Finite Group Databasebeta

← C2×#11732340 #13521516

Subgroups — C2×#11732340 #13521516

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×#6501C211yesmaximal, characteristic
2C22×C4×C22⋊D7C211yesmaximal, characteristic, complemented
3C22×#6446C211yesmaximal, characteristic, complemented
4C22×#6446C211yesmaximal, characteristic, complemented
5C2×C7×#386C211yesmaximal, characteristic, complemented
6C2×#89994C211yesmaximal, characteristic, complemented
7C2×#89984C211yesmaximal, characteristic, complemented
8C2×#89728C211yesmaximal, characteristic, complemented
9C2×#89724C211yesmaximal, characteristic, complemented
10C2×#89720C211yesmaximal, characteristic, complemented
11C2×#89723C211yesmaximal, characteristic, complemented
12#11732340C2116yesmaximal, direct product factor
13C2×#89440C211yesmaximal, characteristic, complemented
14C2×D7×#95C211yesmaximal, characteristic, complemented
15C2×#89433C211yesmaximal, characteristic, complemented
16C2×#89419C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C23×C4×D7C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C2×#6501—28no—
34C2×#6501C2218yes—
35C2×C4×C22⋊D7—28no—
36C2×C4×C22⋊D7C2218yescomplemented
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C22×C4⋊Dic7C2211yescharacteristic
42C22×C4⋊Dic7C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C2×#6446—28no—
49C2×#6446—28no—
50C2×#6446C2218yescomplemented
51C2×#6446C2218yescomplemented
52C7×#386C2218yescomplemented
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55#89994C2218yescomplemented
56#89984C2218yescomplemented
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62C2×C7⋊#95C2211yescharacteristic
63#89728C2218yescomplemented
64#89724C2218yescomplemented
65#89723C2218yescomplemented
66#89720C2218yescomplemented
67#89440C2218yescomplemented
68D7×#95C2218yescomplemented
69#89433C2218yescomplemented
70#89419C2218yescomplemented
71C2×#2425—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—42no—
78C22×C7×D4C2314yes—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—42no—
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2314yes—
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—24no—
89C22×C22⋊D7—24no—
90C22×C22⋊D7—24no—
91C22×C22⋊D7—24no—
92C22×C22⋊D7—24no—
93C22×C22⋊D7D418yes—
94C22×C22⋊D7C2314yes—
95C22×C22⋊D7C2314yes—
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C22×C4×D7—24no—
104C22×C4×D7—24no—
105C22×C4×D7—24no—
106C22×C4×D7—24no—
107C22×C4×D7—24no—
108C22×C4×D7—24no—
109C22×C4×D7—24no—
110C22×C4×D7—42no—
111C22×C4×D7—42no—
112C22×C4×D7C2314yes—
113C22×C4×D7C2314yes—
114C22×C4×D7C2314yes—
115C2×C7×C22⋊C4—24no—
116C2×C7×C22⋊C4—24no—
117C2×C7×C22⋊C4—24no—
118C2×C7×C22⋊C4C2314yes—
119C2×C7×C22⋊C4C2314yes—
120C2×C7×C22⋊C4C2314yes—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7—24no—
126C2×C22⋊Dic7—42no—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132C2×C22⋊Dic7C2314yes—
133#6501—232no—
134C4×C22⋊D7—232no—
135C2×(C2×D7)⋊C4—24no—
136C2×(C2×D7)⋊C4D418yescomplemented
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×C4⋊Dic7—24no—
140C2×C4⋊Dic7—24no—
141C2×C4⋊Dic7—24no—
142C2×C4⋊Dic7—42no—
143C2×C4⋊Dic7C2314yes—
144C2×C4⋊Dic7C2314yes—
145C2×C4⋊Dic7C2314yes—
146C2×C4⋊Dic7C2314yes—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4—24no—
149C2×Dic7⋊C4—24no—
150C2×Dic7⋊C4—24no—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×Dic7⋊C4C2314yes—
155C2×C4×Dic7—24no—
