Finite Group Databasebeta

← C2×#11740090 #13521525

Subgroups — C2×#11740090 #13521525

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×C7×#121C211yesmaximal, characteristic
2C22×#6498C211yesmaximal, characteristic, complemented
3C22×#6498C211yesmaximal, characteristic, complemented
4C22×D4×Dic7C211yesmaximal, characteristic, complemented
5C2×#89994C211yesmaximal, characteristic, complemented
6C2×#89992C211yesmaximal, characteristic, complemented
7C2×#89992C211yesmaximal, characteristic, complemented
8C2×#89982C211yesmaximal, characteristic, complemented
9C22×C7⋊#95C211yesmaximal, characteristic, complemented
10#11740090C2116yesmaximal, direct product factor
11C2×#89756C211yesmaximal, characteristic, complemented
12C2×#89744C211yesmaximal, characteristic, complemented
13C2×#89724C211yesmaximal, characteristic, complemented
14C2×#89720C211yesmaximal, characteristic, complemented
15C2×#89717C211yesmaximal, characteristic, complemented
16C2×#89714C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C24×C4×C7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C24×Dic7C2211yescharacteristic
23C24×Dic7C2211yescharacteristic
24C2×C7×#121—28no—
25C2×C7×#121C2218yes—
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×C22⋊Dic7C2211yescharacteristic
36C22×C22⋊Dic7C2211yescharacteristic
37C22×C22⋊Dic7C2211yescharacteristic
38C2×#6498—28no—
39C2×#6498—28no—
40C2×#6498C2218yescomplemented
41C2×#6498C2218yescomplemented
42C2×D4×Dic7—28no—
43C2×D4×Dic7C2218yescomplemented
44C22×C4⋊Dic7C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×Dic7⋊C4C2211yescharacteristic
48C22×Dic7⋊C4C2211yescharacteristic
49C22×Dic7⋊C4C2211yescharacteristic
50C22×Dic7⋊C4C2211yescharacteristic
51C22×C4×Dic7C2211yescharacteristic
52#89994C2218yescomplemented
53#89992C2218yescomplemented
54#89992C2218yescomplemented
55#89982C2218yescomplemented
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62C2×C7⋊#95C2211yescharacteristic
63C2×C7⋊#95C2211yescharacteristic
64C2×C7⋊#95C2218yescomplemented
65#89756C2218yescomplemented
66#89744C2218yescomplemented
67#89724C2218yescomplemented
68#89720C2218yescomplemented
69#89717C2218yescomplemented
70#89714C2218yescomplemented
71C2×#2425—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C25×C7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—24no—
78C22×C7×D4—24no—
79C22×C7×D4—24no—
80C22×C7×D4—24no—
81C22×C7×D4—24no—
82C22×C7×D4—42no—
83C22×C7×D4D418yes—
84C22×C7×D4C2314yes—
85C22×C7×D4C2314yes—
86C22×C7×D4C2314yes—
87C23×C4×C7—24no—
88C23×C4×C7—24no—
89C23×C4×C7—42no—
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C23×C4×C7C2314yes—
93C23×C4×C7C2311yescharacteristic
94C23×C4×C7C2311yescharacteristic
95C23×Dic7—24no—
96C23×Dic7—24no—
97C23×Dic7—24no—
98C23×Dic7—24no—
99C23×Dic7—24no—
100C23×Dic7—24no—
101C23×Dic7—24no—
102C23×Dic7—42no—
103C23×Dic7—42no—
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C23×Dic7C2311yescharacteristic
108C23×Dic7C2311yescharacteristic
109C23×Dic7C2314yes—
110C23×Dic7C2314yes—
111C23×Dic7C2314yes—
112C23×Dic7C2311yescharacteristic
113C23×Dic7C2311yescharacteristic
114C23×Dic7C2311yescharacteristic
115C7×#121—232no—
116C2×C7×C4⋊C4—24no—
117C2×C7×C4⋊C4C2314yes—
118C2×C7×C22⋊C4—24no—
119C2×C7×C22⋊C4—24no—
120C2×C7×C22⋊C4C2314yes—
121C2×C7×C22⋊C4C2314yes—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7—24no—
126C2×C22⋊Dic7—24no—
127C2×C22⋊Dic7—24no—
128C2×C22⋊Dic7—24no—
