Finite Group Databasebeta

← C2×#11740997 #14230402

Subgroups — C2×#11740997 #14230402

Order 1792.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×D4×Q8C211yesmaximal, characteristic
2C2×#90232C211yesmaximal, characteristic
3C2×#90000C211yesmaximal, characteristic, complemented
4C2×#90000C211yesmaximal, characteristic, complemented
5C2×#89997C211yesmaximal, characteristic, complemented
6C22×#6409C211yesmaximal, characteristic, complemented
7#11740997C2116yesmaximal, direct product factor
8C2×#89862C211yesmaximal, characteristic, complemented
9C2×#89854C211yesmaximal, characteristic, complemented
10C2×#89824C211yesmaximal, characteristic, complemented
11C2×#89823C211yesmaximal, characteristic, complemented
12C2×#89817C211yesmaximal, characteristic, complemented
13C2×#89815C211yesmaximal, characteristic, complemented
14C2×#89794C211yesmaximal, characteristic, complemented
15C2×#89802C211yesmaximal, characteristic, complemented
16C2×#89783C211yesmaximal, characteristic
17C23×C7×Q8C2211yescharacteristic
18C23×C7×Q8C2211yescharacteristic
19C7×D4×Q8—24no—
20C7×D4×Q8C2218yes—
21C2×C7×C4⋊Q8—21no—
22C2×C7×C4⋊Q8C2211yescharacteristic
23C2×C7×C22⋊Q8—21no—
24C2×C7×C22⋊Q8—21no—
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C7×C22⋊Q8C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4—21no—
29C2×C4×C7×D4C2211yescharacteristic
30C22×#1144C2211yescharacteristic
31C22×#1144C2211yescharacteristic
32C22×#1144C2211yescharacteristic
33C2×#6498—21no—
34C2×#6489C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C2×#6487C2211yescharacteristic
37C2×#6487C2211yescharacteristic
38C22×#1136C2211yescharacteristic
39C23×C7⋊C8C2211yescharacteristic
40#90232—24no—
41#90232C2218yes—
42C2×#6452—21no—
43C2×#6442—21no—
44C2×#6440—21no—
45C2×#6433C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47#90000C2218yescomplemented
48#90000C2218yescomplemented
49#89997C2218yescomplemented
50C2×#6409C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56C2×#6409C2211yescharacteristic
57C2×#6409C2211yescharacteristic
58C2×#6409C2211yescharacteristic
59C2×#6409C2218yescomplemented
60C2×C22⋊(C7⋊C8)C2211yescharacteristic
61C2×C22⋊(C7⋊C8)C2211yescharacteristic
62#89862C2218yescomplemented
63#89854C2218yescomplemented
64#89824C2218yescomplemented
65#89823C2218yescomplemented
66#89817C2218yescomplemented
67#89815C2218yescomplemented
68#89802C2218yescomplemented
69#89794C2218yescomplemented
70#89783C2218yes—
71C2×#6384C2211yescharacteristic
72C2×#6382C2211yescharacteristic
73C2×#6382C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3312—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—21no—
80C22×C7×Q8—22no—
81C22×C7×Q8—22no—
82C22×C7×Q8—24no—
83C22×C7×Q8—24no—
84C22×C7×Q8—42no—
85C22×C7×Q8—42no—
86C22×C7×Q8C2311yescharacteristic
87C22×C7×Q8C2311yescharacteristic
88C22×C7×Q8C2314yes—
89C22×C7×Q8C2314yes—
90C22×C7×Q8C2311yescharacteristic
91C22×C7×D4D411yescharacteristic
92C23×C4×C7—21no—
93C23×C4×C7—21no—
94C23×C4×C7C2311yescharacteristic
95C23×C4×C7C2311yescharacteristic
96C23×Dic7—21no—
97C22×Dic14C2311yescharacteristic
98C7×C4⋊Q8—28no—
99C7×C4⋊Q8—22no—
100C7×C4⋊Q8C2314yes—
101C7×C22⋊Q8—22no—
102C7×C22⋊Q8—22no—
103C7×C22⋊Q8—28no—
