282no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—78no—
566C2×C22⋊C4—74no—
567C2×C22⋊C4—74no—
568C2×C22⋊C4—74no—
569C2×C22⋊C4—74no—
570C2×C22⋊C4—74no—
571C2×C22⋊C4—74no—
572C2×C22⋊C4—74no—
573C2×C22⋊C4—74no—
574C2×C22⋊C4—74no—
575C2×C22⋊C4—74no—
576C2×C22⋊C4—74no—
577C2×C22⋊C4—74no—
578C2×C22⋊C4—74no—
579C2×C22⋊C4—1432no—
580C2×C22⋊C4—144no—
581C2×C22⋊C4—144no—
582C2×C22⋊C4—144no—
583C2×C22⋊C4—144no—
584C2×C22⋊C4—144no—
585C2×C22⋊C4—144no—
586C2×C22⋊C4—144no—
587C2×C22⋊C4—144no—
588C2×C22⋊C4—144no—
589C2×C22⋊C4—282no—
590C2×C22⋊C4—282no—
591C2×C22⋊C4—282no—
592C2×C22⋊C4C22×D714yes—
593C2×C22⋊C4C22×D714yes—
594C2×C22⋊C4C22×D714yes—
595C2×C42—74no—
596C2×C42—144no—
597#95—74no—
598#95—74no—
599#95—74no—
600#95—74no—
601#95—74no—
602#95—74no—
603C22×C7—24no—
604C22×C7—232no—
605C22×C7—24no—
606C22×C7—24no—
607C22×C7—24no—
608C22×C7—24no—
609C22×C7—24no—
610C22×C7—24no—
611C22×C7—24no—
612C22×C7—24no—
613C22×C7—24no—
614C22×C7—24no—
615C22×C7—24no—
616C22×C7—24no—
617C22×C7—24no—
618C22×C7—24no—
619C22×C7—464no—
620C22×C7—42no—
621C22×C7—42no—
622C22×C7—42no—
623C22×C7—416no—
624C22×C7—416no—
625C22×C7—416no—
626C22×C7—42no—
627C22×C7—42no—
628C22×C7—42no—
629C22×C7—42no—
630C22×C7—42no—
631C22×C7—42no—
632C22×C7—42no—
633C22×C7—42no—
634C22×C7—42no—
635C22×C7C2×#12314yes—
636C22×C7C2×#12318yescomplemented
637C22×C7#52514yes—
638C22×C7#53814yes—
639C22×C7D4214yes—
640C22×C7#54614yes—
641C22×C7#54614yes—
642C22×C7#55114yes—
643C22×C7C23×D411yescharacteristic
644C22×C7C23×D411yescharacteristic
645C22×C7C22×#4111yescharacteristic
646C22×C7C22×#4111yescharacteristic
647C22×C7C22×#4111yescharacteristic
648C22×C7C2×H(5,𝔽2)11yescharacteristic
649C22×C7C2×H(5,𝔽2)11yescharacteristic
650C4×C7—24no—
651C4×C7—42no—
652C4×C7—42no—
653Dic7—24no—
654Dic7—24no—
655Dic7—42no—
656Dic7—42no—
657Dic7—42no—
658Dic7—42no—
659Dic7—42no—
660Dic7—42no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—232no—
666C24—28no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—28no—
673C24—28no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—28no—
688C24—28no—
689C24—44no—
690C24—44no—
691C24—416no—
692C24—416no—
693C24—416no—
694C24—416no—
695C24—416no—
696C24—416no—
697C24D4×D714yes—
698C24#115914yes—
699C24#115914yes—
700C24#115914yes—
701C24C2×C22⋊D714yes—
702C24C2×C22⋊D714yes—
703C24C23×D712yes—
704C24C23×D712yes—
705C24C23×D712yes—
706C24C23×D712yes—
707C24C23×D711yescharacteristic
708C2×D4—232no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—416no—
718C2×D4—416no—
719C2×D4C2×C22⋊D7116yes—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—74no—
729C22×C4—74no—
730C22×C4—72no—
731C22×C4—72no—
732C22×C4—72no—
733C22×C4—72no—
734C22×C4—72no—
735C22×C4—72no—
736C22×C4—72no—
737C22×C4—72no—
738C22×C4—148no—
739C22×C4—148no—
740C22×C4—148no—
741C22×C4—142no—
742C22×C4—142no—
743C22×C4—142no—
744C22×C4—142no—
745C22×C4—142no—
746C22×C4—142no—
747C22×C4—142no—
748C22×C4—142no—
749C22×C4—142no—
750C22×C4—142no—
751C22×C4—142no—