129C2×C22⋊Dic7—42no—
130C2×C22⋊Dic7D418yescomplemented
131C2×C22⋊Dic7C2314yes—
132C2×C22⋊Dic7C2314yes—
133C2×C22⋊Dic7C2314yes—
134C2×C22⋊Dic7C2314yes—
135C2×C22⋊Dic7C2314yes—
136C2×C22⋊Dic7C2314yes—
137C2×C22⋊Dic7C2314yes—
138C2×C22⋊Dic7C2314yes—
139C2×C22⋊Dic7C2314yes—
140#6498—232no—
141#6498—232no—
142D4×Dic7—232no—
143C2×C4⋊Dic7—24no—
144C2×C4⋊Dic7C2314yes—
145C2×Dic7⋊C4—24no—
146C2×Dic7⋊C4—24no—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4—24no—
149C2×Dic7⋊C4—24no—
150C2×Dic7⋊C4—42no—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×Dic7⋊C4C2314yes—
155C2×Dic7⋊C4C2314yes—
156C2×Dic7⋊C4C2314yes—
157C2×C4×Dic7—24no—
158C2×C4×Dic7C2314yes—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×#123—71no—
168C22×#123—71no—
169C22×#121D711yescharacteristic
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×#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×C7—22no—
194C24×C7—22no—
195C24×C7—22no—
196C24×C7—22no—
197C24×C7—22no—
198C24×C7—22no—
199C24×C7—22no—
200C24×C7C2×D414yes—
201C24×C7C2×D414yes—
202C24×C7C2×D414yes—
203C24×C7#4114yes—
204C24×C7C2412yes—
205C24×C7C2412yes—
206C24×C7C2412yes—
207C24×C7C2411yescharacteristic
208C2×C7×D4—232no—
209C2×C7×D4—28no—
210C2×C7×D4—28no—
211C2×C7×D4—28no—
212C2×C7×D4—28no—
213C2×C7×D4—28no—
214C2×C7×D4—28no—
215C2×C7×D4—28no—
216C2×C7×D4—44no—
217C2×C7×D4—416no—
218C2×C7×D4—416no—
219C2×C7×D4C2×D4116yes—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—28no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—28no—
232C22×C4×C7—44no—
233C22×C4×C7—416no—
234C22×C4×C7C2×D414yes—
235C22×C4×C7#4114yes—
236C22×C4×C7C2412yes—
237C22×C4×C7C2412yes—
238C22×C4×C7C2412yes—
239C22×C4×C7C2412yes—
240C22×Dic7—22no—
241C22×Dic7—22no—
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—28no—
254C22×Dic7—28no—
255C22×Dic7—28no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—28no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7—22no—
264C22×Dic7—22no—
265C22×Dic7—28no—
266C22×Dic7—28no—
267C22×Dic7—28no—
268C22×Dic7—44no—
269C22×Dic7—44no—
270C22×Dic7—416no—
271C22×Dic7—416no—
272C22×Dic7—416no—
273C22×Dic7C2×D414yes—
274C22×Dic7C2×D414yes—
275C22×Dic7#4114yes—
276C22×Dic7C2412yes—
277C22×Dic7C2412yes—
278C22×Dic7C2412yes—
279C22×Dic7C2412yes—
280C22×Dic7C2412yes—
281C22×Dic7C2412yes—
282C22×Dic7C2412yes—
283C22×Dic7C2412yes—
284C7×C4⋊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—28no—
293C22⋊Dic7—28no—
294C22⋊Dic7—44no—
295C22⋊Dic7C2×D4116yescomplemented
296C4⋊Dic7—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4—28no—
299Dic7⋊C4—28no—
300Dic7⋊C4—28no—
301Dic7⋊C4—28no—
302Dic7⋊C4—44no—
303C4×Dic7—28no—
304C23×D4C2×D711yescharacteristic
305C23×D4C2×D711yescharacteristic
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—28no—
316C2×#121C2×D718yes—
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⋊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×C42—71no—
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—22no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—22no—
381C23×C7—22no—
382C23×C7—22no—
383C23×C7—22no—
384C23×C7—44no—
385C23×C7—44no—
386C23×C7—44no—
387C23×C7—44no—
388C23×C7—44no—
389C23×C7—44no—
390C23×C7—44no—
391C23×C7—44no—
392C23×C7—44no—
393C23×C7—44no—
394C23×C7—44no—
395C23×C7#121116yes—
396C23×C7C22×D414yes—
397C23×C7C22×D412yes—
398C23×C7C22×D414yes—
399C23×C7C22×D414yes—
400C23×C7C22×D412yes—
401C23×C7C2×#4114yes—