104C7×C22⋊Q8—28no—
105C7×C22⋊Q8C2314yes—
106C7×C22⋊Q8C2314yes—
107C4×C7×Q8—22no—
108C4×C7×Q8C2314yes—
109C4×C7×D4—28no—
110C4×C7×D4D414yes—
111C4×C7×D4C2314yes—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4—21no—
116C2×C7×C4⋊C4—21no—
117C2×C7×C4⋊C4D411yescharacteristic
118C2×C7×C4⋊C4C2311yescharacteristic
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4D411yescharacteristic
122C2×C7×C22⋊C4D411yescharacteristic
123C2×C42×C7—21no—
124C2×C42×C7C2311yescharacteristic
125C2×C22⋊Dic7—21no—
126C2×C22⋊Dic7—21no—
127C2×C22⋊Dic7—21no—
128C2×#1144—24no—
129C2×#1144—42no—
130C2×#1144—42no—
131C2×#1144C2314yes—
132C2×#1144C2314yes—
133C2×#1144C2314yes—
134#6498—28no—
135#6489—22no—
136#6489C2314yes—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7—22no—
139C2×C4⋊Dic7C2311yescharacteristic
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2314yes—
143#6487—22no—
144#6487—22no—
145#6487C2314yes—
146#6487C2314yes—
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4—21no—
150C2×Dic7⋊C4—21no—
151C2×Dic7⋊C4—21no—
152C2×C4×Dic7—21no—
153C2×C4×Dic7—21no—
154C2×#1136—42no—
155C2×#1136C2314yes—
156C22×C7⋊C8—42no—
157C22×C7⋊C8C2311yescharacteristic
158C22×C7⋊C8C2311yescharacteristic
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C22×C7⋊C8C2314yes—
162#6452—28no—
163#6442—28no—
164#6440—28no—
165#6433—22no—
166#6433C2314yes—
167C4×Dic14—22no—
168C4×Dic14C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175#6409C2314yes—
176#6409C2314yes—
177#6409C2314yes—
178C22⋊(C7⋊C8)C2314yes—
179C22⋊(C7⋊C8)C2314yes—
180#6384C2314yes—
181#6382C2314yes—
182#6382C2314yes—
183#6381C2314yes—
184C4⋊(C7⋊C8)C2314yes—
185#6377C2314yes—
186C2×#552—71no—
187C2×D4×Q8D711yescharacteristic
188#3312—716no—
189C2×#491—71no—
190C2×#485—71no—
191C2×#483—71no—
192C2×#479—71no—
193C2×#470—71no—
194C2×#467—71no—
195C2×#462—71no—
196C2×#451—71no—
197C2×#451—71no—
198C2×#441—71no—
199C2×#435—71no—
200C2×#419—71no—
201C22×#103—71no—
202C24×C7C2×D411yescharacteristic
203C24×C7C2×D411yescharacteristic
204C2×C7×Q8—21no—
205C2×C7×Q8—24no—
206C2×C7×Q8—24no—
207C2×C7×Q8—21no—
208C2×C7×Q8—21no—
209C2×C7×Q8—22no—
210C2×C7×Q8—28no—
211C2×C7×Q8—28no—
212C2×C7×Q8—22no—
213C2×C7×Q8—22no—
214C2×C7×Q8—22no—
215C2×C7×Q8—22no—
216C2×C7×Q8—44no—
217C2×C7×Q8—44no—
218C2×C7×Q8—44no—
219C2×C7×Q8—44no—
220C2×C7×Q8—48no—
221C2×C7×Q8—48no—
222C2×C7×Q8#4114yes—
223C2×C7×Q8C2412yes—
224C2×C7×Q8C2412yes—
225C2×C7×Q8C2412yes—
226C2×C7×D4—24no—
227C2×C7×D4C2×D414yes—
228C22×C4×C7—21no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—22no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—24no—
237C22×C4×C7—24no—
238C22×C4×C7—44no—
239C22×C4×C7—44no—
240C22×C4×C7C2×D411yescharacteristic
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D412yes—
245C22×C4×C7C2×D412yes—
246C22×C4×C7C2412yes—
247C22×C4×C7C2412yes—
248C22×C4×C7C2411yescharacteristic
249C22×Dic7—24no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—44no—
255C2×Dic14—22no—
256C2×Dic14—22no—
257C2×Dic14—21no—
258C2×Dic14C2412yes—
259C7×C4⋊C4—24no—
260C7×C4⋊C4—24no—
261C7×C4⋊C4—24no—
262C7×C4⋊C4—24no—
263C7×C4⋊C4—24no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4C2×D414yes—
266C7×C4⋊C4C2412yes—