156C2×C4×Dic7C2314yes—
157#6446—232no—
158#6446—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×D4—71no—
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×#386D711yescharacteristic, complemented
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×C7—22no—
194C24×C7—22no—
195C24×C7—22no—
196C24×C7C2×D414yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7C2×D414yes—
205C23×D7C2×D414yes—
206C23×D7#4114yes—
207C23×D7C2412yes—
208C2×C7×D4—28no—
209C2×C7×D4—28no—
210C2×C7×D4—44no—
211C2×C7×D4—416no—
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—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—28no—
225C22×C4×C7—28no—
226C22×C4×C7—44no—
227C22×C4×C7—416no—
228C22×C4×C7C2×D414yes—
229C22×C4×C7#4114yes—
230C22×C4×C7#4114yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2412yes—
236C2×C22⋊D7—232no—
237C2×C22⋊D7—28no—
238C2×C22⋊D7—28no—
239C2×C22⋊D7—28no—
240C2×C22⋊D7—28no—
241C2×C22⋊D7—28no—
242C2×C22⋊D7—416no—
243C2×C22⋊D7C2×D4116yes—
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—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7C2×D414yes—
264C22×Dic7C2×D414yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C2×C4×D7—28no—
273C2×C4×D7—28no—
274C2×C4×D7—28no—
275C2×C4×D7—28no—
276C2×C4×D7—28no—
277C2×C4×D7—28no—
278C2×C4×D7—28no—
279C2×C4×D7—44no—
280C2×C4×D7—44no—
281C2×C4×D7—416no—
282C2×C4×D7—416no—
283C2×C4×D7—416no—
284C7×C22⋊C4—28no—
285C7×C22⋊C4—28no—
286C7×C22⋊C4—28no—
287C22⋊Dic7—28no—
288C22⋊Dic7—28no—
289C22⋊Dic7—28no—
290C22⋊Dic7—28no—
291C22⋊Dic7—28no—
292C22⋊Dic7—44no—
293(C2×D7)⋊C4—28no—
294(C2×D7)⋊C4C2×D4116yescomplemented
295C4⋊Dic7—28no—
296C4⋊Dic7—28no—
297C4⋊Dic7—28no—
298C4⋊Dic7—44no—
299Dic7⋊C4—28no—
300Dic7⋊C4—28no—
301Dic7⋊C4—28no—
302Dic7⋊C4—28no—
303C4×Dic7—28no—
304C23×D4—71no—
305C23×D4—71no—
306C23×D4C2×D711yescharacteristic
307C24×C4—71no—
308C24×C4—71no—
309C24×C4—71no—
310C24×C4C2×D711yescharacteristic
311C2×#123—78no—
312C2×#123—78no—
313C2×#123—148no—
314C2×#123—148no—
315C2×#121—78no—
316C2×#121—148no—
317C2×C4×D4—78no—
318C2×C4×D4—148no—
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⋊C4—71no—
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⋊C4C2×D711yescharacteristic
336C22×C22⋊C4C2×D711yescharacteristic
337C22×C22⋊C4C2×D711yescharacteristic
338C22×C42—71no—
339#398—78no—
340#397—78no—
341#396—78no—
342#394—78no—
343#389—78no—
344#388—78no—
345#386—78no—
346#386C2×D718yescomplemented
347#385—78no—
348#380—78no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—78no—
356C2×#95C2×D711yescharacteristic
357C2×#95C2×D711yescharacteristic
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—28no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7—44no—
384C23×C7—44no—
385C23×C7C22×D414yes—
386C23×C7C22×D412yes—
387C23×C7C22×D412yes—
388C23×C7C2×#4112yes—
389C23×C7C2×#4112yes—
390C23×C7C2×#4112yes—
391C23×C7H(5,𝔽2)12yes—
392C23×C72−1+412yes—
393C23×C7C2511yescharacteristic
394C22×D7—28no—
395C22×D7—28no—
396C22×D7—28no—
397C22×D7—28no—
398C22×D7—28no—
399C22×D7—28no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—22no—
403C22×D7—22no—
404C22×D7#121116yes—
405C22×D7C22×D414yes—
406C22×D7C22×D414yes—
407C22×D7C2×#4114yes—
408C7×D4—416no—
409C2×C4×C7—28no—
410C2×C4×C7—28no—
411C2×C4×C7—28no—
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—22no—
423C2×C4×C7—22no—
424C2×C4×C7—416no—
425C2×C4×C7—44no—
426C2×C4×C7—44no—
427C2×C4×C7C22×D414yes—