752C22×C4—142no—
753C22×C4—148no—
754C22×C4—142no—
755C22×C4—142no—
756C22×C4—142no—
757C22×C4—142no—
758C22×C4—142no—
759C22×C4—142no—
760C22×C4—142no—
761C22×C4—142no—
762C22×C4—142no—
763C22×C4—142no—
764C22×C4—148no—
765C22×C4—148no—
766C22×C4—284no—
767C22×C4—284no—
768C22×C4—284no—
769C22×C4—2816no—
770C22×C4—2816no—
771C22×C4—2816no—
772C22×C4C2×C22⋊D714yes—
773C22×C4C23×D712yes—
774C22×C4C23×D712yes—
775C22×C4C23×D712yes—
776C4⋊C4—148no—
777C4⋊C4—148no—
778C4⋊C4—148no—
779C4⋊C4—284no—
780C4⋊C4—284no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—716no—
785C22⋊C4—148no—
786C22⋊C4—148no—
787C22⋊C4—148no—
788C22⋊C4—148no—
789C22⋊C4—148no—
790C22⋊C4—148no—
791C22⋊C4—148no—
792C22⋊C4—148no—
793C22⋊C4—148no—
794C22⋊C4—284no—
795C22⋊C4—284no—
796C22⋊C4—284no—
797C42—148no—
798C2×C7—28no—
799C2×C7—44no—
800C2×C7—44no—
801C2×C7—44no—
802C2×C7#241818yescomplemented
803C2×C7C22×#12311yescharacteristic
804C2×C7C2×#52511yescharacteristic
805C2×C7C2×#53811yescharacteristic
806C2×C7C2×D4211yescharacteristic
807C2×C7C2×#54611yescharacteristic
808C2×C7C2×#54611yescharacteristic
809C2×C7C2×#55111yescharacteristic
810C23—28no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—232no—
821C23—28no—
822C23—28no—
823C23—28no—
824C23—28no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—28no—
829C23—28no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—416no—
849C23—416no—
850C23—416no—
851C23—416no—
852C23—416no—
853C23—4128no—
854C23—44no—
855C23—44no—
856C23—416no—
857C23—44no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23#6498116yescomplemented
868C23C2×D4×D714yes—
869C23C2×D4×D712yes—
870C23C2×#115914yes—
871C23C2×#115914yes—
872C23C2×#115914yes—
873C23C2×#115912yes—
874C23C2×#115912yes—
875C23C2×#115912yes—
876C23#654812yes—
877C23#654812yes—
878C23C22×C22⋊D714yes—
879C23C22×C22⋊D714yes—
880C23C22×C22⋊D712yes—
881C23C24×D711yescharacteristic
882D4—232no—
883D4—416no—
884D4—416no—
885C2×C4—28no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—44no—
895C2×C4—44no—
896C2×C4—74no—
897C2×C4—74no—
898C2×C4—148no—
899C2×C4—148no—
900C2×C4—142no—
901C2×C4—142no—
902C2×C4—142no—
903C2×C4—142no—
904C2×C4—142no—
905C2×C4—142no—
906C2×C4—142no—
907C2×C4—142no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—142no—
915C2×C4—142no—
916C2×C4—142no—
917C2×C4—142no—
918C2×C4—142no—
919C2×C4—142no—
920C2×C4—142no—
921C2×C4—142no—
922C2×C4—2816no—
923C2×C4—2816no—
924C2×C4—2816no—
925C2×C4—284no—
926C2×C4—284no—
927C2×C4—284no—
928C2×C4—284no—
929C2×C4—284no—
930C2×C4—284no—
931C2×C4C22×C22⋊D714yes—
932C7C2×#241811yescharacteristic, complemented, Sylow
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—232no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—464no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—416no—
963C22—416no—
964C22—416no—
965C22#9027714yes—
966C22#9027814yes—
967C22#9028214yes—
968C22#9028414yes—
969C22C2×#649814yes—
970C22C2×#649818yescomplemented
971C22D4×C22⋊D714yes—