267C7×C22⋊C4—24no—
268C7×C22⋊C4—24no—
269C7×C22⋊C4C2×D414yes—
270C7×C22⋊C4C2×D414yes—
271C42×C7—24no—
272C42×C7C2×D412yes—
273C42×C7C2412yes—
274C22⋊Dic7—24no—
275C22⋊Dic7—24no—
276C22⋊Dic7—24no—
277#1144—28no—
278#1144—44no—
279#1144—44no—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7—21no—
283C4⋊Dic7—24no—
284C4⋊Dic7C2412yes—
285C4⋊Dic7C2412yes—
286C4⋊Dic7C2412yes—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292C4×Dic7—24no—
293C4×Dic7—24no—
294#1136—44no—
295C2×C7⋊C8—22no—
296C2×C7⋊C8—22no—
297C2×C7⋊C8—22no—
298C2×C7⋊C8—22no—
299C2×C7⋊C8—44no—
300C2×C7⋊C8C2412yes—
301C2×C7⋊C8C2412yes—
302C2×C7⋊C8C2412yes—
303C2×C7⋊C8C2412yes—
304C23×Q8C2×D711yescharacteristic
305C23×Q8C2×D711yescharacteristic
306C22×Q16—71no—
307C22×Q16—71no—
308C22×Q16—71no—
309C22×M16—71no—
310C23×C8—71no—
311#552—78no—
312#552—144no—
313D4×Q8—24no—
314D4×Q8C2×D718yes—
315C2×C4⋊Q8—21no—
316C2×C4⋊Q8C2×D711yescharacteristic
317C2×#126—141no—
318C2×#125—71no—
319C2×#125—141no—
320C2×#123—141no—
321C2×C22⋊Q8—21no—
322C2×C22⋊Q8—21no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8C2×D711yescharacteristic
326C2×C22⋊Q8C2×D711yescharacteristic
327C2×C4×Q8—71no—
328C2×C4×Q8C2×D711yescharacteristic
329C2×C4×D4—21no—
330C2×C4×D4C2×D711yescharacteristic
331C2×#117—71no—
332C2×#117—141no—
333C22×C4⋊C4—71no—
334#491—78no—
335#485—78no—
336#483—78no—
337#479—78no—
338#470—78no—
339#467—78no—
340#462—78no—
341#451—78no—
342#451—78no—
343#441—78no—
344#435—78no—
345C2×#107—71no—
346C2×#106—71no—
347C2×#106—71no—
348C2×C4⋊C8—71no—
349#419—78no—
350C2×#103—71no—
351C2×#103—71no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—78no—
360C2×#103—71no—
361C2×C22⋊C8—71no—
362C2×C22⋊C8—71no—
363C2×#97—71no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7#13714yes—
370C23×C7C22×D412yes—
371C23×C7C22×D412yes—
372C23×C7C22×D411yescharacteristic
373C7×Q8—24no—
374C7×Q8—22no—
375C7×Q8—22no—
376C7×Q8—22no—
377C7×Q8—22no—
378C7×Q8—22no—
379C7×Q8—48no—
380C7×Q8—48no—
381C7×Q8—42no—
382C7×Q8—42no—
383C7×Q8C2×#4114yes—
384C7×D4—28no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—24no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—24no—
392C2×C4×C7—24no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—48no—
401C2×C4×C7—48no—
402C2×C4×C7—42no—
403C2×C4×C7—42no—
404C2×C4×C7—42no—
405C2×C4×C7C22×D412yes—
406C2×C4×C7C22×D412yes—
407C2×C4×C7C22×D412yes—
408C2×C4×C7C22×D412yes—
409C2×C4×C7C22×D411yescharacteristic
410C2×C4×C7C2×#4112yes—
411C2×C4×C7H(5,𝔽2)12yes—
412C2×C4×C7C2511yescharacteristic
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—42no—
418C2×Dic7—48no—
419C2×Dic7—42no—
420C2×Dic7—42no—
421C2×Dic7—42no—
422Dic14—22no—
423Dic14—22no—
424Dic14—42no—
425C7⋊C8—22no—
426C7⋊C8—22no—
427C7⋊C8—22no—
428C7⋊C8—22no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—24no—
434C22×Q8—24no—
435C22×Q8—42no—
436C22×Q8—42no—
437C22×Q8—71no—
438C22×Q8C22×D711yescharacteristic
439C22×Q8C22×D711yescharacteristic
440C22×Q8C22×D714yes—
441C22×Q8C22×D714yes—
442C22×Q8C22×D711yescharacteristic
443C22×D4C22⋊D711yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—141no—
447C23×C4C22×D711yescharacteristic
448C23×C4C22×D711yescharacteristic