428C2×C4×C7C2×#4114yes—
429C2×C4×C7C2×#4114yes—
430C22⋊D7—232no—
431C22⋊D7—416no—
432C2×Dic7—28no—
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—44no—
454C2×Dic7—44no—
455C2×Dic7—44no—
456C2×Dic7—44no—
457C2×Dic7—44no—
458C2×Dic7C22×D414yes—
459C2×Dic7C22×D414yes—
460C4×D7—416no—
461C4×D7—416no—
462C4×D7—416no—
463C25—71no—
464C25C22×D711yescharacteristic
465C25C22×D711yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—42no—
469C22×D4—78no—
470C22×D4—74no—
471C22×D4—74no—
472C22×D4—144no—
473C22×D4—144no—
474C22×D4—144no—
475C22×D4—144no—
476C22×D4—144no—
477C22×D4C22×D714yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—74no—
489C23×C4—74no—
490C23×C4—74no—
491C23×C4—144no—
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×C4C22×D711yescharacteristic
501C23×C4C22×D711yescharacteristic
502C23×C4C22×D714yes—
503C23×C4C22×D711yescharacteristic
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506#123—1432no—
507#123—1432no—
508#121—1432no—
509C4×D4—1432no—
510C2×C4⋊C4—74no—
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—144no—
525C2×C4⋊C4—282no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—78no—
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—74no—
537C2×C22⋊C4—74no—
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×D714yes—
546C2×C22⋊C4C22×D714yes—
547C2×C22⋊C4C22×D714yes—
548C2×C42—74no—
549C2×C42—144no—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95—74no—
555#95—74no—
556#95C22×D714yes—
557#95C22×D714yes—
558C22×C7—24no—
559C22×C7—24no—
560C22×C7—24no—
561C22×C7—42no—
562C22×C7—416no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—88no—
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—24no—
589C2×D7—232no—
590C2×D7—24no—
591C2×D7—24no—
592C2×D7—24no—
593C2×D7—24no—
594C2×D7—24no—
595C2×D7C2×#12118yes—
596C4×C7—24no—
597C4×C7—24no—
598C4×C7—24no—
599C4×C7—42no—
600C4×C7—42no—
601Dic7—24no—
602Dic7—24no—
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—22no—
619C24—22no—
620C24—22no—
621C24—74no—
622C24—74no—
623C24—74no—
624C24—72no—
625C24—142no—
626C24—142no—
627C24—142no—
628C24—142no—
629C24D4×D714yes—
630C24C23×D712yes—
631C24C23×D712yes—
632C24C23×D711yescharacteristic
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—44no—
636C2×D4—416no—
637C2×D4—716no—
638C2×D4—148no—
639C2×D4—1432no—
640C2×D4—148no—
641C2×D4—148no—
642C2×D4—148no—
643C2×D4—148no—
644C2×D4—2816no—
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—22no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—44no—
660C22×C4—416no—
661C22×C4—74no—
662C22×C4—74no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—148no—
671C22×C4—148no—
672C22×C4—148no—
673C22×C4—148no—
674C22×C4—148no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
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—142no—
692C22×C4—142no—
693C22×C4—142no—
694C22×C4—148no—
695C22×C4—148no—
696C22×C4—284no—
697C22×C4—284no—
698C22×C4—2816no—
699C22×C4—2816no—
700C22×C4—2816no—
701C22×C4#115714yes—
702C22×C4D4×D714yes—
703C22×C4#115914yes—
704C22×C4C23×D712yes—
705C22×C4C23×D712yes—
706C22×C4C23×D712yes—
707C22×C4C23×D712yes—
708C22×C4C23×D712yes—
709C4⋊C4—148no—
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—28no—
719C22⋊C4—28no—
720C22⋊C4—716no—
721C22⋊C4—148no—
722C22⋊C4—148no—
723C22⋊C4—148no—
724C22⋊C4—148no—
725C22⋊C4—148no—
726C22⋊C4—148no—
727C22⋊C4—284no—
728C42—148no—