402C23×C7C2×#4112yes—
403C23×C7C2×#4112yes—
404C23×C7C2×#4112yes—
405C23×C7H(5,𝔽2)12yes—
406C23×C72−1+412yes—
407C23×C7C2511yescharacteristic
408C7×D4—232no—
409C7×D4—416no—
410C7×D4—416no—
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—416no—
424C2×C4×C7—44no—
425C2×C4×C7—44no—
426C2×C4×C7C22×D414yes—
427C2×C4×C7C2×#4114yes—
428C2×Dic7—28no—
429C2×Dic7—28no—
430C2×Dic7—28no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
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—416no—
453C2×Dic7—416no—
454C2×Dic7—416no—
455C2×Dic7—44no—
456C2×Dic7—44no—
457C2×Dic7—44no—
458C2×Dic7—44no—
459C2×Dic7—44no—
460C2×Dic7C22×D414yes—
461C2×Dic7C22×D414yes—
462C2×Dic7C2×#4114yes—
463C25C22×D711yescharacteristic
464C25C22×D711yescharacteristic
465C25C22×D711yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—42no—
474C22×D4C22⋊D718yes—
475C22×D4C22×D714yes—
476C22×D4C22×D714yes—
477C22×D4C22×D714yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—74no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
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—144no—
499C23×C4—282no—
500C23×C4—282no—
501C23×C4C22×D711yescharacteristic
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D714yes—
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506#123—1432no—
507#123—1432no—
508#121—232no—
509C4×D4—1432no—
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—24no—
528C2×C22⋊C4—78no—
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—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—144no—
545C2×C22⋊C4—282no—
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#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×C7—42no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7—42no—
580C22×C7—88no—
581C22×C7C2×#12118yes—
582C22×C7C2×#12114yes—
583C22×C7#52914yes—
584C22×C7#53914yes—
585C22×C7#54614yes—
586C22×C7#54614yes—
587C22×C7#54714yes—
588C22×C7#54714yes—
589C22×C7C23×D411yescharacteristic
590C22×C7C23×D411yescharacteristic
591C22×C7C22×#4111yescharacteristic
592C22×C7C22×#4111yescharacteristic
593C22×C7C22×#4111yescharacteristic
594C22×C7C2×H(5,𝔽2)11yescharacteristic
595C22×C7C2×2−1+411yescharacteristic
596C4×C7—24no—
597C4×C7—24no—
598C4×C7—42no—
599C4×C7—42no—
600Dic7—24no—
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—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24D4×D714yes—
626C24#115914yes—
627C24C2×C22⋊D714yes—
628C24C2×C22⋊D714yes—
629C24C23×D712yes—
630C24C23×D712yes—
631C24C23×D712yes—
632C24C23×D711yescharacteristic
633C2×D4—232no—
634C2×D4—28no—
635C2×D4—28no—
636C2×D4—28no—
637C2×D4—28no—
638C2×D4—28no—
639C2×D4—28no—
640C2×D4—28no—
641C2×D4—44no—
642C2×D4—416no—
643C2×D4—416no—
644C2×D4C2×C22⋊D7116yes—
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—28no—
656C22×C4—28no—
657C22×C4—44no—
658C22×C4—416no—
659C22×C4—74no—
660C22×C4—74no—
661C22×C4—74no—
662C22×C4—72no—
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—142no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—148no—
683C22×C4—148no—
684C22×C4—142no—
685C22×C4—148no—
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—142no—
697C22×C4—148no—
698C22×C4—284no—
699C22×C4—284no—
700C22×C4—2816no—
701C22×C4—2816no—
702C22×C4—2816no—
703C22×C4#115914yes—
704C22×C4C2×C22⋊D714yes—
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—28no—
719C22⋊C4—716no—
720C22⋊C4—148no—
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—28no—