972C22#9049714yes—
973C22C22×D4×D711yescharacteristic
974C22C22×#115911yescharacteristic
975C22C22×#115911yescharacteristic
976C22C22×#115911yescharacteristic
977C22C2×#654811yescharacteristic
978C22C2×#654811yescharacteristic
979C22C23×C22⋊D711yescharacteristic
980C4—24no—
981C4—42no—
982C4—42no—
983C4—144no—
984C4—144no—
985C4—282no—
986C4—282no—
987C4—282no—
988C4—282no—
989C4—282no—
990C4—282no—
991C2—28no—
992C2—44no—
993C2—44no—
994C2—44no—
995C2#1174003018yesdirect product factor
996C2C2×#9027711yescharacteristic
997C2C2×#9028411yescharacteristic
998C2C2×#9027811yescharacteristic
999C2C2×#9028211yescharacteristic
1000C2C22×#649811yescharacteristic
1001C2C2×#9049711yescharacteristic
1002C2C2×D4×C22⋊D711yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC22×C7×#120C2
socleC24×C7C24
hypercenterC22×#120D7
hypocenterC7C2×#2418
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊Dic7C2semidirect
3. C22×#6498C2semidirect
4. C22×D4×Dic7C2semidirect
5. C2×#90019C2semidirect
6. C2×#89994C2semidirect
7. C2×#89994C2semidirect
8. C2×#89992C2semidirect
9. C2×#89992C2semidirect
10. #11740030C2direct (N × H)
11. C2×#89721C2semidirect
12. C2×#89725C2semidirect
13. C2×#89716C2semidirect
14. C2×#89716C2semidirect
15. C2×#89718C2semidirect
16. C2×#89714C2semidirect
23. C24×Dic7C22semidirect
40. C22×C22⋊Dic7C22semidirect
41. C22×C22⋊Dic7C22semidirect
42. C22×C22⋊Dic7C22semidirect
43. C22×C22⋊Dic7C22semidirect
45. C2×#6498C22semidirect
47. C2×D4×Dic7C22semidirect
48. C22×C4⋊Dic7C22semidirect
49. C22×Dic7⋊C4C22semidirect
50. C22×Dic7⋊C4C22semidirect
51. C22×Dic7⋊C4C22semidirect
52. C22×Dic7⋊C4C22semidirect
53. C22×C4×Dic7C22semidirect
54. #90019C22semidirect
55. #89994C22semidirect
56. #89994C22semidirect
57. #89992C22semidirect
58. #89992C22semidirect
59. C2×C7⋊#95C22semidirect
60. C2×C7⋊#95C22semidirect
61. C2×C7⋊#95C22semidirect
62. C2×C7⋊#95C22semidirect
63. C2×C7⋊#95C22semidirect
64. C2×C7⋊#95C22semidirect
65. #89725C22semidirect
66. #89721C22semidirect
67. #89718C22semidirect
68. #89716C22semidirect
69. #89716C22semidirect
70. #89714C22semidirect
118. C23×Dic7C23semidirect
139. C2×C22⋊Dic7D4semidirect
150. C2×C22⋊Dic7C23semidirect
151. C2×C22⋊Dic7C23semidirect
152. C2×C22⋊Dic7C23semidirect
156. C2×C4⋊Dic7C23semidirect
161. C2×Dic7⋊C4C23semidirect
162. C2×Dic7⋊C4C23semidirect
163. C2×Dic7⋊C4C23semidirect
164. C2×Dic7⋊C4C23semidirect
166. C2×C4×Dic7C23semidirect
167. C7⋊#95C23semidirect
168. C7⋊#95C23semidirect
169. C7⋊#95C23semidirect
170. C7⋊#95C23semidirect
171. C7⋊#95C23semidirect
172. C7⋊#95C23semidirect
319. C22⋊Dic7C2×D4semidirect
437. C23×C7#123semidirect
636. C22×C7C2×#123semidirect
802. C2×C7#2418semidirect
867. C23#6498semidirect
932. C7C2×#2418semidirect
970. C22C2×#6498semidirect
995. C2#11740030direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1202
C23×C22⋊Dic72
C22×#64982
C22×D4×Dic72
C2×#900192
C2×#899942
C2×#899922
#117400302
C2×#897212
C2×#897252
C2×#897162
C2×#897182
C2×#897142
C2×#24187