729C2×C7—44no—
730C2×C7—82no—
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—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—716no—
768C23—74no—
769C23—74no—
770C23—74no—
771C23—148no—
772C23—148no—
773C23—148no—
774C23—148no—
775C23—148no—
776C23—142no—
777C23—148no—
778C23—142no—
779C23—142no—
780C23—142no—
781C23C2×#115712yes—
782C23C2×D4×D714yes—
783C23C2×D4×D712yes—
784C23C2×D4×D712yes—
785C23C2×#115912yes—
786C23#654812yes—
787C23D7×#4112yes—
788C23#655412yes—
789C23C24×D711yescharacteristic
790D4—416no—
791D4—1432no—
792D4—2816no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
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—22no—
808C2×C4—416no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—74no—
812C2×C4—74no—
813C2×C4—148no—
814C2×C4—148no—
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—142no—
834C2×C4—2816no—
835C2×C4—2816no—
836C2×C4—2816no—
837C2×C4—284no—
838C2×C4—284no—
839C2×C4—284no—
840C2×C4—284no—
841C2×C4—284no—
842C2×C4C2×#115714yes—
843C2×C4C2×D4×D714yes—
844C2×C4C2×#115914yes—
845C7C2×#242511yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—416no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—78no—
862C22—88no—
863C22—144no—
864C22—144no—
865C22—144no—
866C22—144no—
867C22—1432no—
868C22—144no—
869C22—144no—
870C22#9018114yes—
871C22#9024214yes—
872C22#9024814yes—
873C22#9028214yes—
874C22D7×#12114yes—
875C22#9030214yes—
876C22#9035114yes—
877C22C22×#115711yescharacteristic
878C22C22×D4×D711yescharacteristic
879C22C22×D4×D711yescharacteristic
880C22C22×#115911yescharacteristic
881C22C2×#654811yescharacteristic
882C22C2×D7×#4111yescharacteristic
883C22C2×#655411yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—144no—
890C4—144no—
891C4—282no—
892C4—282no—
893C4—282no—
894C4—282no—
895C4—282no—
896C2—44no—
897C2—82no—
898C2—148no—
899C2#1173234018yesdirect product factor
900C2C2×#9018111yescharacteristic
901C2C2×#9024811yescharacteristic
902C2C2×#9024211yescharacteristic
903C2C2×#9028211yescharacteristic
904C2C2×#9030211yescharacteristic
905C2C2×D7×#12111yescharacteristic
906C2C2×#9035111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC22×#6501C2
hypercenterC2×#386D7
hypocenterC7C2×#2425
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D7C2semidirect
3. C22×#6446C2semidirect
4. C22×#6446C2semidirect
5. C2×C7×#386C2semidirect
6. C2×#89994C2semidirect
7. C2×#89984C2semidirect
8. C2×#89728C2semidirect
9. C2×#89724C2semidirect
10. C2×#89720C2semidirect
11. C2×#89723C2semidirect
12. #11732340C2direct (N × H)
13. C2×#89440C2semidirect
14. C2×D7×#95C2semidirect
15. C2×#89433C2semidirect
16. C2×#89419C2semidirect
36. C2×C4×C22⋊D7C22semidirect
50. C2×#6446C22semidirect
51. C2×#6446C22semidirect
52. C7×#386C22semidirect
55. #89994C22semidirect
56. #89984C22semidirect
63. #89728C22semidirect
64. #89724C22semidirect
65. #89723C22semidirect
66. #89720C22semidirect
67. #89440C22semidirect
68. D7×#95C22semidirect
69. #89433C22semidirect
70. #89419C22semidirect
136. C2×(C2×D7)⋊C4D4semidirect
179. C2×#386D7semidirect
294. (C2×D7)⋊C4C2×D4semidirect
346. #386C2×D7semidirect
731. C2×C7#2425semidirect
845. C7C2×#2425semidirect
899. C2#11732340direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65012
C22×C4×C22⋊D72
C22×#64462
C2×C7×#3862
C2×#899942
C2×#899842
C2×#897282
C2×#897242
C2×#897202
C2×#897232
#117323402
C2×#894402
C2×D7×#952
C2×#894332
C2×#894192
C2×#24257