730C2×C7—44no—
731C2×C7—82no—
732C2×C7#242518yescomplemented
733C2×C7C22×#12111yescharacteristic
734C2×C7C2×#52911yescharacteristic
735C2×C7C2×#53911yescharacteristic
736C2×C7C2×#54611yescharacteristic
737C2×C7C2×#54611yescharacteristic
738C2×C7C2×#54711yescharacteristic
739C2×C7C2×#54711yescharacteristic
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—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23#6502116yes—
778C23C2×D4×D714yes—
779C23C2×D4×D712yes—
780C23C2×#115914yes—
781C23C2×#115912yes—
782C23C2×#115912yes—
783C23#654812yes—
784C23D7×#4112yes—
785C23#655412yes—
786C23C22×C22⋊D714yes—
787C23C22×C22⋊D714yes—
788C23C22×C22⋊D712yes—
789C23C24×D711yescharacteristic
790D4—232no—
791D4—416no—
792D4—416no—
793C2×C4—28no—
794C2×C4—28no—
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—416no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—74no—
809C2×C4—74no—
810C2×C4—74no—
811C2×C4—148no—
812C2×C4—148no—
813C2×C4—148no—
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—142no—
834C2×C4—142no—
835C2×C4—2816no—
836C2×C4—2816no—
837C2×C4—2816no—
838C2×C4—284no—
839C2×C4—284no—
840C2×C4—284no—
841C2×C4—284no—
842C2×C4—284no—
843C2×C4C2×#115914yes—
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—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—88no—
869C22#9029114yes—
870C22#9029314yes—
871C22#9030114yes—
872C22#9030214yes—
873C22C2×#650218yes—
874C22C2×#650214yes—
875C22#9049714yes—
876C22#9051514yes—
877C22C22×D4×D711yescharacteristic
878C22C22×#115911yescharacteristic
879C22C22×#115911yescharacteristic
880C22C2×#654811yescharacteristic
881C22C2×D7×#4111yescharacteristic
882C22C2×#655411yescharacteristic
883C22C23×C22⋊D711yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—144no—
889C4—144no—
890C4—144no—
891C4—282no—
892C4—282no—
893C4—282no—
894C4—282no—
895C4—282no—
896C2—28no—
897C2—44no—
898C2—82no—
899C2#1174009018yesdirect product factor
900C2C2×#9029111yescharacteristic
901C2C2×#9029311yescharacteristic
902C2C2×#9030211yescharacteristic
903C2C2×#9030111yescharacteristic
904C2C22×#650211yescharacteristic
905C2C2×#9049711yescharacteristic
906C2C2×#9051511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC22×C7×#121C2
socleC24×C7C24
hypercenterC22×#121D7
hypocenterC7C2×#2425
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
2. C22×#6498C2semidirect
3. C22×#6498C2semidirect
4. C22×D4×Dic7C2semidirect
5. C2×#89994C2semidirect
6. C2×#89992C2semidirect
7. C2×#89992C2semidirect
8. C2×#89982C2semidirect
9. C22×C7⋊#95C2semidirect
10. #11740090C2direct (N × H)
11. C2×#89756C2semidirect
12. C2×#89744C2semidirect
13. C2×#89724C2semidirect
14. C2×#89720C2semidirect
15. C2×#89717C2semidirect
16. C2×#89714C2semidirect
40. C2×#6498C22semidirect
41. C2×#6498C22semidirect
43. C2×D4×Dic7C22semidirect
52. #89994C22semidirect
53. #89992C22semidirect
54. #89992C22semidirect
55. #89982C22semidirect
64. C2×C7⋊#95C22semidirect
65. #89756C22semidirect
66. #89744C22semidirect
67. #89724C22semidirect
68. #89720C22semidirect
69. #89717C22semidirect
70. #89714C22semidirect
130. C2×C22⋊Dic7D4semidirect
295. C22⋊Dic7C2×D4semidirect
732. C2×C7#2425semidirect
845. C7C2×#2425semidirect
899. C2#11740090direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C22×#64982
C22×D4×Dic72
C2×#899942
C2×#899922
C2×#899822
C22×C7⋊#952
#117400902
C2×#897562
C2×#897442
C2×#897242
C2×#897202
C2×#897172
C2×#897142
C2×#24257