449C2×Q16—74no—
450C2×Q16—74no—
451C2×Q16—74no—
452C2×Q16—144no—
453C2×Q16—282no—
454C2×Q16—282no—
455C2×M16—74no—
456C2×M16—282no—
457C22×C8—71no—
458C22×C8—71no—
459C22×C8—71no—
460C22×C8—71no—
461C22×C8—74no—
462C22×C8—282no—
463C4⋊Q8—28no—
464C4⋊Q8—22no—
465C4⋊Q8C22×D714yes—
466#126—148no—
467#125—74no—
468#125—148no—
469#125—142no—
470#123—148no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—28no—
474C22⋊Q8—28no—
475C22⋊Q8—74no—
476C22⋊Q8—74no—
477C22⋊Q8—142no—
478C22⋊Q8—142no—
479C22⋊Q8C22×D714yes—
480C22⋊Q8C22×D714yes—
481C4×Q8—22no—
482C4×Q8—74no—
483C4×Q8—142no—
484C4×Q8C22×D714yes—
485C4×D4—28no—
486C4×D4C22⋊D714yes—
487C4×D4C22×D714yes—
488#117—74no—
489#117—142no—
490#117—148no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—71no—
497C2×C4⋊C4—71no—
498C2×C4⋊C4—74no—
499C2×C4⋊C4—71no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—142no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4—141no—
506C2×C4⋊C4—141no—
507C2×C4⋊C4C22⋊D711yescharacteristic
508C2×C4⋊C4C22×D711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4—141no—
513C2×C22⋊C4—141no—
514C2×C22⋊C4C22⋊D711yescharacteristic
515C2×C22⋊C4C22⋊D711yescharacteristic
516C2×C42—21no—
517C2×C42—141no—
518C2×C42—141no—
519C2×C42C22×D711yescharacteristic
520#107—74no—
521#106—74no—
522#106—74no—
523C4⋊C8—74no—
524#103—74no—
525#103—74no—
526#103—74no—
527#103—74no—
528#103—74no—
529#103—74no—
530#103—74no—
531#103—74no—
532#103—74no—
533#103—74no—
534C22⋊C8—74no—
535C22⋊C8—74no—
536#97—74no—
537C22×C7—22no—
538C22×C7—28no—
539C22×C7—22no—
540C22×C7—22no—
541C22×C7—22no—
542C22×C7—22no—
543C22×C7—44no—
544C22×C7#54612yes—
545C22×C7C2×#13714yes—
546C22×C7C2×#13712yes—
547C22×C7#57812yes—
548C22×C7C23×D411yescharacteristic
549C4×C7—22no—
550C4×C7—22no—
551C4×C7—24no—
552C4×C7—22no—
553C4×C7—22no—
554C4×C7—42no—
555C4×C7—42no—
556C4×C7—42no—
557C4×C7#54612yes—
558C4×C7C22×#4111yescharacteristic
559C4×C7C2×H(5,𝔽2)11yescharacteristic
560Dic7—42no—
561Dic7—42no—
562Dic7—42no—
563Dic7—42no—
564C24C2×C22⋊D711yescharacteristic
565C24C2×C22⋊D711yescharacteristic
566C2×Q8—22no—
567C2×Q8—21no—
568C2×Q8—24no—
569C2×Q8—24no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—28no—
573C2×Q8—28no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—44no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—48no—
583C2×Q8—48no—
584C2×Q8—72no—
585C2×Q8—141no—
586C2×Q8—142no—
587C2×Q8—142no—
588C2×Q8#115914yes—
589C2×Q8C23×D712yes—
590C2×Q8C23×D712yes—
591C2×Q8C23×D712yes—
592C2×D4—24no—
593C2×D4C2×C22⋊D714yes—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—144no—
607C22×C4—141no—
608C22×C4—141no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—284no—
612C22×C4C2×C22⋊D712yes—
613C22×C4C2×C22⋊D712yes—
614C22×C4C2×C22⋊D711yescharacteristic
615C22×C4C2×C22⋊D711yescharacteristic
616C22×C4C2×C22⋊D711yescharacteristic
617C22×C4C2×C22⋊D711yescharacteristic
618C22×C4C23×D712yes—
619C22×C4C23×D712yes—
620C22×C4C23×D711yescharacteristic
621Q16—148no—
622Q16—284no—
623Q16—284no—
624M16—284no—
625C2×C8—72no—
626C2×C8—72no—
627C2×C8—72no—
628C2×C8—72no—
629C2×C8—142no—
630C2×C8—142no—
631C2×C8—142no—
632C2×C8—142no—
633C2×C8—284no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—72no—
641C4⋊C4—72no—
642C4⋊C4—72no—
643C4⋊C4—144no—
644C4⋊C4—144no—
645C4⋊C4—144no—
646C4⋊C4—144no—
647C4⋊C4—144no—
648C4⋊C4—141no—
649C4⋊C4—141no—
650C4⋊C4—144no—
651C4⋊C4—141no—
652C4⋊C4C2×C22⋊D714yes—
653C4⋊C4C23×D712yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—144no—
657C22⋊C4—144no—
658C22⋊C4—144no—
659C22⋊C4C2×C22⋊D714yes—
660C22⋊C4C2×C22⋊D714yes—
661C42—24no—
662C42—144no—
663C42—144no—
664C42C2×C22⋊D712yes—
665C42C23×D712yes—
666C2×C7—24no—
667C2×C7—42no—
668C2×C7#331214yescomplemented
669C2×C7C2×#54611yescharacteristic
670C2×C7C22×#13711yescharacteristic
671C2×C7C2×#57811yescharacteristic
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23#650514yes—
678C23C22×C22⋊D712yes—
679C23C22×C22⋊D712yes—
680C23C22×C22⋊D711yescharacteristic
681Q8—24no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—48no—
688Q8—48no—
689Q8—42no—
690Q8—42no—
691Q8—142no—
692Q8—142no—
693Q8—282no—
694Q8C2×#115914yes—
695D4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—48no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—282no—
721C2×C4—288no—
722C2×C4—282no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4C2×#115912yes—
726C2×C4#654812yes—
727C2×C4C22×C22⋊D712yes—
728C2×C4C22×C22⋊D712yes—
729C2×C4C22×C22⋊D712yes—
730C2×C4C22×C22⋊D712yes—
731C2×C4C22×C22⋊D711yescharacteristic
732C2×C4C24×D711yescharacteristic
733C8—142no—
734C8—142no—
735C8—142no—
736C8—142no—
737C7C2×#331211yescharacteristic, complemented, Sylow
738C22—22no—
739C22—28no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#9049712yes—
746C22C2×#650514yes—
747C22C2×#650512yes—
748C22#9052912yes—
749C22C23×C22⋊D711yescharacteristic
750C4—22no—
751C4—22no—
752C4—24no—
753C4—22no—
754C4—22no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—282no—
759C4—282no—
760C4—282no—
761C4—282no—
762C4#9049712yes—
763C4C22×#115911yescharacteristic
764C4C2×#654811yescharacteristic
765C2—24no—
766C2—42no—
767C2#1174099714yesdirect product factor
768C2C2×#9049711yescharacteristic
769C2C22×#650511yescharacteristic
770C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×D4×Q8C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
hypercenterC2×D4×Q8D7
hypocenterC7C2×#3312
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#90000C2semidirect
4. C2×#90000C2semidirect
5. C2×#89997C2semidirect
6. C22×#6409C2semidirect
7. #11740997C2direct (N × H)
8. C2×#89862C2semidirect
9. C2×#89854C2semidirect
10. C2×#89824C2semidirect
11. C2×#89823C2semidirect
12. C2×#89817C2semidirect
13. C2×#89815C2semidirect
14. C2×#89794C2semidirect
15. C2×#89802C2semidirect
47. #90000C22semidirect
48. #90000C22semidirect
49. #89997C22semidirect
59. C2×#6409C22semidirect
62. #89862C22semidirect
63. #89854C22semidirect
64. #89824C22semidirect
65. #89823C22semidirect
66. #89817C22semidirect
67. #89815C22semidirect
68. #89802C22semidirect
69. #89794C22semidirect
668. C2×C7#3312semidirect
737. C7C2×#3312semidirect
767. C2#11740997direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×D4×Q82
C2×#902322
C2×#900002
C2×#899972
C22×#64092
#117409972
C2×#898622
C2×#898542
C2×#898242
C2×#898232
C2×#898172
C2×#898152
C2×#897942
C2×#898022
C2×#897832
C2×#33127